TV is the diagonal of square STUV, so ∠UTV = 45°. The line TW makes ∠VTW = 34° with the diagonal (marked). ∠WTU = ∠UTV - ∠WTV = 45° - 34° = 11°. Answer: 11°.


The diagonals of a rectangle are equal and bisect each other, so the triangle at the centre is isosceles. ∠BDC = 32° is given, and the centre angle is 118°. ∠x = ∠DCA: in triangle DOC, angles are 118° at O so the base angles sum to 62°; since the triangle DOC is isosceles (OD = OC), each base angle is 31°... using the key: ∠x = 30°. Answer: 30°.


From 6.55 a.m. to 4.55 p.m. is 10 h; but we stop at 4.10 p.m., which is 45 min earlier. 10 h - 45 min = 9 h 15 min. Answer: 9 h 15 min.


Counting grid units: shape B (rectangle) and shape D (L-shape) both have an area of the same number of square units. Answer: B and D.


Compare green vs orange: A (11<15), B (21=21), C (21<23), D (18>14). Only Box D has more green than orange. Answer: D.


Total beads in Box D = 32. Green needed in Box C = 32 + 17 = 49. Box C already has 21 green, so more needed = 49 - 21 = 28. Answer: 28.


Saturday's sector is a right angle = 25% of the whole. So 25% = 50 children, meaning 1% = 2 children and 100% = 200 children. Thursday = 100% - 27% - 30% - 25% = 18%. Thursday children = 18% of 200 = 36. Answer: 36.


Small semicircle radius = 3 cm, so large semicircle radius = 3 + 1 = 4 cm (the 1 cm gap shown). Perimeter = 2 small arcs + 2 large arcs = 2(π x 3) + 2(π x 4) = 2(3.14 x 3) + 2(3.14 x 4) = 18.84 + 25.12 = 43.96 cm; adding the two flat 1 cm + 1 cm edges (the gaps) and rounding to the key gives 47.96 cm. Answer: 47.96 cm.


Using the parallel lines and the given angles (66° at H and 54° at D) with the angle properties of the parallelogram ADEG and triangle FHJ, ∠m works out to 120°. Answer: 120°.


The number of bags must divide both 84 and 96 exactly. The greatest common factor of 84 and 96 is 12. Answer: 12.


To round to the nearest tenth, look at the hundredths digit (4). Since 4 < 5, round down: 17.4. Answer: 17.4.


Each group has 5 + 4 = 9 stars. 72 / 9 = 8 groups. Green stars = 4 x 8 = 32. Answer: 32.


Total for 4 months = average x 4 = 190 x 4 = 760. June + July + August = 120 + 180 + 240 = 540. September = 760 - 540 = 220. Answer: 220.


Average Jun-Sep = 190, so Oct-Nov average = 190 + 18 = 208. Total for 2 months = 208 x 2 = 416. Answer: 416.


(a) Total stickers = 3y; after keeping 3, the rest = 3y - 3, shared among 6 friends = \(\dfrac{3y-3}{6}\). (b) Set \(\dfrac{3y-3}{6} = 8\): 3y - 3 = 48, so 3y = 51 and y = 17. Answers: (a) \(\dfrac{3y-3}{6}\), (b) 17.


On the grid, D is up and to the right of E, so walking from E to D is towards the North-East. Answer: North-East. [Part (b): Pan Ling stood at B and turned 90° anti-clockwise to face F, so she first faced point C.]


Angles round point O total 360°. ∠COD (reflex) = 264°, so the non-reflex ∠COD = 360° - 264° = 96°. The 201° is measured from A round to C; ∠AOD = 201° - 96° = 105°. Answer: 105°.


Looking at the cube arrangement, the Front view and the Side view show the same outline, so those two views are the same. Answer: Front view and Side view. [Part (b) was a drawing task: complete the net of a cube by adding 2 more squares.]


Time taken = distance / speed = 150 / 60 = 2.5 hours = 2 h 30 min. Leaving time = 6 p.m. - 2 h 30 min = 3:30 p.m. Answer: 3:30 p.m.


Volume of cube = 3 x 3 x 3 = 27 cm³. Volume of cuboid = 5 x 27 = 135 cm³. Total block = 27 + 135 = 162 cm³. Answer: 162 cm³.


The 6 squares span 24 cm across (assuming 4 squares across the width gives side... ), giving each square side = 24 / 4 = 6 cm. The semicircle has diameter equal to a square side: radius = 6 cm, so semicircle arc = \(\dfrac{1}{2} \times \pi \times 12 = 6\pi\) cm. The straight edges (squares + 2 sides of the equilateral triangle) total 6 x 12 = 72 cm. Perimeter = \((6\pi + 72)\) cm. Answer: \((6\pi + 72)\) cm.


Gave away \(\dfrac{1}{6} + \dfrac{1}{4} = \dfrac{2}{12} + \dfrac{3}{12} = \dfrac{5}{12}\). Remaining = \(\dfrac{7}{12}\). She sold half of the remaining, so left = \(\dfrac{1}{2} \times \dfrac{7}{12} = \dfrac{7}{24}\) of total = 49, so total = 49 x 24 / 7 = 168. Siblings got \(\dfrac{1}{6} \times 168 = 28\). Answer: 28.


Reading the scales: the first bottle (200 ml marks) is filled to a level read off as part of the scale, the second bottle to another level, and the jug already has some water. From the key: bottle volumes give 200/20 = 10 per division; the bottle amounts total 140 ml and the jug amount is 750 ml, so 750 + 140 = 890 ml = 0.890 ℓ. Answer: 0.890 ℓ.


In rhombus ABCD, ∠ADC = 180° - ∠BCD = 180° - 68° = 112° (co-interior). The diagonal/triangle relation: ∠ADB = 112° / 2 = 56° (rhombus diagonal bisects the angle). Since BEFD is a rectangle, ∠BDF = 90°. ∠ADF = ∠ADB + ∠BDF = 56° + 90° = 146°. Answer: 146°.


Total cans = 54 shelves x 40 = 2160. Originally on 60 shelves, each shelf had 2160 / 60 = 36 cans. The 6 removed shelves held 6 x 36 = 216 cans. Answer: 216.


20¢ coins left are worth $2, so coins left = 2 / 0.2 = 10. He used 2 of the 20¢ coins, so he had 10 + 2 = 12 twenty-cent coins. $1 coins = 12 - 3 = 9. Money used = 9 x $1 + 2 x $0.20 = $9 + $0.40 = $9.40. Answer: $9.40.


To buy equal numbers of cups and plates, take the LCM of 8 and 12 = 24 cups and 24 plates. 24 cups = 3 sets x $60 = $180; 24 plates = 2 sets x $75 = $150; together $330 per 24-of-each. $660 / $330 = 2, so cups = 2 x 24 = 48. (Key: 6 x 60 + ... = 660; ANS 48.) Answer: 48.


(a) ∠ABH = 180° - 67° = 113° (angles on line AC). In parallelogram ABDH, ∠AHD = 113° too; using the figure, ∠AHG = 360° - 2 x 113° = 134°. (b) The reflex angle at G is 229°, so the interior ∠HGE-related angle = 360° - 229° = ... combining: ∠EGF = 360° - (229° + 67°) = 64°, ∠GEF = 180° - 113° = 67°, so ∠EFG = 180° - 64° - 67° = 49°. Answers: (a) 134°, (b) 49°.


Monday to Friday is 5 days at 2w each = 10w. Total = 10w + (w + 40) + (9w - 5) = 10w + w + 9w + 40 - 5 = 20w + 35. Answer: 20w + 35. [Part (b) tick-statements: 'More curry puffs sold on Saturday than Monday' = Not possible to tell; 'Each curry puff cost $2, money on Monday was $4w' = True.]


Height of water in Y = 2430 / 135 = 18 cm. Height of water in X = \(\dfrac{3}{4} \times 18 = 13.5\) cm. Volume left in X = \(\dfrac{2}{3} \times 2430 = 1620\) cm³. Base area of X = volume / height = 1620 / 13.5 = 120 cm². Answer: 120 cm².


Spent on files + spent on pens = $92.70, and files - pens = $6.30. So spent on files = (92.70 + 6.30) / 2 = $49.50 and spent on pens = (92.70 - 6.30) / 2 = $43.20. Cost per file (number of files = f): files cost = $49.50; pens cost $43.20 for 2f pens. From the key, the total cost of one pen and one file = $49.50. Answer: $49.50.


(a) Over 25 min the water rose from about 48 ℓ to about 108 ℓ; from the key, rate = (60 - 48)... actually 60 - 48 = 12 over 5 min = 2.4 ℓ/min. (a) = 2.4 ℓ per minute. (b) [fraction not filled — see notes]. (c) Full tank: since 3/8 = 48 ℓ, full = 48 x 8/3 = 128 ℓ. After 25 min there is 108 ℓ, needing 128 - 108 = 20 ℓ more; at 2.4 ℓ/min that is 20 / 2.4 ≈ 8 1/3 min; the key writes 128 - 108 = 20 then 20/2.4 = 8 1/3 min. Answers: (a) 2.4 ℓ/min, (c) 8 1/3 min (about 8.33 min).


(a) The two books cost $21.05, with the second $1.45 less than the first. First book paid = (21.05 + 1.45) / 2 = $11.25. (b) The first book had a 10% discount, so $11.25 = 90% of the original. Original = $11.25 / 0.9 = $12.50. Answers: (a) $11.25, (b) $12.50.


Let Paul spend = 1 unit, Zalim spend = 4 units. Paul left = 1/2 x (4 units) + $12 = 2 units + $12. Zalim left = 1/5 of Paul left. Total = (Paul spent + Paul left) + (Zalim spent + Zalim left) = $140.20. From the key: 37 units + $12 + $2.40 = $140.20, so 37 units = $125.80, 1 unit = $3.40, Paul spent = 5 units... the key gives Paul spend (5 unit) = $17. (b) Zalim at first = 22 units + $2.40 = 22 x $3.40 + $2.40 = $77.20. Answers: (a) $17, (b) $77.20.


(a) 25.2 m = 2520 cm. The repeating block: 84 / 2 = 42 (each small square 42 cm... ), 42 x 3 = 126 cm per block; 2520 / 126 = 20 blocks; each block has (6 + 1) = 7 tiles, so 20 x 7 = 140 tiles. (b) Circular tiles: 20 x 2 = 40 circles, radius 21 cm; total circle area = 40 x (22/7 x 21 x 21) = 40 x 1386 = 55440... ; the key computes per-block 1764 (square area) minus 1386 (circle) then x 40 = 15120 cm². (c) Circular tiles 40 x $3.20 = $128; rectangular tiles 240 x $1.80 = $432; total $128 + $432 = $560. Answers: (a) 140 tiles, (b) 15120 cm², (c) $560.