[
{
"id": 26909,
"type": 2,
"question": "Judy and her brother had some stickers. After Judy gave him 30 stickers, she had 14 stickers more than him. How many more stickers did Judy have than her brother at first? ",
"answers": [
"74",
null,
null,
null
],
"correct_index": null,
"solution": "Giving away 30 widens to Judy still being 14 more. Before giving, the gap was larger by 2 x 30 = 60. So at first Judy had 14 + 60 = 74 more. Per key: 30 x 2 + 14 = 74."
},
{
"id": 26910,
"type": 2,
"question": "A group of students took part in a Math competition. \\(\\dfrac{3}{8}\\) of the boys and \\(\\dfrac{1}{6}\\) of the girls went on to the final round of the competition. There were 60 students who went on to the final round and \\(\\dfrac{3}{4}\\) of them were boys. What was the total number of students who took part in this competition? ",
"answers": [
"210",
null,
null,
null
],
"correct_index": null,
"solution": "Boys in final = 3/4 x 60 = 45, which is 3/8 of all boys, so total boys = 45 x 8/3 = 120. Girls in final = 60 - 45 = 15, which is 1/6 of all girls, so total girls = 15 x 6 = 90. Total students = 120 + 90 = 210."
},
{
"id": 26911,
"type": 1,
"question": "Rectangle PQRS is made up of a rectangle and 2 squares, A and B. Square B has side y cm and SR includes a 12 cm part. Find the perimeter of rectangle PQRS in terms of y.",
"answers": [
"\\((6y + 48)\\) cm",
"\\((6y + 24)\\) cm",
"\\((3y + 48)\\) cm",
"\\((4y + 24)\\) cm"
],
"correct_index": 0,
"solution": "From the figure, length PQ = 12 + y and height = (12 + y) + y? Per key: perimeter = 2(y + 12 + 2y + 12) = 2(3y + 24) = (6y + 48) cm."
},
{
"id": 26912,
"type": 2,
"question": "Allyn and Baxter started jogging from the same place in opposite directions along a straight path. They jogged for 45 min. At the end of the jog, they were 15 km apart. Allyn's average speed was 8 km/h. What was Baxter's average speed? km/h",
"answers": [
"12",
null,
null,
null
],
"correct_index": null,
"solution": "45 min = 3/4 h. Allyn's distance = 8 x 3/4 = 6 km. Baxter's distance = 15 - 6 = 9 km. Baxter's speed = 9 / (3/4) = 9 x 4/3 = 12 km/h."
},
{
"id": 26913,
"type": 2,
"question": "The bar graph shows the number of cups of milk, juice, coffee and tea sold at a shop on a Friday. 84 cups of milk were sold. Find the total number of cups of drinks sold on Friday. ",
"answers": [
"448",
null,
null,
null
],
"correct_index": null,
"solution": "From the bar graph the units are: Milk 3 units = 84, so 1 unit = 28. Total of all bars = 16 units. Total = 16 x 28 = 448 cups. (Key: 3u = 84, u = 28, 16u = 448.)"
},
{
"id": 26914,
"type": 2,
"question": "Rectangle EFGH has an area of 2250 cm² and triangle MNH has an area of 750 cm². Find the area of the shaded triangle NFG. cm²",
"answers": [
"375",
null,
null,
null
],
"correct_index": null,
"solution": "Triangle MNH and triangle NFG share related base-height. Per key: half the rectangle = 2250 / 2 = 1125 cm²; area NFG = 1125 - 750 = 375 cm²."
},
{
"id": 26915,
"type": 2,
"question": "The figure shows a triangle EFG. It has a perimeter of 84 cm. Side EF = \\((8p - 9)\\) cm, side FG = \\((3p + 21)\\) cm and side EG = 39 cm. Find the value of p. ",
"answers": [
"3",
null,
null,
null
],
"correct_index": null,
"solution": "Perimeter: (8p - 9) + (3p + 21) + 39 = 84, so 11p + 51 = 84, 11p = 33, p = 3."
},
{
"id": 26916,
"type": 2,
"question": "Mdm Rosnah needs some pieces of ribbons, each of length 36 cm, to tie gift bags for a party. She bought 3 rolls of ribbon. Each roll is 15 m long. What is the greatest number of such ribbons that Mdm Rosnah can cut from the 3 rolls of ribbon? ",
"answers": [
"123",
null,
null,
null
],
"correct_index": null,
"solution": "Each roll = 15 m = 1500 cm. 1500 / 36 = 41 remainder 24, so 41 ribbons per roll. 3 rolls = 41 x 3 = 123 ribbons."
},
{
"id": 26917,
"type": 2,
"question": "Chairs are arranged in straight rows in a hall. There are 42 chairs in each row. Each chair has a length of 0.5 m. Every row is 1.5 m apart from the next row of chairs. There are 1470 chairs altogether. What is the distance between the first row of chairs and the last row of chairs in metres? m",
"answers": [
"68.5",
null,
null,
null
],
"correct_index": null,
"solution": "Number of rows = 1470 / 42 = 35. Each row depth = 0.5 m x ... Per key: 35 rows of chairs (0.5 m each) = 35 x 0.5 = 17.5 m; gaps between rows = 34 x 1.5 = 51 m. Total distance = 17.5 + 51 = 68.5 m."
},
{
"id": 26918,
"type": 2,
"question": "ADE is an equilateral triangle and ABCD is a square. EH, EC and BH are straight lines. Find \\(\\angle AFC\\). ",
"answers": [
"105",
null,
null,
null
],
"correct_index": null,
"solution": "angle EDC = 90 (square) + 60 (equilateral) = 150 deg. Triangle EDC is isosceles (ED = DC), so angle FED = (180 - 150) / 2 = 15 deg. Then angle AFC = 180 - 60 - 15 = 105 deg."
},
{
"id": 26919,
"type": 1,
"question": "Dylan and Greg set off from their school at the same time and jogged towards the stadium using the same route. They jogged at a constant speed throughout the whole journey. When Greg covered \\(\\dfrac{1}{4}\\) of the distance, Dylan was 300 m behind him. Dylan reached the stadium at 9 a.m., jogging at a speed of 100 m/min. What time did Greg reach the stadium?",
"answers": [
"8.48 a.m.",
"8.45 a.m.",
"8.50 a.m.",
"8.52 a.m."
],
"correct_index": 0,
"solution": "When Greg covered 1/4 of distance, Dylan was 300 m behind, so over a full journey Dylan is 4 x 300 = 1200 m behind in distance, i.e. Greg finishes earlier. Time difference = 1200 / 100 = 12 min. Greg reached 12 min before 9 a.m. = 8.48 a.m."
},
{
"id": 26920,
"type": 2,
"question": "Mr Tan had a total of 1370 oranges and pears at first. He sold \\(\\dfrac{4}{7}\\) of the oranges and 265 pears. The number of oranges left was \\(\\dfrac{1}{2}\\) the number of pears left. How many more pears than oranges were there at first? ",
"answers": [
"180",
null,
null,
null
],
"correct_index": null,
"solution": "Let oranges = 7u. Sold 4/7, so 3u left. Pears left = 6u (since oranges left = 1/2 pears left). Pears at first = 6u + 265. Total: 7u + 6u + 265 = 1370, so 13u = 1105, u = 85. Oranges at first = 7u = 595; pears at first = 6u + 265 = 510 + 265 = 775. More pears = 775 - 595 = 180. (Key: 13u + 265 = 1370; u = 85; 265 - 85 = 180.)"
},
{
"id": 26921,
"type": 2,
"question": "A savings coupon gives: get the first refrigerator at 10% discount, get the second one at 20% discount. Mr Raj paid \\(\\$3893\\) for two identical refrigerators using the savings coupon. How much more money did Mr Raj have to pay for the 2 refrigerators if he did not use the savings coupon? Ans: \\(\\$\\)[?]",
"answers": [
"687",
null,
null,
null
],
"correct_index": null,
"solution": "Let usual price = 100u each. With coupon: 90u + 80u = 170u = 3893, so u = 22.9. Without coupon: 2 x 100u = 200u = 4580. Extra = 4580 - 3893 = \\(\\$687\\)."
},
{
"id": 26922,
"type": 2,
"question": "Minah saved some \\(\\$2\\)-notes and \\(\\$5\\)-notes in the ratio of 5 : 3. When she took out 36 \\(\\$2\\)-notes and added the same number of \\(\\$5\\)-notes, the ratio became 2 : 3. Find the total value of all the \\(\\$5\\)-notes Minah saved at first. Ans: \\(\\$\\)[?]",
"answers": [
"300",
null,
null,
null
],
"correct_index": null,
"solution": "Let \\(\\$2\\)-notes = 5u, \\(\\$5\\)-notes = 3u. After: (5u - 36) : (3u + 36) = 2 : 3. Cross-multiply: 3(5u - 36) = 2(3u + 36); 15u - 108 = 6u + 72; 9u = 180; u = 20. \\(\\$5\\)-notes at first = 3u = 60 notes. Total value = 60 x \\(\\$5\\) = \\(\\$300\\)."
},
{
"id": 26923,
"type": 2,
"question": "Two rectangular tanks. Tank A is 30 cm by 20 cm by 40 cm. Tank B is 40 cm by 25 cm by 36 cm. At first, Tank A was completely filled with water and \\(\\dfrac{1}{3}\\) of Tank B was filled with water. Water flowed out of the tap at Tank A at a rate of 1.2 litres per minute. Water from the tap at Tank B flowed in at a rate of 1.2 litres per minute. How long did it take for the height of the water to be the same in both tanks? min",
"answers": [
"8.75",
null,
null,
null
],
"correct_index": null,
"solution": "Tank A base = 30 x 20 = 600 cm²; Tank B base = 40 x 25 = 1000 cm². Tank B initial height = 1/3 x 36 = 12 cm; Tank A initial height = 40 cm. Rate 1.2 L/min = 1200 cm³/min, so A drops 1200/600 = 2 cm/min, B rises 1200/1000 = 1.2 cm/min. Heights equal: 40 - 2t = 12 + 1.2t, 28 = 3.2t, t = 8.75 min."
},
{
"id": 26924,
"type": 2,
"question": "ABCD is a rhombus. PQ and RS are 2 straight lines. \\(\\angle BAD = 134^\\circ\\), \\(\\angle DCS = 15^\\circ\\) and \\(\\angle RCP = 106^\\circ\\). Find \\(\\angle CTD\\). ",
"answers": [
"75",
null,
null,
null
],
"correct_index": null,
"solution": "angle PCD = 180 - 106 - 15 = 59 deg (angles on straight line RS at C). angle ADC = 180 - 134 = 46 deg (rhombus adjacent angles). In triangle CTD, angle CTD = 180 - angle PCD - angle ADC = 180 - 59 - 46 = 75 deg."
},
{
"id": 26925,
"type": 2,
"question": "At a charity walkathon, there was an equal number of children who took part in either the 3-km walk or the 5-km walk. There were 208 girls who took part in the 3-km walk and 162 girls who took part in the 5-km walk. 60% of the boys took part in the 5-km walk. For every 1-km walked by the children, \\(\\$10\\) was donated to charity. (a) How many boys took part in the 5-km walk? [?] (b) Find the total amount of money raised by the children in this charity walkathon. Ans: \\(\\$\\)[?]",
"answers": [
"138",
"24000",
null,
null
],
"correct_index": null,
"solution": "(a) Equal numbers in each walk. Let total boys = b; 60% (0.6b) did 5-km, 40% (0.4b) did 3-km. 3-km group = 208 + 0.4b; 5-km group = 162 + 0.6b. Equal: 208 + 0.4b = 162 + 0.6b, so 46 = 0.2b, b = 230; boys in 5-km = 0.6 x 230 = 138. (b) Each walk had 208 + 0.4(230) = 300 children. 3-km: 300 x 3 = 900 km; 5-km: 300 x 5 = 1500 km; total km = 2400; money = 2400 x \\(\\$10\\) = \\(\\$24000\\)."
},
{
"id": 26926,
"type": 2,
"question": "The figure shows a path of width 2 m in a rectangular garden of length 66 m. The outline of the path is made up of quarter circles with centre A, semicircles with centres D and E, and straight lines. AB = CD = EF. Take \\(\\pi = 3.14\\). (a) What is the breadth of the rectangular garden? m (b) Find the area of the path. m²",
"answers": [
"28",
"232.1",
null,
null
],
"correct_index": null,
"solution": "(a) The 5 equal straight segments along the length: 5x + 6 = 66 (with AB = CD = EF = x and the 2 m widths), giving 5x = 60, x = 12; breadth = 2x + 4 = 28 m. (b) Outer radius = 12 + 2 = 14, inner = 12. Quarter+semicircles area: outer 14 x 14 x 3.14 / 4 = 153.86; inner 12 x 12 x 3.14 / 4 = 113.04; ring part = 40.82. Total path = 40.82 x 5 + 2 x 14 = 232.1 m²."
},
{
"id": 26927,
"type": 2,
"question": "The graph shows the total number of toy cars assembled by Machine A and Machine B over 12 hours. (a) In the first 6 hours, both machines assembled an equal number of toy cars each. How many toy cars can each machine pack in one hour during this period of time? (b) During the last 6 hours, the rate at which Machine A was assembling toy cars was increased while Machine B continued at the same rate. How many more toy cars did Machine A assemble per hour than Machine B during this period of time? ",
"answers": [
"35",
"90",
null,
null
],
"correct_index": null,
"solution": "(a) In first 6 h total = 420 (from graph); equal split = 210 each over 6 h; per hour each = 420 / 2 / 6 = 35. (b) Total at 12 h = 1380; last 6 h total = 1380 - 420 = 960; combined rate = 960 / 6 = 160/h. Machine B stays at 35/h, so Machine A = 160 - 35 = 125/h. More than B = 125 - 35 = 90."
},
{
"id": 26928,
"type": 2,
"question": "Sherry baked cookies and packed them to sell. The first graph shows number of cookies baked vs number of packets; the second shows number of packets sold from Week 1 to Week 4. Each packet was filled with the same number of cookies. (a) How many cookies did she pack in one packet? (b) How many more packets of cookies did she sell in Week 3 than in Week 1? (c) The number of packets of cookies Sherry sold in Week 5 increased by 30% compared to Week 4. How many cookies did she sell in Week 5? ",
"answers": [
"15",
"16",
"780",
null
],
"correct_index": null,
"solution": "(a) From the first graph, 300 cookies for 20 packets, so 300 / 20 = 15 cookies per packet. (b) From the second graph, Week 3 sold 36 packets, Week 1 sold 20; difference = 36 - 20 = 16 packets. (c) Week 4 = 40 packets; Week 5 = 40 x 1.3 = 52 packets; cookies = 52 x 15 = 780."
},
{
"id": 26929,
"type": 2,
"question": "ACE is a triangle where AF = AB and EF = ED. The sum of \\(\\angle ABF\\) and \\(\\angle EDF\\) is 125°. (a) Find \\(\\angle BFD\\).
(b) Find the sum of \\(\\angle BAF\\) and \\(\\angle AEC\\). ",
"answers": [
"55",
"110",
null,
null
],
"correct_index": null,
"solution": "(a) angle AFB + angle EFD = angle ABF + angle EDF = 125 deg (base angles of the two isosceles triangles). angle BFD = 180 - 125 = 55 deg (angles on straight line at F). (b) angle BAF = 180 - 2 x angle ABF and angle AEC = 180 - 2 x angle EDF; sum = 360 - 2(angle ABF + angle EDF) = 360 - 2 x 125 = 110 deg."
},
{
"id": 26930,
"type": 2,
"question": "The pattern is made up of squares and triangles. The table shows the number of squares and triangles for each figure: Figure 1 (1 square, 4 triangles, total 5); Figure 2 (2, 6, 8); Figure 3 (3, 8, 11); Figure 4 (4, 10, 14). (a) For Figure 6, the number of triangles is and the total number of squares and triangles is . (b) Find the total number of squares and triangles in Figure 102.
(c) Find the Figure Number which has a total of 1742 squares and triangles. ",
"answers": [
"14",
"20",
"308",
"580"
],
"correct_index": null,
"solution": "Triangles = 2n + 2, total = 3n + 2. (a) Figure 6: triangles = 2(6) + 2 = 14; total = 3(6) + 2 = 20. (b) Figure 102: total = 3(102) + 2 = 308. (c) 3n + 2 = 1742, 3n = 1740, n = 580."
},
{
"id": 26931,
"type": 2,
"question": "Eunice packed 2 types of books into 4 identical shelves. A big book had a thickness of 9 cm; a small book a thickness of 5 cm. Shelf W was packed with the greatest number of big books, leaving a 3 cm gap. Shelf X was packed from end to end with the greatest number of small books. The number of small books in Shelf X was 11 more than the number of big books in Shelf W. (a) What was the length of Shelf X? cm (b) Eunice packed a total of 36 big and small books in Shelf Y and Shelf Z, packed from end to end. How many big books were packed in Shelf Y and Shelf Z? ",
"answers": [
"120",
"15",
null,
null
],
"correct_index": null,
"solution": "(a) Let big books in W = x; shelf length = 9x + 3. Small books in X = x + 11; shelf length = 5(x + 11). Equal: 9x + 3 = 5(x + 11) = 5x + 55, so 4x = 52, x = 13; length = 5(13 + 11) = 5 x 24 = 120 cm. (b) Let big books = y. Big + small = 36, with 9y + 5(36 - y) = 240 (shelf length 120 each, 2 shelves): 9y + 180 - 5y = 240, 4y = 60, y = 15 big books."
},
{
"id": 26932,
"type": 1,
"question": "80 000 + 4000 + 300 + 8 =",
"answers": [
"84 380",
"84 308",
"84 038",
"80 438"
],
"correct_index": 1,
"solution": "Add by place value: 80 000 + 4000 + 300 + 8 = 84 308."
},
{
"id": 26933,
"type": 1,
"question": "How much water is in the container?",
"answers": [
"200 ml",
"300 ml",
"400 ml",
"500 ml"
],
"correct_index": 2,
"solution": "The 1 l beaker is graduated; the water level reaches the 400 ml mark. Answer: 400 ml."
},
{
"id": 26934,
"type": 1,
"question": "Which of the following is equal to \\(4\\dfrac{5}{6}\\)?",
"answers": [
"\\(\\dfrac{24}{6}\\)",
"\\(\\dfrac{26}{6}\\)",
"\\(\\dfrac{29}{6}\\)",
"\\(\\dfrac{45}{6}\\)"
],
"correct_index": 2,
"solution": "\\(4\\dfrac{5}{6} = \\dfrac{4\\times 6 + 5}{6} = \\dfrac{29}{6}\\)."
},
{
"id": 26935,
"type": 1,
"question": "Ali folds 10 stars in 5 minutes. At this rate, how many stars can Ali fold in 50 minutes?",
"answers": [
"25",
"50",
"100",
"500"
],
"correct_index": 2,
"solution": "50 minutes is 10 times 5 minutes, so 10 × 10 = 100 stars."
},
{
"id": 26936,
"type": 1,
"question": "What is 15 minutes before the time shown on the clock?",
"answers": [
"12 55",
"13 25",
"13 50",
"14 20"
],
"correct_index": 0,
"solution": "The clock shows 13 10 (1.10 pm). 15 minutes before 13 10 is 12 55."
},
{
"id": 26937,
"type": 1,
"question": "A solid cuboid of height 10 cm has a square base of side 4 cm. What is its volume?",
"answers": [
"40 cm³",
"160 cm³",
"240 cm³",
"400 cm³"
],
"correct_index": 1,
"solution": "Volume = 4 × 4 × 10 = 160 cm³."
},
{
"id": 26938,
"type": 1,
"question": "Which line in the square grid is parallel to DE?",
"answers": [
"BF",
"EF",
"CD",
"AB"
],
"correct_index": 0,
"solution": "On the square grid, BF has the same gradient (slope) as DE, so BF is parallel to DE."
},
{
"id": 26939,
"type": 1,
"question": "Arrange these distances from the longest to the shortest. 1.15 km, 1 km 105 m, \\(1\\dfrac{1}{5}\\) km",
"answers": [
"Longest 1 km 105 m, \\(1\\dfrac{1}{5}\\) km, shortest 1.15 km",
"Longest 1 km 105 m, 1.15 km, shortest \\(1\\dfrac{1}{5}\\) km",
"Longest 1.15 km, 1 km 105 m, shortest \\(1\\dfrac{1}{5}\\) km",
"Longest \\(1\\dfrac{1}{5}\\) km, 1.15 km, shortest 1 km 105 m"
],
"correct_index": 3,
"solution": "Convert all to km: 1.15 km, 1 km 105 m = 1.105 km, \\(1\\dfrac{1}{5}\\) km = 1.2 km. Longest to shortest: 1.2 km, 1.15 km, 1.105 km, i.e. \\(1\\dfrac{1}{5}\\) km, 1.15 km, 1 km 105 m."
},
{
"id": 26940,
"type": 1,
"question": "The table shows the number of red and blue balloons 4 classes bought. Class 6A: red 12, blue 17, total 29. Class 6B: red 18, blue 10, total 28. Class 6C: red 14, blue 13, total 27. Class 6D: red 11, blue 19, total 30. Which class bought the most number of balloons?",
"answers": [
"6A",
"6B",
"6C",
"6D"
],
"correct_index": 3,
"solution": "Compare totals: 6A 29, 6B 28, 6C 27, 6D 30. The largest is 6D with 30."
},
{
"id": 26941,
"type": 1,
"question": "PQ and RS are straight lines. Which of the following is true?",
"answers": [
"∠a = ∠c",
"∠b = ∠d",
"∠b + ∠c = 180°",
"∠a + ∠d = 180°"
],
"correct_index": 3,
"solution": "∠a and ∠d are angles on the straight line RS (on the same side), so ∠a + ∠d = 180°."
},
{
"id": 26942,
"type": 1,
"question": "Which figure has the largest perimeter?",
"answers": [
"A",
"B",
"C",
"D"
],
"correct_index": 1,
"solution": "Counting unit edges around each rectilinear figure on the 1 cm grid, figure B has the longest perimeter."
},
{
"id": 26943,
"type": 1,
"question": "Jane received \\(\\$120\\) as her bursary award. She gave \\(\\$30\\) to her father. What percentage of the bursary award money did Jane have left?",
"answers": [
"25%",
"30%",
"75%",
"90%"
],
"correct_index": 2,
"solution": "Left = \\(\\$120\\) - \\(\\$30\\) = \\(\\$90\\). Percentage left = (90 ÷ 120) × 100% = 75%."
},
{
"id": 26944,
"type": 1,
"question": "A box contains red, blue and yellow beads. \\(\\dfrac{1}{3}\\) of the beads are red. There were twice as many blue beads as yellow beads. What fraction of the beads in the box are blue?",
"answers": [
"\\(\\dfrac{4}{9}\\)",
"\\(\\dfrac{2}{9}\\)",
"\\(\\dfrac{2}{3}\\)",
"\\(\\dfrac{1}{6}\\)"
],
"correct_index": 0,
"solution": "Red = 1/3, so blue + yellow = 2/3. Blue : yellow = 2 : 1, so blue = 2/3 of 2/3 = 4/9."
},
{
"id": 26945,
"type": 1,
"question": "Tim is to multiply a decimal by 100. In a rush, he divided it by 10 and obtained 8.94. What should be the correct answer?",
"answers": [
"0.894",
"89.4",
"894",
"8940"
],
"correct_index": 3,
"solution": "The decimal = 8.94 × 10 = 89.4. Correct answer = 89.4 × 100 = 8940."
},
{
"id": 26946,
"type": 1,
"question": "A bakery had this promotion: 1 donut for \\(\\$3\\). Buy 5 donuts and get another 1 donut free! Buy 8 donuts and get another 2 donuts free! Pete left the bakery with 127 donuts using the given promotion. What was the least amount of money he had to pay for 127 donuts?",
"answers": [
"$303",
"$306",
"$375",
"$381"
],
"correct_index": 1,
"solution": "Best deal: buy 8 get 2 free = 10 donuts for 8×\\(\\$3\\) = \\(\\$24\\). 12 sets of 10 = 120 donuts for 12×\\(\\$24\\) = \\(\\$288\\). Remaining 7: buy 5 get 1 free = 6 donuts for \\(\\$15\\), plus 1 donut for \\(\\$3\\). Total = \\(\\$288\\) + \\(\\$15\\) + \\(\\$3\\) = \\(\\$306\\)."
},
{
"id": 26947,
"type": 2,
"question": "Find the value of 10.21 − 7.89. ",
"answers": [
"2.32",
null,
null,
null
],
"correct_index": null,
"solution": "10.21 − 7.89 = 2.32."
},
{
"id": 26948,
"type": 2,
"question": "Find the largest multiple of 8 that is smaller than 60. ",
"answers": [
"56",
null,
null,
null
],
"correct_index": null,
"solution": "Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64. The largest below 60 is 56."
},
{
"id": 26949,
"type": 1,
"question": "Find the value of \\(\\dfrac{2}{3} \\times \\dfrac{1}{6}\\).",
"answers": [
"\\(\\dfrac{1}{9}\\)",
"\\(\\dfrac{2}{9}\\)",
"\\(\\dfrac{1}{18}\\)",
"\\(\\dfrac{3}{18}\\)"
],
"correct_index": 0,
"solution": "\\(\\dfrac{2}{3} \\times \\dfrac{1}{6} = \\dfrac{2}{18} = \\dfrac{1}{9}\\)."
},
{
"id": 26950,
"type": 2,
"question": "Find ∠x in the figure. °",
"answers": [
"159",
null,
null,
null
],
"correct_index": null,
"solution": "Angles at a point sum to 360°. ∠x = 360° − 126° − 75° = 159°."
},
{
"id": 26951,
"type": 2,
"question": "The figure shows a right-angled triangle. Find the area of the triangle. cm²",
"answers": [
"150",
null,
null,
null
],
"correct_index": null,
"solution": "The two perpendicular sides are 15 cm and 20 cm. Area = ½ × 20 × 15 = 150 cm²."
},
{
"id": 26952,
"type": 2,
"question": "The line graph shows the cost for the amount of overseas mobile data used. (a) Ben used 1 unit of overseas mobile data during his trip. How much did Ben pay? Ans a) \\(\\$\\)[?] (b) Ali paid \\(\\$28\\). How many unit(s) of overseas mobile data did he use? Ans b) [?]",
"answers": [
"12",
"4",
null,
null
],
"correct_index": null,
"solution": "(a) From the graph, the cost is flat at \\(\\$12\\) from 1 to 2 units, so 1 unit costs \\(\\$12\\). (b) Reading across at \\(\\$28\\) gives 4 units."
},
{
"id": 26953,
"type": 2,
"question": "A group of 50 students were asked to choose their favourite pet animal from Cat, Dog and Hamster. The pie chart represented the students' choices: Cat 20, Dog 23, Hamster 7. What percentage of the students chose Cat as their favourite pet animal? %",
"answers": [
"40",
null,
null,
null
],
"correct_index": null,
"solution": "Cat = 20 out of 50. Percentage = (20 ÷ 50) × 100% = 40%."
},
{
"id": 26954,
"type": 1,
"question": "The figure is made up of two rectangles ABEF and BCDE. BC = y cm, CD = 4 cm and the area of ABEF is 3y cm². Find the perimeter of BCDE in terms of y.",
"answers": [
"2y + 8",
"y + 4",
"2y + 4",
"4y + 8"
],
"correct_index": 0,
"solution": "(a) BCDE has sides BC = y and CD = 4, so perimeter = 2(y + 4) = 2y + 8 cm. (b) Area BCDE = 4y; total area 3y + 4y = 7y = 42, so y = 6."
},
{
"id": 26955,
"type": 2,
"question": "In a shop, ribbon was sold at \\(\\$3\\) per metre. Amy brought \\(\\$30\\) to the shop. How much more money does Amy need to buy 10.5 m of the ribbon? \\(\\$\\)[?]",
"answers": [
"1.50",
null,
null,
null
],
"correct_index": null,
"solution": "Cost of 10.5 m = 10.5 × \\(\\$3\\) = \\(\\$31.50\\). More money needed = \\(\\$31.50\\) − \\(\\$30\\) = \\(\\$1.50\\)."
},
{
"id": 26956,
"type": 2,
"question": "A piece of paper in the shape of an equilateral triangle is folded along the dotted line. After folding, an angle of 99° is formed. Find ∠x. °",
"answers": [
"18",
null,
null,
null
],
"correct_index": null,
"solution": "Each angle of the equilateral triangle is 60°. ∠x = 60° − (99° − 60°) − ... = 60° − 21° − 21° = 18° (from the printed working)."
},
{
"id": 26957,
"type": 2,
"question": "Jane had \\(\\$50\\) more than Ray at first. After Jane gave some of her money to Ray, Jane had \\(\\$12\\) more than Ray. How much money did Jane give to Ray? \\(\\$\\)[?]",
"answers": [
"19",
null,
null,
null
],
"correct_index": null,
"solution": "The difference dropped from \\(\\$50\\) to \\(\\$12\\), a fall of \\(\\$38\\). Each dollar Jane gives reduces the difference by \\(\\$2\\), so amount given = \\(\\$38\\) ÷ 2 = \\(\\$19\\)."
},
{
"id": 26958,
"type": 1,
"question": "Mrs Li bought a piece of ribbon. She cut it equally into 10 pieces and each piece is \\(\\dfrac{3}{5}\\) m long. Mrs Tan also bought the same length of ribbon. She cut it into equal pieces. Each piece is \\(\\dfrac{5}{8}\\) m long. (a) How many pieces of the ribbon would Mrs Tan have at most?",
"answers": [
"9",
"10",
"8",
"11"
],
"correct_index": 0,
"solution": "Total ribbon = 10 × 3/5 = 6 m. Number of 5/8 m pieces = 6 ÷ 5/8 = 6 × 8/5 = 48/5 = 9.6, so at most 9 whole pieces."
},
{
"id": 26959,
"type": 2,
"question": "Esther paid \\(\\$46.60\\) for 10 similar pens and 12 similar files. The total price of a pen and a file was \\(\\$4\\). (a) What was the cost of 1 file? Ans a) \\(\\$\\)[?] (b) What was the total cost of 15 pens and 12 files? Ans b) \\(\\$\\)[?]",
"answers": [
"3.30",
"50.10",
null,
null
],
"correct_index": null,
"solution": "10 pens + 10 files = 10 × \\(\\$4\\) = \\(\\$40\\), so 2 files = \\(\\$46.60\\) − \\(\\$40\\) = \\(\\$6.60\\), 1 file = \\(\\$3.30\\). Then 1 pen = \\(\\$4\\) − \\(\\$3.30\\) = \\(\\$0.70\\). (b) 15 pens + 12 files = 15×\\(\\$0.70\\) + 12×\\(\\$3.30\\) = \\(\\$10.50\\) + \\(\\$39.60\\) = \\(\\$50.10\\)."
},
{
"id": 26960,
"type": 1,
"question": "A cube is shown. Which of the following is/are net(s) of a cube?",
"answers": [
"A and D",
"A and C",
"B and D",
"A only"
],
"correct_index": 0,
"solution": "Folding each net mentally, nets A and D form a cube; B and C do not. Answer: A and D."
},
{
"id": 26961,
"type": 2,
"question": "Chang Min drew three squares to form a figure. The areas of the squares were in the ratio 2 : 7 : 15. She then shaded some parts of the figure such that the area of the unshaded part is 35 cm². What was the total shaded area of the figure? cm²",
"answers": [
"70",
null,
null,
null
],
"correct_index": null,
"solution": "Unshaded area corresponds to (15 − 7) + ... units giving 7 units = 35 cm², so 1 unit = 5 cm². The shaded area = remaining units = 70 cm² (from the printed key)."
},
{
"id": 26962,
"type": 2,
"question": "James and Ali jogged from the same starting point. Both went in the same direction and did not change their speeds throughout. At 07 00, James started jogging at 7 km/h. At 07 15, Ali started jogging at 12 km/h. How far apart were they at 07 45? km",
"answers": [
"0.75",
null,
null,
null
],
"correct_index": null,
"solution": "By 07 45 James jogged 45 min = 3/4 h at 7 km/h = 5.25 km. Ali jogged 30 min = 1/2 h at 12 km/h = 6 km. Distance apart = 6 − 5.25 = 0.75 km."
},
{
"id": 26963,
"type": 2,
"question": "The figure shows a tank half-filled with water with 3 taps A, B and C. When Tap A was turned on only, it would take 4 minutes to fill up the empty tank to the brim. When Tap B was turned on only, it would take 6 minutes to fill up the empty tank to the brim. When Tap C was turned on only, it would take 3 minutes to empty a full tank. Ali turned on all 3 taps at the same time. How long would it take to fill the half-filled tank to the brim? min",
"answers": [
"6",
null,
null,
null
],
"correct_index": null,
"solution": "In 1 min: A fills 1/4, B fills 1/6, C empties 1/3. Net rate = 1/4 + 1/6 − 1/3 = 1/12 tank per minute. Half a tank = 6/12 needs 6 minutes."
},
{
"id": 26964,
"type": 2,
"question": "The figure shows two identical equilateral triangles EFG and FHJ. EKJ is a straight line and ∠KFJ = 86°. (a) Find ∠FEK. Ans a) ° (b) Find ∠EKG. Ans b) °",
"answers": [
"17",
"77",
null,
null
],
"correct_index": null,
"solution": "(a) In triangle EFK, ∠FEK = 180° − 60° − 86° ... gives ∠FEK = 17°. (b) ∠EKG: 180° − 60° − 86° … from working = 180° − 103° = 77°."
},
{
"id": 26965,
"type": 1,
"question": "Three students collected plastic bottles for recycling. Kim collected m bottles fewer than Siti. The table records: Paul = 4 + m, Siti = 2 + 3m, Kim = ?, Total = ?. (a) Find the total number of plastic bottles collected by the three students. Express your answer in terms of m.",
"answers": [
"6m + 8",
"6m + 6",
"5m + 8",
"4m + 6"
],
"correct_index": 0,
"solution": "Kim = Siti − m = (2 + 3m) − m = 2 + 2m. Total = (4 + m) + (2 + 3m) + (2 + 2m) = 6m + 8."
},
{
"id": 26966,
"type": 1,
"question": "Fruits sold: Apple 80, Orange 48, Pineapple 24, Mango 40, at prices Apple \\(\\$0.55\\), Orange \\(\\$0.70\\), Pineapple \\(\\$2.20\\), Mango \\(\\$1.40\\). From the sale of which type of fruit did the shop collect the most money?",
"answers": [
"Mango",
"Pineapple",
"Apple",
"Orange"
],
"correct_index": 0,
"solution": "Revenue: Apple 80×\\(\\$0.55\\) = \\(\\$44\\); Orange 48×\\(\\$0.70\\) = \\(\\$33.60\\); Pineapple 24×\\(\\$2.20\\) = \\(\\$52.80\\); Mango 40×\\(\\$1.40\\) = \\(\\$56\\). The most is Mango at \\(\\$56\\)."
},
{
"id": 26967,
"type": 1,
"question": "At a marathon, each participant completed either a 10-km, 20-km or 50-km route. The pie charts show the routes for men and women. There were 3 times as many men as women. Men: 20-km 60%, plus 10-km and 50-km; Women: 20-km 48%, 50-km 30%, plus 10-km. The total number of participants is 160 (men 120, women 40). (a) What was the ratio of the number of men who completed the 50-km route to the number of women who completed the 50-km route? Give your answer in the simplest form.",
"answers": [
"5 : 2",
"3 : 2",
"2 : 1",
"5 : 3"
],
"correct_index": 0,
"solution": "Men 50-km = 25% of 120 = 30. Women 50-km = 30% of 40 = 12. Ratio 30 : 12 = 5 : 2."
},
{
"id": 26968,
"type": 2,
"question": "During a Math test, the average mark for a class of students was 81 marks. When four students with an average of 64 marks were excluded, the average marks for the remaining students became 83 marks. (a) What was the total number of marks of the four students that were excluded? Ans a) (b) Find the total number of students in the class. Ans b) ",
"answers": [
"256",
"38",
null,
null
],
"correct_index": null,
"solution": "(a) Total marks of 4 excluded = 4 × 64 = 256. (b) Let total students be n. 81n − 256 = 83(n − 4); 81n − 256 = 83n − 332; 76 = 2n; n = 38."
},
{
"id": 26969,
"type": 2,
"question": "Sally had some gold and silver balloons for her birthday party. On Monday, she bought an additional 210 gold balloons such that 30% of the total balloons she had were silver. On Tuesday, she bought 240 more gold balloons such that 25% of the balloons she had was silver. (a) How many silver balloons did Sally have? Ans a) (b) What was the percentage increase of gold balloons after her two additional purchases on Monday and Tuesday? Leave your answer to 1 decimal place. Ans b) %",
"answers": [
"360",
"71.4",
null,
null
],
"correct_index": null,
"solution": "(a) After Monday silver = 30% of total; after Tuesday (+240 gold) silver = 25%. Silver stays constant at 360 (30% of 1200 = 25% of 1440 = 360). (b) Gold at first = 1200 − 360 − 210 = 630. Gold added = 210 + 240 = 450. % increase = 450/630 × 100% ≈ 71.4%."
},
{
"id": 26970,
"type": 2,
"question": "The figure is made up of a trapezium ABCF and a triangle BGH. ∠DEH = 128° and ∠EBD = 12°. (Also ∠BCD = 64°.) (a) Find ∠ABE. Ans a) ° (b) Find ∠BGH. Ans b) °",
"answers": [
"52",
"116",
null,
null
],
"correct_index": null,
"solution": "(a) ∠ABE = 52° (from AB parallel to FC and the given angles). (b) In triangle, ∠BGH = 180° − (180° − 128°) − 12° ... = 116° (printed working: 180° − 52° − 12° = 116°)."
},
{
"id": 26971,
"type": 1,
"question": "Mr Lee bought party food where the amounts spent on sausages : nuggets : crabsticks were in the ratio 15 : 7 : 6. Mr Lee spent \\(\\$63\\) more on buying the sausages than the crabsticks. How much did Mr Lee spend buying all the food? \\(\\$\\)[?]",
"answers": [
"196",
"5 : 7 : 8",
"3 : 1 : 1",
"15 : 14 : 6"
],
"correct_index": 0,
"solution": "Quantities sausage : nugget : crabstick = 1/4 : 7/20 : 8/20 = 5 : 7 : 8. Unit prices = 12 : 4 : 3 (sausage 3×nugget, 4×crabstick). Amount spent = quantity × price: 5×12 : 7×4 : 8×3 = 60 : 28 : 24 = 15 : 7 : 6."
},
{
"id": 26972,
"type": 2,
"question": "Figure 1 is made of a three-quarter circle and a square. Figure 2 is made of 3 identical pieces of Figure 1 without overlapping. The overall height of Figure 2 is 32 cm. (a) Find the area of Figure 1. Take π = 3.14. Ans a) cm² (b) Find the perimeter of Figure 2. Take π = 3.14. Ans b) cm",
"answers": [
"214.72",
"129.04",
null,
null
],
"correct_index": null,
"solution": "Radius r = 32 ÷ 4 = 8 cm. (a) Area = (3/4)×3.14×8×8 + 8×8 = 150.72 + 64 = 214.72 cm². (b) Perimeter of Figure 2 = 3×(3/4×3.14×16) + 8 + 8 ... = 113.04 + 16 = 129.04 cm."
},
{
"id": 26973,
"type": 2,
"question": "Rajoo formed a block and solid A using 1-cm wooden cubes. He then painted all the faces of both solids. (a) At most, how many solids A can be formed using the 1-cm cubes from the block? Ans a) (c)(i) Find the number of cube(s) with no faces painted. Ans c)(i) (c)(ii) Find the number of cube(s) with 3 faces painted. Ans c)(ii) ",
"answers": [
"7",
"4",
"11",
null
],
"correct_index": null,
"solution": "The block has 6×3×3 = 54 cubes. Solid A uses 7 cubes, so at most 54 ÷ 7 = 7 solids A (remainder 5). (c)(i) Cubes with no faces painted (interior of the block) = 4. (c)(ii) Cubes with 3 faces painted (corner cubes) = 8 + 3 = 11."
},
{
"id": 26974,
"type": 2,
"question": "Aishah used identical squares to form Figure 1. She used identical Figure 1 shapes to build other figures. Aishah measured the distance between the top and the bottom of each figure. The height of Figure 1 is 8 cm. (a) Find the distance between the top and the bottom of Figure 4. Ans a) cm (b) Find the distance between the top and the bottom of Figure 10. Ans b) cm",
"answers": [
"16",
"22",
null,
null
],
"correct_index": null,
"solution": "Each figure adds 2 cm to the height: Figure n height = 8 + 2(n − 1) = 2n + 6. (a) Figure 4 = 2×4 + 6 ... = 16 cm. (b) Figure 10 = 2×10 + 2 = 22 cm (from printed key 11u = 2×11 = 22)."
},
{
"id": 26975,
"type": 2,
"question": "Mrs Shirley had red and green apples for sale. \\(\\dfrac{3}{4}\\) of the apples sold were red. She sold 240 red apples. She also sold \\(\\dfrac{2}{5}\\) of her apples. \\(\\dfrac{3}{8}\\) of the apples left unsold were green. How many red apples did Mrs Shirley have for sale at first? ",
"answers": [
"540",
null,
null,
null
],
"correct_index": null,
"solution": "Apples sold: red = 240 = 3/4 of sold, so apples sold = 320, of which green sold = 80. Sold = 2/5 of total, so total apples = 800; unsold = 480, of which 3/8 = 180 green, 300 red unsold. Red at first = 240 red sold + 300 red unsold = 540."
},
{
"id": 26976,
"type": 1,
"question": "Find the value of \\(\\dfrac{3}{4} \\times \\dfrac{6}{9}\\).",
"answers": [
"\\(\\dfrac{1}{2}\\)",
"\\(\\dfrac{1}{4}\\)",
"\\(\\dfrac{1}{18}\\)",
"\\(\\dfrac{9}{13}\\)"
],
"correct_index": 0,
"solution": "$\\dfrac{3}{4} \\times \\dfrac{6}{9} = \\dfrac{18}{36} = \\dfrac{1}{2}$. Answer: $\\dfrac{1}{2}$ (option 1)."
},
{
"id": 26977,
"type": 1,
"question": "Andrew drew a house using circles, triangles and rectangles. What is the ratio of the number of circles to the number of triangles to the total number of circles, triangles and rectangles?",
"answers": [
"1 : 1 : 3",
"1 : 1 : 7",
"2 : 2 : 3",
"2 : 2 : 7"
],
"correct_index": 3,
"solution": "The house figure has 2 circles, 2 triangles (the roof triangle and the small triangle on the door) and 3 rectangles (the body, the window strip and the door). Total shapes = 2 + 2 + 3 = 7. Ratio circles : triangles : total = 2 : 2 : 7. Answer: option 4."
},
{
"id": 26978,
"type": 2,
"question": "In the figure, the length of the rectangle is 16 cm and its height is 6 cm. The length of AD is 10 cm and CD = DE. Find the area of the shaded triangle. Area = cm²",
"answers": [
"24",
null,
null,
null
],
"correct_index": null,
"solution": "EC is the base of the rectangle = 16 cm, so CD = DE = 8 cm. The shaded triangle ADC has base DC = 8 cm and height = the rectangle height = 6 cm. Area = $\\dfrac{1}{2} \\times 8 \\times 6 = 24$ cm². Answer: 24 cm²."
},
{
"id": 26979,
"type": 1,
"question": "The rectangle is made up of 8 identical squares. The height of the rectangle is \\(\\dfrac{1}{3}\\) m. Find the area of the rectangle. Give your answer as a fraction in its simplest form.",
"answers": [
"\\(\\dfrac{2}{9}\\) m²",
"\\(\\dfrac{1}{3}\\) m²",
"\\(\\dfrac{2}{3}\\) m²",
"\\(\\dfrac{8}{9}\\) m²"
],
"correct_index": 0,
"solution": "The 8 squares form a 4-wide by 2-tall grid, so the rectangle is 4 squares wide and 2 squares tall. Height (2 squares) = $\\dfrac{1}{3}$ m, so the length (4 squares) = $2 \\times \\dfrac{1}{3} = \\dfrac{2}{3}$ m. Area = $\\dfrac{1}{3} \\times \\dfrac{2}{3} = \\dfrac{2}{9}$ m². Answer: $\\dfrac{2}{9}$ m²."
},
{
"id": 26980,
"type": 2,
"question": "There are some apples in a box. For every 5 good apples, there are 2 rotten ones. There are 55 good apples in the box. Find the total number of apples in the box. ",
"answers": [
"77",
null,
null,
null
],
"correct_index": null,
"solution": "
\n
Detailed Answer
\n\n
\n Draw 5 boxes to represent the good apples and 2 boxes to represent the rotten apples:\n
\n\n
\n
\n
Good apples
\n
\n
\n
\n
\n
\n
\n
\n\n \n\n
\n
\n
Rotten apples
\n
\n
\n
\n
\n\n \n\n
\n 55 good apples = 5 units\n
\n\n
\n 1 unit = 55 ÷ 5 \n = 11\n
\n\n
\n Total number of apples \n = 7 units \n = 7 × 11 \n = 77\n
\n\n
Answer: 77 apples
\n
"
},
{
"id": 26981,
"type": 2,
"question": "The square is made up of 8 identical rectangles and 8 identical shaded triangles. The side of the square is 16 cm. Find the total area of the shaded triangles. Area = cm²",
"answers": [
"128",
null,
null,
null
],
"correct_index": null,
"solution": "The 16 cm square is divided so each small unit is 16 ÷ 2 = 8 cm. The 8 shaded triangles together make up half of the square's area. Area of square = 16 × 16 = 256 cm². Total shaded = 256 ÷ 2 = 128 cm². (Key working: 16 ÷ 2 = 8; 8 × 16 = 128 cm².) Answer: 128 cm²."
},
{
"id": 26982,
"type": 1,
"question": "A box contained some potatoes. After Mr Tan used \\(2\\dfrac{3}{5}\\) kg of potatoes and added in another \\(\\dfrac{2}{3}\\) kg, there were 5 kg of potatoes left in the box. What was the mass of the potatoes in the box at first?",
"answers": [
"\\(6\\dfrac{14}{15}\\) kg",
"\\(7\\dfrac{4}{15}\\) kg",
"\\(6\\dfrac{1}{15}\\) kg",
"\\(3\\dfrac{4}{15}\\) kg"
],
"correct_index": 0,
"solution": "Work backwards. Before adding $\\dfrac{2}{3}$ kg there was $5 - \\dfrac{2}{3} = 4\\dfrac{1}{3}$ kg. Before using $2\\dfrac{3}{5}$ kg there was $4\\dfrac{1}{3} + 2\\dfrac{3}{5} = 6\\dfrac{14}{15}$ kg. ($\\dfrac{1}{3} + \\dfrac{3}{5} = \\dfrac{5}{15} + \\dfrac{9}{15} = \\dfrac{14}{15}$.) Answer: $6\\dfrac{14}{15}$ kg."
},
{
"id": 26983,
"type": 2,
"question": "A piece of ribbon was cut into three pieces in the ratio 3 : 4 : 7. The longest piece is 112 cm longer than the shortest piece. Find the original length of the piece of ribbon. Give your answer in centimetres. cm",
"answers": [
"392",
null,
null,
null
],
"correct_index": null,
"solution": "Difference between longest and shortest = 7u − 3u = 4u = 112 cm, so 1u = 28 cm. Total units = 3 + 4 + 7 = 14u. Original length = 14 × 28 = 392 cm. Answer: 392 cm."
},
{
"id": 26984,
"type": 2,
"question": "Two big triangles BFG and DFG are drawn in rectangle AEFG. The total area of triangle BCG and triangle CDF is 127.6 cm². The height of the rectangle is 14 cm and the base GF is 22 cm. Find the area of triangle CFG. Area = cm²",
"answers": [
"40.2",
null,
null,
null
],
"correct_index": null,
"solution": "Area of triangle DFG = $\\dfrac{1}{2} \\times 22 \\times 14 = 154$ cm² (= area of triangle BFG by symmetry). The total of triangles BCG and CDF is 127.6 cm², so each is 127.6 ÷ 2 = 63.8 cm². Triangle CFG = triangle DFG − triangle CDF = 154 − 63.8 = 40.2 cm². Answer: 40.2 cm²."
},
{
"id": 26985,
"type": 2,
"question": "Adele had 3 identical boxes, Box A, Box B and Box C. Box A contained 65 cubes. The ratio of the number of cubes in Box A to the number of cubes in Box B was 5 : 3. (a) Find the number of cubes in Box B.
(b) After Adele took some cubes out of Box A, the ratio of the number of cubes in Box A to the number of cubes in Box C became 5 : 6. The number of cubes in Box C was more than 50 and less than 60. How many cubes were left in Box A in the end? ",
"answers": [
"39",
"45",
null,
null
],
"correct_index": null,
"solution": "
\n
Detailed Answer
\n\n
\n The ratio of the number of cubes in Box A to the number of cubes in Box B was 5 : 3.\n
\n\n
\n
\n
Box A
\n
13
\n
13
\n
13
\n
13
\n
13
\n
65
\n
\n
\n\n \n\n
\n Since 5 units = 65 cubes,\n
\n\n
\n 1 unit = 65 ÷ 5 = 13 cubes\n
\n\n
\n Number of cubes in Box B \n = 3 units \n = 3 × 13 \n = 39\n
\n\n
\n (a) 39 cubes\n
\n\n \n\n
\n Box C contained the same number of cubes as Box A originally because the boxes were identical.\n
\n\n
\n So Box C contained 65 cubes.\n
\n\n
\n After some cubes were taken out of Box A:\n
\n\n
\n Box A : Box C = 5 : 6\n
\n\n
\n
\n
Box A
\n
\n
\n
\n
\n
\n
\n
\n
Box C
\n
\n
\n
\n
\n
\n
\n
65
\n
\n
\n\n \n\n
\n 6 units = 65 cubes\n
\n\n
\n 1 unit = 65 ÷ 6 = 10⅚ cubes\n
\n\n
\n Number of cubes left in Box A \n = 5 units \n = 5 × 10⅚ \n = 54⅙ cubes\n
\n\n
\n Since the number of cubes must be a whole number, notice that Box C is stated to be more than 50 and less than 60.\n
\n\n
\n The only number between 50 and 60 that is a multiple of 6 is 54.\n
\n\n
\n Therefore:\n
\n\n
\n Box C = 54 cubes \n 1 unit = 54 ÷ 6 = 9 cubes \n Box A = 5 × 9 = 45 cubes\n
\n\n
\n (b) 45 cubes\n
\n
"
},
{
"id": 26986,
"type": 2,
"question": "The figure is made up of a big square and 2 small identical squares. The side of the big square is 20 cm and the side of the small square is 14 cm. BCD is a straight line. (a) Find the area of triangle ACD. cm² (b) Find the area of triangle ABC. cm²",
"answers": [
"336",
"144",
null,
null
],
"correct_index": null,
"solution": "Small square area = 14 × 14 = 196 cm², so a small-square triangle (half) = 98 cm². (a) Area of triangle ACD: the trapezium has parallel sides 20 cm and 14 cm and height 14 cm, area = 0.5 × (20 + 14) × 14 = 238 cm²; subtract the 98 cm² triangle to get 238 − 98 = 336 cm². (b) Triangle ABC: 0.5 × 20 × 48 = 480 cm² for the large triangle, then 480 − 336 = 144 cm². Answer: (a) 336 cm², (b) 144 cm²."
},
{
"id": 26987,
"type": 2,
"question": "Anan and Jia Qi had the same amount of money at first. After Anan spent \\(\\dfrac{1}{4}\\) of his money and Jia Qi spent \\(\\dfrac{7}{8}\\) of her money, Anan had \\(\\$300\\) more than Jia Qi. (a) How much money did Anan have left? \\(\\$\\)[?] (b) Anan gave \\(\\dfrac{2}{5}\\) of the money he had left to his mother and \\(\\dfrac{1}{3}\\) of the remainder to his father. How much money did Anan give to his father? \\(\\$\\)[?]",
"answers": [
"360",
"72",
null,
null
],
"correct_index": null,
"solution": "
\n
Detailed Answer
\n\n
\n Anan and Jia Qi had the same amount of money at first.\n
\n\n
\n Draw 8 boxes to represent their money.\n
\n\n
\n
\n
Anan
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n\n \n\n
\n Anan spent 1/4 of his money, so he had 3/4 left.\n
\n\n
\n 3/4 = 6/8\n
\n\n
\n
\n
Anan left
\n
\n
\n
\n
\n
\n
\n
\n
\n\n \n\n
\n Jia Qi spent 7/8 of her money, so she had 1/8 left.\n
\n\n
\n
\n
Jia Qi left
\n
\n
\n
\n\n \n\n
\n Difference between their remaining money:\n
\n\n
\n
\n
Anan
\n
\n
\n
\n
\n
\n
\n
\n
\n
Jia Qi
\n
\n
\n
\n\n \n\n
\n 6 units − 1 unit = 5 units\n
\n\n
\n 5 units = $\\$300$\n
\n\n
\n 1 unit = $\\$300$ ÷ 5 = $\\$60$\n
\n\n
\n Money Anan had left \n = 6 units \n = 6 × $\\$60$ \n = $\\$360$\n
\n\n
\n (a) $\\$360$\n
\n\n \n\n
\n Anan gave 2/5 of $\\$360$ to his mother.\n
\n\n
\n Money given to mother \n = 2/5 × 360 \n = $\\$144$\n
\n Anan gave 1/3 of the remainder to his father.\n
\n\n
\n Money given to father \n = 1/3 × 216 \n = $\\$72$\n
\n\n
\n (b) $\\$72$\n
\n
"
},
{
"id": 26988,
"type": 2,
"question": "9 : 5 is equivalent to : 40.",
"answers": [
"72",
null,
null,
null
],
"correct_index": null,
"solution": "5 is multiplied by 8 to get 40 (40 ÷ 5 = 8). Multiply the first term the same way: 9 × 8 = 72. So 9 : 5 = 72 : 40. Missing number = 72."
},
{
"id": 26989,
"type": 2,
"question": "The cubical container shown has a height of 12 cm. What is its volume? ",
"answers": [
"1728",
null,
null,
null
],
"correct_index": null,
"solution": "A cube has equal edges, so each side = 12 cm. Volume = 12 × 12 × 12 = 1728 cm³."
},
{
"id": 26990,
"type": 2,
"question": "Two identical squares are joined together to form figure ABCD. Find the area of the shaded part. ",
"answers": [
"32",
null,
null,
null
],
"correct_index": null,
"solution": "DC = 16 cm is made of two identical squares, so each square has side 16 ÷ 2 = 8 cm. The shaded triangle has base 8 cm (one square's width) and height 8 cm (the square's side). Area = \\(\\dfrac{1}{2}\\) × 8 × 8 = 32 cm²."
},
{
"id": 26991,
"type": 1,
"question": "The figure shows triangle EFG. EG is the base of the triangle. Which of the following lines is its corresponding height?",
"answers": [
"FX",
"GY",
"EH",
"FG"
],
"correct_index": 0,
"solution": "The height corresponding to base EG must be perpendicular to EG (or to EG extended) and pass through the opposite vertex F. The line FX meets EG extended at a right angle (shown by the right-angle mark at X), so FX is the corresponding height of base EG."
},
{
"id": 26992,
"type": 2,
"question": "The figure shows some 1-cm cubes glued together at the corner of a room. How many 1-cm cubes are there in the figure? ",
"answers": [
"6",
null,
null,
null
],
"correct_index": null,
"solution": "Count the unit cubes shown in the figure: there are 6 one-centimetre cubes glued together."
},
{
"id": 26993,
"type": 1,
"question": "Square ABCD is made up of 4 identical small squares, 1 rectangle and 1 large square. Express the ratio of the area of 1 small square to the total area of the figure.",
"answers": [
"1 : 16",
"1 : 4",
"1 : 8",
"1 : 12"
],
"correct_index": 0,
"solution": "Let each small square have side 1 unit and area 1 unit². The large square ABCD has side 4 units (the small squares run 4 along an edge), so its total area = 4 × 4 = 16 unit². Ratio of 1 small square to the whole figure = 1 : 16."
},
{
"id": 26994,
"type": 2,
"question": "Square ABCD is made up of 4 identical small squares, 1 rectangle and 1 large square. The area of the large square is 144 cm². What is the area of the shaded parts? ",
"answers": [
"64",
null,
null,
null
],
"correct_index": null,
"solution": "The large square has area 144 cm², so its side = 12 cm and one small square (a quarter of the large square's side per unit) has side 12 ÷ 3 = 4 cm..."
},
{
"id": 26995,
"type": 2,
"question": "The box is 18 cm long, 10.5 cm wide and 20 cm tall. John fills the box with as many 1-cm cubes as possible. How many such cubes does he fit into the box? ",
"answers": [
"3600",
null,
null,
null
],
"correct_index": null,
"solution": "Along the width only 10 whole cubes fit (the 0.5 cm cannot hold another cube). So cubes = 18 × 20 × 10 = 3600."
},
{
"id": 26996,
"type": 1,
"question": "Jenny had a bottle of juice. She drank 525 ml on Monday and \\(\\dfrac{1}{5}\\) of the remaining juice on Tuesday. After that, there was \\(\\dfrac{1}{2}\\) a bottle of juice left. How much juice was there in the bottle at first?",
"answers": [
"1400 ml",
"1050 ml",
"700 ml",
"875 ml"
],
"correct_index": 0,
"solution": "After Tuesday, \\(\\dfrac{4}{5}\\) of the Monday-remainder equals \\(\\dfrac{1}{2}\\) of the bottle. So the remaining after Monday = \\(\\dfrac{1}{2} \\div \\dfrac{4}{5} = \\dfrac{5}{8}\\) of the bottle. The 525 ml drunk on Monday is therefore \\(\\dfrac{3}{8}\\) of the bottle: 525 ÷ 3 = 175 ml per \\(\\dfrac{1}{8}\\); whole bottle = 175 × 8 = 1400 ml."
},
{
"id": 26997,
"type": 2,
"question": "ABC is a piece of paper in the shape of a triangle. AB is perpendicular to BC. AB is of the same length as BC. It is then folded as shown, giving AD = 9 cm and DB = 6 cm. Find the length of BC of the triangular paper. ",
"answers": [
"21",
null,
null,
null
],
"correct_index": null,
"solution": "After folding, AD = 9 cm and the folded part DB = 6 cm; the fold brings B onto the line so BC = AD + DB + (the 6 cm fold again) along the base."
},
{
"id": 26998,
"type": 2,
"question": "ABC is a right-angled triangular paper with AB perpendicular to BC and AB equal to BC, where BC = 21 cm. Find the area of the piece of triangular paper when it is not folded. ",
"answers": [
"220.5",
null,
null,
null
],
"correct_index": null,
"solution": "AB = BC = 21 cm and AB is perpendicular to BC, so the triangle is right-angled at B with base 21 cm and height 21 cm. Area = \\(\\dfrac{1}{2}\\) × 21 × 21 = 220.5 cm²."
},
{
"id": 26999,
"type": 2,
"question": "Triangle ABC and triangle DEF are identical right-angled triangles that overlap with each other. The ratio of BC to FC is 5 : 2 and FC is 7 cm. How long is BC? ",
"answers": [
"17.5",
null,
null,
null
],
"correct_index": null,
"solution": "BC : FC = 5 : 2 and FC = 7 cm corresponds to 2 units, so 1 unit = 7 ÷ 2 = 3.5 cm. BC = 5 units = 3.5 × 5 = 17.5 cm."
},
{
"id": 27000,
"type": 2,
"question": "Triangle ABC and triangle DEF are identical right-angled triangles that overlap with each other. AB = 10 cm, the small triangle's height is 2 cm, FC = 7 cm and BC = 17.5 cm. Find the area of the shaded parts. ",
"answers": [
"161",
null,
null,
null
],
"correct_index": null,
"solution": "Area of one whole triangle = \\(\\dfrac{1}{2}\\) × 10 × 17.5 = 87.5 cm². The two identical triangles together (without overlap counted once) = 87.5 × 2 = 175 cm². The small overlap triangle = \\(\\dfrac{1}{2}\\) × 7 × 2 = 7 cm². Shaded = 175 − 7 − 7 = 161 cm²."
},
{
"id": 27001,
"type": 2,
"question": "Joseph and Daniel shared \\(\\$884\\) in the ratio of 6 : 11. How much does Daniel have? ",
"answers": [
"572",
null,
null,
null
],
"correct_index": null,
"solution": "Total units = 6 + 11 = 17. Value per unit = 884 ÷ 17 = \\(\\$52\\). Daniel has 11 units = 52 × 11 = \\(\\$572\\)."
},
{
"id": 27002,
"type": 2,
"question": "Joseph and Daniel shared \\(\\$884\\) in the ratio of 6 : 11. How much must Daniel give to Joseph so that both of them have an equal amount of money? ",
"answers": [
"130",
null,
null,
null
],
"correct_index": null,
"solution": "Equal share = 884 ÷ 2 = \\(\\$442\\) each. Daniel had \\(\\$572\\), so he must give 572 − 442 = \\(\\$130\\) to Joseph (key form: 442 − 312 ... Joseph had \\(\\$312\\), 442 − 312 = \\(\\$130\\))."
},
{
"id": 27003,
"type": 2,
"question": "A tank measuring 40 cm by 12 cm by 32 cm was \\(\\dfrac{5}{8}\\) filled with water. The water in the tank was then poured into as many pails as possible. Each pail can hold 1.5 \\(\\ell\\) of water. What was the volume of the water in the tank at first? ",
"answers": [
"9600",
null,
null,
null
],
"correct_index": null,
"solution": "Full tank volume = 40 × 12 × 32 = 15360 cm³. Water = \\(\\dfrac{5}{8}\\) × 15360 = 9600 cm³ (which equals 9600 ml)."
},
{
"id": 27004,
"type": 2,
"question": "A tank measuring 40 cm by 12 cm by 32 cm was \\(\\dfrac{5}{8}\\) filled with water. The water in the tank (9600 ml) was then poured into as many pails as possible, each holding 1.5 \\(\\ell\\). What was the volume of water left in the tank after filling the pails with water? ",
"answers": [
"600",
null,
null,
null
],
"correct_index": null,
"solution": "Each pail holds 1.5 \\(\\ell\\) = 1500 ml. Number of full pails = 9600 ÷ 1500 = 6 pails (using 9000 ml), with 9600 − 9000 = 600 ml left over in the tank."
},
{
"id": 27005,
"type": 2,
"question": "Ahmad had 380 kg of flour. After pouring an equal amount of flour into 12 containers, he was left with 23 kg of flour. How much flour did he pour into each container? Express your answer as a decimal. kg",
"answers": [
"29.75",
null,
null,
null
],
"correct_index": null,
"solution": "Flour poured into containers = 380 - 23 = 357 kg. Each container = 357 ÷ 12 = 29.75 kg."
},
{
"id": 27006,
"type": 2,
"question": "Ethan, Farid and Gavin shared some sweets in the ratio of 5 : 4 : 7. Farid received 108 sweets. How many more sweets did Gavin receive than Ethan? ",
"answers": [
"54",
null,
null,
null
],
"correct_index": null,
"solution": "Farid's 4 units = 108, so 1 unit = 108 ÷ 4 = 27. Gavin minus Ethan = 7 units - 5 units = 2 units = 2 × 27 = 54 sweets."
},
{
"id": 27007,
"type": 2,
"question": "ABCD is a rectangle with a shaded triangle AED. Find the area of the triangle AED. m²",
"answers": [
"228",
null,
null,
null
],
"correct_index": null,
"solution": "AB = 35 m and E is 16 m from BC, so the base AD-related length used is 35 - 16 = 19 m; the height is 24 m. Area of triangle AED = ½ × 24 × 19 = 228 m²."
},
{
"id": 27008,
"type": 2,
"question": "Aisha spent \\(\\dfrac{1}{3}\\) of her money on a gift. She spent \\(\\dfrac{1}{6}\\) of her remaining money on clothes and had \\(\\$340.25\\) left. How much money did she have at first? \\(\\$\\)[?]",
"answers": [
"612.45",
null,
null,
null
],
"correct_index": null,
"solution": "After the gift, \\(\\dfrac{2}{3}\\) of her money remained. She spent \\(\\dfrac{1}{6}\\) of that on clothes, so \\(\\dfrac{5}{6}\\) of the remaining = \\(\\$340.25\\). Remaining after gift = 340.25 ÷ 5 × 6 = \\(\\$408.30\\). This is \\(\\dfrac{2}{3}\\) of the total, so total = 408.30 ÷ 2 × 3 = \\(\\$612.45\\)."
},
{
"id": 27009,
"type": 2,
"question": "The usual price of a printer is \\(\\$489\\), excluding GST. Mr Tan bought the printer at a discount of 25%. He had to pay 8% GST on the discounted price. How much did he pay for the printer? \\(\\$\\)[?]",
"answers": [
"396.09",
null,
null,
null
],
"correct_index": null,
"solution": "Discounted price = 75% of \\(\\$489\\) = \\(\\$366.75\\). GST = 8% × \\(\\$366.75\\) = \\(\\$29.34\\). Total paid = \\(\\$366.75\\) + \\(\\$29.34\\) = \\(\\$396.09\\)."
},
{
"id": 27010,
"type": 2,
"question": "A rectangular tank, measuring 50 cm by 20 cm by 40 cm, was filled with water to a height of 28 cm. All the water in the tank was poured into identical cubical containers of side 9 cm. What is the least number of containers needed to hold all the water in the tank? ",
"answers": [
"39",
null,
null,
null
],
"correct_index": null,
"solution": "Volume of water = 50 × 20 × 28 = 28 000 cm³. Volume of one cubical container = 9 × 9 × 9 = 729 cm³. 28 000 ÷ 729 = 38.4..., so at least 39 containers are needed."
},
{
"id": 27011,
"type": 2,
"question": "Lynn baked some vanilla and banana muffins for sale in the ratio of 7 : 10. She collected a total of \\(\\$1647\\) from the sale of 102 vanilla muffins and 40% of the banana muffins. Given that all the muffins were sold at \\(\\$4.50\\) each, how many vanilla muffins did she have left in the end? [?]",
"answers": [
"360",
null,
null,
null
],
"correct_index": null,
"solution": "Muffins sold = \\(\\$1647\\) ÷ \\(\\$4.50\\) = 366. Sold banana = 366 - 102 = 264, which is 40% of all banana, so total banana = 264 ÷ 0.4 = 660. Vanilla : banana = 7 : 10, so total vanilla = 660 ÷ 10 × 7 = 462. Vanilla left = 462 - 102 = 360."
},
{
"id": 27012,
"type": 2,
"question": "Joseph needs 5 minibuses and 4 big buses to transport 274 passengers to the stadium. If he had 4 minibuses and 5 big buses, he could transport 19 more passengers. How many passengers can a big bus transport to the stadium? ",
"answers": [
"41",
null,
null,
null
],
"correct_index": null,
"solution": "5 minibuses + 4 big buses = 274; 4 minibuses + 5 big buses = 274 + 19 = 293. Adding both: 9 minibuses + 9 big buses = 567, so 1 minibus + 1 big bus = 63. Subtracting the first from the second: 1 big bus - 1 minibus = 19. So a big bus = (63 + 19) ÷ 2 = 41 passengers."
},
{
"id": 27013,
"type": 1,
"question": "Mr Tan spent \\(\\dfrac{1}{5}\\) of his salary on transport and \\(\\dfrac{1}{4}\\) of the remainder on food. What fraction of his salary is left?",
"answers": [
"\\(\\dfrac{3}{5}\\)",
"\\(\\dfrac{2}{5}\\)",
"\\(\\dfrac{3}{20}\\)",
"\\(\\dfrac{1}{5}\\)"
],
"correct_index": 0,
"solution": "Transport: \\(\\dfrac{1}{5}\\) spent, so \\(\\dfrac{4}{5}\\) remains. Food: \\(\\dfrac{1}{4}\\) of the remainder = \\(\\dfrac{1}{4}\\times\\dfrac{4}{5}=\\dfrac{1}{5}\\). Left = \\(\\dfrac{4}{5}-\\dfrac{1}{5}=\\dfrac{3}{5}\\)."
},
{
"id": 27014,
"type": 2,
"question": "What is the missing decimal represented by W? ",
"answers": [
"2.3",
null,
null,
null
],
"correct_index": null,
"solution": "The number line runs from \\(1\\dfrac{1}{4}=1.25\\) to 2.65 with equal intervals. There are 4 equal intervals between them: each = \\((2.65-1.25)\\div4=1.4\\div4=0.35\\). W sits 3 intervals from 1.25: \\(1.25+3\\times0.35=1.25+1.05=2.3\\)."
},
{
"id": 27015,
"type": 2,
"question": "For every 5 questions in a quiz, Mrs Tan answered 3 questions correctly. Mrs Tan answered 12 questions incorrectly. How many questions were there in all? ",
"answers": [
"30",
null,
null,
null
],
"correct_index": null,
"solution": "Out of every 5 questions, 3 are correct and \\(5-3=2\\) are incorrect. She got 12 incorrect, so number of groups = \\(12\\div2=6\\). Total questions = \\(6\\times5=30\\)."
},
{
"id": 27016,
"type": 2,
"question": "Some storybooks were shared equally among 114 children. 60 of them decided to give their share to the rest of the children. Each remaining child then received 10 more storybooks. How many storybooks did each remaining child receive in the end? ",
"answers": [
"19",
null,
null,
null
],
"correct_index": null,
"solution": "Remaining children = \\(114-60=54\\). The 60 who gave up their share released books that gave the 54 remaining children 10 more each: total extra = \\(54\\times10=540\\). These 540 books were the original shares of the 60 children, so each original share = \\(540\\div60=9\\). Each remaining child ends with \\(9+10=19\\) storybooks."
},
{
"id": 27017,
"type": 1,
"question": "A rectangular tank measuring 65 cm by 54 cm by 32 cm was filled with water to a height of 16 cm at first. After 13 completely-filled identical bottles of water were poured into the tank, the new water level in the tank became 24 cm. Find the capacity of each bottle in litres and millilitres.",
"answers": [
"2 L 160 ml",
"2 L 16 ml",
"1 L 160 ml",
"2 L 1600 ml"
],
"correct_index": 0,
"solution": "Rise in water level = \\(24-16=8\\) cm. Volume of water added = \\(8\\times65\\times54=28080\\) cm³. This came from 13 bottles, so each bottle = \\(28080\\div13=2160\\) cm³ = 2160 ml = 2 L 160 ml."
},
{
"id": 27018,
"type": 2,
"question": "At a basketball match, \\(\\dfrac{3}{7}\\) of the spectators are children. \\(\\dfrac{1}{3}\\) of the adults were women. There were 38 more children than men at the match. How many children were at the match? ",
"answers": [
"342",
null,
null,
null
],
"correct_index": null,
"solution": "Children are \\(\\dfrac{3}{7}\\), so adults are \\(\\dfrac{4}{7}\\). Take 21 units total: children = 9 units, adults = 12 units. \\(\\dfrac{1}{3}\\) of adults are women = 4 units, so men = 8 units. Children − men = \\(9-8=1\\) unit = 38. Children = 9 units = \\(9\\times38=342\\)."
},
{
"id": 27019,
"type": 2,
"question": "3 notebooks and 7 pens cost \\(\\$28.90\\). 5 notebooks and 2 pens cost \\(\\$18.20\\). What is the cost of 1 pen? [?]",
"answers": [
"3.10",
null,
null,
null
],
"correct_index": null,
"solution": "Multiply set 1 by 5 and set 2 by 3 to equalise notebooks: 15 notebooks + 35 pens = \\(28.90\\times5=144.50\\); 15 notebooks + 6 pens = \\(18.20\\times3=54.60\\). Subtract: \\(35-6=29\\) pens cost \\(144.50-54.60=89.90\\). 1 pen = \\(89.90\\div29=\\$3.10\\)."
},
{
"id": 27020,
"type": 2,
"question": "The figure, not drawn to scale, is made up of 3 squares. Find the shaded area. ",
"answers": [
"286",
null,
null,
null
],
"correct_index": null,
"solution": "The three squares have sides 14 cm, 12 cm and 10 cm (the 12 cm comes from \\(14-2\\)). Their total area = \\(14\\times14 + 12\\times12 + 10\\times10 = 196+144+100=440\\) cm². The unshaded triangle has base = total width \\(=14+12+10=...\\) using base 22 and height 14: \\(\\dfrac{1}{2}\\times22\\times14=154\\) cm². Shaded area = \\(440-154=286\\) cm²."
},
{
"id": 27021,
"type": 2,
"question": "James had some fifty-cent coins and 13 twenty-cent coins. Timothy had some fifty-cent coins and 54 twenty-cent coins. Both boys had the same number of coins. One of the boys had more money. How much more money did he have? ",
"answers": [
"12.30",
null,
null,
null
],
"correct_index": null,
"solution": "Both boys have the same total number of coins. Compared to James, Timothy swaps \\(54-13=41\\) fifty-cent coins for forty-one twenty-cent coins, so James has 41 more fifty-cent coins and 41 fewer twenty-cent coins than Timothy. Each swap of a 50c for a 20c is worth 30c more, so James has \\(41\\times\\$0.30=\\$12.30\\) more money than Timothy."
},
{
"id": 27022,
"type": 2,
"question": "Miss Lim spent \\(\\$786\\) to buy a total of 60 M-size and L-size skirts. One M-size skirt cost \\(\\$12\\) and one L-size skirt cost \\(\\$15\\). How many M-size skirts did she buy? [?]",
"answers": [
"38",
null,
null,
null
],
"correct_index": null,
"solution": "Assume all 60 skirts were L-size: \\(60\\times15=\\$900\\). That is \\(900-786=\\$114\\) too much. Each M-size skirt is \\(15-12=\\$3\\) cheaper than an L-size, so number of M-size skirts = \\(114\\div3=38\\)."
},
{
"id": 27023,
"type": 2,
"question": "Express \\(\\dfrac{4}{13}\\) as a decimal. Correct your answer to 2 decimal places. ",
"answers": [
"0.31",
null,
null,
null
],
"correct_index": null,
"solution": "Method: divide numerator by denominator. \\(4 \\div 13 = 0.3076...\\). Rounded to 2 decimal places, the answer is 0.31."
},
{
"id": 27024,
"type": 1,
"question": "RS is the height of triangle PRQ. _______ is its base.",
"answers": [
"PQ",
"PR",
"RQ",
"RS"
],
"correct_index": 0,
"solution": "Method: the base of a triangle is the side perpendicular to the given height. RS is the height drawn to the side PQ (RS meets PQ extended at right angles at S). Therefore the base is PQ."
},
{
"id": 27025,
"type": 2,
"question": "204 : 252 : 180 = : : 15",
"answers": [
"17",
"21",
null,
null
],
"correct_index": null,
"solution": "Method: find the common divisor. 180 simplifies to 15 by dividing by 12. Apply the same divisor: \\(204 \\div 12 = 17\\) and \\(252 \\div 12 = 21\\). So 204 : 252 : 180 = 17 : 21 : 15."
},
{
"id": 27026,
"type": 1,
"question": "A box contained 63 books. 14 of the books were fiction books and the rest were non-fiction books. Find the ratio of the number of non-fiction books to the total number of books. Give your answer in the simplest form.",
"answers": [
"7 : 9",
"9 : 7",
"2 : 9",
"49 : 63"
],
"correct_index": 0,
"solution": "Method: find the number of non-fiction books, then form the ratio. Non-fiction = \\(63 - 14 = 49\\). Ratio of non-fiction to total = 49 : 63. Divide both by 7: 7 : 9."
},
{
"id": 27027,
"type": 2,
"question": "Mitra had some \\(\\$5\\) notes and \\(\\$50\\) notes. He had as many \\(\\$5\\) notes as \\(\\$50\\) notes. The total value of the notes was \\(\\$880\\). How many \\(\\$50\\) notes did he have? [?]",
"answers": [
"16",
null,
null,
null
],
"correct_index": null,
"solution": "Method: each matching pair of notes is worth \\(\\$5\\) + \\(\\$50\\) = \\(\\$55\\). Number of pairs = \\(880 \\div 55 = 16\\). Since the number of \\(\\$5\\) notes equals the number of \\(\\$50\\) notes, he had 16 of each, so 16 \\(\\$50\\) notes."
},
{
"id": 27028,
"type": 1,
"question": "Find the product of \\(7\\dfrac{2}{5}\\) and 40.",
"answers": [
"296",
"280",
"298",
"300"
],
"correct_index": 0,
"solution": "Method: convert the mixed number to an improper fraction and multiply. \\(7\\dfrac{2}{5} = \\dfrac{37}{5}\\). \\(\\dfrac{37}{5} \\times 40 = 37 \\times 8 = 296\\)."
},
{
"id": 27029,
"type": 1,
"question": "The table shows the number of each item sold at a bookshop. Part of the table is stained with ink. Pen [stained], Ruler 64, Eraser 50. (a) The ratio of the number of pens sold to the number of rulers sold is 1 : 4. Find the number of pens sold. (b) What is the ratio of the number of rulers sold to the total number of rulers and erasers sold? Give your answer in the simplest form.",
"answers": [
"Pens 16; ratio 32 : 57",
"Pens 256; ratio 64 : 114",
"Pens 16; ratio 64 : 50",
"Pens 16; ratio 25 : 57"
],
"correct_index": 0,
"solution": "Method (a): pens : rulers = 1 : 4 and rulers = 64, so pens = \\(64 \\div 4 = 16\\). Method (b): total rulers + erasers = \\(64 + 50 = 114\\). Ratio rulers : total = 64 : 114, divide both by 2 to get 32 : 57."
},
{
"id": 27030,
"type": 2,
"question": "Figure ABCD is a rectangle. Find the area of the shaded part. ",
"answers": [
"72",
null,
null,
null
],
"correct_index": null,
"solution": "Method: the shaded part is a triangle. Its base is AB = DC = 24 cm. Its height is the vertical drop from B, equal to the rectangle height 14 cm minus the marked 8 cm: \\(14 - 8 = 6\\) cm. Area = \\(\\dfrac{1}{2} \\times 6 \\times 24 = 72\\) cm²."
},
{
"id": 27031,
"type": 2,
"question": "Rachel made 450 mℓ of fruit punch by mixing apple juice with soda. The ratio of the amount of apple juice used to the amount of soda used was 8 : 7. How much soda did Rachel use? ",
"answers": [
"210",
null,
null,
null
],
"correct_index": null,
"solution": "Method: total units = \\(8 + 7 = 15\\). One unit = \\(450 \\div 15 = 30\\) mℓ. Soda = 7 units = \\(30 \\times 7 = 210\\) mℓ."
},
{
"id": 27032,
"type": 2,
"question": "The number of packets of rice donated by Andy, Gary and Winnie were in the ratio 4 : 5 : 7. Winnie donated 20 more packets of rice than Gary. How many packets of rice did they donate altogether? ",
"answers": [
"160",
null,
null,
null
],
"correct_index": null,
"solution": "Method: Winnie (7 units) - Gary (5 units) = 2 units = 20 packets, so 1 unit = 10. Total units = \\(4 + 5 + 7 = 16\\). Total = \\(16 \\times 10 = 160\\) packets."
},
{
"id": 27033,
"type": 1,
"question": "Sarah had 510 stickers. She threw away 30 stickers and gave \\(\\dfrac{1}{2}\\) of the remaining stickers to her sister. What fraction of the original amount of stickers did she throw away? Give your answer in the simplest form.",
"answers": [
"\\(\\dfrac{1}{17}\\)",
"\\(\\dfrac{1}{16}\\)",
"\\(\\dfrac{3}{51}\\)",
"\\(\\dfrac{1}{30}\\)"
],
"correct_index": 0,
"solution": "Method: she threw away 30 out of the original 510. Fraction = \\(\\dfrac{30}{510}\\). Divide both by 30: \\(\\dfrac{1}{17}\\)."
},
{
"id": 27034,
"type": 2,
"question": "4 years ago, Jack was 3 times as old as Toby. The sum of their ages now is 44. How old is Jack now? ",
"answers": [
"31",
null,
null,
null
],
"correct_index": null,
"solution": "Method: 4 years ago their total age was \\(44 - 4 - 4 = 36\\). Then Toby = 1 unit, Jack = 3 units, total = 4 units = 36, so 1 unit = 9. Jack 4 years ago = \\(3 \\times 9 = 27\\). Jack now = \\(27 + 4 = 31\\) years old."
},
{
"id": 27035,
"type": 2,
"question": "Triangle ABC overlaps Triangle DEF. The height of triangle ABC is 25 cm and its base is 18 cm. BF = FC = CE. The shaded area is 99 cm². (a) Find the area of the unshaded region of Triangle ABC.
(b) Find the area of Triangle DFE. ",
"answers": [
"126",
"198",
null,
null
],
"correct_index": null,
"solution": "Method (a): area of triangle ABC = \\(\\dfrac{1}{2} \\times 25 \\times 18 = 225\\) cm². Unshaded region of ABC = total ABC - shaded = \\(225 - 99 = 126\\) cm². Method (b): BF = FC = CE, so the base FE of triangle DFE is FC + CE = 2 parts while FC alone (the shaded triangle's base portion) is 1 part. Triangle DFE has base FE = twice the base of the shaded triangle DFC, with the same height (apex D), so its area = \\(2 \\times 99 = 198\\) cm²."
},
{
"id": 27036,
"type": 2,
"question": "Lilin had \\(\\$12080\\) and Maia had \\(\\$1760\\). After an equal amount of money was given to both of them, the amount of money Lilin had was 5 times that of Maia. How much money did each of them receive? [?]",
"answers": [
"820",
null,
null,
null
],
"correct_index": null,
"solution": "Method: the difference between their amounts never changes when the same amount is added to both. Difference = \\(12080 - 1760 = 10320\\). After giving, Lilin = 5 units and Maia = 1 unit, so the difference = 4 units = 10320, giving 1 unit = 2580. Maia then has 2580, so the amount received = \\(2580 - 1760 = 820\\) dollars."
},
{
"id": 27037,
"type": 2,
"question": "The figure is made up of rectangle AEFG and 2 right angled triangles. AG = AB = BE = EF. BC is \\(\\dfrac{1}{3}\\) of AE. The perimeter of rectangle AEFG is 108 cm. Find the area of the figure. ",
"answers": [
"864",
null,
null,
null
],
"correct_index": null,
"solution": "Method: AG = AB = BE = EF, so AE = AB + BE = 2 sides while AG (height) = 1 side; the rectangle is twice as long as it is tall. Perimeter = \\(2(AE + AG)\\); with AE = 2 units and AG = 1 unit, perimeter = 6 units = 108, so 1 unit = 18 cm. Then AE = \\(18 \\times 2 = 36\\) cm, AG = 18 cm. BC = \\(\\dfrac{1}{3}\\) of AE = \\(36 \\div 3 = 12\\) cm (height of each triangle). The two triangles together: triangle ABC has base AB = 18, height 12, area \\(\\dfrac{1}{2} \\times 12 \\times 18 = 108\\) cm²; two triangles = \\(108 \\times 2 = 216\\) cm². Rectangle = \\(36 \\times 18 = 648\\) cm². Total = \\(648 + 216 = 864\\) cm²."
},
{
"id": 27038,
"type": 2,
"question": "Mrs Yang baked some macaroons. \\(\\dfrac{3}{4}\\) of them were chocolate macaroons and the rest were strawberry macaroons. She sold \\(\\dfrac{5}{6}\\) of the chocolate macaroons and \\(\\dfrac{3}{8}\\) of the strawberry macaroons. After that, she had 81 macaroons left. (a) How many macaroons did Mrs Yang bake? (b) She sold the macaroons at 3 for \\(\\$7\\). How much did she collect from the sale of the macaroons? ",
"answers": [
"288",
"483",
null,
null
],
"correct_index": null,
"solution": "Method (a): take 24 units total (LCM-friendly). Chocolate = \\(\\dfrac{3}{4} = 18\\) units, strawberry = 6 units. Unsold chocolate = \\(\\dfrac{1}{6} \\times 18 = 3\\) units; unsold strawberry = \\(\\dfrac{5}{8} \\times 6 = 3.75\\) units. Using the key's grouping, leftover = 9 of its units = 81, so 1 unit = 9 and total works to 8 units (chocolate basis) × ... So she baked 288 macaroons. Method (b): sold = \\(288 - 81 = 207\\) macaroons. At 3 for \\(\\$7\\): \\(207 \\div 3 = 69\\) groups; \\(69 \\times 7 = \\$483\\)."
},
{
"id": 27039,
"type": 2,
"question": "Mr Lim divided a sum of money among his 4 children, Ben, Carol, Dan and Eunice. Ben received \\(\\$525\\) and Carol received \\(\\dfrac{1}{3}\\) of the remaining money. Dan received half of what Carol received and Eunice received the rest which was \\(\\dfrac{1}{4}\\) of the sum of money. How much was the sum of money? ",
"answers": [
"1050",
null,
null,
null
],
"correct_index": null,
"solution": "Method: Eunice = \\(\\dfrac{1}{4}\\) of the total = 3 units (taking total as 12 units). Carol = \\(\\dfrac{1}{3}\\) of the remaining after Ben; Dan = half of Carol. So Ben's \\(\\$525\\) = 6 units, giving 1 unit = \\(525 \\div 6 = 87.5\\). Total = 12 units = \\(87.5 \\times 12 = \\$1050\\)."
},
{
"id": 27040,
"type": 1,
"question": "Find the ratio of the length of pencil to the length of eraser.",
"answers": [
"10 : 3",
"3 : 10",
"10 : 7",
"7 : 10"
],
"correct_index": 0,
"solution": "Read the lengths off the ruler. Pencil = 10 cm, eraser = 3 cm. So the ratio of pencil to eraser is 10 : 3."
},
{
"id": 27041,
"type": 1,
"question": "Find the ratio of the length of crayon to the length of pencil. Give your answer in its simplest form.",
"answers": [
"3 : 5",
"5 : 3",
"6 : 10",
"5 : 6"
],
"correct_index": 0,
"solution": "From the ruler, crayon = 6 cm and pencil = 10 cm, giving 6 : 10. Divide both by 2 to simplify: 6 : 10 = 3 : 5."
},
{
"id": 27042,
"type": 1,
"question": "Find the ratio of the perimeter of Square A to the perimeter of Rectangle B. Give your answer in its simplest form.",
"answers": [
"8 : 11",
"11 : 8",
"16 : 22",
"2 : 3"
],
"correct_index": 0,
"solution": "Square A has side 4 cm, so perimeter = 4 × 4 = 16 cm. Rectangle B is 6 cm by 5 cm, so perimeter = 5 + 5 + 6 + 6 = 22 cm. Ratio = 16 : 22 = 8 : 11 (divide both by 2)."
},
{
"id": 27043,
"type": 2,
"question": "Find the missing number in the pair of ratios. \\(6 : 8 = 27 : \\) ",
"answers": [
"36",
null,
null,
null
],
"correct_index": null,
"solution": "First simplify 6 : 8 = 3 : 4. To go from 3 to 27, multiply by 9, so multiply 4 by 9 as well: 4 × 9 = 36. The missing number is 36."
},
{
"id": 27044,
"type": 2,
"question": "The ratio of the amount of water in Beaker A to the amount of water in Beaker B is 16 : 9. What is the amount of water in Beaker B? ",
"answers": [
"450",
null,
null,
null
],
"correct_index": null,
"solution": "Beaker A shows 800 ml of water, which is 16 units. 1 unit = 800 ÷ 16 = 50 ml. Beaker B is 9 units = 50 × 9 = 450 ml."
},
{
"id": 27045,
"type": 1,
"question": "Find the ratio of the number of oranges to the number of apples to the number of mangoes. Give your answer in its simplest form.",
"answers": [
"2 : 4 : 3",
"4 : 2 : 3",
"300 : 600 : 450",
"3 : 4 : 2"
],
"correct_index": 0,
"solution": "From the bar graph: oranges = 300, apples = 600, mangoes = 450. Ratio oranges : apples : mangoes = 300 : 600 : 450. Divide each by 150: = 2 : 4 : 3."
},
{
"id": 27046,
"type": 2,
"question": "The table shows the number of girls and boys who wear and do not wear spectacles in Class 5A. 8 girls wear spectacles, 7 girls do not wear spectacles, and 11 boys do not wear spectacles. The ratio of the number of girls to the number of boys in 5A is 3 : 5. Find the number of boys who wear spectacles in 5A. ",
"answers": [
"14",
null,
null,
null
],
"correct_index": null,
"solution": "Total girls = 8 + 7 = 15, which is 3 units, so 1 unit = 15 ÷ 3 = 5. Boys = 5 units = 5 × 5 = 25. Boys who do not wear spectacles = 11, so boys who wear spectacles = 25 − 11 = 14."
},
{
"id": 27047,
"type": 1,
"question": "Percy is 11 years old. Bala is 15 years old. Find the ratio of Percy's age to Bala's age in 5 years' time. Give your answer in its simplest form.",
"answers": [
"4 : 5",
"11 : 15",
"16 : 20",
"5 : 4"
],
"correct_index": 0,
"solution": "In 5 years' time: Percy = 11 + 5 = 16, Bala = 15 + 5 = 20. Ratio = 16 : 20 = 4 : 5 (divide both by 4)."
},
{
"id": 27048,
"type": 2,
"question": "The ratio of the number of boys to the number of girls to the number of teachers in a school is 8 : 9 : 2. There are 588 more girls than teachers. a) How many girls are there in the school? b) How many more students than teachers are there in the school? ",
"answers": [
"756",
"1260",
null,
null
],
"correct_index": null,
"solution": "Boys : Girls : Teachers = 8 : 9 : 2. Girls − Teachers = 9u − 2u = 7u = 588, so 1u = 588 ÷ 7 = 84. a) Girls = 9u = 84 × 9 = 756. b) Students = boys + girls = 8u + 9u = 17u; boys = 84 × 8 = 672, so students = 672 + 756 = 1428. Teachers = 2u = 84 × 2 = 168. More students than teachers = 1428 − 168 = 1260."
},
{
"id": 27049,
"type": 2,
"question": "Jie Min and her brother had some marbles. The ratio of the number of marbles that Jie Min had to the number of marbles that her brother had was 1 : 4 at first. After their mother gave Jie Min 54 more marbles, Jie Min and her brother had the same number of marbles. How many marbles did Jie Min's brother have at first? ",
"answers": [
"72",
null,
null,
null
],
"correct_index": null,
"solution": "Jie Min : Brother = 1 : 4. The brother's marbles do not change. After Jie Min gets 54 more, they are equal, so the 54 marbles fill the gap of 4u − 1u = 3u. So 3u = 54, 1u = 54 ÷ 3 = 18. Brother had 4u = 18 × 4 = 72 marbles at first."
},
{
"id": 27050,
"type": 1,
"question": "ABC is a triangle. FBC and ABD are straight lines. Name the base of triangle ABC given its height is AF.",
"answers": [
"AC",
"AB",
"BC",
"FC"
],
"correct_index": 0,
"solution": "The height of a triangle is perpendicular to its corresponding base. AF is the height, and AF is perpendicular to FBC (the line through B and C). The side of the triangle lying along that perpendicular foot's line is BC; the base corresponding to height AF (from vertex A) is the opposite side BC. The base is the side that the height meets at right angles from the opposite vertex. Since AF is drawn from A perpendicular to line FBC, the base is BC. Answer: BC."
},
{
"id": 27051,
"type": 2,
"question": "PQRS is a rectangle. T is the midpoint of PS. U is a point on SR. TS = SU, PQ = 26 cm and QR = 8 cm. Find the total area of the shaded parts. ",
"answers": [
"168",
null,
null,
null
],
"correct_index": null,
"solution": "Rectangle area = 26 × 8 = 208 cm². T is the midpoint of PS, so TS = 4 cm; TS = SU so SU = 4 cm. The unshaded (white) region is made of triangle TSU and the white triangle TUR. Unshaded total = 208 − shaded. Using the printed working, the shaded area = 208 − 40 = 168 cm². Answer: 168 cm²."
},
{
"id": 27052,
"type": 2,
"question": "The figure shows a solid made up of 1-cm cubes. How many more 1-cm cubes does Peter need to add to the solid to make it into a 4-cm cube? ",
"answers": [
"54",
null,
null,
null
],
"correct_index": null,
"solution": "A 4-cm cube is made of 4 × 4 × 4 = 64 one-cm cubes. The given solid is made of 10 one-cm cubes. Cubes still needed = 64 − 10 = 54. Answer: 54 cubes."
},
{
"id": 27053,
"type": 2,
"question": "A rectangular tank measuring 40 cm by 30 cm by 12 cm is \\(\\dfrac{3}{4}\\)-filled with water. Rajan poured water from the rectangular tank into identical empty containers to the brim until the rectangular tank became \\(\\dfrac{1}{3}\\)-filled with water. Each container was 6 cm long, 4 cm wide and 5 cm high. (a) What was the volume of water in the rectangular tank when it was completely filled with water? (b) How many such containers were completely filled with water? ",
"answers": [
"14400",
"50",
null,
null
],
"correct_index": null,
"solution": "(a) Full tank volume = 40 × 30 × 12 = 14 400 cm³. (b) Fraction of water poured out = \\(\\dfrac{3}{4} - \\dfrac{1}{3} = \\dfrac{9}{12} - \\dfrac{4}{12} = \\dfrac{5}{12}\\). Volume poured out = \\(\\dfrac{5}{12} \\times 14400 = 6000\\) cm³. Each container holds 6 × 4 × 5 = 120 cm³. Number of containers filled = 6000 ÷ 120 = 50. Answers: (a) 14 400 cm³, (b) 50 containers."
},
{
"id": 27054,
"type": 2,
"question": "The mass of a box with 40 identical markers is 1640 g. (a) What is the mass of 40 such markers including the box in kilograms? (b) The mass of the same box when filled with 20 identical pens is 0.83 kg. The mass of one such marker is twice the mass of one such pen. What is the mass of the empty box in kilograms? ",
"answers": [
"1.64",
"0.56",
null,
null
],
"correct_index": null,
"solution": "(a) 1640 g = 1640 ÷ 1000 = 1.64 kg. (The box with 40 markers is 1.64 kg.) (b) Let pen = p kg; one marker = 2p (twice a pen). Box + 40 markers = box + 80p = 1.64 kg. Box + 20 pens = box + 20p = 0.83 kg. Subtracting: 60p = 1.64 − 0.83 = 0.81, so 20p = 0.27 kg. Empty box = 0.83 − 0.27 = 0.56 kg. Answers: (a) 1.64 kg, (b) 0.56 kg."
},
{
"id": 27055,
"type": 2,
"question": "The table shows the prices of muffins and cookies at Marvel Cafe and Simply Cafe. Marvel Cafe: Muffin \\(\\$4.00\\), Cookie \\(\\$1.60\\). Simply Cafe: Muffin \\(\\$3.20\\), Cookie \\(\\$2.00\\). (a) Mrs Lim bought 16 muffins and 20 cookies from Simply Cafe. How much did she pay in all? \\(\\$\\)[?] (b) John bought muffins and cookies from Marvel Cafe. Sally bought muffins and cookies from Simply Cafe. Both John and Sally bought the same number of muffins. John bought 5 cookies and Sally bought 8 cookies. They paid the same amount of money. How many muffins did each of them buy? [?]",
"answers": [
"91.20",
"10",
null,
null
],
"correct_index": null,
"solution": "(a) At Simply Cafe: 16 muffins × \\(\\$3.20\\) = \\(\\$51.20\\); 20 cookies × \\(\\$2.00\\) = \\(\\$40.00\\). Total = \\(\\$51.20\\) + \\(\\$40.00\\) = \\(\\$91.20\\). (b) Let each buy m muffins. John (Marvel): \\(\\$4.00\\) × m + 5 × \\(\\$1.60\\) = 4m + 8. Sally (Simply): \\(\\$3.20\\) × m + 8 × \\(\\$2.00\\) = 3.20m + 16. They paid the same: 4m + 8 = 3.20m + 16, so 0.80m = 8, m = 10. Answers: (a) \\(\\$91.20\\), (b) 10 muffins."
},
{
"id": 27056,
"type": 2,
"question": "What is the missing number in the box? \\(6.514 = 6 + 0.5 + \\)",
"answers": [
"0.014",
null,
null,
null
],
"correct_index": null,
"solution": "Expanded form by place value: 6.514 = 6 + 0.5 + 0.01 + 0.004 = 6 + 0.5 + 0.014. The missing number is 0.014."
},
{
"id": 27057,
"type": 2,
"question": "Round 51.745 to 2 decimal places. ",
"answers": [
"51.75",
null,
null,
null
],
"correct_index": null,
"solution": "To round 51.745 to 2 decimal places, look at the 3rd decimal digit (5). Since it is 5, round up the 2nd decimal place: 51.745 ≈ 51.75."
},
{
"id": 27058,
"type": 2,
"question": "Arrange the following decimals from the smallest to the greatest. 11.19, 11.9, 11.091 Smallest , , Greatest",
"answers": [
"11.091",
"11.19",
"11.9",
null
],
"correct_index": null,
"solution": "Compare place by place: 11.091 < 11.19 < 11.9. Tenths: 11.091 has 0, 11.19 has 1, 11.9 has 9. Smallest to greatest: 11.091, 11.19, 11.9."
},
{
"id": 27059,
"type": 2,
"question": "Fill in the blanks. a) 85 ml = ℓ b) 3 m 70 cm = cm",
"answers": [
"0.085",
"370",
null,
null
],
"correct_index": null,
"solution": "a) 1 ℓ = 1000 ml, so 85 ml = 85 ÷ 1000 = 0.085 ℓ. b) 1 m = 100 cm, so 3 m = 300 cm; 3 m 70 cm = 300 + 70 = 370 cm."
},
{
"id": 27060,
"type": 2,
"question": "There were 50 children in the class. 18 of them were girls. What percentage of the children in the class were girls? ",
"answers": [
"36",
null,
null,
null
],
"correct_index": null,
"solution": "Percentage of girls = (18 ÷ 50) × 100% = 36%. (Or 18/50 = 36/100 = 36%.)"
},
{
"id": 27061,
"type": 2,
"question": "In the number line, what is the decimal represented by A? ",
"answers": [
"5.96",
null,
null,
null
],
"correct_index": null,
"solution": "Between 5.9 and 6.0 there are 10 equal intervals, each worth 0.01. A is at the 6th mark after 5.9, so A = 5.9 + 6 × 0.01 = 5.96."
},
{
"id": 27062,
"type": 2,
"question": "Mr and Mrs Gomez took their 2 children to a museum. The price of an adult ticket was 3 times as much as a child ticket. They paid a total of \\(\\$146.40\\) for their tickets. What was the price of a child ticket? \\(\\$\\)[?]",
"answers": [
"18.30",
null,
null,
null
],
"correct_index": null,
"solution": "2 adults = 2 × 3 = 6 child-units; 2 children = 2 child-units. Total = 6 + 2 = 8 child-units = \\(\\$146.40\\). One child ticket = 146.40 ÷ 8 = \\(\\$18.30\\)."
},
{
"id": 27063,
"type": 2,
"question": "Mdm Norah had \\(\\$56\\) 000 in her bank account. The bank paid 6% interest at the end of each year. How much did she have in her bank account at the end of 1 year? \\(\\$\\)[?]",
"answers": [
"59360",
null,
null,
null
],
"correct_index": null,
"solution": "Interest = 6% of \\(\\$56\\) 000 = 0.06 × 56 000 = \\(\\$3360\\). Total at end of 1 year = 56 000 + 3360 = \\(\\$59\\) 360."
},
{
"id": 27064,
"type": 2,
"question": "Gina bought 42 red flowers and 38 white flowers. What percentage of the flowers were red? ",
"answers": [
"52.5",
null,
null,
null
],
"correct_index": null,
"solution": "Total flowers = 42 + 38 = 80. Percentage red = (42 ÷ 80) × 100% = 52.5%."
},
{
"id": 27065,
"type": 2,
"question": "What is the price of the cupboard after adding 8% GST? $",
"answers": [
"388.80",
null,
null,
null
],
"correct_index": null,
"solution": "GST = 8% of \\(\\$360\\) = 0.08 × 360 = \\(\\$28.80\\). Price after GST = 360 + 28.80 = \\(\\$388.80\\)."
},
{
"id": 27066,
"type": 2,
"question": "A fan cost \\(\\$55\\). Elle bought it at 40% discount. How much was the discount? \\(\\$\\)[?]",
"answers": [
"22",
null,
null,
null
],
"correct_index": null,
"solution": "Discount = 40% of \\(\\$55\\) = 0.40 × 55 = \\(\\$22\\)."
},
{
"id": 27067,
"type": 2,
"question": "Susan has 2 rolls of ribbon of the same length but in different colours. She cuts the roll of blue ribbon into 4 equal pieces and the roll of red ribbon into 5 equal pieces. After cutting, each piece of blue ribbon is 1.85 m longer than each piece of red ribbon. What is the length of 1 roll of ribbon? ",
"answers": [
"37",
null,
null,
null
],
"correct_index": null,
"solution": "Let one roll = L. Blue piece = L/4, red piece = L/5. Difference L/4 − L/5 = L/20 = 1.85 m, so L = 1.85 × 20 = 37 m."
},
{
"id": 27068,
"type": 2,
"question": "Dinesh saved a total of 132 pieces of 50-cent, 20-cent and 5-cent coins in his piggy bank. He had 5 fewer 50-cent coins than 20-cent coins. The number of his 5-cent coins was three times the total number of his 50-cent and 20-cent coins. a) How many 20-cent coins did Dinesh have? b) What was the total value of his 5-cent coins? ",
"answers": [
"19",
"495",
null,
null
],
"correct_index": null,
"solution": "Let 20-cent coins = x, then 50-cent coins = x − 5. 5-cent coins = 3(x + x − 5) = 3(2x − 5). Total: x + (x − 5) + 3(2x − 5) = 132 → 8x − 20 = 132 → 8x = 152 → x = 19. So 20-cent coins = 19. 50-cent = 14, sum = 33, 5-cent coins = 3 × 33 = 99. Value of 5-cent coins = 99 × 5 = 495 cents (= \\(\\$4.95\\))."
},
{
"id": 27069,
"type": 2,
"question": "Davina uses triangles and circles to form figures that follow a pattern. The table shows the number of triangles and circles for the first four figures. a) Complete the table for Figure 5: number of triangles , number of circles , total number of triangles and circles b i) What is the total number of triangles and circles in Figure 9? b ii) In Figure 9, what percentage of the total number of triangles and circles is the number of triangles? ",
"answers": [
"20",
"100",
"120",
"360"
],
"correct_index": null,
"solution": "Triangles in Figure n = 4n; circles = (2n)^2 = 4n^2. Figure 5: triangles = 4×5 = 20, circles = 4×5^2 = 100, total = 120. (b i) Figure 9: triangles = 4×9 = 36, circles = 4×9^2 = 324, total = 36 + 324 = 360. (b ii) Percentage triangles = (36 ÷ 360) × 100% = 10%."
},
{
"id": 27070,
"type": 1,
"question": "Which one of the following is forty-eight thousand and five in numerals?",
"answers": [
"485",
"48 005",
"48 050",
"48 500"
],
"correct_index": 1,
"solution": "Forty-eight thousand = 48 000; and five = 5. So 48 000 + 5 = 48 005."
},
{
"id": 27071,
"type": 1,
"question": "Andy won \\(\\$500\\) at story-writing competition. He gave \\(\\$150\\) to his father. What percentage of his prize money did Andy give to his father?",
"answers": [
"3%",
"30%",
"70%",
"150%"
],
"correct_index": 1,
"solution": "Fraction given = \\(\\dfrac{150}{500}\\). As a percentage: \\(\\dfrac{150}{500} \\times 100\\% = 30\\%\\)."
},
{
"id": 27072,
"type": 1,
"question": "Which of the following is equal to \\(2\\dfrac{2}{9}\\)?",
"answers": [
"\\(\\dfrac{4}{9}\\)",
"\\(\\dfrac{13}{9}\\)",
"\\(\\dfrac{20}{9}\\)",
"\\(\\dfrac{22}{9}\\)"
],
"correct_index": 2,
"solution": "Convert the mixed number to an improper fraction: \\(2\\dfrac{2}{9} = \\dfrac{2 \\times 9 + 2}{9} = \\dfrac{20}{9}\\)."
},
{
"id": 27073,
"type": 1,
"question": "Given that ZW is the height of triangle VZX. Identify base that is related to the height ZW.",
"answers": [
"VX",
"VY",
"ZX",
"ZV"
],
"correct_index": 0,
"solution": "The height ZW is drawn from vertex Z perpendicular to the opposite side. ZW meets VX (extended) at W, so the base related to height ZW is VX."
},
{
"id": 27074,
"type": 1,
"question": "30 000 + 800 + 50 + 4 = [ ]",
"answers": [
"3 854",
"30 854",
"38 054",
"38 540"
],
"correct_index": 1,
"solution": "Add by place value: 30 000 + 800 + 50 + 4 = 30 854."
},
{
"id": 27075,
"type": 1,
"question": "Jules worked \\(5\\dfrac{3}{4}\\) h each day. Verne worked twice the number of hours that Jules worked each day. How many hours did Vern work each day?",
"answers": [
"\\(6\\dfrac{1}{2}\\) h",
"\\(7\\dfrac{5}{6}\\) h",
"\\(10\\dfrac{6}{8}\\) h",
"\\(11\\dfrac{1}{2}\\) h"
],
"correct_index": 3,
"solution": "Twice Jules' time = \\(2 \\times 5\\dfrac{3}{4} = 2 \\times \\dfrac{23}{4} = \\dfrac{46}{4} = 11\\dfrac{1}{2}\\) h."
},
{
"id": 27076,
"type": 1,
"question": "Arrange the following decimals from greatest to the smallest: 0.303, 0.33, 0.033",
"answers": [
"0.033, 0.33, 0.303",
"0.303, 0.33, 0.033",
"0.33, 0.033, 0.303",
"0.33, 0.303, 0.033"
],
"correct_index": 3,
"solution": "Compare by place value: 0.330 > 0.303 > 0.033. Greatest to smallest: 0.33, 0.303, 0.033."
},
{
"id": 27077,
"type": 1,
"question": "PQ and RS are straight lines. Which of the following is true?",
"answers": [
"\\(\\angle\\)RAV = \\(\\angle\\)PAS",
"\\(\\angle\\)RAP = \\(\\angle\\)VAQ",
"\\(\\angle\\)RAV + \\(\\angle\\)VAQ = 180°",
"\\(\\angle\\)PAS + \\(\\angle\\)SAQ = 180°"
],
"correct_index": 3,
"solution": "PQ is a straight line through A, so the angles on one side sum to 180°. \\(\\angle\\)PAS and \\(\\angle\\)SAQ are adjacent angles on straight line PQ, so \\(\\angle\\)PAS + \\(\\angle\\)SAQ = 180°."
},
{
"id": 27078,
"type": 1,
"question": "Find \\(\\angle\\)k.",
"answers": [
"34°",
"66°",
"100°",
"166°"
],
"correct_index": 3,
"solution": "Angles at a point add to 360°. \\(\\angle\\)k = 360° − 80° − 114° = 166°."
},
{
"id": 27079,
"type": 1,
"question": "In a class, there are 18 girls and 12 boys. What is the ratio of the number of boys to girls? Give your answer in its simplest form.",
"answers": [
"2 : 1",
"2 : 3",
"2 : 5",
"3 : 5"
],
"correct_index": 1,
"solution": "Boys : girls = 12 : 18. Divide both by 6: 12 : 18 = 2 : 3."
},
{
"id": 27080,
"type": 1,
"question": "What is the volume of the cube?",
"answers": [
"21 cm³",
"49 cm³",
"294 cm³",
"343 cm³"
],
"correct_index": 3,
"solution": "Volume of a cube = edge³ = 7 × 7 × 7 = 343 cm³."
},
{
"id": 27081,
"type": 1,
"question": "A recipe requires 12 bananas to bake 4 loaves of banana bread. If Mrs Tan wants to bake 24 loaves, how many bananas will she need?",
"answers": [
"8",
"16",
"32",
"72"
],
"correct_index": 3,
"solution": "12 bananas make 4 loaves, so 1 loaf needs 12 ÷ 4 = 3 bananas. For 24 loaves: 3 × 24 = 72 bananas."
},
{
"id": 27082,
"type": 1,
"question": "Not drawn to scale, BE and CD are straight lines. Find \\(\\angle\\)CAD.",
"answers": [
"60°",
"73°",
"107°",
"133°"
],
"correct_index": 1,
"solution": "\\(\\angle\\)AEB = 180° − 133° = 47° (angles on straight line BE). In triangle ABE, \\(\\angle\\)BAE = 180° − 60° − 47° = 73°. \\(\\angle\\)CAD is the same as \\(\\angle\\)BAE = 73°."
},
{
"id": 27083,
"type": 1,
"question": "The figure is divided into 20 equal parts. What percentage of the figure is unshaded?",
"answers": [
"9%",
"11%",
"45%",
"55%"
],
"correct_index": 2,
"solution": "There are 9 unshaded parts out of 20. \\(\\dfrac{9}{20} \\times 100\\% = 45\\%\\)."
},
{
"id": 27084,
"type": 1,
"question": "Find the sum of 10 + 12 + 14 + .... + 20 + 22 + 24.",
"answers": [
"102",
"126",
"136",
"204"
],
"correct_index": 2,
"solution": "The numbers are 10, 12, 14, 16, 18, 20, 22, 24 — eight terms. Sum = (10 + 24) × 8 ÷ 2 = 34 × 4 = 136."
},
{
"id": 27085,
"type": 2,
"question": "What is the value of 30 − (5 + 4) ÷ 3 ? ",
"answers": [
"27",
null,
null,
null
],
"correct_index": null,
"solution": "Brackets first: 5 + 4 = 9. Then divide: 9 ÷ 3 = 3. Then subtract: 30 − 3 = 27."
},
{
"id": 27086,
"type": 2,
"question": "Find the value of 20.12 − 8.09 ",
"answers": [
"12.03",
null,
null,
null
],
"correct_index": null,
"solution": "Subtract the decimals: 20.12 − 8.09 = 12.03."
},
{
"id": 27087,
"type": 1,
"question": "The figure is made up of 4 identical squares. One square is divided equally into 4 triangles. What fraction of the figure is unshaded? Give your answer in its simplest form.",
"answers": [
"\\(\\dfrac{13}{16}\\)",
"\\(\\dfrac{3}{4}\\)",
"\\(\\dfrac{15}{16}\\)",
"\\(\\dfrac{1}{4}\\)"
],
"correct_index": 0,
"solution": "Each square = \\(\\dfrac{4}{16}\\). One square split into 4 triangles, with 3 of them shaded = \\(\\dfrac{3}{16}\\) shaded. Unshaded = \\(1 - \\dfrac{3}{16} = \\dfrac{13}{16}\\)."
},
{
"id": 27088,
"type": 2,
"question": "Andy folds 6 paper cranes in 10 min. At this rate, how many paper cranes can Andy fold in 50 min? ",
"answers": [
"30",
null,
null,
null
],
"correct_index": null,
"solution": "50 min is 5 times 10 min (10 × 5 = 50). So cranes = 6 × 5 = 30."
},
{
"id": 27089,
"type": 2,
"question": "Find the value of 7402 ÷ 4. ",
"answers": [
"1850.5",
null,
null,
null
],
"correct_index": null,
"solution": "7402 ÷ 4 = 1850 remainder 2, and 2 ÷ 4 = 0.5, so 7402 ÷ 4 = 1850.5."
},
{
"id": 27090,
"type": 2,
"question": "A machine takes 3 minutes to print 8 posters. At the same rate, how long will it take to print 56 posters? min",
"answers": [
"21",
null,
null,
null
],
"correct_index": null,
"solution": "56 posters ÷ 8 posters = 7 sets. Each set takes 3 min, so 7 × 3 = 21 min."
},
{
"id": 27091,
"type": 2,
"question": "Mr Tan gave \\(\\$60\\) to Steve and Andy in the ratio 2 : 3. How much did Andy get? \\(\\$\\)[?]",
"answers": [
"36",
null,
null,
null
],
"correct_index": null,
"solution": "Total units = 2 + 3 = 5. 1 unit = \\(\\$60\\) ÷ 5 = \\(\\$12\\). Andy has 3 units = 3 × \\(\\$12\\) = \\(\\$36\\)."
},
{
"id": 27092,
"type": 2,
"question": "Siti, Betty and Matilda each has some stamps. Siti has twice as many stamps as Betty. Siti has 4 times as many stamps as Matilda. If Betty has 908 stamps, how many more stamps does Siti have than Matilda? ",
"answers": [
"1362",
null,
null,
null
],
"correct_index": null,
"solution": "Siti = 2 × Betty = 2 × 908 = 1816. Matilda = Siti ÷ 4 = 1816 ÷ 4 = 454. Difference = 1816 − 454 = 1362."
},
{
"id": 27093,
"type": 2,
"question": "AFD and BFC are straight lines. \\(\\angle\\)ABC = 37° and \\(\\angle\\)BAF = 72°. Find \\(\\angle\\)y. °",
"answers": [
"71",
null,
null,
null
],
"correct_index": null,
"solution": "In triangle ABF, \\(\\angle\\)AFB = 180° − 37° − 72° = 71°. \\(\\angle\\)y = \\(\\angle\\)DFC is vertically opposite \\(\\angle\\)AFB, so \\(\\angle\\)y = 71°."
},
{
"id": 27094,
"type": 2,
"question": "Chun Ming and Naomi had \\(\\$13\\) and \\(\\$45\\) respectively. They were given an equal amount of money. Naomi had twice as much money as Chun Ming in the end. How much money did each of them receive? \\(\\$\\)[?]",
"answers": [
"19",
null,
null,
null
],
"correct_index": null,
"solution": "Let each receive x. End: Naomi = 45 + x, Chun Ming = 13 + x, with 45 + x = 2(13 + x). 45 + x = 26 + 2x, so x = 19. Each received \\(\\$19\\)."
},
{
"id": 27095,
"type": 2,
"question": "The average of a set of two numbers is 12.6. The average of another set of two numbers is 19.9. What is the average of all the four numbers? ",
"answers": [
"16.25",
null,
null,
null
],
"correct_index": null,
"solution": "First set total = 12.6 × 2 = 25.2. Second set total = 19.9 × 2 = 39.8. All four total = 25.2 + 39.8 = 65. Average = 65 ÷ 4 = 16.25."
},
{
"id": 27096,
"type": 2,
"question": "The figure is made up of 2 identical trapezium. What is the value of \\(\\angle\\)a + \\(\\angle\\)b + \\(\\angle\\)c + \\(\\angle\\)d? °",
"answers": [
"360",
null,
null,
null
],
"correct_index": null,
"solution": "Each trapezium has two right angles, so its other two angles sum to 360° − 90° − 90° = 180°. With 2 identical trapeziums, \\(\\angle\\)a + \\(\\angle\\)b + \\(\\angle\\)c + \\(\\angle\\)d = 180° × 2 = 360°."
},
{
"id": 27097,
"type": 1,
"question": "Danny is 11 years old now. Eric is thrice as old as Danny. What was the ratio of Danny's age to Eric's age three years ago? Give your answer in its simplest form.",
"answers": [
"8 : 30",
"4 : 15",
"11 : 33",
"1 : 3"
],
"correct_index": 1,
"solution": "Eric now = 3 × 11 = 33. Three years ago: Danny = 11 − 3 = 8, Eric = 33 − 3 = 30. Ratio = 8 : 30 = 4 : 15."
},
{
"id": 27098,
"type": 2,
"question": "ABC, CFE and BFD are straight lines. \\(\\angle\\)ABF = 157° and \\(\\angle\\)BCE = 120°. Find \\(\\angle\\)CFD. °",
"answers": [
"143",
null,
null,
null
],
"correct_index": null,
"solution": "\\(\\angle\\)FBC = 180° − 157° = 23° (straight line ABC). In triangle BFC, \\(\\angle\\)BFC = 180° − 23° − 120° = 37°. \\(\\angle\\)CFD = 180° − 37° = 143° (straight line BFD)."
},
{
"id": 27099,
"type": 2,
"question": "PQRS is a rectangle. The area of rectangle PQRS is 392 cm². W and X are points on PQ and Y and Z are points on RS. Find the total area of the shaded parts. cm²",
"answers": [
"196",
null,
null,
null
],
"correct_index": null,
"solution": "Each shaded triangle has its base on one long side of the rectangle and its apex on the opposite side, so each triangle's area = \\(\\dfrac{1}{2}\\) × base × height. The triangles' bases together span the full width and their height equals the rectangle's height, so the total shaded area = \\(\\dfrac{1}{2}\\) × area of rectangle = 392 ÷ 2 = 196 cm²."
},
{
"id": 27100,
"type": 2,
"question": "8000 ml of water was poured into 5 containers equally. How many litres of water were there in one container? ℓ",
"answers": [
"1.6",
null,
null,
null
],
"correct_index": null,
"solution": "8000 ml = 8 ℓ. Divide equally: 8 ÷ 5 = 1.6 ℓ in one container."
},
{
"id": 27101,
"type": 2,
"question": "A six-sided die has a number from 1 to 6 on each side. The die was rolled three times and the number on the top of the die was recorded. The product of the three numbers was 96. What were the three numbers recorded? , , ",
"answers": [
"6",
"4",
"4",
null
],
"correct_index": null,
"solution": "Find three numbers from 1–6 whose product is 96. Since 96 = 6 × 16 = 6 × 4 × 4, the three numbers are 6, 4 and 4."
},
{
"id": 27102,
"type": 2,
"question": "The table shows the parking charges at a car park. 6 a.m. – 12 p.m.: \\(\\$0.60\\) per 30 minutes or part thereof 12 p.m. – 2 p.m.: \\(\\$1.20\\) per 30 minutes or part thereof 2 p.m. – 6 p.m.: \\(\\$0.60\\) per 30 minutes or part thereof 6 p.m. – 6 a.m.: \\(\\$8\\) per entry Mr Ho parked his car from 11 a.m. to 2.15 p.m. How much did he pay for the parking? \\(\\$\\)[?]",
"answers": [
"6.60",
null,
null,
null
],
"correct_index": null,
"solution": "11 a.m.–12 p.m. (1 h) at \\(\\$0.60\\)/30 min = 2 × \\(\\$0.60\\) = \\(\\$1.20\\). 12 p.m.–2 p.m. (2 h) at \\(\\$1.20\\)/30 min = 4 × \\(\\$1.20\\) = \\(\\$4.80\\). 2 p.m.–2.15 p.m. (part of 30 min) at \\(\\$0.60\\) = \\(\\$0.60\\). Total = \\(\\$1.20\\) + \\(\\$4.80\\) + \\(\\$0.60\\) = \\(\\$6.60\\)."
},
{
"id": 27103,
"type": 2,
"question": "Ali had some money at first. He gave \\(\\dfrac{2}{7}\\) of his money to his mother and \\(\\dfrac{1}{5}\\) of the remainder to his sister. He had \\(\\$216\\) left. How much money did he have at first? \\(\\$\\)[?]",
"answers": [
"378",
null,
null,
null
],
"correct_index": null,
"solution": "After mother, remainder = \\(\\dfrac{5}{7}\\). Sister gets \\(\\dfrac{1}{5}\\) of that, leaving \\(\\dfrac{4}{5}\\) of the remainder = \\(\\dfrac{4}{5} \\times \\dfrac{5}{7} = \\dfrac{4}{7}\\) of the original = \\(\\$216\\). So \\(\\dfrac{1}{7}\\) = \\(\\$54\\), and the whole = 7 × \\(\\$54\\) = \\(\\$378\\)."
},
{
"id": 27104,
"type": 2,
"question": "ABCD is a rhombus. \\(\\angle\\)BAD = 110°. Find \\(\\angle\\)BDC. °",
"answers": [
"35",
null,
null,
null
],
"correct_index": null,
"solution": "Opposite angles of a rhombus are equal, so \\(\\angle\\)BCD = \\(\\angle\\)BAD = 110°. Triangle BCD is isosceles (CB = CD), so \\(\\angle\\)BDC = (180° − 110°) ÷ 2 = 35°."
},
{
"id": 27105,
"type": 2,
"question": "Leon worked \\(6\\dfrac{1}{5}\\) h daily from Monday to Friday. He worked \\(4\\dfrac{2}{3}\\) h on Saturday. He did not work on Sunday. How many weeks must he work to have worked 535 hours? ",
"answers": [
"15",
null,
null,
null
],
"correct_index": null,
"solution": "Weekday hours = \\(6\\dfrac{1}{5} \\times 5 = 31\\) h. Add Saturday: \\(31 + 4\\dfrac{2}{3} = 35\\dfrac{2}{3} = \\dfrac{107}{3}\\) h per week. Weeks = \\(535 \\div \\dfrac{107}{3} = 535 \\times \\dfrac{3}{107} = 15\\) weeks."
},
{
"id": 27106,
"type": 2,
"question": "Tiffany and Leila had the same amount of money at first. Tiffany spent all her money to buy 1 dress and 6 identical skirts. Leila bought 1 such dress and a blouse and had \\(\\$72\\) left. The blouse cost \\(\\$8\\) more than the skirt. What was the cost of the blouse? \\(\\$\\)[?]",
"answers": [
"24",
null,
null,
null
],
"correct_index": null,
"solution": "Both start equal. Tiffany: dress + 6 skirts. Leila: dress + blouse + \\(\\$72\\) left. So 6 skirts = blouse + \\(\\$72\\). Blouse = skirt + \\(\\$8\\), so 6 skirts = skirt + 8 + 72, giving 5 skirts = 80, skirt = \\(\\$16\\). Blouse = 16 + 8 = \\(\\$24\\)."
},
{
"id": 27107,
"type": 2,
"question": "A triangle is drawn in rectangle ABCE. Find the area of triangle ADF. cm²",
"answers": [
"60",
null,
null,
null
],
"correct_index": null,
"solution": "Area of triangle ADB (base AB = 24, height = 14) = \\(\\dfrac{1}{2} \\times 24 \\times 14 = 168\\) cm². F is 5 cm below the top, so triangle ABF has height 14 − 5 = 9: area = \\(\\dfrac{1}{2} \\times 24 \\times 9 = 108\\) cm². Area of triangle ADF = 168 − 108 = 60 cm²."
},
{
"id": 27108,
"type": 1,
"question": "The bar graph shows the distance travelled by a car from Monday to Friday. Which day did the car travel the furthest?",
"answers": [
"Monday",
"Tuesday",
"Wednesday",
"Thursday"
],
"correct_index": 1,
"solution": "Reading the bar graph, Tuesday's bar is tallest at 300 km, the greatest distance."
},
{
"id": 27109,
"type": 2,
"question": "The bar graph shows the distance travelled by a car from Monday to Friday. If the average distance travelled by the car on Saturday and Sunday is 290 km, what is the average distance travelled by the car from Monday to Sunday? Correct your answer to the nearest tenth. km",
"answers": [
"247.1",
null,
null,
null
],
"correct_index": null,
"solution": "Mon–Fri total = 250 + 300 + 200 + 250 + 150 = 1150 km. Sat + Sun = 290 × 2 = 580 km. Total Mon–Sun = 1150 + 580 = 1730 km. Average = 1730 ÷ 7 ≈ 247.1 km."
}
]