{
"paper": {
"school": "Anglo-Chinese School (Junior)",
"year": 2023,
"level": "P6",
"label": "Prelim",
"source_prefix": "ACS 2023 P6 Prelim",
"has_answer_key": true,
"notes": "Two papers in one PDF. Paper 1 = Booklet A (Q1-15, MCQ) + Booklet B (Q16-30). Paper 2 = Q1-17. Manifest numbers questions P1-1..P1-30 then P2-1..P2-17 to avoid collisions; source label preserves paper+question. Printed answer key on last pages used and cross-checked."
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "Express 56 hundredths as a decimal.",
"answer0": "0.056",
"answer1": "0.56",
"answer2": "5.6",
"answer3": "56.0",
"correct_answer": 1,
"skill_id": 158,
"difficulty_id": 1,
"explanation": "56 hundredths = 56/100 = 0.56. Answer: (2) 0.56.",
"hints": ["Hundredths is the 2nd decimal place.", "56 ÷ 100 moves the decimal two places left."],
"source": "ACS 2023 P6 Prelim Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 2."
},
{
"n": 2,
"type_id": 1,
"question": "Round 84 596 to the nearest thousand.",
"answer0": "80 000",
"answer1": "84 000",
"answer2": "84 600",
"answer3": "85 000",
"correct_answer": 3,
"skill_id": 150,
"difficulty_id": 1,
"explanation": "The hundreds digit is 5, so round up: 84 596 → 85 000. Answer: (4) 85 000.",
"hints": ["Look at the hundreds digit to decide.", "5 or more rounds the thousands up."],
"source": "ACS 2023 P6 Prelim Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 4."
},
{
"n": 3,
"type_id": 1,
"question": "Which one of the following fractions is closest to 1?",
"answer0": "\\(\\dfrac{7}{8}+\\dfrac{1}{7}\\)",
"answer1": "\\(\\dfrac{8}{7}\\)",
"answer2": "\\(\\dfrac{8}{9}\\)",
"answer3": "\\(\\dfrac{9}{8}\\)",
"correct_answer": 2,
"skill_id": 159,
"difficulty_id": 2,
"explanation": "Compare each value's distance from 1. \\(\\dfrac{7}{8}+\\dfrac{1}{7}=\\dfrac{49+8}{56}=\\dfrac{57}{56}\\) (off by 1/56). \\(\\dfrac{8}{7}\\) off by 1/7. \\(\\dfrac{8}{9}\\) off by 1/9. \\(\\dfrac{9}{8}\\) off by 1/8. The smallest gap is 1/56, but among single fractions options 3 and 4: 1/9 < 1/8. Comparing all four, option 1 is closest (1/56). Printed key: (3) 8/9. Using key.",
"hints": ["Find how far each is from 1.", "Smaller difference means closer to 1."],
"source": "ACS 2023 P6 Prelim Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 3 (8/9). Note: option (1) 7/8+1/7 = 57/56 is mathematically closer to 1 (off 1/56); the school key marks (3). Followed printed key."
},
{
"n": 4,
"type_id": 1,
"question": "How many sixths are there in \\(2\\dfrac{2}{3}\\)?",
"answer0": "16",
"answer1": "14",
"answer2": "12",
"answer3": "8",
"correct_answer": 0,
"skill_id": 206,
"difficulty_id": 1,
"explanation": "\\(2\\dfrac{2}{3}=\\dfrac{8}{3}=\\dfrac{16}{6}\\), so there are 16 sixths. Answer: (1) 16.",
"hints": ["Convert the mixed number to an improper fraction.", "Rewrite with denominator 6."],
"source": "ACS 2023 P6 Prelim Q4",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 1."
},
{
"n": 5,
"type_id": 1,
"question": "Which of the following lines is perpendicular to AC?",
"answer0": "AB",
"answer1": "CD",
"answer2": "ED",
"answer3": "FB",
"correct_answer": 3,
"skill_id": 143,
"difficulty_id": 2,
"explanation": "On the square grid, AC is a diagonal; the line FB meets AC at right angles. Answer: (4) FB.",
"hints": ["Look for the line that crosses AC at 90°.", "Use the grid squares to check the right angle."],
"source": "ACS 2023 P6 Prelim Q5",
"image_needed": true,
"image_page": 3,
"image_bbox": [0.40, 0.30, 0.70, 0.47],
"image_loc": "grid figure with points A,B,C,D,E,F in upper-middle of page below the question",
"image_options": false,
"image_file": "q5.png",
"notes": "Key: 4."
},
{
"n": 6,
"type_id": 1,
"question": "The average mass of a group of 3 boys is 38 kg. Hashim, whose mass is 42 kg, joined the group. What is the average mass of the new group?",
"answer0": "24 kg",
"answer1": "39 kg",
"answer2": "40 kg",
"answer3": "52 kg",
"correct_answer": 1,
"skill_id": 203,
"difficulty_id": 2,
"explanation": "Total of 3 boys = 3 × 38 = 114 kg. New total = 114 + 42 = 156 kg over 4 people. Average = 156 ÷ 4 = 39 kg. Answer: (2) 39 kg.",
"hints": ["Total = average × number of items.", "Add Hashim, then divide by the new count of 4."],
"source": "ACS 2023 P6 Prelim Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 2."
},
{
"n": 7,
"type_id": 1,
"question": "Find the area of triangle ABC.",
"answer0": "96 cm²",
"answer1": "114 cm²",
"answer2": "190 cm²",
"answer3": "228 cm²",
"correct_answer": 1,
"skill_id": 186,
"difficulty_id": 2,
"explanation": "Base AC = 16 + 3 = 19 cm, height = 12 cm. Area = ½ × 19 × 12 = 114 cm². Answer: (2) 114 cm².",
"hints": ["The base is the whole bottom side (16 + 3).", "Area = ½ × base × height."],
"source": "ACS 2023 P6 Prelim Q7",
"image_needed": true,
"image_page": 4,
"image_bbox": [0.30, 0.13, 0.80, 0.30],
"image_loc": "triangle ABC with 20 cm, 12 cm, 16 cm, 3 cm labels, top of page below question",
"image_options": false,
"image_file": "q7.png",
"notes": "Key: 2. Base = 16+3 = 19 cm."
},
{
"n": 8,
"type_id": 1,
"question": "The pie chart shows how Rory spent his pocket money last month. He spent $30 more on item D than item C. How much did he spend on item B?",
"answer0": "$70",
"answer1": "$60",
"answer2": "$45",
"answer3": "$25",
"correct_answer": 2,
"skill_id": 235,
"difficulty_id": 3,
"explanation": "D = 35%. The angle between C and D is a right angle (90% mark shows C is 25%? ) — using the chart, C = 35% − difference. D − C corresponds to $30; D = 35% so C = 20% (right angle = 25% of 360°… ) giving 1% = $30 ÷ (35−20) → $2 per 1%? Following the key, B = 45%? Printed key: (3) $45. Using printed key value $45.",
"hints": ["The right-angle mark equals 25% of the circle.", "Use the $30 difference between D and C to find the value of 1%."],
"source": "ACS 2023 P6 Prelim Q8",
"image_needed": true,
"image_page": 4,
"image_bbox": [0.38, 0.49, 0.62, 0.66],
"image_loc": "pie chart with sectors A,B,C,D(35%) and a right-angle mark, middle of page",
"image_options": false,
"image_file": "q8.png",
"notes": "Key: 3 ($45). Pie sectors A, B, C, D=35%, one right angle marked; D is $30 more than C."
},
{
"n": 9,
"type_id": 1,
"question": "A piece of paper is folded and a symmetrical figure is cut out from it. Which one shows half of the symmetrical figure that is cut out, with the dotted line as the line of symmetry?",
"answer0": "Figure (1)",
"answer1": "Figure (2)",
"answer2": "Figure (3)",
"answer3": "Figure (4)",
"correct_answer": 2,
"skill_id": 234,
"difficulty_id": 3,
"explanation": "Reflecting the cut-out half across the dotted line of symmetry reproduces the full notched figure. Option (3) matches. Answer: (3).",
"hints": ["Imagine reflecting each option across the dotted line.", "The reflected shape must rebuild the original cut figure."],
"source": "ACS 2023 P6 Prelim Q9",
"image_needed": true,
"image_options": true,
"image_page": 5,
"image_bbox": [0.30, 0.12, 0.72, 0.24],
"image_loc": "folded-paper notched figure at top; four option diagrams below labelled (1)-(4)",
"image_file": "q9.png",
"notes": "Key: 3. image_options: option diagrams q9_opt0..q9_opt3 to be cropped; main figure q9.png. Stem figure is geometric symmetry shapes."
},
{
"n": 10,
"type_id": 1,
"question": "A cuboid has a square base area of 25 cm². The area of the shaded face is 35 cm². What is the volume of the cuboid?",
"answer0": "125 cm³",
"answer1": "175 cm³",
"answer2": "245 cm³",
"answer3": "875 cm³",
"correct_answer": 1,
"skill_id": 227,
"difficulty_id": 2,
"explanation": "Square base 25 cm² → side = 5 cm. Shaded (side) face 35 cm² = 5 × height → height = 7 cm. Volume = base area × height = 25 × 7 = 175 cm³. Answer: (2) 175 cm³.",
"hints": ["Square base area gives the base side length.", "Use the shaded face to find the height, then V = base × height."],
"source": "ACS 2023 P6 Prelim Q10",
"image_needed": true,
"image_page": 6,
"image_bbox": [0.40, 0.11, 0.66, 0.25],
"image_loc": "cuboid drawing with shaded face labelled 35 cm², top-middle of page",
"image_options": false,
"image_file": "q10.png",
"notes": "Key: 2."
},
{
"n": 11,
"type_id": 1,
"question": "ABCF is a trapezium and CDEF is a parallelogram. AF // BC, \\(\\angle\\)EDC = 110° and \\(\\angle\\)BCF = 52°. Find \\(\\angle\\)AFE.",
"answer0": "122°",
"answer1": "128°",
"answer2": "140°",
"answer3": "162°",
"correct_answer": 3,
"skill_id": 200,
"difficulty_id": 3,
"explanation": "In parallelogram CDEF, \\(\\angle\\)CFE = \\(\\angle\\)EDC = 110° (opposite angles). \\(\\angle\\)BCF = 52°; since AF // BC, \\(\\angle\\)AFC = 52° (alternate angles). \\(\\angle\\)AFE = \\(\\angle\\)AFC + \\(\\angle\\)CFE = 52° + 110° = 162°. Answer: (4) 162°.",
"hints": ["Opposite angles of a parallelogram are equal.", "AF // BC gives alternate angles; add the two parts at F."],
"source": "ACS 2023 P6 Prelim Q11",
"image_needed": true,
"image_page": 6,
"image_bbox": [0.28, 0.50, 0.72, 0.74],
"image_loc": "trapezium+parallelogram figure A,B,C,D,E,F with 110° and 52° marked, middle of page",
"image_options": false,
"image_file": "q11.png",
"notes": "Key: 4."
},
{
"n": 12,
"type_id": 1,
"question": "Jonathan used 4 identical right-angled triangles to form a figure PQRST. PT = 12 cm. The perimeter of the figure is 40 cm. Find the area of PQRST.",
"answer0": "48 cm²",
"answer1": "96 cm²",
"answer2": "144 cm²",
"answer3": "192 cm²",
"correct_answer": 1,
"skill_id": 186,
"difficulty_id": 3,
"explanation": "PT = 12 cm is split by R into two equal heights of 6 cm each (the common short side of the triangles). The 4 outer slanted edges total the perimeter 40 cm → each slant = 10 cm. Each right triangle has legs 6 and 8 (since 6-8-10), area = ½ × 6 × 8 = 24 cm². Four triangles: 4 × 24 = 96 cm². Answer: (2) 96 cm².",
"hints": ["The perimeter is made of the 4 equal slant edges.", "Find the legs of each right triangle, then total 4 areas."],
"source": "ACS 2023 P6 Prelim Q12",
"image_needed": true,
"image_page": 7,
"image_bbox": [0.24, 0.16, 0.52, 0.37],
"image_loc": "fan of 4 right-angled triangles P,Q,R,S,T with PT=12 cm marked, upper-left of page",
"image_options": false,
"image_file": "q12.png",
"notes": "Key: 2."
},
{
"n": 13,
"type_id": 1,
"question": "The table shows the parking charges for a motorist in a shopping centre.
7 am to 6 pm — 1st hour: $2.20; subsequent 30 minutes or part thereof: $1.50.
After 6 pm — $2.50 per entry.
Mr Lim parked his car from 4 p.m. to 7 p.m. How much parking charges did he pay?",
"answer0": "$6.20",
"answer1": "$6.90",
"answer2": "$7.70",
"answer3": "$8.50",
"correct_answer": 2,
"skill_id": 167,
"difficulty_id": 3,
"explanation": "4 pm to 6 pm (2 h, day rate): 1st hour $2.20 + two more 30-min blocks $1.50 × 2 = $3.00 → $5.20. After 6 pm to 7 pm = $2.50 per entry. Total = $5.20 + $2.50 = $7.70. Answer: (3) $7.70.",
"hints": ["Split the parking into before 6 pm and after 6 pm.", "Count the 30-minute blocks after the first hour."],
"source": "ACS 2023 P6 Prelim Q13",
"image_needed": true,
"image_page": 7,
"image_bbox": [0.24, 0.55, 0.78, 0.66],
"image_loc": "parking-charge table, middle of page (table can also be read from stem text)",
"image_options": false,
"image_file": "q13.png",
"notes": "Key: 3. Table also transcribed into the stem so the figure is optional."
},
{
"n": 14,
"type_id": 1,
"question": "There were a total of 800 adults and children at a stadium. 70% of them were adults. Some adults left the stadium and the ratio of the number of adults to the number of children became 5 : 3. How many adults left the stadium?",
"answer0": "60",
"answer1": "70",
"answer2": "160",
"answer3": "210",
"correct_answer": 1,
"skill_id": 209,
"difficulty_id": 3,
"explanation": "Adults = 70% × 800 = 560; children = 240 (unchanged). New ratio 5 : 3, so 3 units = 240 → 1 unit = 80, 5 units (adults) = 400. Adults left = 560 − 400 = 160. Answer: (3) 160. Printed key: 70. Note discrepancy.",
"hints": ["Children stay the same; only adults leave.", "Use the children's number as the fixed 3-unit part of 5 : 3."],
"source": "ACS 2023 P6 Prelim Q14",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Printed key: 3. Correct value 160 is option (3); the answer key letter '3' = option (3) = 160, consistent. (The earlier read of key as '70' was option position; key value 160.)"
},
{
"n": 15,
"type_id": 1,
"question": "Su Lin and Tina made some necklaces over 2 days. On Monday, Su Lin made 17 more necklaces than Tina. On Tuesday, Su Lin made 30 necklaces and Tina made 11 necklaces. At the end of the 2 days, Tina made \\(\\dfrac{1}{4}\\) of the total number of necklaces. How many necklaces did Su Lin make?",
"answer0": "54",
"answer1": "57",
"answer2": "64",
"answer3": "72",
"correct_answer": 0,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "Let Tina's Monday count = t. Tina total = t + 11; Su Lin total = (t + 17) + 30 = t + 47. Tina is 1/4 of total, so Su Lin is 3/4 → Su Lin = 3 × Tina: t + 47 = 3(t + 11) → t + 47 = 3t + 33 → 2t = 14 → t = 7. Su Lin = 7 + 47 = 54. Answer: (1) 54.",
"hints": ["Tina = 1/4 of total means Su Lin = 3 × Tina.", "Set up totals from each day and solve for the unknown."],
"source": "ACS 2023 P6 Prelim Q15",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 1."
},
{
"n": 16,
"type_id": 2,
"question": "Find the value of 85 + 4 × (15 − 6 ÷ 3). [?]",
"answer0": "137",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 155,
"difficulty_id": 2,
"explanation": "Brackets first: 6 ÷ 3 = 2, then 15 − 2 = 13. Then 4 × 13 = 52. Finally 85 + 52 = 137.",
"hints": ["Work inside the brackets first (division before subtraction).", "Then multiply, then add."],
"source": "ACS 2023 P6 Prelim Q16",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 137."
},
{
"n": 17,
"type_id": 2,
"question": "Find the value of \\(9000 + 9 + \\dfrac{9}{100} + \\dfrac{9}{1000}\\). Give your answer as a decimal. [?]",
"answer0": "9009.099",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 158,
"difficulty_id": 2,
"explanation": "9/100 = 0.09 and 9/1000 = 0.009. Sum = 9000 + 9 + 0.09 + 0.009 = 9009.099.",
"hints": ["Convert each fraction to a decimal.", "Line up the place values before adding."],
"source": "ACS 2023 P6 Prelim Q17",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 9009.099."
},
{
"n": 18,
"type_id": 2,
"question": "What is the length of the clip? [?]",
"answer0": "2.75",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 184,
"difficulty_id": 1,
"explanation": "The clip spans from the 3.5 cm mark to the 6.25 cm mark on the ruler. Length = 6.25 − 3.5 = 2.75 cm.",
"hints": ["Read the ruler marks at both ends of the clip.", "Subtract the start reading from the end reading."],
"source": "ACS 2023 P6 Prelim Q18",
"image_needed": true,
"image_page": 9,
"image_bbox": [0.22, 0.62, 0.78, 0.78],
"image_loc": "paper clip lying over a centimetre ruler marked 3 to 7, lower half of page",
"image_options": false,
"image_file": "q18.png",
"notes": "Key: 2.75 (answer in cm)."
},
{
"n": 19,
"type_id": 2,
"question": "The figure is made up of 1-cm cubes. What is the volume of the figure? [?]",
"answer0": "13",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 189,
"difficulty_id": 2,
"explanation": "Count the unit cubes in the solid: 13 cubes. Each is 1 cm³, so volume = 13 cm³.",
"hints": ["Count every small cube, including hidden ones.", "Each cube is 1 cm³."],
"source": "ACS 2023 P6 Prelim Q19",
"image_needed": true,
"image_page": 10,
"image_bbox": [0.30, 0.10, 0.80, 0.30],
"image_loc": "staircase arrangement of 1-cm cubes, top of page",
"image_options": false,
"image_file": "q19.png",
"notes": "Key: 13 (answer in cm³). Count-to-verify: 13 cubes."
},
{
"n": 20,
"type_id": 1,
"question": "The figure shows a circle drawn inside a square. A shaded square is then drawn inside the circle. What fraction of the figure is shaded?",
"answer0": "\\(\\dfrac{1}{2}\\)",
"answer1": "\\(\\dfrac{1}{4}\\)",
"answer2": "\\(\\dfrac{2}{3}\\)",
"answer3": "\\(\\dfrac{3}{4}\\)",
"correct_answer": 0,
"skill_id": 223,
"difficulty_id": 3,
"explanation": "The inner shaded square's diagonal equals the circle's diameter, which equals the side of the outer square. A square drawn on a diagonal has half the area of the square built on that diagonal as its side; the shaded square is half the area of the outer square. So the shaded fraction = 1/2.",
"hints": ["The diagonal of the shaded square equals the side of the big square.", "A square has half the area of the square on its diagonal."],
"source": "ACS 2023 P6 Prelim Q20",
"image_needed": true,
"image_page": 10,
"image_bbox": [0.30, 0.42, 0.62, 0.62],
"image_loc": "outer square (rotated) with inscribed circle and shaded inner square, middle of page",
"image_options": false,
"image_file": "q20.png",
"notes": "Key: 1/2. Made MCQ because the answer is a fraction."
},
{
"n": 21,
"type_id": 1,
"question": "Arrange the following from the smallest to the greatest.
\\(\\dfrac{21}{5}\\), 2.15, \\(2\\dfrac{1}{5}\\)",
"answer0": "2.15, \\(2\\dfrac{1}{5}\\), \\(\\dfrac{21}{5}\\)",
"answer1": "\\(\\dfrac{21}{5}\\), 2.15, \\(2\\dfrac{1}{5}\\)",
"answer2": "\\(2\\dfrac{1}{5}\\), 2.15, \\(\\dfrac{21}{5}\\)",
"answer3": "2.15, \\(\\dfrac{21}{5}\\), \\(2\\dfrac{1}{5}\\)",
"correct_answer": 0,
"skill_id": 158,
"difficulty_id": 2,
"explanation": "Convert to decimals: 21/5 = 4.2, 2.15 = 2.15, 2 1/5 = 2.2. Smallest to greatest: 2.15, 2 1/5, 21/5. Answer: (1).",
"hints": ["Convert every number to a decimal first.", "Then order the decimals from smallest to largest."],
"source": "ACS 2023 P6 Prelim Q21",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 2.15, 2 1/5, 21/5. Made MCQ because the ordered answer contains a fraction and a mixed number."
},
{
"n": 22,
"type_id": 2,
"question": "POS is a straight line. \\(\\angle\\)QOS = 138° and \\(\\angle\\)POR = 130°. Find \\(\\angle\\)QOR. [?]",
"answer0": "88",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 194,
"difficulty_id": 2,
"explanation": "On straight line POS: \\(\\angle\\)POQ = 180° − 138° = 42°; \\(\\angle\\)ROS = 180° − 130° = 50°. \\(\\angle\\)QOR = 180° − 42° − 50° = 88°.",
"hints": ["Angles on a straight line sum to 180°.", "Find POQ and ROS first, then subtract from 180°."],
"source": "ACS 2023 P6 Prelim Q22",
"image_needed": true,
"image_page": 11,
"image_bbox": [0.18, 0.50, 0.56, 0.62],
"image_loc": "rays Q and R from point O on straight line POS, 130° and 138° marked, middle-left of page",
"image_options": false,
"image_file": "q22.png",
"notes": "Key: 88° (answer in degrees)."
},
{
"n": 23,
"type_id": 0,
"question": "The square grid shows the positions of points A, B, C, D, E, F and G.
(a) In what direction is point E from point B?
(b) Kayel stood at one of the points facing C. After he turned 45° anti-clockwise, he faced G. Which point was Kayel at?",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 234,
"difficulty_id": 2,
"explanation": "(a) E is to the lower-right of B → Southeast. (b) Standing at a point, facing C then turning 45° anti-clockwise to face G: that point is F.",
"hints": ["Use the N arrow to set the compass directions.", "Sketch the facing direction and turn it 45° anti-clockwise."],
"source": "ACS 2023 P6 Prelim Q23",
"image_needed": true,
"image_page": 12,
"image_bbox": [0.40, 0.14, 0.74, 0.34],
"image_loc": "square grid with labelled points A-G and a North arrow, top-middle of page",
"image_options": false,
"image_file": "q23.png",
"notes": "type_id 0: part (a) answer 'Southeast' is a word/direction (no numeric FIB), and (b) answer 'F' is a letter; per rules direction/letter answers cannot be FIB. Skipped on insert. Key: (a) Southeast, (b) F."
},
{
"n": 24,
"type_id": 2,
"question": "A box with 24 erasers has a mass of 0.67 kg. The same box with 44 similar erasers has a mass of 1.21 kg. Find the mass of 1 eraser. Express your answer in kg. [?]",
"answer0": "0.027",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 167,
"difficulty_id": 2,
"explanation": "Extra 44 − 24 = 20 erasers add 1.21 − 0.67 = 0.54 kg. Mass of 1 eraser = 0.54 ÷ 20 = 0.027 kg.",
"hints": ["The mass difference comes only from the extra erasers.", "Divide the extra mass by the extra number of erasers."],
"source": "ACS 2023 P6 Prelim Q24",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 0.027 kg."
},
{
"n": 25,
"type_id": 2,
"question": "Shane had a rectangular piece of paper ABCD. \\(\\angle\\)AFD = 74°. He folded it along line AE and AF. Find \\(\\angle\\)y. [?]",
"answer0": "29",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 143,
"difficulty_id": 3,
"explanation": "In right-angled triangle ADF, \\(\\angle\\)DAF = 90° − 74° = 16°. By folding along AF, the fold angle is preserved, so the corner angle 90° splits: 90° − 16° = 74°, then the two equal folded angles share 90° − 32° → \\(\\angle\\)y = (90° − 32°) ÷ 2 = 29°. (Key working: 90 − 74 = 16 × 2 = 32; (90 − 32)/2 = 29.)",
"hints": ["Folding makes equal angles on each side of the crease.", "Use the 90° corner of the rectangle minus the folded angles."],
"source": "ACS 2023 P6 Prelim Q25",
"image_needed": true,
"image_page": 13,
"image_bbox": [0.14, 0.44, 0.88, 0.66],
"image_loc": "before-folding rectangle ABCD with 74° at F and after-folding figure, two diagrams across middle of page",
"image_options": false,
"image_file": "q25.png",
"notes": "Key: 29° (answer in degrees)."
},
{
"n": 26,
"type_id": 0,
"question": "Rectangle ACDF is made up of a square and a rectangle. The perimeter of rectangle ACDF is (2y + 15) cm. The perimeter of the square ABEF is 16 cm.
(a) Find the perimeter of rectangle BCDE in terms of y. Give your answer in its simplest form.
(b) Find the perimeter of the rectangle BCDE when y = 3.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 239,
"difficulty_id": 3,
"explanation": "Square ABEF has perimeter 16 cm → side = 4 cm. (a) Perimeter of BCDE = perimeter of ACDF − the two square sides counted twice = (2y + 15) − 4 − 4 = (2y + 7) cm. (b) When y = 3: 2(3) + 7 = 13 cm.",
"hints": ["Find the square's side from its perimeter (16 ÷ 4).", "Subtract the shared/extra square sides from the big rectangle's perimeter."],
"source": "ACS 2023 P6 Prelim Q26",
"image_needed": true,
"image_page": 14,
"image_bbox": [0.28, 0.13, 0.58, 0.30],
"image_loc": "rectangle ACDF split into square ABEF and rectangle BCDE, top-middle of page",
"image_options": false,
"image_file": "q26.png",
"notes": "type_id 0: part (a) answer is an algebraic expression (2y + 7) which cannot be a numeric FIB; part (b) is 13. Skipped on insert. Key: (a) 2y + 7 cm, (b) 13 cm."
},
{
"n": 27,
"type_id": 0,
"question": "The table shows the price of economical rice at four different stalls at a hawker centre.
A: lowest $4.20, highest $8.80; B: lowest $6.00, highest $10.30; C: lowest $3.70, highest $6.20; D: lowest $4.60, highest $12.50.
(a) Raymond wanted to buy food from 2 of the stalls. He had $8. Which two stalls could he buy food from?
(b) Xue Ling had $20. She bought food from one of the stalls and had $9.50 left. Which stall did she buy her food from?",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 147,
"difficulty_id": 2,
"explanation": "(a) Cheapest two combined: A + C = 4.20 + 3.70 = 7.90 ≤ 8, so stalls A and C. (b) She spent 20 − 9.50 = $10.50; the only stall whose price range includes $10.50 is D (4.60–12.50). Stall D.",
"hints": ["For (a) add the two lowest prices and keep within $8.", "For (b) the amount spent is $10.50; find the stall whose range covers it."],
"source": "ACS 2023 P6 Prelim Q27",
"image_needed": true,
"image_page": 15,
"image_bbox": [0.16, 0.14, 0.84, 0.30],
"image_loc": "price table for stalls A-D (lowest/highest price), top of page (also transcribed in stem)",
"image_options": false,
"image_file": "q27.png",
"notes": "type_id 0: answers are stall letters (A & C; D), which are letter answers — cannot be numeric FIB and exact-match is fragile. Skipped on insert. Key: (a) A and C, (b) D."
},
{
"n": 28,
"type_id": 2,
"question": "BIG SALE!!! Buy first toaster oven at 10% discount. Buy second toaster oven at 20% discount. Price of 2nd toaster oven should be equal to or lower than price of 1st toaster oven.
Uncle Jaime bought 2 toaster ovens at the sale. The two toaster ovens were priced at $40 and $60. How much did he pay for the two toaster ovens? [?]",
"answer0": "86",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 176,
"difficulty_id": 3,
"explanation": "To pay the least, the higher price ($60) takes the 10% (first) and the lower price ($40) takes the 20% (second), satisfying 2nd ≤ 1st. First oven: 60 × 0.90 = $54. Second oven: 40 × 0.80 = $32. Total = 54 + 32 = $86.",
"hints": ["Decide which oven is the '1st' (10% off) and which is the '2nd' (20% off).", "Apply each discount, then add the two prices."],
"source": "ACS 2023 P6 Prelim Q28",
"image_needed": true,
"image_page": 16,
"image_bbox": [0.18, 0.10, 0.86, 0.40],
"image_loc": "BIG SALE poster with two toaster ovens and discount labels, top half of page",
"image_options": false,
"image_file": "q28.png",
"notes": "Key: $86 (answer in dollars). Poster gives the discount conditions (also in stem)."
},
{
"n": 29,
"type_id": 0,
"question": "The line graph shows the amount of water in a tank from 1 p.m. to 5 p.m. The tank was 20% filled at 1 p.m. Water flowed into the tank from 1 p.m. to 5 p.m.
(a) During which 1-hour interval was the flow into the tank the greatest?
(b) At 5 p.m., what fraction of the tank was filled with water?",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 147,
"difficulty_id": 3,
"explanation": "(a) The steepest rise on the line graph is from 2 p.m. to 3 p.m. (from 12 L to 21 L, a rise of 9 L), the greatest 1-hour increase. (b) At 1 p.m. tank was 20% full = 6 L, so full tank = 30 L. At 5 p.m. there were 30 L → 30/30, but graph shows ~22 L of the 30 L capacity → fraction = 22/30 = 11/15 (key writes 22/30 = 73.3%).",
"hints": ["The steepest section of the line is the greatest flow.", "Use the 1 p.m. value (20% = 6 L) to find the full tank capacity."],
"source": "ACS 2023 P6 Prelim Q29",
"image_needed": true,
"image_page": 17,
"image_bbox": [0.20, 0.14, 0.82, 0.50],
"image_loc": "line graph volume of water vs time 1pm-5pm, upper half of page",
"image_options": false,
"image_file": "q29.png",
"notes": "type_id 0: (a) answer is a time interval '2 p.m. to 3 p.m.' (a range of words), (b) answer is a fraction 11/15 — neither is a clean numeric FIB. Skipped on insert. Key: (a) 2 p.m.–3 p.m., (b) 22/30 (= 11/15)."
},
{
"n": 30,
"type_id": 0,
"question": "ABCD is a trapezium and AD = BC. Each of the statements is either true, false or not possible to tell from the information given. For each statement, decide your answer.
Statement 1: AB // CD.
Statement 2: \\(\\angle\\)ADE + \\(\\angle\\)CBE = 90°.
Statement 3: The shaded area is greater than the unshaded area.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "Statement 1 (AB // CD): True — it is a trapezium with AB parallel to CD. Statement 2 (∠ADE + ∠CBE = 90°): False. Statement 3 (shaded area greater than unshaded): False.",
"hints": ["A trapezium has one pair of parallel sides.", "Compare the shaded triangle with the rest of the figure."],
"source": "ACS 2023 P6 Prelim Q30",
"image_needed": true,
"image_page": 18,
"image_bbox": [0.30, 0.12, 0.66, 0.28],
"image_loc": "trapezium ABCD with shaded triangle DEB, top of page",
"image_options": false,
"image_file": "q30.png",
"notes": "type_id 0: a true/false/not-possible tick-table — an interactive match format with no app question type. Skipped on insert. Key: True, False, False."
},
{
"n": 31,
"type_id": 2,
"question": "A bag of sweets was shared equally among a group of 36 students. 12 of them gave up all of their sweets to the rest of the students. As a result, the rest of the students received 5 more sweets each. How many sweets were there in the bag at first? [?]",
"answer0": "360",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "The remaining 36 − 12 = 24 students each got 5 more sweets → 24 × 5 = 120 sweets came from the 12 who gave up theirs. So each original share = 120 ÷ 12 = 10 sweets. Total at first = 36 × 10 = 360.",
"hints": ["Find the total extra sweets the 24 students received.", "Those extra sweets came from the 12 students' shares."],
"source": "ACS 2023 P6 Prelim Paper 2 Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q1. Key: 360."
},
{
"n": 32,
"type_id": 2,
"question": "A box contained some red and yellow balls. At first, the number of red balls to the number of yellow balls is 1 : 3. After \\(\\dfrac{1}{4}\\) of the red balls and \\(\\dfrac{3}{8}\\) of the yellow balls were taken out, there were 63 balls left in the box. How many yellow balls were there in the box at first? [?]",
"answer0": "72",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 214,
"difficulty_id": 3,
"explanation": "Ratio R : Y = 1 : 3. To use 1/4 and 3/8 cleanly, scale to R : Y = 6 : 18 (so total 24 units). Removed: 1/4 of red = 1.5 units (use ×... ) — using key's units R:Y = 8:24: removed 1/4 of 8 = 2, and 3/8 of 24 = 9, removed 11 units, left 32 − 11 = 21 units = 63 → 1 unit = 3. Yellow at first = 24 units × 3 = 72.",
"hints": ["Choose units so 1/4 of red and 3/8 of yellow are whole numbers.", "Set the leftover units equal to 63 to find one unit."],
"source": "ACS 2023 P6 Prelim Paper 2 Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q2. Key: 24u = 72 (yellow at first = 72)."
},
{
"n": 33,
"type_id": 2,
"question": "The table shows the amount of money Jamie spent at a restaurant for the first three weeks. Week 1: $36; Week 2: $39; Week 3: $37; Week 4: ?
Jamie will get a free meal if the average amount of money he spent for three of the four weeks is $40 or more. What is the smallest amount Jamie must spend in Week 4 to receive the free meal? [?]",
"answer0": "44",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 204,
"difficulty_id": 3,
"explanation": "Average of 3 weeks ≥ $40 → total of the best 3 weeks ≥ 3 × 40 = $120. Take Week 4 with the two highest existing weeks (39 and 37): Week 4 + 39 + 37 ≥ 120 → Week 4 ≥ 120 − 76 = $44. Smallest amount = $44.",
"hints": ["Average of 3 weeks of $40 needs a total of $120.", "Pair Week 4 with the two largest of the first three weeks."],
"source": "ACS 2023 P6 Prelim Paper 2 Q3",
"image_needed": true,
"image_page": 21,
"image_bbox": [0.36, 0.15, 0.66, 0.28],
"image_loc": "weekly amount-spent table, top-middle of page (also in stem)",
"image_options": false,
"image_file": "q33.png",
"notes": "Paper 2 Q3. Key: 3×40=120; 120−39−37=44."
},
{
"n": 34,
"type_id": 0,
"question": "In the grid, 2 sides of a trapezium PQRS have been drawn. Complete the drawing of trapezium PQRS where PQ is parallel to RS and RS is twice as long as PQ. Label dot S.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 201,
"difficulty_id": 2,
"explanation": "On the dot grid, draw S so that RS is parallel to PQ and RS = 2 × PQ, then join the sides to complete trapezium PQRS.",
"hints": ["RS must be parallel to PQ.", "Make RS exactly twice the length of PQ along the grid."],
"source": "ACS 2023 P6 Prelim Paper 2 Q4",
"image_needed": true,
"image_page": 21,
"image_bbox": [0.26, 0.58, 0.72, 0.84],
"image_loc": "isometric/square dot grid with P, Q, R marked, lower half of page",
"image_options": false,
"image_file": "q34.png",
"notes": "type_id 0: a draw/construct task on a grid — interactive, no app question type. Skipped on insert. Key: drawing (S labelled to complete the trapezium)."
},
{
"n": 35,
"type_id": 2,
"question": "The figure is made up of a rectangle, a square and a quadrant. Find the area of the shaded part. (Take \\(\\pi = 3.14\\)) [?]",
"answer0": "12.57",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 221,
"difficulty_id": 3,
"explanation": "From the key working: lower shaded triangle = ½ × 14 × 14 = 98 — this refers to the full construction; the final shaded area uses the quadrant: shaded part = ¼ × π × 4 × 4 = ¼ × 3.14 × 16 ≈ 12.57 cm² (the small upper shaded region between the square and the quarter circle of radius 4 cm). Final answer ≈ 12.57 cm².",
"hints": ["Identify the quadrant's radius from the 4 cm width.", "Area of a quadrant = ¼ × π × r²."],
"source": "ACS 2023 P6 Prelim Paper 2 Q5",
"image_needed": true,
"image_page": 22,
"image_bbox": [0.30, 0.12, 0.56, 0.42],
"image_loc": "tall composite figure: rectangle/square with a quadrant arc and shaded regions, 4 cm and 14 cm marked, upper-left of page",
"image_options": false,
"image_file": "q35.png",
"notes": "Paper 2 Q5. Key working: ½×14×14=98; ½×4×4=8; ¼×22/7×4×4=12.57. Final shaded answer 12.57 cm²."
},
{
"n": 36,
"type_id": 2,
"question": "Mrs Lee wrote the word RESILIENCE repeatedly: R E S I L I E N C E R E S I L I E N C E R E S I L I E N C E …
(a) How many 'E's are there in the 1st 100 letters? [?]
(b) How many letters are there altogether up to the 101st 'E'? [?]",
"answer0": "30",
"answer1": "437",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 6,
"difficulty_id": 3,
"explanation": "RESILIENCE has 10 letters with 3 E's (positions 2, 7, 10). (a) 100 letters = 10 full blocks → 10 × 3 = 30 E's. (b) Each block has 3 E's. 101 = 33 × 3 + 2, so 33 full blocks (33 × 10 = 330 letters, 99 E's) then 2 more E's. The 100th E is the 2nd E of block 34 (at local position 7) → 330 + 7 = 337; the 101st E is the 3rd E of block 34 (local position 10) → 330 + 10 = 340 letters. (Key writes 10 × 43 + 7 = 437; using the printed key value 437.)",
"hints": ["Each RESILIENCE block has 3 E's in 10 letters.", "Divide 101 by 3 to count blocks, then add the leftover letters."],
"source": "ACS 2023 P6 Prelim Paper 2 Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q6. Key: (a) 30, (b) 437. Note: my recomputation gives 340 for (b); the printed key states 437 (10×43+7) — used the printed key value as source of truth and flagged the discrepancy."
},
{
"n": 37,
"type_id": 2,
"question": "The table shows the number of seashells collected by 3 boys. Jim: 17; Ken: x; Leo: 6x − 5.
(b) If the average number of seashells the 3 boys collected is 39, what is the value of x? [?]",
"answer0": "15",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 241,
"difficulty_id": 3,
"explanation": "Total = 17 + x + (6x − 5) = 7x + 12. Average 39 over 3 boys → total = 39 × 3 = 117. So 7x + 12 = 117 → 7x = 105 → x = 15.",
"hints": ["Add the three expressions to get the total (7x + 12).", "Average × 3 = total; solve for x."],
"source": "ACS 2023 P6 Prelim Paper 2 Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q7. Only part (b) is a numeric FIB (x = 15). Part (a) answer is the expression 7x + 12 (algebraic, not numeric) so it is omitted from the FIB; recorded in explanation. Key: (a) 7x+12, (b) x=15."
},
{
"n": 38,
"type_id": 2,
"question": "Alisha bought candles of 3 different fragrances. The bar graph shows the number of each type of candle she bought. The number of candles is not shown on the scale.
(a) What percentage of the candles Alisha bought were mint candles? [?]
(b) The price of each rose candle is $12.80. Alisha spent $153.60 on rose candles. How many vanilla candles did she buy? [?]",
"answer0": "50",
"answer1": "24",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 148,
"difficulty_id": 3,
"explanation": "From the bar graph the units are Rose : Vanilla : Mint = 2 : 4 : 6 (total 12). (a) Mint = 6/12 = 50%. (b) Rose candles = 153.60 ÷ 12.80 = 12; if Rose = 2 units then 1 unit = 6, so Vanilla = 4 units = 24. (Key: 153.60/12.8 × 2 = 24.)",
"hints": ["Read the bar lengths as equal units to find the ratio.", "Find the number of rose candles first, then scale to vanilla."],
"source": "ACS 2023 P6 Prelim Paper 2 Q8",
"image_needed": true,
"image_page": 25,
"image_bbox": [0.18, 0.13, 0.78, 0.36],
"image_loc": "horizontal bar graph Rose/Vanilla/Mint number of candles, upper part of page",
"image_options": false,
"image_file": "q38.png",
"notes": "Paper 2 Q8. Key: (a) 3/6 = 50%, (b) 153.60/12.8 ×2 = 24. Bar graph needed for (a)."
},
{
"n": 39,
"type_id": 2,
"question": "ABCG is a parallelogram and CDEF is a trapezium. EF = ED and BCD is a straight line. \\(\\angle\\)AGC = 113°, \\(\\angle\\)GFC = 115°, \\(\\angle\\)EFD = 56° and \\(\\angle\\)CDF = 48°.
(a) Find \\(\\angle\\)FCD. [?]
(b) Find \\(\\angle\\)CGF. [?]",
"answer0": "76",
"answer1": "28",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 197,
"difficulty_id": 3,
"explanation": "(a) In triangle FCD, angles sum to 180°: \\(\\angle\\)FCD = 180° − \\(\\angle\\)CDF − \\(\\angle\\)DFC = 180° − 48° − 56° = 76°. (b) \\(\\angle\\)GCF = 180° − \\(\\angle\\)AGC = 180° − 113° = 67° (co-interior, parallelogram); triangle GCF: \\(\\angle\\)GFC = 115°? Using key: 180 − 67 − 67 = ... and 180 − 115 − 37 = 28°. \\(\\angle\\)CGF = 28°.",
"hints": ["Use the angle sum of triangle FCD for part (a).", "Use parallel-line angles from the parallelogram, then the triangle GCF angle sum."],
"source": "ACS 2023 P6 Prelim Paper 2 Q9",
"image_needed": true,
"image_page": 26,
"image_bbox": [0.16, 0.13, 0.74, 0.36],
"image_loc": "parallelogram ABCG + trapezium CDEF figure with 113°,115°,56°,48° marked, upper part of page",
"image_options": false,
"image_file": "q39.png",
"notes": "Paper 2 Q9. Key: (a) 180−48−56=76; (b) 180−115−37=28."
},
{
"n": 40,
"type_id": 2,
"question": "Munirah cycled from her home to a park. On her way, she had to cycle past a library. She cycled at an average speed of 15 km/h for \\(\\dfrac{1}{2}\\) h from her home to the library. She then cycled the remaining \\(\\dfrac{2}{5}\\) of the journey for 45 minutes.
(a) What was the distance she cycled from her home to the library? [?]
(b) What was her average speed for the whole journey? [?]",
"answer0": "7.5",
"answer1": "10",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 219,
"difficulty_id": 3,
"explanation": "(a) Home→library distance = speed × time = 15 × ½ = 7.5 km. (b) Home→library is 3/5 of the journey (since the remaining is 2/5): 3 units = 7.5 km → 1 unit = 2.5 km, 2 units = 5 km. Total distance = 7.5 + 5 = 12.5 km. Total time = ½ h + 45 min = ½ + ¾ = 1¼ h. Average speed = 12.5 ÷ 1¼ = 10 km/h.",
"hints": ["Distance = speed × time for the first leg.", "Total distance ÷ total time gives the average speed (convert minutes to hours)."],
"source": "ACS 2023 P6 Prelim Paper 2 Q10",
"image_needed": true,
"image_page": 27,
"image_bbox": [0.20, 0.10, 0.84, 0.22],
"image_loc": "Home–Library–Park route pictograph, top of page",
"image_options": false,
"image_file": "q40.png",
"notes": "Paper 2 Q10. Key: (a) 15×½=7.5 km; (b) 12.5/(½+¾)=10 km/h. Answer (a) in km, (b) in km/h."
},
{
"n": 41,
"type_id": 2,
"question": "ABGF and BCDG are rhombuses. \\(\\angle\\)ABF = 31°, \\(\\angle\\)CBG = 40° and EF is parallel to DG.
(a) Find \\(\\angle\\)FGD. [?]
(b) Find \\(\\angle\\)DFE. [?]",
"answer0": "118",
"answer1": "39",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 200,
"difficulty_id": 3,
"explanation": "(a) In rhombus ABGF, diagonal BF bisects, and \\(\\angle\\)BGF = 180° − 2 × 31° = 118°? Using key: 180 − 62 = 118, so \\(\\angle\\)FGD = 118°. (b) Using key: (180 − 102)/2 = 39, so \\(\\angle\\)DFE = 39°.",
"hints": ["Opposite angles of a rhombus are equal; adjacent angles sum to 180°.", "Use the parallel lines EF // DG to transfer angles."],
"source": "ACS 2023 P6 Prelim Paper 2 Q11",
"image_needed": true,
"image_page": 28,
"image_bbox": [0.28, 0.12, 0.70, 0.46],
"image_loc": "two rhombuses ABGF and BCDG with points A-G and E, 31° and 40° marked, upper-middle of page",
"image_options": false,
"image_file": "q41.png",
"notes": "Paper 2 Q11. Key: (a) 180−62=118; (b) (180−102)/2=39."
},
{
"n": 42,
"type_id": 1,
"question": "The pie chart shows the amount of pasta sold from Monday to Thursday. Monday = \\(\\dfrac{1}{4}\\). The ratio of the amount of pasta sold on Wednesday to the amount of pasta sold on Monday was 3 : 2. What fraction of the amount of pasta was sold on Wednesday?",
"answer0": "\\(\\dfrac{3}{8}\\)",
"answer1": "\\(\\dfrac{1}{4}\\)",
"answer2": "\\(\\dfrac{2}{8}\\)",
"answer3": "\\(\\dfrac{3}{4}\\)",
"correct_answer": 0,
"skill_id": 235,
"difficulty_id": 3,
"explanation": "Monday = 1/4 = 2/8. Wednesday : Monday = 3 : 2, so if Monday = 2 units = 2/8, then 1 unit = 1/8 and Wednesday = 3 units = 3/8.",
"hints": ["Write Monday's 1/4 as a number of units matching the ratio.", "Wednesday is 3 units when Monday is 2 units."],
"source": "ACS 2023 P6 Prelim Paper 2 Q12",
"image_needed": true,
"image_page": 29,
"image_bbox": [0.38, 0.12, 0.62, 0.30],
"image_loc": "pie chart with Monday (1/4) and Wednesday sectors, top-middle of page",
"image_options": false,
"image_file": "q42.png",
"notes": "Paper 2 Q12(a). Made MCQ because the answer is a fraction (3/8). Key: 1/4 = 2/8, 3u = 3/8. Part (b) of Q12 (draw bars) is a drawing task, omitted."
},
{
"n": 43,
"type_id": 2,
"question": "Mr. Kassim had some mangoes and apples for sale. He sold 144 mangoes. 40% of the fruits he sold were apples.
(a) How many fruits did Mr Kassim sell altogether? [?]
(b) He sold 30% of his fruits. 70% of the fruits left unsold were mangoes. How many apples did Mr. Kassim have at first? [?]",
"answer0": "240",
"answer1": "264",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 207,
"difficulty_id": 3,
"explanation": "(a) 40% sold were apples → 60% sold were mangoes = 144. 60% = 144 → 100% = 240 fruits sold. (b) 30% of all fruits = 240, so total fruits = 800 (100%). Unsold = 70% = 560 fruits; 70% of unsold were mangoes → 30% of 560 = 168 unsold apples. Apples sold = 40% of 240 = 96. Apples at first = 168 + 96 = 264.",
"hints": ["For (a) the 144 mangoes are 60% of the fruits sold.", "For (b) find total fruits from the 30% sold, then add unsold and sold apples."],
"source": "ACS 2023 P6 Prelim Paper 2 Q14",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q14. Key: (a) 60%=144→240; (b) 30%=240→100%=800, 70%=560, 30%=168, 168+96=264."
},
{
"n": 44,
"type_id": 2,
"question": "Raju, Sam and Tristan had a total of $435. Raju spent \\(\\dfrac{4}{5}\\) of his money, Sam spent \\(\\dfrac{2}{3}\\) and Tristan spent \\(\\dfrac{3}{4}\\) of his money. In the end, Raju had $55 more than Sam and Tristan had $10 more than Sam. How much money did Tristan have at first? [?]",
"answer0": "80",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "Raju left = 1/5, Sam left = 1/3, Tristan left = 1/4. Let Sam's leftover = s. Raju left = s + 55, Tristan left = s + 10. From the key: Raju at first = 5×(Sam left) form, working gives 1 unit = $10, Tristan at first = 4 units + (4 × 10) = $80.",
"hints": ["Write each person's leftover as a fraction of their start.", "Use the '$55 more' and '$10 more than Sam' relationships with the $435 total."],
"source": "ACS 2023 P6 Prelim Paper 2 Q15",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q15. Key: (435−40−275)/12u=10; 1u=10; T = 10×4+40 = 80."
},
{
"n": 45,
"type_id": 2,
"question": "Matt bought some Dino Brand and Lion Brand correction tapes. Dino Brand: 4 for $8.50. Lion Brand: 3 for $7.25. \\(\\dfrac{1}{3}\\) of the correction tapes Matt bought was Lion Brand correction tapes. He spent $198 more on Dino Brand correction tapes. How much did he spend on the correction tapes? [?]",
"answer0": "720",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "Lion is 1/3, Dino is 2/3, so Dino : Lion = 2 : 1. Take a group of (4 Dino, ... ) using LCM: per group Dino = 4 tapes ($8.50) and Lion = 3 tapes ($7.25) → but to keep 2:1 use sets: 4 Dino × 3 sets = 12, etc. Key working: Dino set cost per group $25.50, Lion $14.50, difference $11 per 18-group; $198 ÷ $11 = 18 groups; total = (25.5 + 14.5) × 18 = $720.",
"hints": ["Dino is twice Lion in count; choose matching set sizes.", "The $198 difference equals (Dino spend − Lion spend) per group × number of groups."],
"source": "ACS 2023 P6 Prelim Paper 2 Q16",
"image_needed": true,
"image_page": 35,
"image_bbox": [0.20, 0.13, 0.70, 0.30],
"image_loc": "two price labels: Dino Brand '4 for $8.50' and Lion Brand '3 for $7.25', upper part of page (prices also in stem)",
"image_options": false,
"image_file": "q45.png",
"notes": "Paper 2 Q16. Key: 4×3 set=12; 3×2 set=6; 8.5×3=25.5; 7.25×2=14.5; 25.5−14.5=11; 198/11=18; (25.5+14.5)×18=$720."
},
{
"n": 46,
"type_id": 2,
"question": "Two rectangular tanks are shown. Tank A: base 60 cm × 10 cm, height 40 cm. Tank B: base 50 cm × 20 cm, height 35 cm. At the beginning, Tank A was \\(\\dfrac{1}{10}\\) filled with water and Tank B was \\(\\dfrac{2}{5}\\) filled with water. Both tanks had taps turned on at the same time and water flowed from both taps at the same rate of 1.2 litres per minute.
(a) How long will it take for the height of the water to be the same in both tanks? [?]
(b) At what height will this happen? [?]",
"answer0": "200",
"answer1": "18",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 193,
"difficulty_id": 3,
"explanation": "Initial heights: Tank A = 1/10 × 40 = 4 cm; Tank B = 2/5 × 35 = 14 cm. Height difference = 14 − 4 = 10 cm. Base areas: A = 60 × 10 = 600 cm²; B = 50 × 20 = 1000 cm² (key uses surface difference 1000 − 600 = 400 cm²). Per the key: 400 cm² difference, 400 × 10 / 1200 = 3 min 20 sec; then height = 1200 × 3min20s /1000 + ... = 18 cm. (a) ≈ 3 min 20 s (200 s); (b) ≈ 18 cm.",
"hints": ["Find each tank's starting water height first.", "Equal flow into different base areas changes height at different rates."],
"source": "ACS 2023 P6 Prelim Paper 2 Q17",
"image_needed": true,
"image_page": 36,
"image_bbox": [0.14, 0.10, 0.88, 0.32],
"image_loc": "two labelled tanks A and B with dimensions, top of page (dimensions also in stem)",
"image_options": false,
"image_file": "q46.png",
"notes": "Paper 2 Q17. Key working: 40×1/10=4cm; 35×2/5=14cm; diff 10cm; 50×20−60×10=400; 400×10/1200=3min20sec; final height +14cm = 18cm. (a) answered as 200 seconds (3 min 20 s); (b) 18 cm. Flag: key working ambiguous — used printed final values."
}
]
}