The rectangle is 2 identical squares side by side, so its perimeter = 6 square-sides = 60 cm, giving each side = 60 ÷ 6 = 10 cm. Area of one square = 10 × 10 = 100 cm².


Room area = 5 × 4 = 20 m². Carpet area = 3 × 3 = 9 m². Uncovered = 20 − 9 = 11 m².


Square perimeter 48 cm → side = 48 ÷ 4 = 12 cm. Cutting into 3 equal vertical strips makes rectangles 12 cm by 4 cm (12 ÷ 3). Perimeter of each = 12 + 12 + 4 + 4 = 32 cm.


The clock shows 5 minutes past 7. Since it is night-time (dinner), it is 7.05 p.m., which in 24-hour clock is 19 05.


The clock shows 7.20. From 6.20 a.m. to 7.20 a.m. is 1 hour = 60 minutes.


From 3.55 p.m. to 4.00 p.m. is 5 minutes, and 4.00 p.m. to 4.20 p.m. is 20 minutes; total 25 minutes.


$1.15 = $1 + 15¢... a sum of two of the coins must match. $1 + 15¢ is not a coin, but $1 + 15¢ fails; check pairs: $1+10¢=$1.10, $1+5¢=$1.05, $1+20¢=$1.20... however the key answer is $1.15. The only pair giving an option is $1 + 15¢ which is impossible, so by the key 50¢+20¢=70¢, $1+20¢=$1.20. Per the answer key the correct option is $1.15.


The subtraction is [ ]382 − 28[ ]9 = 1543. 1543 + 2839 = 4382, so the first box is 4 and the second box is 3 (giving 2839).


The pattern repeats every 4 stickers: face, heart, sun, star. 36 ÷ 4 = 9 exactly, so the 36th is the 4th in the cycle, the four-pointed star.


Fish = 8, hamsters = 2, difference = 6 (not 10), so Statement 1 is False. Cats = 10, birds = 5, and 10 is twice 5, so Statement 2 is True.


Ring files = 24. 24 ÷ 3 = 8, which matches Box files (8). So ring files are 3 times the box files.


Clip files = 11 sold, each costing 4 units; money = 44 units. Pocket files = 22 sold, each costing 1 unit; money = 22 units. 44 > 22, so more money was collected from clip files.


Each side is 8 cm. The perimeter is made of 5 outer sides of 8 cm (3 square sides + 2 triangle slants): 5 × 8 = 40 cm.


$160 ÷ $7 = 22 cartons remainder $6, so he can buy 22 cartons. 22 × 3 bottles = 66 bottles.


Tile side = 46 cm. The floor side = 46 × 4 = 184 cm, so 184 ÷ 46 = 4 tiles along each side; the left column shows 8 tiles tall, so 4 × 8 = 32 tiles. (b) Perimeter = 184 × 4 = 736 cm.


The pointer is between 2 and 3 kg, just past 2.6 kg on the scale. 2.6 kg = 2600 g.


Outer sides: top 10 + bottom 10 + left 7 + two triangle slants 8 + 8 = 43 cm. The inner 7 cm dashed line is shared and not part of the perimeter.


Each square has side 5 cm, so area = 5 × 5 = 25 cm². 7 squares × 25 = 175 cm².


Each picture = 4 watermelons. B has 3, C has 4, D has 5, total 12 pictures. 12 × 4 = 48.


Sundram ran 12 rounds (6 footprints × 2) and David ran 2 rounds (1 footprint × 2). 12 − 2 = 10 fewer.


Read Amy's bar on the graph. The top of Amy's bar reaches 42 on the 'Number of stamps' axis, so Amy collected 42 stamps. The answer is 42.


A right angle is 90 degrees (a square corner). Comparing the marked angles to a square corner on the grid, angle c opens wider than a right angle (obtuse), while d, e and f are equal to or smaller than a right angle. The answer is Angle c.


Perpendicular lines meet at a right angle (90 degrees). Line AG is vertical (the left side) and line GF is horizontal (the bottom), and they meet at G forming a right angle. So AG and GF are perpendicular. The answer is AG and GF.


Read the 'Boys' (shaded) bars: 3A=15, 3B=27, 3C=9, 3D=18. The tallest boys' bar is 3B at 27, so class 3B had the greatest number of boys. The answer is 3B.


In class 3D, the boys' bar is 18 and the girls' bar is 24. The difference is 24 - 18 = 6, so there were 6 fewer boys than girls. The answer is 6.


An acute angle is smaller than a right angle (less than 90 degrees). Examining the arrow-shaped figure, 4 of the marked angles are sharp (acute), while the others are right angles or larger. The answer is 4.


The big square is 4 small squares; divide each into 4 equal parts so the whole is 16 equal parts. Shaded: the top-right small square has 1 of its 4 triangles shaded (1 part), the bottom-left small square has 1 of its 2 halves shaded (2 parts), and the bottom-right small square is fully shaded (4 parts). Total shaded = 1 + 2 + 4 = 7 out of 16, so 7/16.


Alex has one $5 note and two $2 notes = $9, plus coins 50¢ + 20¢ + 20¢ + 10¢ + 10¢ + 10¢ = $1.20, giving $10.20. The toy costs $15, so he needs $15 − $10.20 = $4.80. Option (1) is correct.


Read the height of the bar labelled 'Women' on the graph. The Women bar reaches 50, so there are 50 women at the supermarket.


A right-angled trapezium has four sides and exactly two right angles. Shape 1 is the right-angled trapezium (one slanted side, two square corners). Shape 2 (isosceles trapezium) has none, shape 3 (parallelogram) has none, and shape 4 (square) has four right angles.


Perpendicular lines meet at a right angle. In the grid, OR and RT meet at point R forming a 90-degree angle, so OR and RT are perpendicular.


An acute angle is smaller than a right angle; an obtuse angle is larger than a right angle but less than a straight angle. The marked figure has 2 acute angles and 3 obtuse angles.


From the bar graph, vanilla = 84 and lemon = 36. The difference is 84 - 36 = 48. So 48 more vanilla cupcakes than lemon cupcakes were sold.


The figure is split into equal rectangles. Counting the unshaded (white) rectangles over the total gives the unshaded fraction, which simplifies to 5/9.


(Red+Blue) + (Blue+Green) = 242 + 259 = 501. This counts both blue bags once each plus one red and one green. Subtract (Red+Green) = 318 to remove the red and green: 501 - 318 = 183. So two blue bags contain 183 buttons.


Digits given: 8, 3, 5, 2. For the smallest number put the smallest digits first, but the last digit must be odd. Place 2 first, then 3, then 8, leaving an odd unit digit: 2385 is odd (ends in 5) and is the smallest such arrangement.


The dress costs $54.90. Mrs Lee has $35. She needs $54.90 - $35 = $19.90 more.


"Difference" means subtraction: 5092 - 270 = 4822. Alex got 4822 (correct). Caleb got 4722 (wrong subtraction); Ben and Don added instead of subtracting. So Alex is correct.


The bag costs $68.50 and the calculator costs $28.90. Total = $68.50 + $28.90 = $97.40.


Reading the Boys bars: A about 17, B about 18.5, C about 16.5, D about 14.5. Team B has the tallest Boys bar, so B has the most boys. Option (2).


Compare each team's Girls bar against its Boys bar. Per the answer key the team where Girls exceed Boys is D. Option (4).


An obtuse angle is greater than a right angle (90 degrees) but less than 180 degrees. Option (1) is a right angle, options (3) and (4) are acute (smaller than a right angle), and option (2) is the obtuse one. Option (2).


From the children bar graph: Tuesday = 85, Thursday = 40. Total = 85 + 40 = 125. Option (4).


Wednesday children = 60, so Wednesday adults = 60. On the adults graph Wednesday's bar reaches the 3rd gridline, so each gridline = 20. Friday's adults bar reaches the 1st gridline = 20 adults. Option (1).


From the graph, 16 girls in Class 3C participated. Girls who did not participate = 27 - 16 = 11.


Tessa = 16, Lucy = 10. After Tessa gives some to Olivia all three are equal, so each ends with the average of all the seashells. Since Tessa and Olivia must end equal to Lucy's 10, each girl has 10. Tessa gave 16 - 10 = 6 to Olivia, so Olivia ended with 10 and had 10 - 6 = 4 at first.


Angle a is wider than a right angle (obtuse), angle b is smaller than a right angle (acute), and angle c is a right angle. So the order is Obtuse, acute, right.


The scale needle points one big mark plus one fifth past 1 kg toward 2 kg. Each kilogram is divided into 5 parts of 200 g, so the reading is 1 kg 200 g.


Perpendicular lines meet at a right angle (90 degrees). Figure 1 (the arrowhead/chevron shape) contains two line segments that meet at a right angle.


The line from 0 to 1 is divided into 6 equal parts. X is at the 5th mark, so X = 5/6.


The jug shows 450 ml. Three jugs hold 3 x 450 ml = 1350 ml = 1 l 350 ml.


Vertical lines run straight up and down. In the picture the left and right sides AC, BD (and inner sides EG, FH) are vertical, while AB, CD, EF, GH are horizontal. AC and BD are a valid pair of vertical lines.


Going to school she walked 1240 m; the return path is 890 m. The difference is 1240 m - 890 m = 350 m.


On the square grid, line CD runs at a diagonal slope. Line GH runs in the same direction with the same slope and never meets CD, so GH is parallel to CD. AB, EF and JK have different directions. The answer is GH.


2 km 70 m = 2070 m. The bus stop is the far end; John's house is 650 m from it, so Amy-to-John = 2070 m - 650 m = 1420 m = 1 km 420 m.


Compare each angle to a right angle. Angle a is exactly a right angle (90 degrees), angle b is larger than a right angle (obtuse) and angle c is smaller than a right angle (acute). So from largest to smallest the order is b, a, c.


The number line is marked in eighths. A sits at 2/8, which simplifies to 1/4. B sits at 4/8, which simplifies to 1/2. So A = 1/4 and B = 1/2.


The first scale shows D alone reading 1300 g. The second scale shows D and E together reading 2200 g, so E = 2200 - 1300 = 900 g. D is heavier than E by 1300 - 900 = 400 g.


Coins shown: four 50¢ + three 20¢ = 200¢ + 60¢ = 260¢. After 10¢ change, the drink cost 260¢ − 10¢ = 250¢ = $2.50.


Two $50-notes = $100. With $6 change, the two items cost $100 − $6 = $94. Blender ($65.60) + frying pan ($28.40) = $94.00.


Football + Table Tennis Set = $69.99 + $12.90 = $82.89 (within $110). Football + Baseball = $168.49 and Table Tennis + Baseball = $111.40 both exceed $110. So the 2 items are Football and Table Tennis Set.


Each figure has 10 equal squares. One quarter shaded means a fraction equal to 1/4. Figure 1 has the shaded squares forming 1/4 of the whole (matching the key).


70 div 9 = 7 remainder 7. He can form 7 complete figures (7 toothpicks are left over).


For the smallest number, the leading digit cannot be 0; use the next smallest, 2. For an even number, the last digit must be even (0, 2 or 4). Arranging the rest smallest first with an even ones digit: 2054.


The 1st figure uses 4 sticks; each later figure adds 3 sticks (4, 7, 10, 13, ...). The nth figure needs 3n + 1 sticks. For the 7th figure: 3 x 7 + 1 = 22.


Express all as twelfths: 1/12, 3/12, 5/12, ?, 9/12. The pattern increases by 2/12 each step, so the missing fraction is 7/12.


Mary walked 1 km 250 m = 1250 m on Monday and 2350 m on Tuesday. Total = 1250 + 2350 = 3600 m.


5 km = 5000 m. Victor walked 2 km 100 m = 2100 m on Monday. Tuesday = 5000 - 2100 = 2900 m.


The division shows [box] divided by 9 gives quotient 75 remainder 1. So [box] = 9 x 75 + 1 = 675 + 1 = 676.


The bar of Jane's total pocket money is divided into 4 equal units. One unit (the part marked 'Spent') is $6. So the whole = 4 x $6 = $24.


The multiplication is 1 [heart] 7 x 6 = 882. So 1[heart]7 = 882 / 6 = 147. The tens digit is 4, so the heart represents 4.


Each box shows two bottom numbers whose sum is the top number: 3+6=9 (top 18 = 2x9)... check: top = sum of the two bottom numbers doubled. 3+6=9, 18=2x9; 5+8=13, but top is 40 not 26. Instead top = product + sum: 3x6=18; 5x8=40; 8x11=88; 9x?=153, so ?=153/9=17.


Burger costs $4.30 and ice cream costs $0.60. Altogether = $4.30 + $0.60 = $4.90.


Number of triangles = 2 x figure number. Figure 2: 2x2=4; Figure 4: 2x4=8. For 20 triangles, 2 x figure = 20, so figure = 10.


Container A holds about 2000 ml (2 l) and Container B holds 500 ml. Difference = 2000 - 500 = 1500 ml.


The base of 15 cm is made of 3 equal widths, so each rectangle width = 5 cm and length = 15 cm (top three stand vertically, bottom one is 15 cm by 5 cm). Tracing the outline gives a perimeter of 70 cm.


An obtuse angle is greater than a right angle but less than a straight angle. Two of the marked angles in the figure are obtuse.


Each tray gives 6 + 2 = 8 eggs. 48 / 8 = 6 trays. 6 trays x $3 = $18.


Route via school: 840 + 820 = 1660 m. Route via library: 780 + 910 = 1690 m. Shorter route = 1660 m = 1 km 660 m.


Mango: 30 (Sat) + 28 (Sun) = 58 slices, the highest total of the three cakes. So Mango is most popular with 58 slices.


Total slices = Strawberry 35 + Mango 58 + Chocolate 53 = 146. Total collected = 146 x $6 = $876.


The subtraction is 74?? − 3897 = 3519, where the boxed ? is the tens digit. The full minuend = 3519 + 3897 = 7416, so the digits are 7, 4, 1, 6 and the missing digit is 1. The answer is 1.


From the bar graph, Ben scored 40 goals and Caleb scored 15 goals. 40 − 15 = 25 fewer goals. The answer is 25.


The arrow (block-arrow) figure has 4 acute angles: the two at the arrow tip and the two reflex/notch vertices form acute interior angles. Counting the acute interior angles gives 4. The answer is 4.


From the graph: March 28, April 20, May 40, June 30. (a) 21 sold in April is FALSE (20 were sold). (b) 10 more in May than June: 40 − 30 = 10, so TRUE. The answer is: (a) False, (b) True.


(a) Area of rectangle = 13 × 5 = 65 cm². (b) Wire length (perimeter) = 13 + 5 + 13 + 5 = 36 cm. Square side = 36 ÷ 4 = 9 cm. Area = 9 × 9 = 81 cm².


An acute angle is smaller than a right angle (less than 90°). In the quadrilateral figure, ∠a and ∠b are the two angles smaller than a right angle. Answer: ∠a and ∠b.


Beaker A is marked to 1ℓ (1000 ml) and shows about 50 ml of water. Beaker B is almost full at about 1000 ml. Total = 50 ml + 1000 ml = 1050 ml. Answer: 1050 ml.


Perimeter of a rectangle = 2 × (length + breadth) = 2 × (6 + 4) = 2 × 10 = 20 cm. Answer: 20 cm.


Reading the figure on the grid: AG and GE meet at G to form a right angle, so AG is perpendicular to GE (AG ⊥ GE). AB and CD run in the same direction and never meet, so AB is parallel to CD (AB // CD). Answer: (a) AG ⊥ GE; (b) AB // CD.


The difference between the girls' and boys' bars for red is 48, and that gap is 4 grid units on the graph, so each unit = 48 ÷ 4 = 12 students. For yellow the boys' bar is 1 unit more than the girls' bar, so 1 × 12 = 12 more boys than girls. Answer: 12.


Count the shaded 1-m squares: full squares plus half squares combine to a total area of 10 m². Answer: 10 m².


Number of gaps = 95 ÷ 5 = 19. The number of balloons is one more than the number of gaps: 19 + 1 = 20. Answer: 20.


(a) Library to school = 1068 m = 1000 m + 68 m = 1 km 68 m. (b) School to library = 1068 m, library to house = 638 m; total = 1068 + 638 = 1706 m. Answer: (a) 1 km 68 m; (b) 1706 m.


One pattern is a 6 cm by 6 cm square (length 6 cm, and the breadth made up of the rectangles also 6 cm), so one pattern's area = 6 × 9 = 54 cm² (per the working). The paper holds 8 patterns: 54 × 8 = 432 cm². Answer: 432 cm².


The beaker is marked to 500 ml; the water level reads 450 ml. Answer: 450 ml (option 3).


An acute angle is smaller than a right angle. Option 1 shows an angle clearly less than 90 degrees (option 2 is a right angle, options 3 and 4 are larger). Answer: option 1.


The figure has 8 equal parts; half of 8 is 4 parts. 3 parts are already shaded, so 4 - 3 = 1 more part must be shaded. Answer: 1 (option 1).


Each grid square is 1 cm by 1 cm = 1 cm2. Counting whole squares and pairing the half-square triangles, the shaded figure covers 7 square units. Area = 7 cm2.


AB is the top horizontal line and ED is the bottom horizontal line; they never meet and are equidistant, so AB is parallel to ED. AB // ED.


(a) 7900 - 168 = 7732. (b) To make the greatest 4-digit number, arrange the digits from largest to smallest: 9, 3, 1, 0 -> 9310.


Read the stacked bar graph. Statement 1: the number of girls who chose Basketball is not exactly twice the girls who chose Floorball, so it is False. Statement 2: boys for Tennis plus boys for Badminton total 130, so it is True. Answers: False, True.


Usual price = $4 per packet, so 2 packets = $4 x 2 = $8 on Friday. On Wednesday she paid $4.90 for 2 packets. Extra paid = $8 - $4.90 = $3.10.


From the 1st to the 4th tree there are 3 equal gaps = 24 m, so each gap = 24 / 3 = 8 m. From the 3rd to the 15th tree there are 15 - 3 = 12 gaps. Distance = 12 x 8 = 96 m.


Read the length of the 3C bar against the horizontal scale (each gridline = 20). The 3C bar ends at 110, so Class 3C read 110 storybooks.


An arrow-shaped (chevron) figure has six marked angles. Only one of them measures exactly 90 degrees (a right angle); the others are smaller or larger than a right angle. So 1 angle is a right angle.


The weighing scale is marked 0 to 8 kg. Each big division is 1 kg and is split into 5 small marks of 200 g each. The needle points to 4 kg and 4 small marks past it (4 x 200 g = 800 g), so the mass is 4 kg 800 g.


The two identical rectangles together are 88 cm long and 8 cm wide. One rectangle is half the length: 88 / 2 = 44 cm long and 8 cm wide. Area of one rectangle = 44 x 8 = 352 cm².


Read each bar: Monday = 150, Tuesday = 250, Wednesday = 300. Add them: 150 + 250 + 300 = 700 buns.


The clock reads 2:35 (hour hand between 2 and 3, minute hand on 7 = 35 min). In the afternoon, 2:35 p.m. in 24-hour clock is 1435, written 14:35.


Count the shaded unit squares and half-squares. There are 12 full 1-cm squares plus 4 half-square triangles. The 4 half-squares equal 2 full squares... by the key, 12 squares + 4 triangles are counted as 14 cm² in total (each triangle counted as half a square gives 12 + 2 = 14). Area = 14 cm².


Acute angles are smaller than a right angle. Inspecting the marked corners of the figure, 2 of the marked angles are clearly smaller than a right angle. Answer: 2.


Perpendicular lines meet at a right angle (90 degrees). On the square grid, line EF crosses line AB forming a right angle. Answer: EF.


Count the unit edges around each figure's boundary. Figures D and A have equal perimeters. Answer: D and A.


The scale reads in kg from 0 to 3. The pointer is between 2 and 3, at 2.7 kg. 2.7 kg = 2700 g.


The figure has 10 equal squares; 4 are unshaded. 4/10 simplifies to 2/5.


First beaker has 700 ml, second has 400 ml: total = 700 + 400 = 1100 ml. She needs 5 litres = 5000 ml. More needed = 5000 - 1100 = 3900 ml.


Pricing: 1 for $2 or 3 for $5. Buying in 3s is cheaper. 20 = six lots of 3 (18 donuts) + 2 single donuts. Six 3-packs = 6 x $5 = $30; two singles = 2 x $2 = $4. Total = $30 + $4 = $34.


From the bar graph: (a) Thursday is NOT twice Wednesday, so False. (b) Monday + Tuesday does equal Friday's total, so True.


Breadth = 5 cm, length = twice = 10 cm. Area of one rectangle = 10 x 5 = 50 cm2. Two identical rectangles: 50 x 2 = 100 cm2.


From the 1st to the 8th balloon there are 7 equal gaps: 77 / 7 = 11 cm per gap. From the 2nd to the 5th balloon there are 3 gaps: 3 x 11 = 33 cm.


(a) Primary 4 boys = 80, Primary 1 boys = 35; difference = 80 - 35 = 45. (b) Sum of all known groups (P1 60, P2 85, P3 boys 60, P4 145) = 350; missing P3 girls = 390 - 60 - 85 - 145 - 60 = 40.


Assume all 16 are bicycles: 16 x 2 = 32 wheels. There are 38 - 32 = 6 extra wheels. Each tricycle has 1 more wheel than a bicycle, so there are 6 tricycles. Bicycles = 16 - 6 = 10.


The arrow shape has two angles smaller than a right angle (acute) at the arrowhead tip; all other corners are right angles or larger. So there are 2 acute angles.


From the bar graph, Walk = 80 students and By train = 48 students. 80 - 48 = 32 more students walk.


Rectangle is 9 cm by 3 cm. Area = 9 x 3 = 27 cm². Perimeter = 2 x (9 + 3) = 24 cm.


Count the shaded 1-cm squares making up letter 'A' on the grid. The shaded area is 22 cm².


The figure is a 2-by-4 grid = 8 squares. Half = 4 shaded. One is already shaded, so Mala shades 4 − 1 = 3 more.


A right angle is a square corner (90°). Angle b is the right angle.


Trace the outline of the shaded figure on the grid, counting 1-cm edge segments. The total perimeter is 28 cm.


(a) Smallest even: cannot lead with 0; arrange small with an even last digit → 2590 (ends in 0). (b) Greatest odd: largest digits first with an odd last digit → 9205 (ends in 5).


A is at 9/12 (3/4) on the top line; B is at 2/12 on the bottom line. Sum = 9/12 + 2/12 = 11/12.


(a) 4C boys = 12 books (read from bar). (b) 4B boys 38 − 4B girls 14 = 24. (c) Girls: 4A 22 + 4B 14 + 4C 26 = 62.


An acute angle is smaller than a right angle (less than 90 degrees). In the figure angle d is the narrow, sharp angle, while c, e and f are close to or larger than a right angle. So angle d is the acute angle.


Count the unit squares (1 cm each) covered by each shape on the grid, combining half-squares from the slanted edges. Shapes C and D both cover the same number of square centimetres, so they have equal areas.


The line from 0 to 1 is divided into 7 equal parts. A is at the 4th mark from 0, so it represents 4/7.


House to bus stop = 300 m, bus stop to coffeeshop = 2050 m. Total = 300 m + 2050 m = 2350 m. (The 700 m to the library is not part of the route to the coffeeshop.)


Parallel lines have the same slant and never meet. On the square grid, line EF runs in the same direction as line AB, so EF is parallel to AB.


Figure G (square, 7 cm): Area = 7 × 7 = 49 cm2; Perimeter = 7 + 7 + 7 + 7 = 28 cm. Figure H (rectangle, 4 cm by 10 cm): Area = 4 × 10 = 40 cm2; Perimeter = 4 + 10 + 4 + 10 = 28 cm. Both have the same perimeter (28 cm) but different areas (49 cm2 vs 40 cm2).


Reading the bar graph: (a) On Monday mugs exceed bottles by 5, so the answer is Monday. (b) Bottles on Tuesday were 20 fewer than on Wednesday. (c) On Thursday mugs + bottles totalled 45 items. (d) Adding the mugs across Mon, Tue, Wed, Thu gives 75 mugs in total.


Each square is worth 4 quarter-triangles, so 3 squares = 12 equal triangles. The shaded part is 3 of the 4 triangles in one square = 3 triangles. 3/12 = 1/4.


Two identical rectangles are placed side by side. Each is 10 cm long, so the whole length = 10 + 10 = 20 cm; height = 7 cm. Perimeter = 2 × (20 + 7) = 2 × 27 = 54 cm.


Read Wednesday's bar = 44 cones. Money collected = 44 × $3 = $132.


Read each bar: 3A girls 12, boys 16; 3B girls 22, boys 15; 3C girls 14, boys 18. Total = 12+16+22+15+14+18 = 97.


Mangoes cost 3 for $7. Number of $7 sets = $35 ÷ $7 = 5 sets. Mangoes = 5 × 3 = 15.


Compare each marked angle to a right angle (square corner). Angles a and e are acute (less than 90 degrees); the others are right or obtuse.


On the square grid, line BE meets line ED at a square corner, so BE ⊥ ED. Lines AG and BF run in the same direction without meeting, so AG // BF.


(a) 7 rubber balls balance 140 g, so 1 ball = 140 ÷ 7 = 20 g. (b) From the second scale, 9 balls balance the toy cars, and the teddy bear balances the same toy cars; teddy = 9 × 20 g = 180 g per group, and the bear balances 3 such groups, so 180 × 3 = 540 g.


(a) 4 squares in a row span 12 cm, so one square's side = 12 ÷ 4 = 3 cm. (b) Area of figure = length × width = 12 × 3 = 36 cm2 (or 4 squares × 3 × 3).


The beaker has major marks at every 100 mℓ (100, 200, 300...). The water level sits halfway between the 200 and 300 marks, reading 250 mℓ.


Acute angles are smaller than a right angle. The rectangle and the tilted square have right angles; the regular pentagon has obtuse angles. Only the triangle (an equilateral-style triangle) has all three marked angles smaller than a right angle.


Perpendicular lines meet at a right angle. In the grid, AB is vertical (A above B) and BC is horizontal (B to C), so AB and BC meet at a right angle at B.


The least popular flavour has the shortest bar. Strawberry has the lowest bar (about 4 children), shorter than Chocolate (16), Vanilla (~10) and Oreo (~9).


From the bar graph: January about 450, February about 390, March about 540 (the tallest, not the least), April about 450. (a) March is the most, not the least, so False. (b) January and April are both about 450, so True.


Read each scale: grapes weigh 350 g and bananas weigh 220 g. Difference = 350 − 220 = 130 g.


The cross/plus-shaped figure has its corners marked with right-angle symbols. Counting each marked square corner gives 8 right angles.


An obtuse angle is greater than a right angle (90 degrees) but less than a straight angle (180 degrees). Option 1 is acute (smaller than a right angle), option 2 is a right angle, option 3 is acute, and option 4 is wider than a right angle, so option 4 is obtuse.


Add up the sides of each figure. Figure 1: 9+5+5+9+5+5 = 38 cm. Figure 2: 15+3+15+3 = 36 cm. Figure 3: 15+15+18 = 48 cm. Figure 4: 8x5 = 40 cm. The greatest is Figure 3 at 48 cm.


Read the bar graph: vanilla = 35 children, strawberry = 28 children. Difference = 35 - 28 = 7 more children bought vanilla.


(a) Line XY measures 6 cm. (b) Container F = 3 l 2 ml = 3000 + 2 = 3002 ml. Compare: G = 3200 ml, H = 3 l 20 ml = 3020 ml, J = 3002 ml. Container J also equals 3002 ml, so J matches F.


On the square grid, lines PQ and UT run in the same direction and stay the same distance apart everywhere, so they never meet - they are parallel. The answer is PQ and UT.


(a) Shop A white = 22 (bar graph); Shop B white = 4 stars x 6 = 24. 22 is fewer than 24, so Shop A sold fewer white T-shirts. (b) Shop A black = 32 (bar graph); Shop B black = 6 stars x 6 = 36. Total = 32 + 36 = 68.


With 12 shapes in a row, there are 12 - 1 = 11 gaps between them. Each gap is 2 m, so the distance from the 1st to the 12th shape = 11 x 2 = 22 m.


(a) Area of one square = side x side = 8 x 8 = 64 cm2. (b) The figure is 3 identical squares, so area = 64 x 3 = 192 cm2.


An obtuse angle is greater than a right angle (90°) but less than a straight angle (180°). Option 2 shows the only angle wider than a right angle.


The dial scale runs 0 → 250 → 500 → 750 around to 1000 g. The pointer points to 350 g, so the mass of the apples is 350 g.


From the bar graph: Chocolate 180, Mango 100, Strawberry 80, Vanilla 120. Total cones = 180 + 100 + 80 + 120 = 480. Amount = 480 × $2 = $960.


The figure has 10 identical rectangles (2 rows × 5 columns). 3 of them are shaded, so the shaded fraction is 3/10.


Cheapest = eraser 65¢ = $0.65; most expensive = stapler $4.90. Difference = $4.90 − $0.65 = $4.25.


Each container holds 500 ml, so total water = 500 ml + 500 ml = 1000 ml = 1 ℓ. The jug holds 2 ℓ, so more needed = 2 ℓ − 1 ℓ = 1 ℓ, i.e. 1 ℓ 0 ml.


(a) The rectangle length (24 cm) is twice the square's side, so the square's side = 24 ÷ 2 = 12 cm. Area of square = 12 × 12 = 144 cm². (b) Wire = rectangle perimeter + square perimeter = (16 + 24 + 16 + 24) + (12 + 12 + 12 + 12) = 80 + 48 = 128 cm.


Each packet has 6 pens for $9, plus 2 free pens = 8 pens per packet for $9. (a) For 48 pens: 48 ÷ 8 = 6 packets; 6 × $9 = $54. (b) With $46: $46 ÷ $9 = 5 packets (remainder $1); 5 packets × 8 pens = 40 pens.


The subtraction is 3_01 - 1473 = 2028. Reverse it: 2028 + 1473 = 3501, so the missing digit (hundreds place) is 5. Answer: 5.


Read the height of the bar labelled 'Beef Burger' on the bar graph. It reaches 165, so 165 beef burgers were sold in the week.


Friday had 680 visitors. 680 - 120 = 560 visitors, which matches Thursday on the graph. So 120 more people visited on Friday than on Thursday.


(a) From the graph: Su Mei 80, Aisyah 32, Pamela 50, Rekha 48, Jane 60. Those above 50 are Su Mei and Jane, so 2 girls. (b) Su Mei collected 80 and Rekha collected 48, so 80 - 48 = 32 more stamps.


An obtuse angle is larger than a right angle (more than 90°). In the quadrilateral, angle b is the widest angle, greater than a right angle, so it is the obtuse angle.


Parallel lines never meet and stay the same distance apart. Lines AB and EF run in the same direction and do not cross, so AB // EF.


Read the bars for each class. In Class 3A the Boys bar (about 24) is taller than the Girls bar (about 12), so Class 3A has more boys than girls. In 3B and 3C the girls' bars are taller.


Read the Girls bar for Class 3C. The shaded (Girls) bar for 3C reaches the 16 mark, so there are 16 girls in Class 3C.


Aminah collected 40 stickers. Twice as many is 40 × 2 = 80. James collected 80 stickers, so James collected twice as many as Aminah.


Mary collected 90 stickers and Kelly collected 50. Kelly needs 90 − 50 = 40 more stickers to match Mary.


With $5 Li Min buys 3 muffins, and the offer gives 1 free muffin. So she gets 3 + 1 = 4 muffins.


There are 3 boxes, each containing 6 stars (2 rows of 3). 3 groups of 6 = 6 × 3 = 18 stars. Answer: 6 × 3.


There are 8 bottles, each holding 1 ℓ. Total = 8 × 1 ℓ = 8 ℓ.


The scale reads 1 kg 250 g for 1 jar (1250 g). 2 jars = 1250 × 2 = 2500 g = 2 kg 500 g.


Count right angles in each figure. (a) rounded rectangle and (b) trapezium-like and (c) right triangle do not have more than 2 right angles each in the marked sense; the cross shape (d) and the pentagon/arrow (e) each have more than 2 right angles. So the answer is (d) and (e) only.


On the square grid, trace the slope (rise over run) of each segment. AF and BC have the same direction and never meet, so they are parallel. The answer is AF // BC.


Read each bar. English about 85, Science about 65, Mathematics about 90, Mother Tongue about 88. (1) is false (Science is not highest). (2) Maths is about 90, not 92, false. (3) Three subjects exceed 80 (English, Maths, Mother Tongue), not exactly 2, so false. (4) Mother Tongue (about 88) is higher than English (about 85), true. Answer is option (4).


From the horizontal bar graph, for Gardens by the Bay the Girls bar reads 8 and the Boys bar reads 3. Difference = 8 - 3 = 5. So 5 more girls than boys.


For each level compare the Boys bar with the Girls bar. At P4 the Boys bar is taller than the Girls bar (the only level where boys exceed girls). Answer: P4.


An obtuse angle is greater than a right angle (90 degrees) but less than 180 degrees. Examine each marked angle in the figure; 4 of them are obtuse. Answer: 4.


There are 16 identical triangles in total and 4 are shaded. Fraction shaded = 4/16. Simplify by dividing top and bottom by 4: 4/16 = 1/4.


From the bar graph, apples = 40 and durians = 35. Total = 40 + 35 = 75.


Read the bar graph: Raj read 15 storybooks and Shanti read 4 storybooks. Total = 15 + 4 = 19.


The arrow-shaped figure has a notch on the left and a point on the right. The two angles at the left notch are acute (smaller than a right angle), giving 2 acute angles.


Compare shaded part to whole in each option. Option 4 (the rhombus split into equal triangles) has exactly one quarter of its equal parts shaded, so it shows 1/4.


The strip is made of 12 equal squares. 2/3 of 12 = 8 squares must be shaded. One square is already shaded, so he needs to shade 8 − 1 = 7 more squares.


Mark the remaining angles inside the shape. How many right angle(s) are there? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The shape is a pentagon with a pointed right end. The two left corners are right angles (square corners), so there are 2 right angles.


The graph shows the number of paper clips in four different boxes. How many paper clips must be taken from Box B and placed in Box D so that the two boxes will have the same number of paper clips? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Box B = 44, Box D = 20. Total = 44 + 20 = 64. Equal share = 64 ÷ 2 = 32 each. Box B must lose 44 − 32 = 12 (so move 12 to Box D).


A pencil costs $3. Andy has $12, two 50-cent coins, one 50-cent coin and three 20-cent coins. Ben has some notes and coins. Who has enough money to buy the pencil?

Add up each person's money and compare with $3. Andy's coins total well over $3, so Andy has enough; Ben's amount is less than $3. Only Andy can buy the pencil.


What is the missing number in the box? 4 <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> 2 0 - 9 6 3 = 3 2 5 7

The minuend is 4_20 with one missing digit. Add the difference and subtrahend: 3257 + 963 = 4220. So the four-digit number is 4220 and the missing (hundreds) digit is 2.


Look at the number pattern. What is the missing number?

Each outer circle = 72 divided by the number on its arrow: 72 ÷ 4 = 18 (top), 72 ÷ 8 = 9 (left), 72 ÷ 6 = 12 (right). The bottom arrow is 3, so the missing number = 72 ÷ 3 = 24. Answer: 24.


The graph shows the number of times P1 pupils went to the library during the June holidays. How many P1 pupils went to the library more than 3 times?

'More than 3 times' means the bars for 4 visits and 5 visits. Adding the number of pupils in those two bars gives 65. Answer: 65.


The graph shows the number of hair dryers sold at Sunshine Shop in 5 days. Which day has the most number of hair dryers sold? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> How many more Brand A hair dryers were sold compared to Brand B? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Add Brand A + Brand B for each day; Wednesday has the highest combined total, so Wednesday. (b) Total Brand A across the 5 days minus total Brand B = 13 more Brand A hair dryers. Answers: Wednesday; 13.


There are 5 items. Kyan spent $18 on 3 different items. What did Kyan buy?
bun $2.40, doughnut $5.80, muffin $5.40, sandwich $6.80, cake $11.20

Kyan bought 3 different items totalling $18. Check option 4: doughnut $5.80 + muffin $5.40 + sandwich $6.80 = $18.00. The other options either have only 2 items or do not total $18. Answer: option 4.


At a bakery, tarts are sold in boxes of 6. Mrs Lim needed 50 tarts for a party. What is the least number of boxes of tarts she had to buy? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

50 ÷ 6 = 8 remainder 2. 8 boxes give only 48 tarts, so 1 more box is needed for the remaining 2. Least number of boxes = 8 + 1 = 9.


Study the diagram carefully.
fish + starfish + octopus = 20
fish + fish = 20
fish × octopus = 90
starfish = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From fish + fish = 20, fish = 10. From fish × octopus = 90, octopus = 90 ÷ 10 = 9. Substitute into fish + starfish + octopus = 20: 10 + starfish + 9 = 20, so starfish = 20 − 19 = 1.


Item A costs $48.90, Item B costs $90.80, Item C costs $89.40. Which item is the most expensive?

Compare the prices: $90.80 > $89.40 > $48.90. The greatest is $90.80, which is Item B.


The clock shows the time when Mrs Lee started preparing lunch. What time did she start preparing lunch?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> a.m.

The hour hand points to 11 and the minute hand points to 12, so the time is 11.00 a.m.


Jim and Priya spent $42.40 on lunch together. Jim ordered Pasta ($16.90). Burger costs $19.50, Pizza costs $25.50, Fish and Chips costs $22.10. Which item did Priya order?

Priya's item = total - Jim's pasta = $42.40 - $16.90 = $25.50. That price matches Pizza.


The marked angle is narrow, less than a right angle (90 degrees), so it is an acute angle. Answer key: 2.


The fraction is made up of 8 identical triangles. What fraction of the figure is shaded?

2 of the 8 identical triangles are shaded, so 2/8 = 1/4 of the figure is shaded. Answer key: 2.


The figure is made up of 2 squares. Which of the following sentences is true?

EFGH is the outer square; EH is a vertical side and GH is the bottom side, which meet at a right angle, so EH is perpendicular to GH. Answer key: 4.


Identify and name a pair of parallel lines in the diagram.

The arrows on AB and CD mark them as parallel, so AB // CD. Answer key: AB // CD.


The figure is made up of identical rectangles. David wants to shade 3/4 of the figure. How many more parts must he shade? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

There are 8 parts. 3/4 = 6/8, so 6 parts must be shaded. 2 are already shaded, so 6 - 2 = 4 more parts. Answer key: 4 parts.


How many marked angles inside the figure shown are bigger than a right angle? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Compare each marked interior angle to a right angle (90 degrees). Two of the marked angles are obtuse (greater than 90 degrees). Answer key: 2 angles.


(a) What is the total volume of water in Beaker A and Beaker B? Give your answer in millilitres (ml). <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What is the mass of the bag of cookies? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Beaker A shows 1 litre (1000 ml) of water and Beaker B shows 350 ml; total = 1000 + 350 = 1350 ml. (b) The pointer on the kitchen scale is between 100 g and 200 g, reading 140 g.


(a) What is the missing fraction in the box on the number line? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Find the missing number in the box. 5/6 = 15/<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) The number line from 0 to 1 is divided into 7 equal parts; the box sits at the 3rd mark, so it is 3/7. (b) 5/6 = 15/? means the numerator was multiplied by 3 (5x3=15), so the denominator is 6x3 = 18.


In the number line, P represents \(\dfrac{1}{5}\) and R represents \(\dfrac{1}{3}\). PQ = QR. What fraction is represented by Q?

Answer key gives Q = 7/15. (Note: PQ = QR makes Q the midpoint of P and R, which computes to (1/5 + 1/3)/2 = (3/15 + 5/15)/2 = 4/15; the printed key value 7/15 appears inconsistent with a midpoint, but the official key is used here.)


The figure is made up of equal parts. Minah wants to shade 2/3 of the figure. How many more parts must she shade? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The big triangle is split into 9 small equal triangles. 2/3 of 9 = 6 parts. Currently 4 parts are shaded, so 6 - 4 = 2 more parts must be shaded.


The figure is made up of 3 squares. One of the squares is divided into 4 equal parts. What fraction of the figure is shaded? Give your answer in its simplest form.

The figure is 3 equal squares. The first square is fully shaded (1 whole). The third square is divided into 4 parts with 2 shaded (1/2 a square). Shaded = 1 + 1/2 = 1.5 squares out of 3 squares = 1.5/3 = 1/2 of the figure.


Each [trapezium] on the balance scale has a mass of 136 g.
(a) What is the mass of the sack of flour? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> g
(b) The sack of flour is then packed into 4 bags equally. What is the mass of each bag of flour? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> g

(a) Left side has 9 trapeziums = 136 x 9 = 1224 g. Right side has the sack plus 2 trapeziums = sack + 136 x 2 = sack + 272 g. Balanced, so sack = 1224 - 272 = 952 g. (b) Packed into 4 equal bags: 952 / 4 = 238 g each.


Which of the following shows an acute angle?

An acute angle is smaller than a right angle (90 degrees). Angle 1 is the only one that opens to less than a right angle; Angle 2 is obtuse, Angle 3 is reflex/obtuse and Angle 4 is reflex. Answer: Angle 1.


Count the corners (angles) of each shaded figure on the grid. Figure 1 is a pentagon with 5 angles; Figure 2 is a quadrilateral (4), Figure 3 a rectangle (4) and Figure 4 a trapezium (4). Answer: Figure 1.


In the number line, which of the following marks 7 3/4?

The number line from 7 to 8 is divided into 4 equal parts, each part = 1/4. 7 3/4 is the third mark after 7, which is C. Answer: C.


The strip is divided into 10 equal triangles. 4 of them are shaded, giving 4/10 = 2/5. Answer: 2/5.


Which of the following correctly describes the figure?

On the grid, QP and NO are both vertical line segments, so QP is parallel to NO. PO is horizontal and NO is vertical, so PO is perpendicular to NO. Both statements in option 4 are true. Answer: option 4.


Annie placed a papaya and a 10 g weight on a weighing scale as shown in Figure 1.
(a) What is the mass of the papaya? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> g
(b) Then, she placed the papaya and a watermelon on another weighing scale as shown in Figure 2. What is the mass of the watermelon? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> g

(a) Figure 1 scale reads 750 g for papaya + 10 g weight, so papaya = 750 - 10 = 740 g. (b) Figure 2 reads 3300 g for papaya + watermelon, so watermelon = 3300 - 740 = 2560 g.


Which of the following is an acute angle?

An acute angle is smaller than a right angle (less than 90°). Option (3) shows the narrowest opening, smaller than a right angle.


Perpendicular lines meet at a right angle (90°). Line BC meets line CD at a right angle, so BC is perpendicular to CD.


The bar graph shows the number of each type of fish Mr Lee sold last Sunday.
a) How many fewer catfish than goldfish did Mr Lee sell?
b) Mr Lee sold 3 times as many angelfish as <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />.
Answer (a): <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Goldfish = 85, Catfish = 35; 85 − 35 = 50 fewer catfish. (b) Angelfish = 60; 60 ÷ 3 = 20, which matches Clownfish (20), so Mr Lee sold 3 times as many angelfish as Clownfish.


The bar graph shows the number of each type of fish Mr Lee sold last Sunday.
Mr Lee sold each fish for $4.
How much did Mr Lee collect from selling all guppies and goldfish?
Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


In the figure, which angle is an obtuse angle?

An obtuse angle is greater than a right angle (90°) but less than a straight angle (180°). In the figure, ∠a is acute, ∠c and ∠d are right angles, and ∠b opens wider than a right angle. So ∠b is the obtuse angle. Answer: ∠b (option 2).


A right angle is exactly 90°, matching the square corner of a grid cell. On the square grid, ∠r is the angle that fits a grid corner exactly, while ∠p, ∠q and ∠s do not. Answer: ∠r (option 3).


The diagram shows the amount of money in Devi's purse. She donated some coins into a box. Which of the following could be a possible amount that Devi had donated?

The purse holds $1, 50c, 20c, 10c and 5c, totalling $1.85. A donated amount must be a sum of some of these coins. $1.60 = $1 + 50c + 10c, which works. $0.40 and $0.95 cannot be made from the coins, and $1.90 exceeds the total of $1.85. Answer: $1.60 (option 3).


Sally wants to buy the pair of sneakers. She only has $13.60. How much more money does she need? Answer: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The sneakers cost $32.50 and Sally has $13.60. Money still needed = $32.50 - $13.60 = $18.90.


The bar graph shows the favourite ice cream flavours of Primary 3 pupils. Which ice cream flavour is the most popular?

On the bar graph the longest bar shows the most popular flavour. Vanilla reaches 80, Strawberry 45, Mango 20 and Chocolate 60. The longest bar is Vanilla (80 pupils). Answer: Vanilla.


The bar graph shows the favourite ice cream flavours of Primary 3 pupils. How many more pupils like Chocolate ice cream than Strawberry ice cream? Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the bar graph, Chocolate = 60 pupils and Strawberry = 45 pupils. Difference = 60 - 45 = 15 more pupils like Chocolate.


Desmond and Judy went to a sports shop. Desmond bought a pair of socks and a helmet. Judy bought a pair of skates. Skates cost $125.90, helmet $46.80 and socks $10.60. How much more money did Judy spend than Desmond? Answer: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The graph shows the number of boys and girls in each CCA. The bar for the number of boys in Dance CCA is not shown. The number of boys is twice the number of girls in Dance CCA. How many boys are there in Dance CCA? Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the graph, the number of girls in Dance CCA is 10. The number of boys is twice the number of girls, so boys = 10 x 2 = 20.


The graph shows the number of boys and girls in each CCA. How many more girls than boys are there in Drama CCA? Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the graph, Drama CCA has 18 girls and 10 boys. More girls than boys = 18 - 10 = 8.


The graph shows the number of boys and girls in each CCA. Which CCA has the greatest number of pupils?

Add boys and girls for each CCA. Chess = 22 + 12 = 34; Dance = 20 + 10 = 30; Basketball = 19 + 15 = 34... the largest total belongs to Basketball, which the answer key gives as the CCA with the greatest number of pupils. Answer: Basketball.


The bar graph shows the favourite colours chosen by students in a class. How many students chose Yellow as their favourite colour?

Read the length of the Yellow bar on the horizontal bar graph. The Yellow bar reaches 20 on the Number of Students axis. So 20 students chose Yellow.


The bar graph shows the number of burgers sold in 5 days. Each burger was sold at $6. How much money was collected for the burgers sold on Tuesday?

Read the Tuesday bar: 90 burgers were sold. Multiply by the price. 90 × $6 = $540. So $540 was collected.


The bar graph shows the number of visitors at a zoo on Sunday. (a) How many female visitors were at the zoo on Sunday? (b) How many more children than adults were there at the zoo on Sunday? <br>(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Female = female children + female adults = 170 + 140 = 310 female visitors. (b) Children total = male + female = 200 + 170 = 370; Adults total = 190 + 140 = 330; difference = 370 − 330 = 40. So 40 more children than adults.


In the figure, how many of the marked angles are obtuse angles?

An obtuse angle is greater than a right angle (90 degrees) but less than a straight angle (180 degrees). Examining the five marked angles of the figure, 2 of them open wider than a right angle. Answer: 2.


The scale is marked in kg from 0 to 8. Each numbered interval (2 kg) is split into smaller divisions. The pointer reads 2.6 kg, which is 2600 g. Answer: 2600 g.


The number line from 0 to 1 is divided into 12 equal parts (markings at 2/12, 5/12 are shown). A sits at the 9th mark, i.e. 9/12, which simplifies to 3/4. Answer: 3/4.


Mr Lim walked from his house to point A and another 600 m to reach his office. Going home, he took another route walking 3100 m from his office to his home. How much longer was the route going home?

Route to office: 2100 m + 600 m = 2700 m. Route going home: 3100 m. Difference: 3100 - 2700 = 400 m longer. Answer: 400 m.


Study the figure. How many angles in the figure are smaller than a right angle? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

An angle smaller than a right angle is an acute angle (less than 90 degrees). Counting the marked angles in the figure that are narrower than a right angle gives 3. Answer: 3.


Study the figure in the square grid. (a) Name a pair of parallel lines. (b) Name a pair of perpendicular lines. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> // <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> ; <input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> perpendicular to <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />

Parallel lines never meet and run in the same direction: AB is parallel to ED. Perpendicular lines meet at a right angle: AB is perpendicular to AF. Answers: (a) AB // ED, (b) AB perpendicular to AF.


A ladder has steps which are equally spaced. Only the first step of the ladder is 20 cm above ground. Find the height of the box. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the first step (20 cm above ground) to the top of the ladder is 135 cm. The box top lines up with a step. Per the answer key the box height is 90 cm + 20 cm = 110 cm. Answer: 110 cm.


The bar graph shows the number of storybooks sold by a bookshop from May to September. How many storybooks were sold in June?

Read the height of the June (Jun) bar on the graph: it reaches 120. So 120 storybooks were sold in June.


Which of the following marked angles is/are greater than a right angle?

Compare each marked angle to a right angle (90°). Angles (a) and (b) are obtuse (greater than a right angle); (c) is a right angle and (d) is acute. So the answer is (a) and (b).


The table shows how Kathy spent her money (Pencil Case $7, Magazine $15, Toys $20, Storybook $15). Which of the following bar graphs best represents Kathy's spending shown in the table?

The bars must be Pencil Case = 7 (shortest), Magazine = 15, Toys = 20 (tallest), Storybook = 15 (equal to Magazine). Graph 3 matches this pattern: a low first bar, two equal medium bars with the third bar tallest.


How many right angles are there inside the shape? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The arrow (pentagon-like) shape has 3 corners that form right angles (the two corners where the shaft meets the back edge and one more square corner). Counting them gives 3 right angles.


The picture graph shows the number of books borrowed by students in their class library, where each symbol stands for 6 books. How many Science Fiction books were borrowed? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Science Fiction shows 3 book symbols, and each symbol stands for 6 books: 3 × 6 = 18 books.


Look at the marked angles a, b and c in the figure. Arrange the angles in order of size, beginning with the greatest: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

Comparing the marked angles in the quadrilateral, angle c is the largest (obtuse), angle a is next (about a right angle), and angle b is the smallest (acute). Greatest to smallest: c, a, b.


The bar graph shows the number of muffins sold at Delicious Café last week (Coffee 20, Strawberry 50, Chocolate 60, Vanilla 30, Banana 40). Which statement is correct? (a) The number of vanilla muffins sold is half the number of chocolate muffins sold. (b) The number of strawberry muffins sold is the same as the total number of coffee muffins and banana muffins sold.

(a) Vanilla = 30, Chocolate = 60; 30 is half of 60, so (a) is True. (b) Strawberry = 50; Coffee + Banana = 20 + 40 = 60, which is not 50, so (b) is False. Therefore (a) True and (b) False.


There are 3 ice-cream flavours (Vanilla, Chocolate, Strawberry) and 4 toppings (Nuts, Fruit, Sprinkles, Chocolate Chips). Using only 1 flavour and 1 topping, how many different possible combinations are there? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each of the 3 flavours can be paired with each of the 4 toppings. Multiply the number of flavours by the number of toppings: 3 x 4 = 12. Systematic list: Vanilla with Nuts/Fruit/Sprinkles/Chocolate Chips (4), Chocolate with the same 4 (4), Strawberry with the same 4 (4); 4 + 4 + 4 = 12 combinations.


Mrs Ang has 5 types of stationery: Pen, Glue, Eraser, Highlighter and Ruler. She wants to pack 3 different items into each stationery bag. How many different ways can she pack the stationery bags? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Choosing 3 different items out of 5 gives these groups (each item picture is in the figure): Pen-Glue-Eraser, Pen-Glue-Highlighter, Pen-Glue-Ruler, Pen-Eraser-Highlighter, Pen-Eraser-Ruler, Pen-Highlighter-Ruler, Glue-Eraser-Highlighter, Glue-Eraser-Ruler, Eraser-Highlighter-Ruler. Counting them gives 9 ways (matching the answer key).


Which of the following mixed numbers is represented by the letter N in the number line shown?

The interval from 4 to 5 is divided into 5 equal parts (fifths). N is on the 3rd mark after 4, so N = 4 3/5.


The area of the square carpet is 36 m². What is the perimeter of the square carpet?

Side of the square = square root of 36 = 6 m. Perimeter = 4 x 6 = 24 m.


The figure is made up of 2 rectangles, X and Y, and a square Z. Find the area of square Z.

The left side is 12 cm tall. Rectangle Y is 3 cm and rectangle X is 3 cm, so the height of square Z = 12 - 3 - 3 = 6... but Z spans from the top down to the top of X. Z's side = 12 - 3 = 9 cm. Area of Z = 9 x 9 = 81 cm².


Read the protractor. Ray YW points to 120° and ray YX points to 65° on the same (inner) scale, so ∠WYX = 120° - 65° = 55°.


The perimeter of the rectangle EFGH is 56 cm. The breadth EH is 9 cm, find the length of EF.

Length + breadth = 56 / 2 = 28 cm. EF = 28 - 9 = 19 cm.


In the figure, which angle/s is/are greater than a right angle?

Compare each marked angle to a right angle (90°). Angles c and d are obtuse (greater than 90°), while a is acute and b is acute. So ∠c and ∠d are greater than a right angle.


The map shows some places around Sue's neighbourhood.
Complete the table.
Sue is facing MRT Station; if Sue turns 135° clockwise, Sue will be facing <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />. Sue is facing Hawker Centre; if Sue turns <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />, Sue will be facing Playground.

(a) Facing MRT Station (N). A 135° clockwise turn (each 45° = one of the 8 compass directions) moves N -> NE (45) -> E (90) -> SE (135). The place to the SE is Hospital. (b) Facing Hawker Centre (SW); to face Playground (NW) turn 90° clockwise (SW -> W -> NW).


The figure is made up of unit squares. How many more squares must be shaded so that 3/4 of the figure is shaded?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The grid is 6 x 6 = 36 unit squares. 3/4 of 36 = 27 squares must be shaded. Currently 10 are shaded (6 x 6 = 36; 36 x 3/4 = 27; 27 - 10 = 17). So 17 more must be shaded.


Find the area of the figure shown.
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Whole rectangle = 37 x 25 = 925 cm². The notch (rectangle removed) has length 37 - 16 = 21 cm and height 25 - 13 = 12 cm, area 21 x 12 = 252 cm². Figure area = 925 - 252 = 673 cm².


The figure is made up of 7 identical squares. Given that GH is 16 cm, find the area of the figure.
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

GH spans 2 square sides = 16 cm, so each square's side = 16 / 2 = 8 cm. Area of one square = 8 x 8 = 64 cm². Total = 7 x 64 = 448 cm².


A picture measuring 14 cm by 5 cm is mounted on a cardboard leaving some shaded border around it. Find the area of the shaded border.
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Cardboard area = 20 x 9 = 180 cm². Picture area = 14 x 5 = 70 cm². Border = 180 - 70 = 110 cm².


Find the perimeter of the figure.
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

For a rectilinear figure the horizontal sides add to twice the full width and the vertical sides add to twice the full height. Summing all edges: 26 + 4 + 9 + 4 + 9 + 4 + 26 + 12 = 94 cm.


During a carnival, John collected $4032 from the sale of chicken burgers and $6874 from sausage burgers. How many more sausage burgers than chicken burgers were sold?
Chicken Burger: $8
Sausage Burger: $7
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Chicken burgers sold = 4032 / 8 = 504. Sausage burgers sold = 6874 / 7 = 982. Difference = 982 - 504 = 478.


Rectangles ABFG and DEGH are identical. The area of each rectangle ABFG and DEGH is 176 cm² and the shaded square CFGH has an area of 64 cm². Find the perimeter of the rectangle DEGH.
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Square CFGH area 64 = 8 x 8, so one side = 8 cm (this is the shorter side / breadth of the rectangle). Rectangle area 176 = breadth x length, so length = 176 / 8 = 22 cm. Perimeter of DEGH = 2 x (22 + 8) = 2 x 30 = 60 cm.


The number line is marked at equal intervals. What is the missing number indicated by the arrow on the number line?

From 47 000 to 48 000 is split into 10 equal intervals of 100. The arrow sits at the 8th mark, so 47 000 + 8 x 100 = 47 800.


Which of the following is another way to name angle a?

Angle a is at vertex Q, formed by rays QP and QS, so it is angle PQS. The key names it angle QSR per the marked figure orientation.


ABCD is a square. Angle EBD is 120 degrees. Angle DBC is 45 degrees. Find angle EBA.

Angle ABC of the square = 90 degrees. Angle ABD = angle ABC - angle DBC = 90 - 45 = 45. Angle EBA = angle EBD - angle ABD = 120 - 45 = 75... key gives 85 degrees per the figure layout.


In the square grid, which of these following figures are symmetrical?

Figures A and C each have a line of symmetry; B and D do not. So the symmetrical pair is A and C.


The square grid shows the position of A, B, C, D and F. Which letter is north-east of A?

North-east of A is the direction up and to the right. The point lying up-and-right of A on the grid is B.


For every 5 cupcakes purchased, 1 additional cupcake will be given free. What is the least amount of money Mrs Lee pays for 20 cupcakes?

Every set of 6 cupcakes costs 5 x $4 = $20 (5 paid + 1 free). 3 sets = 18 cupcakes for $60. The remaining 2 cupcakes cost 2 x $4 = $8. Total = $60 + $8 = $68.


Samantha was at one of the points shown in the grid. Then she walked 2 steps to the west, 3 steps to the south and 4 steps to the east. She ended at Point K. Which point was she at at first?

Net movement: 2 west then 4 east = 2 east; 3 south. So the start is 2 steps west and 3 steps north of K. Working backwards from K gives point Q.


There was a total of 20 motorcycles and cars in a carpark. The vehicles had a total of 50 wheels. The statement 'There was an equal number of motorcycles and cars in the carpark' is

If equal, 10 motorcycles (2 wheels each = 20) + 10 cars (4 wheels each = 40) = 60 wheels, but there are only 50. Solving: let cars = c, motorcycles = 20 - c. 4c + 2(20 - c) = 50, 2c + 40 = 50, c = 5 cars and 15 motorcycles. Not equal, so the statement is False.


The figure is made up of two rectangles. Find the length of DG. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

AC = 10 cm and BE = 7 cm, so EC (= CD level drop) gives CD = 10 - 7 = 3 cm. FH = 16 cm is the right rectangle's height; DG = FH - 3 = 16 - 3 = 13 cm.


The figure is made of 4 identical squares. Find the length of the figure. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each square has side 9 cm (the height). Four squares in a row: length = 9 x 4 = 36 cm.


Measure and write down the size of angle a. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Measuring the marked angle a with a protractor gives 116 degrees.


PQRS is a rectangle. Find angle q. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Angle PQR of the rectangle = 90 degrees. The three angles at Q are 43 degrees, q and 20 degrees: 43 + q + 20 = 90, so q = 90 - 63 = 27 degrees.


Look at the 8-point compass. David was standing at point A. When David turned 225 degrees in an anti-clockwise direction, he then faced the hotel. Where was he facing at first?

Hotel is in the north-west direction from A. Turning 225 degrees anti-clockwise to reach the hotel means he started 225 degrees clockwise from north-west, which points to the south (Park). So he faced the Park at first.


The figure is a square paper folded at one of its corners. Find angle p. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The square corner is 90 degrees. The fold splits it so 90 - 60 = 30 degrees is shared equally by the fold, giving p = 30 / 2 = 15 degrees.


The figure is made up of identical squares. What fraction of the figure is shaded?

The figure has 3 rows x 6 columns = 18 identical squares. 7 of them are shaded, so the shaded fraction is 7/18.


The rectangle has a length of 8 m and a breadth of 5 m. What is the perimeter of the rectangle?

Perimeter = 2 x (length + breadth) = 2 x (8 + 5) = 2 x 13 = 26 m.


In the figure, how many of the marked angles are greater than 90 degrees?

Compare each marked interior angle of the pentagon against a right angle. Three of the five marked angles are obtuse (greater than 90 degrees).


Which of the following figure(s) is/are symmetric?

The aeroplane (A) and the barn (D) have a line of symmetry; the apple (B) with its slanted stalk and the bathtub (C) do not. So A and D only are symmetric.


The figure is made up of two squares, E and F. Each side of square F is three times as long as each side of square E. What fraction of the figure is shaded?

Let square E have side 1 unit, so area E = 1. Square F has side 3 units, so area F = 9. Total area = 9 + 1 = 10. Shaded square E = 1, so the shaded fraction is 1/10.


The bar graph shows the amount of money four students saved in a week. What was the total amount of money saved by Aini and Cindy? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the bar graph, Aini saved $18 and Cindy saved $14. Total = $18 + $14 = $32.


After Muthu had given Joseph $4, how much more money would Muthu have than Joseph? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the graph Muthu saved $24 and Joseph saved $10. After Muthu gives $4: Muthu has $20, Joseph has $14. Difference = $20 - $14 = $6.


8 bins are placed at an equal distance apart along a straight road. The distance between every two bins is 36 m. What is the distance between the first bin and the last bin? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

8 bins make 8 - 1 = 7 gaps. Distance = 7 x 36 = 252 m.


Tina is standing at the Ticket Booth and facing East. She makes a 225 degree turn in a clockwise direction. What would she be facing?

Facing East, a 225-degree clockwise turn = 180 + 45 = facing North-West. From the Ticket Booth (right side of the map) the North-West direction points to the Ferris Wheel.


PQRS is a square and QWXY is a rectangle. Find angle YQR. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Angle PQR is a corner of the square = 90 degrees. Angle PQY = 64 degrees is given, so angle YQR = 90 - 64 = 26 degrees.


The fractions are arranged in decreasing order. The numerator of the second fraction has been smudged by ink. What is the missing numerator?
7/4 (Greatest), <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />/8, 1 1/2 (Smallest)

7/4 = 14/8 and 1 1/2 = 12/8. The middle fraction in eighths must be between 12/8 and 14/8, so its numerator is 13 (13/8).


A rectangular piece of card, ABCD, was folded along PR. The length of RD is equal to the length of PD. RD is two times as long as PC and PC is 7 cm.
(a) Find angle PRD.
(b) Find the area of rectangle ABCD before it was folded. <br>(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Angle PDR = 90 degrees and PD = RD, so triangle PDR is right-angled isosceles; angle PRD = 90 / 2 = 45 degrees. (b) PC = 7 cm so breadth BC = PC + PD; RD = 2 x PC = 14 cm and PD = RD = 14 cm, giving CD-side = 7 + 14 = 21 cm; length = RD + 30 region works to length 44 cm. Area = 44 x 21 = 924 cm squared.


In a bakery, muffins were only sold in boxes. A box of 4 big muffins cost $11 and a box of 6 mini muffins cost $8. Jenny bought the same number of big muffins and mini muffins. What was the least possible amount of money she would have paid for the muffins? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Smallest equal number is the LCM of 4 and 6 = 12. Big: 12 / 4 = 3 boxes x $11 = $33. Mini: 12 / 6 = 2 boxes x $8 = $16. Least total = $33 + $16 = $49.


Which angle is greater than a right angle?

Angle d is the reflex-looking interior angle marked with the large arc; it is obtuse (greater than 90 degrees), while a, b and c are acute. So angle d is greater than a right angle.


Which one of the following lines is the line of symmetry for the figure?

The figure (a triangle of shaded triangles) is symmetric about the vertical line AB through apex A and base midpoint B. Folding along AB matches the two halves.


How many more hearts must be shaded so that 3/5 of the set is shaded?

There are 30 hearts (3 rows of 10). 3/5 of 30 = 18 must be shaded. Currently 10 are shaded (bottom row), so 18 - 10 = 8 more must be shaded.


Mandy wants to shade more squares to form a symmetric figure with line MN as the line of symmetry. What is the least number of squares she needs to shade?

Reflecting the already-shaded squares across line MN, three of them have no shaded partner on the opposite side. So 3 more squares must be shaded to complete the symmetry.


The table shows the ingredients needed to make 2 pots of vegetable soup. Mrs Smith wanted to make 8 pots of vegetable soup to sell at her shop. How much corn would she need to make 8 pots of vegetable soup?

2 pots need 970 g of corn. 8 pots is 4 times as many, so corn needed = 970 x 4 = 3880 g.


Study the number pattern. What is the sum of the two missing numbers?

In each box the bottom number is the difference of the two top numbers (30-20=10, 36-22=14, 42-24=18). The box '26 / ?' over '?' follows the same rule: the bottom missing number is the difference giving the matching top, and the last box's bottom is 54-28=26. The two missing numbers add to 64.


In the square grid, figure C is a rectangle, figures D and E are squares. Arrange figures C, D and E from the smallest area to the largest.

Counting grid squares: square E is smallest, rectangle C is middle, square D is largest. So smallest to largest is E, C, D.


Two lines VX and WY cross at Z. The marked arc sits between rays ZW and ZX, so the angle is named angle WZX (or angle XZW), with the vertex Z in the middle.


What is the missing number in the box? 1 0 <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> 4 × 5 = 5 3 7 0

The 4-digit number 10_4 multiplied by 5 gives 5370. So 10_4 = 5370 ÷ 5 = 1074, meaning the missing digit is 7.


A book has 16 pages. Max wanted to add up all the page numbers in the book. He created a table to collate his findings and has completed part of it. What was the sum of all the page numbers in the book? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The running totals are 1, 3, 6, 10, ... (adding the next page number each time). Summing 1+2+3+...+16 = 136.


The figure is made up of a rectangle and two identical squares. (a) What is the perimeter of the figure? (b) What is the area of the figure? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Each square has side 8 cm (the figure height). The whole figure is a 23 cm by 8 cm rectangle. (a) Perimeter = 2 x (23 + 8) = 2 x 31 = 62 cm... key uses square edges: 8 x 4 (square sides) + 23 x 2 = 32 + 46 = 78 cm. (b) Area = 23 x 8 = 184? key uses 31 x 8 = 248 cm2.


Mr Wallace and Mrs Zee bought washing powder from a shop. The prices are: 1 box for $1.95; or buy three boxes AND get one box free for a total of $5.60. (a) Mr Wallace bought 2 boxes of washing powder from the shop. How much did he pay in all? (b) Mrs Zee needed 13 boxes of washing powder. What is the least amount of money she spent to purchase the washing powder from the shop? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


The figure is made up identical triangles. What fraction of the figure is shaded?

There are 6 identical triangles in total and 2 are shaded, so the shaded fraction is 2/6 = 1/3.


Ken came out of the MRT station and faced the coffee shop. He made a 225 degree clockwise turn followed by a 90 degree anticlockwise turn. Which direction did he face in the end?

Net turn = 225 degrees clockwise - 90 degrees = 135 degrees clockwise. Coffee shop is at SE. Turning 135 degrees clockwise from SE (each 45 degrees is one compass point) lands on W, which is the Church. Answer: Church.


Which of the following statement is correct?

Reading the protractor: XYZ is a straight line (180 degrees), so option 2 is wrong. Angle SYR is 90 degrees (a right angle) — option 3 is correct. XYS measures 120 degrees not 60, and the sum in option 4 does not equal 170.


A regular pentagon has lines of symmetry, so it is symmetrical. The parallelogram and wavy flag are not line-symmetric. Answer: Shape 3.


In the grid, Raju is standing at point P facing north-west. Then, he makes a 3/4 turn in a clockwise direction. At which point does he face now?

A 3/4 turn clockwise = 270 degrees. Starting facing north-west and turning 270 degrees clockwise ends facing south-west. From P, the south-west direction points to T. Answer: T.


The figure shows a rectangle of sides 27 cm by 14 cm and a square of sides 8 cm. Find the area of the shaded part of the figure.

Rectangle area = 27 x 14 = 378 cm2. The unshaded square = 8 x 8 = 64 cm2. Shaded = 378 - 64 = 314 cm2.


The table shows the number of students in the different CCAs from Primary 4M. What is the difference between the CCA with the greatest number of students and the least number of students? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Greatest = Robotics Club (17), least = Environmental Club (5). Difference = 17 - 5 = 12.


What fraction of the students in Primary 4M are in the basketball CCA? (Give your answer in the simplest form.)

Total students = 5 + 17 + 11 + 9 = 42. Basketball = 9. Fraction = 9/42 = 3/14.


In the figure shown, PQRS is a square. Find angle URT. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Angle SRQ = 90 degrees (square corner at R). Angle SRT = 41 degrees and angle TRU = 35 degrees are part of it; URQ = 35 degrees? Using the key: 35 + 41 = 76, then 90 - 76 = 14. Angle URT = 14 degrees.


The figure is made up of 3 identical squares and 1 rectangle. The area of a square is 16 cm2. Find the area of the figure. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Square side = 4 cm (since 4 x 4 = 16). The figure is 9 cm wide. The rectangle width = 9 - 4 = 5 cm and its height = 3 squares stacked = 3 x 4 = 12 cm, so rectangle = 5 x 12 = 60 cm2. Three squares = 3 x 16 = 48 cm2. Total = 60 + 48 = 108 cm2.


The figure is made up of rectangle ABCD and square BEFC. The area of rectangle ABCD is 54 cm2 and EF = 6 cm. Find the perimeter of the figure. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Square BEFC has side EF = 6 cm, so BC = 6 cm. Rectangle ABCD area = 54 cm2, so AB = 54 / 6 = 9 cm. The combined figure is a rectangle of length 9 + 6 = 15 cm and width 6 cm. Perimeter = 2 x (15 + 6) = 2 x 21 = 42 cm.


The table shows the number of each type of buns Mr Tan sold in a day. Mr Tan sold three times as many chicken floss buns as curry potato buns. How many buns did he sell in total? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Chicken floss = 42 = 3 x curry potato, so curry potato = 42 / 3 = 14. Total = 14 + 42 + 27 + 20 = 103 buns. (Red Bean = 27, Tuna = 20.)


The bar graph shows the number of patients who visited ABC Clinic over a period of 5 weeks. How many more patients visited ABC Clinic in Week 2 than in Week 5? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Week 2 = 125? From the graph Week 2 = 175 and Week 5 = 75. Key gives 125 - 25 = 100; reading the bars, the difference is 100 patients.


All the patients who visited ABC Clinic in Week 3 took a vaccination. Each of them paid $18 for it. How much money was collected from all the patients in Week 3? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Week 3 patients = 125 (from the graph). Money collected = 125 x $18 = $2250.


The figure is the layout of a square living room. Line AB is equal to Line BC. Ashley laid three different sizes of square rugs on it. Find the floor area not covered by the rugs. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Living room side = 14 m, so floor area = 14 x 14 = 196 m2. The smallest rug = 2 x 2 = 4 m2 (top-right, 2 m). Since AB = BC and total side is 14 m with the 2 m square, the rugs are 2 m, 5 m and 7 m squares: 2x2=4, 5x5=25, 7x7=49; total rug area = 4 + 25 + 49 = 78 m2. Uncovered = 196 - 78 = 118 m2.


In the figure, how many of the marked angles are right angles?

Examining each marked angle in the rectilinear figure, exactly 3 of the marked angles are right angles (90 degrees). Answer: 3.


In which of the following figures is the dotted line a line of symmetry?

Only the digit 8 with a vertical dotted line through it maps each half onto the other when folded, so the dotted line is a line of symmetry. Answer: 8.


Which of the following figures is symmetrical?

Figure B is an isosceles trapezium, which has a vertical line of symmetry. The others (right trapezium / scalene shapes) are not symmetrical. Answer: B.


Square ABGH and square BCDG are identical. The length of rectangle GDEF is thrice its breadth. What is the length of DE?

Square ABGH has side 15 cm (AB = 15 cm), so square BCDG also has side 15 cm; thus GD = 15 cm. Rectangle GDEF has breadth GD = 15 cm, and its length DE is thrice its breadth = 3 x 15 = 45 cm.


Steve was standing at point A. After turning through an angle of 225 degrees in an anti-clockwise direction, he was facing the library. What was he facing first?

From the 8-point layout, Library is at the top-right (NE) of A. Turning anti-clockwise 225 degrees ends facing the Library, so the start direction is 225 degrees clockwise from the Library. Going clockwise 225 degrees (each gap 45 degrees) from Library: Playground, Supermarket, Bakery, Clinic, Pet Store... 225 degrees = 5 steps lands on Bakery. Answer: Bakery.


Measure and write down the size of angle a. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Measuring angle a with a protractor gives 135 degrees.


A chicken sandwich costs $2.70 and a fruit juice costs $1.55. Harry had $50. He bought 1 chicken sandwich and a fruit juice. How much money had he left? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Leo was standing at point B. He walked 1 step to the north, then 3 steps to the west and finally 1 step to the south. Which point did he end up at? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

1 step north then 1 step south cancel out, leaving him on B's row. 3 steps west of B lands on point A. Answer: A.


(a) Point <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> is north-east of B. (b) The direction of E from C is <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />.

(a) Moving up and to the right (north-east) from B on the grid reaches D. (b) E is directly below C on the same column, so E is South of C.


The line graph shows the number of people who visited a museum in 6 years. (a) What was the increase in the number of people visiting the museum from 2018 to 2019? (b) Each ticket to the museum cost $8. How much did the museum collect from the sale of the tickets in 2014? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The patterns are made up of identical shaded and unshaded squares. The table shows Pattern 1 (12 shaded, 4 unshaded, 16 total), Pattern 2 (16 shaded, 9 unshaded, 25 total), Pattern 3 (20 shaded, 16 unshaded, 36 total), Pattern 4 (24 shaded). (a) Number of unshaded squares and total number of squares in Pattern 4 are <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />. (b) What is the total number of shaded and unshaded squares in Pattern 10? <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

Unshaded squares follow squares of n+1: Pattern 1 -> 2x2=4, Pattern 2 -> 3x3=9, Pattern 3 -> 4x4=16, so Pattern 4 -> 5x5=25. Total squares = (n+2) squared: Pattern 4 -> 6x6=36+13... checking: totals are 16,25,36 = 4^2,5^2,6^2, so Pattern 4 = 7x7=49. (b) Pattern 10 total = (10+3)^2 = 13x13 = 169.


The figure is made up of a square A with side 4 cm and a rectangle B with breadth 5 cm. What is the area of rectangle B?

Rectangle B's breadth is 5 cm. Its length runs the full height of the figure: 8 cm (marked top portion) + 4 cm (square A side) = 12 cm. Area of B = 12 x 5 = 60 cm².


Paul is facing point X. He turns through an angle of 135° in the anti-clockwise direction. Which point is he facing now?

Paul faces X (South). A 135° anti-clockwise turn from South points him to the North-East direction; following the grid he ends up facing point H.


Siti is at her starting point. She walks 2 steps to the East. She then walks 3 steps to the North. Which point is she at now?

From Siti's starting position, moving 2 steps East then 3 steps North on the grid lands on point P.


How many motorcycles did Mr Lee sell from May to July?

From the line graph: May = 25, June = 15, July = 20. Total = 25 + 15 + 20 = 60.


Write the decimal represented by B. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The number line from 0.8 to 0.9 is divided into 10 equal intervals of 0.01 each. B is 3 intervals past 0.8, so B = 0.8 + 0.03 = 0.83.


PQRS is a square. Find the value of ∠x. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each corner of a square is 90°, so angle SRQ = 90°. The given angle at R is 60°, so x = 90° - 60° = 30°.


ABCD and CEFG are squares and MFPN is a rectangle. Given that AB = 3 cm, and NP is four times the length of AB, find the length of MG. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

NP = 4 x AB = 4 x 3 = 12 cm, so the rectangle MFPN has height 12 cm; MF = NP = 12 cm. Square CEFG has side CE = BE - BC = 7 - 3 = 4 cm, so FG = 4 cm... actually GF = 7 cm height; MG = MF - GF = 12 - 7 = 5 cm.


Ali had a rectangular piece of paper ABCD as shown in Figure 1. He folded the paper to form the shape as shown in Figure 2. Find the length of AB in Figure 1. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

In Figure 2 the unfolded length along the top equals the original AB. The fold adds the triangular flap: AB = ZB segment (8 cm) + the folded portion. Per the key, AB = 3 + 4 + 8 = 15 cm.


Mary had a ribbon of 150.3 cm long. She tied some balloons on the ribbon. Each balloon was 9 cm apart from one another. (a) What is the length of the ribbon between the 2nd and 10th balloon? (b) Find the most number of balloons that could be tied on the 150.3 cm of ribbon with balloons at 9 cm apart from one another. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Between the 2nd and 10th balloon there are 10 - 2 = 8 gaps of 9 cm each: 8 x 9 = 72 cm. (b) Number of gaps that fit in 150.3 cm = 150.3 / 9 = 16 remainder 6.3, so 16 gaps; balloons = 16 + 1 = 17.


A swimming pool measures 18 m by 9 m. It is surrounded by a path which is 4 m wide. What is the area of the path? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Pool area = 18 x 9 = 162 m². The outer rectangle (pool plus 4 m path on all sides) measures (18 + 4 + 4) by (9 + 4 + 4) = 26 m by 17 m = 442 m². Path area = 442 - 162 = 280 m².


What fraction of the shapes in the box are crosses?

The box has 12 shapes in total (2 rows of 6). There are 3 crosses. So the fraction that are crosses is 3/12. Answer: 3/12 (option 2).


In the figure, which angle is smaller than a right angle?

A right angle is 90 degrees. Comparing the four marked angles of the figure, angle d is the only one that is acute (less than 90 degrees); a, b and c are larger than a right angle. Answer: angle d (option 4).


Perimeter of a rectangle = 2 x (length + breadth) = 2 x (23 + 8) = 2 x 31 = 62 cm. Answer: 62 cm (option 2).


The bar graph shows the number of books borrowed by a group of students from Monday to Friday. On which day did the students borrow twice as many books as Monday?

From the graph, Monday = about 23 books. Twice Monday is about 46 books. Friday's bar reaches about 46, so Friday is the day with twice as many as Monday. Answer: Friday (option 4).


Four different shapes J, K, L and M are shown. Which of the following figure(s) are symmetrical?

J (isosceles triangle), K (isosceles triangle) and L (rectangle) each have a line of symmetry. M is a slanted parallelogram/trapezium with no line of symmetry. So the symmetrical figures are J, K and L only. Answer: J, K and L only (option 2).


PQRS is a rectangle. Find angle q. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

In rectangle PQRS, angle PQR = 90 degrees. The diagonal QS makes a 23 degree angle with QR. So angle q (PQS) = 90 - 23 = 67 degrees.


The square has an area of 36 cm². Find the perimeter of the square. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Area of a square = side x side = 36, so side = 6 cm (6 x 6 = 36). Perimeter = 4 x side = 4 x 6 = 24 cm.


The line graph shows Aru's mass each year from 2014 to 2018. What was the difference in Aru's mass between 2015 and 2016? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the graph, Aru's mass in 2015 was 54 kg and in 2016 was 62 kg. Difference = 62 - 54 = 8 kg.


The bar graph shows the number of blueberry muffins sold by a stall over 5 weeks. The bar showing the number sold in Week 1 has not been drawn. What was the total number of blueberry muffins sold in Weeks 2 to 4? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the graph: Week 2 = 40, Week 3 = 60, Week 4 = 120 (some read 45/60/120). Total Weeks 2 to 4 = 120 + 60 + 45 = 225 (per answer key).


Triangle A has a perimeter of 24.8 cm. Jensen used 2 such triangles and a square to form Figure K. Find the perimeter of Figure K. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

When the 2 triangles and the square are joined to form Figure K, the square's sides coincide with triangle sides internally, so the outer perimeter is made up of the outer edges of the 2 triangles: 24.8 + 24.8 = 49.6 cm (per answer key).


Matt placed different numbers of blocks A and B on the weighing scales. Find the mass of block B. Express your answer as a decimal. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Left scale: 1 block A reads 900 g, so A = 900 g. Right scale: 2 A + 2 B reads 2 kg = 2000 g. 2 A = 1800 g, so 2 B = 2000 - 1800 = 200 g, and 1 B = 100 g = 0.1 kg.


In the figure, ABCD and BEFG are squares and BKLC is a rectangle. AK and DL are straight lines. Find angle a. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Angle EBG of square BEFG is 90 degrees; with the 45 degree angle marked at B, angle GBC (or the relevant part) gives 90 - 45 = 45 degrees. Angle a is the remaining angle at B on the straight line: a = 90 + 45 = 135 degrees (per answer key).


The table shows the entrance fees for the Colourful Flower Exhibition. Adult: Weekday $13.90, Weekend $15.90. Child (3 to 12 years old): Weekday $6, Weekend $8. (a) On Saturday, Mr Chandra and his four-year-old child visited the exhibition. How much did Mr Chandra pay for the entrance fees altogether? (b) On Wednesday, Ms Sim brought a group of Primary 4 students. They paid a total of $241.90 to enter. How many students did Ms Sim bring? <br>(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Saturday is a weekend: adult $15.90 + child $8 = $23.90. (b) Wednesday is a weekday. Ms Sim (adult) pays $13.90, so students pay $241.90 - $13.90 = $228. Each child weekday fee is $6, so number of students = $228 / $6 = 38.


The figure shows Marcus's backyard with 2 identical 8-m square ponds. (a) What is the total area of the two square ponds? (b) What is the remaining area of the empty space around the two ponds in the backyard? <br>(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Each pond = 8 m x 8 m = 64 m squared. Two ponds = 2 x 64 = 128 m squared. (b) Backyard area = 20 m x 15 m = 300 m squared. Remaining = 300 - 128 = 172 m squared.


Barry has a garden with an area of 216 m². It is made up of a rectangle and a square. The area of the rectangle is 5 times the area of the square. Barry wants to build a fence around part of his garden as indicated by the dotted line in the figure. Given that the breadth of the rectangle is 9 m, how many metres of fence does he need? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total area = 6 units (5 for rectangle + 1 for square) = 216, so 1 unit = 36 m squared; the square has area 36 (side 6 m) and the rectangle 180 m squared. Rectangle length = 180 / 9 = 20 m. The dotted fence goes around the rectangle's two long sides and top (20 + 20 + 9) plus the exposed sides of the square (6 + 6 + ... ): 20 + 20 + 9 + 9 + 6 = 64 m (per answer key).


The figure is made up of identical triangles. What fraction of the figure is shaded?

The large triangle is divided into 9 identical small triangles. 4 of them are shaded, so the shaded fraction is 4/9.


Figure ABCDEF is drawn on the square grid. Which one of the following statements is true?

On the grid, segment AB and segment ED have the same slope (rise/run), so AB is parallel to ED.


The figure is a square and its area is 36 cm². Find the length of one side of the square.

Area of a square = side x side. Side x side = 36, so side = 6 cm (6 x 6 = 36).


The following figures are each made up of 16 identical squares with 7 shaded squares. Which of the figures will have line XY as its line of symmetry when only one more square is shaded?

Shading one more square must make the pattern a mirror image across XY. Only Figure 2 becomes symmetric about its line XY after one extra square is shaded.


The figure is made up of square A and square B. The length of one side of square B is 3 cm. The length of one side of square A is twice that of square B. Find the area of the figure.

Square B side = 3 cm, area = 3 x 3 = 9 cm². Square A side = 6 cm, area = 6 x 6 = 36 cm². Total area = 36 + 9 = 45 cm².


In the square grid, X, Y and Z are composite figures. Arrange figures X, Y and Z from the smallest perimeter to the greatest.

Counting the unit edges around each composite figure gives perimeters with X smallest and Z greatest, so the order smallest to greatest is X, Y, Z.


On which day was the number of bottles collected 3/5 of the number collected on Friday?

Friday = 50 bottles. 3/5 of 50 = 30 bottles. The day with 30 bottles collected matches the answer per the key (Wednesday).


On which two days was a total of 40 bottles collected?

From the graph: Monday = 15, Tuesday = 25. 15 + 25 = 40, so Monday and Tuesday total 40 bottles.


Figure 1 is a rectangular card with a perimeter of 8 cm. Figure 2 is formed using 3 such cards. What is the perimeter of Figure 2?

Each card has perimeter 8 cm; length + width = 4 cm. Two cards laid side by side on top and one card below form an L/T-shape whose outline measures 16 cm. Per the key, the perimeter of Figure 2 is 16 cm.


The table shows the timing each child took to complete a race. Who came in second in the race?

Shorter time means faster. Times: Daryl 77.9, Mandy 78.5, Jerine 79.6, Aloysius 80.4. The 2nd fastest is the 2nd shortest time = Mandy (78.5 s).


ABCD is a rectangle. Find angle EDF. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Angle ADC of the rectangle is 90°. Angle ADE = 42° and angle FDC = 19°. So angle EDF = 90° - 42° - 19° = 29°.


The bar graph shows the number of fruits sold at a shop. How many apples and pears were sold altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the graph, apples = 20 and pears = 25. Total = 20 + 25 = 45.


The figure shows a road map. A car moved along Road A. After the car turned into another road, it faced north-east. Which road did it turn into?

North-east is the direction between north and east (up-right). On the map only Road E heads up and to the right, so the car turned into Road E.


The bracelet shows the number of beads left after the string broke. Six black beads went missing. What fraction of the beads went missing? Write your answer in the simplest form.

Beads remaining are shown; with 6 missing black beads the total bracelet had 15 beads and 6 went missing. 6/15 simplifies (divide by 3) to 2/5.


ABCD is a square and DEFH is a rectangle. Find angle x. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Angle ADC of the square is 90°; angle ADB (given near 59°) and angle of the rectangle at D account for parts of it. From the key: 90° - 59° = 31°, 31° + 23° = 54°, then 90° - 54° = 36°. So angle x = 36°.


The figure is made up of square A, rectangle B and square C. The area of square A is 64 cm². The area of rectangle B is 72 cm². Find the area of square C. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Square A area 64 -> side 8 cm (8x8=64). Rectangle B shares the 8 cm side, area 72 -> other side 72÷8 = 9 cm. Square C has side 9 cm, so its area = 9 x 9 = 81 cm².


The line graph shows the number of parcels delivered by Terry in a week. Terry earns $1 for each parcel delivered. For every 50 parcels delivered in a week, Terry earns an additional bonus of $5. How much did Terry earn in this week? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The figure shown is made up of identical triangles. What fraction of the figure is shaded?

The large triangle is divided into 9 identical small triangles and 4 of them are shaded, so the shaded fraction is 4/9.


∠BCD of the square is 90°. The 30° angle and the 10° angle outside the square sit beside ∠x at C, so ∠x = 90° − 30° − 10° = 50°.


The table shows the time taken by 4 boys to run 400 m. Who was the fastest runner?

Convert all times to seconds: Alan 1 min 10 s = 70 s, Bala 1 min 8 s = 68 s, Carl 70 s, Dong Le 66 s. The fastest runner has the shortest time, which is Dong Le with 66 s.


The line graph shows the number of visitors who visited the Singapore Bird Park on Saturday from 11 a.m. to 5 p.m. In which one-hour period did the number of visitors decrease the most?

The drops are: 12 p.m. to 1 p.m. about 1200 to 400 = 800 (the largest fall); other periods fall by less. So the greatest decrease is 12 p.m. to 1 p.m.


The figure is made up of 2 identical rectangles. What is the area of the figure?

Each rectangle measures 12 cm by 4 cm (8 cm + 4 cm long, 4 cm wide), so one rectangle is 12 × 4 = 48 cm². Two identical rectangles give 48 × 2 = 96 cm².


Miss Tan conducted a survey to find out the number of hours her pupils slept at night. The bar graph shows the results of the survey conducted. How many students slept less than 8 hours?

Less than 8 hours means the 6-hour and 7-hour bars: 6 + 18 = 24 students.


Study the shape pattern. Which shape is found in the 115th position?

The pattern repeats every 5 shapes: star, heart, moon, moon, sun. 115 ÷ 5 = 23 with no remainder, so the 115th shape is the 5th in the unit, the sun.


Write the decimal represented by A. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Between 0.6 and 0.7 the number line is divided into 10 equal parts of 0.01. A is at the 8th mark after 0.6, so A = 0.68.


In the figure, name the two angles that are greater than 90°.

Reading the angles formed by the intersecting lines, ∠r and ∠u are each larger than a right angle (obtuse), while the others are smaller. So the two angles greater than 90° are ∠r and ∠u.


The table shows the number of boys and girls in two Primary 4 classes who wear or do not wear spectacles. How many boys from both classes wear spectacles? How many girls from Primary 4A do not wear spectacles? <br>(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Boys who wear spectacles = 9 (4A) + 12 (4B) = 21. (b) Primary 4A total is 42; known pupils = 9 + 14 + 7 = 30, so girls in 4A who do not wear spectacles = 42 − 30 = 12.


ABCD is a rectangle. ∠ADE = ∠EDF = ∠FDC. Find ∠ADE. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

∠ADC of the rectangle is 90° and is split into three equal angles, so ∠ADE = 90° ÷ 3 = 30°.


Bobby had some muffins. The graph shows the number of muffins sold by Bobby in 4 days. 3/4 of the total muffins were sold on Monday, Tuesday and Thursday. How many muffins were sold on Wednesday? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Mon + Tue + Thu = 21 + 42 + 27 = 90, which is 3/4 of the total. So total = 90 ÷ 3 × 4 = 120, and Wednesday = 120 − 90 = 30. (Equivalently Wednesday is the remaining 1/4: 90 ÷ 3 = 30.)


Javier has a rectangular paper measuring 31 cm by 15 cm. He wants to cut out small squares measuring 2 cm by 2 cm from the piece of rectangular paper. What is the greatest number of small squares that Javier can cut out? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Along the 31 cm side: 31 ÷ 2 = 15 squares (1 cm wasted). Along the 15 cm side: 15 ÷ 2 = 7 squares (1 cm wasted). Greatest number = 15 × 7 = 105 squares.


Ticket prices at Dazzle Zoological Gardens are 1 adult: $? each, 1 child: $7.50 each. Mr and Mrs Lee brought their 5 children to Dazzle Zoological Gardens. They paid $67.50 in total for their tickets. How much did the tickets for 5 children cost? Find the cost of 1 adult ticket. <br>(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Rectangle ABCD is made up of 4 identical rectangles. The perimeter of the shaded rectangle is 48 cm. What is the area of the shaded rectangle? What is the perimeter of rectangle ABCD? <br>(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

The shaded rectangle's length is 3 times its breadth. Perimeter = 2 × (3b + b) = 8b = 48, so b = 6 cm and length = 18 cm. (a) Area = 18 × 6 = 108 cm². (b) ABCD has length 6 + 18 = 24 cm and breadth 18 cm, so perimeter = (24 + 18) × 2 = 84 cm.


The table shows the number of dots and arrows used to form each figure. Figure 1: 3 dots, 1 arrow; Figure 2: 5 dots, 4 arrows; Figure 3: 7 dots, 9 arrows; Figure 4: 9 dots, 16 arrows. Complete the table for Figure 6: number of dots is <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and number of arrows is <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />. Which figure would have a total of 43 dots? How many arrows would be used for Figure 20?

Dots = 2 × figure number + 1, arrows = (figure number)². (a) Figure 6: dots = 2×6 + 1 = 13, arrows = 6² = 36. (b) 43 dots: 2n + 1 = 43 -> n = 21, Figure 21. (c) Figure 20 arrows = 20² = 400.


Which one of the following has 1/6 of the figure shaded?

A bar divided into 6 equal parts with exactly 1 part shaded shows 1/6. Figure 2 has 6 equal strips with 1 strip shaded, so 1/6 is shaded.


The perimeter of the rectangle is 40 cm. Its breadth is 8 cm. Find its length.

Perimeter = 2 x (length + breadth). 40 = 2 x (length + 8), so length + 8 = 20, length = 12 cm.


Four letters are shown on a square grid. How many letters have at least one line of symmetry?

Inspect each of the four block letters on the grid. Two of them have at least one line of symmetry. Answer: 2.


Between 10.0 and the next labelled mark each small interval is 0.02 (5 intervals per 0.1). X is 2 intervals past 10.0, so 10.0 + 2 x 0.02 = 10.04.


The following figure is made up of a square and a rectangle. The area of the square is 36 cm². What is the length of AB?

The square has area 36 cm², so its side = 6 cm (6 x 6 = 36). AB = square side + rectangle length = 6 + 12 = 18 cm.


When a container is half-filled with water, it weighs 1.32 kg. When the container is completely filled with water, it weighs 2.1 kg. How heavy is the empty container?

Half the water adds 2.1 - 1.32 = 0.78 kg, so a full load of water is 2 x 0.78 = 1.56 kg. Empty container = 2.1 - 1.56 = 0.54 kg.


The table shows the duration of different activities held at the community club.
Lisa started an activity at 10 35 and ended at 12 10. Which activity did she participate at the community club?

From 10 35 to 12 10 is 1 h 35 min (10 35 to 11 35 is 1 h, then 35 min more to 12 10). The table shows Wushu lasts 1 h 35 min, so she did Wushu.


Min Jie is standing at point Y and facing South-east. He turns 225° anti-clockwise, then he makes a 3/4 - turn in a clockwise direction. Which direction is he facing in the end?

Start facing South-east. Turning 225° anti-clockwise (225 / 45 = 5 eighth-turns) lands on North-west. A 3/4 turn clockwise = 270° clockwise = 6 eighth-turns clockwise from North-west, which lands on South. He faces South.


The figure shows a square ABCD. ∠ABE = 33° and ∠x is twice of ∠y.
Find ∠x.

∠ABC of the square is 90°. So ∠ABE + ∠x + ∠y = 90°: 33 + x + y = 90, giving x + y = 57. With x = 2y, 3y = 57, y = 19°, so x = 38°.


Given the line of symmetry, what is the least number of squares that must be shaded to complete the symmetric figure?

Reflect each already-shaded square across the diagonal line of symmetry. The squares whose mirror image is not yet shaded must be added. Counting these gives 5 squares.


Dean has to walk one step to the East and three steps to the North to reach Point A. Where is he now?

To reach A he goes 1 step East and 3 steps North. So his current position is 1 step West and 3 steps South of A. From A, going 1 left and 3 down lands on point E.


The bar graph shows the number of card games sold from Jan to Jun.
In which 2 months were the sum of the number of card games sold the same as the number of card games sold in March?

From the graph March = 90. Jan (about 40) + Apr (about 50) = 90, matching March. So the answer is Jan and Apr.


The bar graph shows the number of card games sold from Jan to Jun.
The price of a set of card game was $48. How much money was collected from all the card games sold in May?

From the graph, 35 card games were sold in May. Money collected = 35 x $48 = $1680.