[
{
"index": 14673,
"id": 25904,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Each angle of the equilateral triangle is 60°.
From the fold, ∠b = 180° − 77° − 60° = 43°.
Then ∠a = 180° − 43° − 43° = 94°.
Printed key: 94°",
"answers": [
"94",
null,
null,
null
],
"correct_index": null
},
{
"index": 14674,
"id": 25905,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) Initial water = 2 × 15 × 15 = 450 cm³.
(b) Leak rate: from 600 cm³ (7 a.m.) the reading rose 150 cm³ per hour, so 1 hour = 150 cm³.
Full con",
"answers": [
"450",
"3",
null,
null
],
"correct_index": null
},
{
"index": 14675,
"id": 25906,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) The number of circles on one side is twice the figure number, so 12 circles per side -> 12 ÷ 2 = Figure 6.
(b) The number of squares in Figure ",
"answers": [
"6",
"225",
"89",
null
],
"correct_index": null
},
{
"index": 14676,
"id": 25907,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Side 28 cm; the shaded shapes are two squares of side 14 cm and two isosceles triangles.
One small square = 14 × 14 = 196 cm²; two squares = 392 cm",
"answers": [
"343",
null,
null,
null
],
"correct_index": null
},
{
"index": 14677,
"id": 25908,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Anna keeps 7/9 of her beads; Brenda keeps 3/7 of hers.
Setting them equal: 7/9 × Anna = 3/7 × Brenda, so 21/27...
gives 49 units (Anna) = 27 uni",
"answers": [
"\\(\\dfrac{24}{59}\\)",
"\\(\\dfrac{216}{531}\\)",
"\\(\\dfrac{168}{531}\\)",
"\\(\\dfrac{59}{24}\\)"
],
"correct_index": 0
},
{
"index": 14678,
"id": 25909,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Add the place values: 70 000 + 9000 + 200 + 5 = 79 205.",
"answers": [
"70 925",
"79 025",
"79 205",
"79 250"
],
"correct_index": 2
},
{
"index": 14679,
"id": 25910,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "In 458 321 the digit 4 occupies the hundred-thousands place (400 000).",
"answers": [
"hundreds",
"thousands",
"ten thousands",
"hundred thousands"
],
"correct_index": 3
},
{
"index": 14680,
"id": 25911,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Convert to sixths: 7/6, 4/3 = 8/6, 1 1/2 = 9/6.
Greatest to smallest: 9/6, 8/6, 7/6, i.e. 1 1/2, 4/3, 7/6.",
"answers": [
"\\(\\dfrac{7}{6}\\) , \\(\\dfrac{4}{3}\\) , \\(1\\dfrac{1}{2}\\)",
"\\(\\dfrac{4}{3}\\) , \\(\\dfrac{7}{6}\\) , \\(1\\dfrac{1}{2}\\)",
"\\(1\\dfrac{1}{2}\\) , \\(\\dfrac{4}{3}\\) , \\(\\dfrac{7}{6}\\)",
"\\(1\\dfrac{1}{2}\\) , \\(\\dfrac{7}{6}\\) , \\(\\dfrac{4}{3}\\)"
],
"correct_index": 2
},
{
"index": 14681,
"id": 25912,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "A typical pear has a mass of about 120 g.
12 g is far too light, while 1200 g (1.2 kg) and 12 000 g (12 kg) are far too heavy.",
"answers": [
"12 g",
"120 g",
"1200 g",
"12 000 g"
],
"correct_index": 1
},
{
"index": 14682,
"id": 25913,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "0.10 lies between 0.08 and 0.17.
0.01 is too small; 0.18 and 0.90 are too large.",
"answers": [
"0.01",
"0.10",
"0.18",
"0.90"
],
"correct_index": 1
},
{
"index": 14683,
"id": 25914,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "From 2.0 kg to 2.5 kg there are 10 intervals, so each interval is 0.05 kg.
A is 4 intervals past 2.5 kg: 2.5 + 4 x 0.05 = 2.70 kg.",
"answers": [
"2.70 kg",
"2.75 kg",
"2.90 kg",
"3.00 kg"
],
"correct_index": 0
},
{
"index": 14684,
"id": 25915,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Volume = length x breadth x height = 5 x 5 x 8 = 200 cm³.",
"answers": [
"40 cm³",
"200 cm³",
"240 cm³",
"320 cm³"
],
"correct_index": 1
},
{
"index": 14685,
"id": 25916,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "48 posters is 48 ÷ 6 = 8 times as many as 6 posters, so it takes 8 x 2 = 16 min.",
"answers": [
"8 min",
"12 min",
"16 min",
"24 min"
],
"correct_index": 2
},
{
"index": 14686,
"id": 25917,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Angles q, r and s lie on one side of the straight line AB at the same point, so they sum to 180°.",
"answers": [
"\\(\\angle r = \\angle u\\)",
"\\(\\angle q + \\angle r = 180°\\)",
"\\(\\angle q + \\angle r + \\angle s = 180°\\)",
"\\(\\angle q + \\angle r + \\angle s + \\angle t = 360°\\)"
],
"correct_index": 2
},
{
"index": 14687,
"id": 25918,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "The hundreds digit is 9 (≥5), so round up: 87 954 rounds to 88 000.",
"answers": [
"80 000",
"87 000",
"88 000",
"90 000"
],
"correct_index": 2
},
{
"index": 14688,
"id": 25919,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Convert to cm: Ali 160 cm, Bala 132 cm, Chenle 145 cm, Danial 150 cm.
The tallest is Ali (160 cm).",
"answers": [
"Ali",
"Bala",
"Chenle",
"Danial"
],
"correct_index": 0
},
{
"index": 14689,
"id": 25920,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Purple : yellow = 56 : 24.
Dividing both by 8 gives 7 : 3.",
"answers": [
"3 : 7",
"7 : 3",
"3 : 10",
"7 : 10"
],
"correct_index": 1
},
{
"index": 14690,
"id": 25921,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Evaluate: 32÷100 = 0.32, 32÷1000 = 0.032, 320÷100 = 3.2, 320÷1000 = 0.32.
The greatest is 320÷100 = 3.2.",
"answers": [
"\\(32 \\div 100\\)",
"\\(32 \\div 1000\\)",
"\\(320 \\div 100\\)",
"\\(320 \\div 1000\\)"
],
"correct_index": 2
},
{
"index": 14691,
"id": 25922,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "2/3 of the number is 12, so 1/3 is 6 and the whole number is 18.
Half of 18 is 9.",
"answers": [
"8",
"9",
"18",
"4"
],
"correct_index": 1
},
{
"index": 14692,
"id": 25923,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "The smallest cuboid that contains the solid is 2 x 2 x 2 = 8 unit cubes.
The figure shown has 4 cubes, so 8 - 4 = ...
(A 2x2x2 cuboid holds 8 cu",
"answers": [
"5",
"7",
"12",
"22"
],
"correct_index": 1
},
{
"index": 14693,
"id": 25924,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Brackets first: 6 + 8 = 14.
Then 14 ÷ 2 = 7, 7 x 3 = 21.
Finally 50 - 21 = 29.",
"answers": [
"29",
null,
null,
null
],
"correct_index": null
},
{
"index": 14694,
"id": 25925,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Rate = total volume ÷ time = 28 ℓ ÷ 7 min = 4 ℓ/min.",
"answers": [
"4",
null,
null,
null
],
"correct_index": null
},
{
"index": 14695,
"id": 25926,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64...
The largest one below 60 is 56.",
"answers": [
"56",
null,
null,
null
],
"correct_index": null
},
{
"index": 14696,
"id": 25927,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "45 ÷ 200 = 45/200.
Divide numerator and denominator by 5: 9/40, which is in simplest form.",
"answers": [
"\\(\\dfrac{9}{40}\\)",
"\\(\\dfrac{45}{200}\\)",
"\\(\\dfrac{9}{20}\\)",
"\\(\\dfrac{18}{80}\\)"
],
"correct_index": 0
},
{
"index": 14697,
"id": 25928,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "5 ÷ 9 = 0.555..., so 4 5/9 = 4.555..., which rounds to 4.56 (2 d.p.).",
"answers": [
"4.56",
null,
null,
null
],
"correct_index": null
},
{
"index": 14698,
"id": 25929,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Interest = 2% of \\(\\$20\\) 000 = 2/100 x \\(\\$20\\) 000 = \\(\\$400\\).",
"answers": [
"400",
null,
null,
null
],
"correct_index": null
},
{
"index": 14699,
"id": 25930,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "After Jackson gives 10 chocolates, Kala has 40 + 10 + 10 = 60 more than Jackson.
Since Kala = 5 x Jackson, the difference of 4 units = 60, so 1 uni",
"answers": [
"15",
null,
null,
null
],
"correct_index": null
},
{
"index": 14700,
"id": 25931,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "The right angle is at A, with legs AB = 8 cm and AC = 6 cm.
Area = 1/2 x 8 x 6 = 24 cm².",
"answers": [
"24",
null,
null,
null
],
"correct_index": null
},
{
"index": 14701,
"id": 25932,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Double the first set: 4 pencils + 8 notebooks = \\(\\$52\\). Subtract the second set (4 pencils + 2 notebooks = \\(\\$22\\)): 6 notebooks = \\(\\$30\\), so 1 n",
"answers": [
"5",
null,
null,
null
],
"correct_index": null
},
{
"index": 14702,
"id": 25933,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Total area = 12 units (the largest oval).
Unshaded area = 12u - 3u = ...
per key: total = 12u, unshaded = 10u - 3u = 7u, so fraction unshaded = ",
"answers": [
"\\(\\dfrac{7}{12}\\)",
"\\(\\dfrac{5}{12}\\)",
"\\(\\dfrac{3}{12}\\)",
"\\(\\dfrac{10}{12}\\)"
],
"correct_index": 0
},
{
"index": 14703,
"id": 25934,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Total time 2.00 to 4.50 pm = 2 h 50 min.
First hour = \\(\\$6\\). Remaining 1 h 50 min = 110 min = 4 blocks of 30 min (4 x \\(\\$2.50\\) = \\(\\$10\\)). Tot",
"answers": [
"16",
null,
null,
null
],
"correct_index": null
},
{
"index": 14704,
"id": 25935,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "After completing rhombus ABCD on the dot grid, the measured angle BAD is 70°.
(Key Q29b = 70°.)",
"answers": [
"70",
null,
null,
null
],
"correct_index": null
},
{
"index": 14705,
"id": 25936,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Angle DEF = 58°, so along straight line DA the angle CFE folds: ∠CFE = 180° - 58° - 90° = 32°.
The fold makes ∠AFB = 90° - 32° - 32° = 26°.
(Key",
"answers": [
"26",
null,
null,
null
],
"correct_index": null
},
{
"index": 14706,
"id": 25937,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "There are 12 rectangles in total and 5 are shaded, so the fraction shaded is 5/12.",
"answers": [
"\\(\\dfrac{5}{12}\\)",
"\\(\\dfrac{7}{12}\\)",
"\\(\\dfrac{5}{7}\\)",
"\\(\\dfrac{1}{2}\\)"
],
"correct_index": 0
},
{
"index": 14707,
"id": 25938,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "VZY is a straight line (180°).
At Z there is a right angle (90°) and an angle of 32°.
So ∠a = 180° - 90° - 32° = 58°.",
"answers": [
"58",
null,
null,
null
],
"correct_index": null
},
{
"index": 14708,
"id": 25939,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Tank volume = 35 x 8 x 12 = 3360 cm³.
The empty (unfilled) part is 2/5: 2/5 x 3360 = 1344 cm³ = 1344 ml.",
"answers": [
"1344",
null,
null,
null
],
"correct_index": null
},
{
"index": 14709,
"id": 25940,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "WX is parallel to ZY (trapezium), so co-interior angles ∠XWZ + ∠WZY = 180° — True.
For (b): with ∠Y = 120° and WZ = WX, working through the angles ",
"answers": [
"(a) True, (b) False",
"(a) False, (b) True",
"(a) True, (b) Not possible to tell",
"(a) Not possible to tell, (b) False"
],
"correct_index": 0
},
{
"index": 14710,
"id": 25941,
"type": 2,
"flags": [
"ANS0(20)_NOT_IN_SOLUTION"
],
"solution_preview": "Opposite triangles in such a figure have equal areas, and each pair (W+Z and X+Y) is half the rectangle.",
"answers": [
"20",
null,
null,
null
],
"correct_index": null
},
{
"index": 14711,
"id": 25942,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Before buying, he had 9 - 2 1/2 = 6 1/2 kg.
Adding back what he used: 6 1/2 + 4 3/5 = 11 1/10 kg at first.",
"answers": [
"\\(11\\dfrac{1}{10}\\) kg",
"\\(6\\dfrac{1}{2}\\) kg",
"\\(11\\dfrac{9}{10}\\) kg",
"\\(7\\dfrac{1}{10}\\) kg"
],
"correct_index": 0
},
{
"index": 14712,
"id": 25943,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "The 24 extra cars have 24 x 4 = 96 wheels.
Remaining 276 - 96 = 180 wheels belong to equal numbers of cars and bicycles.
Each car+bicycle set ha",
"answers": [
"30",
null,
null,
null
],
"correct_index": null
},
{
"index": 14713,
"id": 25944,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "The difference 3.09 - 1.05 = 2.04 kg stays the same and equals 3 units (B is 4 units, A is 1 unit).
So 1 unit = 0.68 kg = A after removal.
Remov",
"answers": [
"0.37",
null,
null,
null
],
"correct_index": null
},
{
"index": 14714,
"id": 25945,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Total of 6 boys = 6 x 52 = 312 kg.
Total of remaining 4 boys = 4 x 48 = 192 kg.
The 2 boys who left = 312 - 192 = 120 kg, so their average = 120",
"answers": [
"60",
null,
null,
null
],
"correct_index": null
},
{
"index": 14715,
"id": 25946,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Total pocket money in a week = \\(\\$8\\) x 7 = \\(\\$56\\).
She spends \\(\\$5.60\\) x 5 = \\(\\$28\\) on weekdays, so she saves \\(\\$56\\) - \\(\\$28\\) = \\(\\$28\\",
"answers": [
"10",
null,
null,
null
],
"correct_index": null
},
{
"index": 14716,
"id": 25947,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Total = 16 equal units = 80, so 1 unit = 5 students.
(a) Badminton + Table Tennis = 10 units = 50 students.
(b) Basketball = 30 students; 30/80 ",
"answers": [
"50",
"37.5",
null,
null
],
"correct_index": null
},
{
"index": 14717,
"id": 25948,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Make the mango parts equal: Shop A 4:3 x2 = 8:6, Shop B 3:2 x3 = 9:6.
Apples differ by 9 - 8 = 1 unit = 70.
Shop B total = 9 + 6 = 15 units = 15",
"answers": [
"1050",
null,
null,
null
],
"correct_index": null
},
{
"index": 14718,
"id": 25949,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) Triangle ABG is isosceles (AB = BG) with base angle 65°, so ∠ABG = 180° - 65° - 65° = 50°.
(b) ∠DCF = 180° - 112° = 68° (rhombus).
In triang",
"answers": [
"50",
"29",
null,
null
],
"correct_index": null
},
{
"index": 14719,
"id": 25950,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) Discount = 35% of (2 x \\(\\$450\\) = \\(\\$900\\)) = 35/100 x \\(\\$900\\) = \\(\\$315\\).
(b) Usual backpack price = 40% x \\(\\$450\\) = \\(\\$180\\).
Disc",
"answers": [
"315",
"117",
null,
null
],
"correct_index": null
},
{
"index": 14720,
"id": 25951,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) Total discount over the original 68 files = 68 x \\(\\$3.40\\) = \\(\\$231.20\\).
This pays for 19 extra files less the \\(\\$3.20\\) left: 19 files = \\",
"answers": [
"12",
"1047.20",
null,
null
],
"correct_index": null
},
{
"index": 14721,
"id": 25952,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Ali keeps 2/3, Betty keeps 3/5; these are equal.
Letting equal leftover = L, Ali = 3/2 L (in units), Betty = 5/3 L; working in units the total is 1",
"answers": [
"(a) $3000, (b) $112.50",
"(a) $2700, (b) $112.50",
"(a) $3000, (b) $450",
"(a) $2700, (b) $150"
],
"correct_index": 0
},
{
"index": 14722,
"id": 25953,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) QRST is a square; area = 4 x area of triangle PRQ = 4 x 16 = 64 cm², so side RQ = 8 cm.
(b) Areas: square QRST = 64; triangle SRZ = 1/2 x 8 x 5",
"answers": [
"8",
"278.5",
null,
null
],
"correct_index": null
},
{
"index": 14723,
"id": 25954,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Eighty thousand = 80 000; two hundred = 200.
So 80 000 + 200 = 80 200.
Answer: 80 200.",
"answers": [
"8200",
"80 200",
"800 200",
"820 000"
],
"correct_index": 1
},
{
"index": 14724,
"id": 25955,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "\\(\\dfrac{1}{50}=\\dfrac{2}{100}=0.02\\).
So \\(1\\dfrac{1}{50}=1.02\\).
Answer: 1.02.",
"answers": [
"1.02",
"1.15",
"1.2",
"1.5"
],
"correct_index": 0
},
{
"index": 14725,
"id": 25956,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "27 words is 3 times 9 words (27 / 9 = 3).
Time = 8 x 3 = 24 seconds.
Answer: 24 seconds.",
"answers": [
"16 seconds",
"24 seconds",
"26 seconds",
"32 seconds"
],
"correct_index": 1
},
{
"index": 14726,
"id": 25957,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "The clock shows 8.50 (hour hand near 9, minute hand on 10 = 50 min), i.e. 20 50 in 24-hour evening time.
15 minutes after 20 50 is 21 05.
Answer",
"answers": [
"20 35",
"20 50",
"21 05",
"22 58"
],
"correct_index": 2
},
{
"index": 14727,
"id": 25958,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Volume = length x breadth x height = 5 x 5 x 2 = 50 cm³.
Answer: 50 cm³.",
"answers": [
"10 cm³",
"20 cm³",
"50 cm³",
"100 cm³"
],
"correct_index": 2
},
{
"index": 14728,
"id": 25959,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Each grid square is 1 cm.
Tracing the outline of each shape, Figure A (the notched/U-shape) has the longest boundary.
Answer: Figure A.",
"answers": [
"Figure A",
"Figure B",
"Figure C",
"Figure D"
],
"correct_index": 0
},
{
"index": 14729,
"id": 25960,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "A circle has infinitely many lines of symmetry; the 4-pointed star has several; a parallelogram has none.
The arrow has exactly one line of symmetr",
"answers": [
"Circle",
"Four-pointed star",
"Arrow",
"Parallelogram"
],
"correct_index": 2
},
{
"index": 14730,
"id": 25961,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Three lines pass through the point.
∠a and ∠c are vertically opposite angles (∠a between R and the upper line; ∠c between S and the lower line), so",
"answers": [
"∠a = ∠c",
"∠b = ∠e",
"∠a + ∠c = 180°",
"∠a + ∠b + ∠c = 180°"
],
"correct_index": 0
},
{
"index": 14731,
"id": 25962,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Rounded to the nearest hundred gives 24 000 means the number lies in 23 950 to 24 049.
Of the options, only 24 009 rounds to 24 000.
(23 099 to ",
"answers": [
"23 099",
"23 940",
"24 009",
"24 050"
],
"correct_index": 2
},
{
"index": 14732,
"id": 25963,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "The figure that has exactly one third of its area shaded is option (4).
Answer: option (4).",
"answers": [
"Cross of 5 squares with 1 shaded",
"Square with a shaded triangle",
"Hexagon split into 6 triangles, 2 shaded",
"Figure of squares with one shaded"
],
"correct_index": 3
},
{
"index": 14733,
"id": 25964,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Footballs = 15% of 40 = 6.
Volleyballs = 35% of 40 = 14.
Rest = 40 - 6 - 14 = 20, split equally so basketballs = 10.
Footballs + basketballs ",
"answers": [
"10",
"16",
"20",
"26"
],
"correct_index": 1
},
{
"index": 14734,
"id": 25965,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Total mass = 3 x 55 = 165 kg.
John + Angel = 165 - 56 = 109 kg.
With John - Angel = 11: John = (109 + 11) / 2 = 60 kg (Angel = 49 kg).
Answer",
"answers": [
"54.5 kg",
"60 kg",
"98 kg",
"100 kg"
],
"correct_index": 1
},
{
"index": 14735,
"id": 25966,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Cubes may be added only where they do not change the top view or front view outline.
Filling the hidden gaps behind the visible solid allows up to ",
"answers": [
"1",
"2",
"3",
"5"
],
"correct_index": 3
},
{
"index": 14736,
"id": 25967,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Square perimeter = 4 x 0.2 = 0.8 m.
Triangle perimeter = 3 x 0.24 = 0.72 m.
Total = 0.8 + 0.72 = 1.52 m.
Answer: 1.52 m.",
"answers": [
"0.08 m",
"0.44 m",
"0.76 m",
"1.52 m"
],
"correct_index": 3
},
{
"index": 14737,
"id": 25968,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "In triangle ABC each angle is 60°.
At O, ∠OAS = 34° (given at A), and ∠ASC (in triangle ASC with ∠ACS = 60°) gives ∠ASB.
∠BSP works out to 94°.<",
"answers": [
"34°",
"86°",
"94°",
"146°"
],
"correct_index": 2
},
{
"index": 14738,
"id": 25969,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "2.4 ÷ 200 = 2.4 ÷ 2 ÷ 100 = 1.2 ÷ 100 = 0.012.
Answer: 0.012.",
"answers": [
"0.012",
null,
null,
null
],
"correct_index": null
},
{
"index": 14739,
"id": 25970,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "18% of 600 = 0.18 x 600 = 108.
Answer: 108.",
"answers": [
"108",
null,
null,
null
],
"correct_index": null
},
{
"index": 14740,
"id": 25971,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "\\(\\dfrac{4}{7}\\times\\dfrac{49}{16}=\\dfrac{4\\times49}{7\\times16}=\\dfrac{7}{4}=1\\dfrac{3}{4}\\).
Answer: \\(1\\dfrac{3}{4}\\).",
"answers": [
"\\(1\\dfrac{3}{4}\\)",
"\\(1\\dfrac{1}{4}\\)",
"\\(2\\dfrac{1}{4}\\)",
"\\(\\dfrac{7}{4}\\)"
],
"correct_index": 0
},
{
"index": 14741,
"id": 25972,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Lily starts facing the Staff Room (south).
A 1/4-turn (90°) right faces her to the Science Garden.
A 225° anticlockwise turn from there (225° = ",
"answers": [
"Basketball Court",
"Foyer",
"Library",
"Computer Lab"
],
"correct_index": 0
},
{
"index": 14742,
"id": 25973,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "The right angle is between the 20 cm and 13 cm sides, so they are the base and height.
Area = 1/2 x 20 x 13 = 130 cm².
Answer: 130 cm².",
"answers": [
"130",
null,
null,
null
],
"correct_index": null
},
{
"index": 14743,
"id": 25974,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) 40 − (20 − 4) ÷ 4 × 3 = 40 − 16 ÷ 4 × 3 = 40 − 4 × 3 = 40 − 12 = 28.
(b) Multiples of 8: ..., 48, 56, 64.
The largest below 60 is 56.
Ans",
"answers": [
"28",
"56",
null,
null
],
"correct_index": null
},
{
"index": 14744,
"id": 25975,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "\\(2-\\dfrac{2}{3}-\\dfrac{1}{6}=2-\\dfrac{4}{6}-\\dfrac{1}{6}=2-\\dfrac{5}{6}=1\\dfrac{1}{6}\\).
Answer: \\(1\\dfrac{1}{6}\\).",
"answers": [
"\\(1\\dfrac{1}{6}\\)",
"\\(1\\dfrac{1}{2}\\)",
"\\(\\dfrac{5}{6}\\)",
"\\(1\\dfrac{5}{6}\\)"
],
"correct_index": 0
},
{
"index": 14745,
"id": 25976,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "7.68 + 3.40 = 11.08.
Answer: 11.08.",
"answers": [
"11.08",
null,
null,
null
],
"correct_index": null
},
{
"index": 14746,
"id": 25977,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Convert all to kg: 3.055 kg; 3 kg 250 g = 3.25 kg; \\(3\\dfrac{1}{8}\\) kg = 3.125 kg.
Heaviest to lightest: 3.25 > 3.125 > 3.055, i.e. 3 kg 250 g, \\(",
"answers": [
"3 kg 250 g, \\(3\\dfrac{1}{8}\\) kg, 3.055 kg",
"3.055 kg, \\(3\\dfrac{1}{8}\\) kg, 3 kg 250 g",
"\\(3\\dfrac{1}{8}\\) kg, 3 kg 250 g, 3.055 kg",
"3 kg 250 g, 3.055 kg, \\(3\\dfrac{1}{8}\\) kg"
],
"correct_index": 0
},
{
"index": 14747,
"id": 25978,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "The jug is marked up to 2 ℓ.
The water level reads 1800 mℓ (i.e. 1.8 ℓ).
Answer: 1800 mℓ.",
"answers": [
"1800",
null,
null,
null
],
"correct_index": null
},
{
"index": 14748,
"id": 25979,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) Reading the line graph at 08 10 gives 64°C.
(b) The temperature is 80°C and above from 08 15 to 08 35, a span of 20 minutes.
Answers: 64°C; ",
"answers": [
"64",
"20",
null,
null
],
"correct_index": null
},
{
"index": 14749,
"id": 25980,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "1 bracelet = 205 ÷ 5 = 41 cm.
16 bracelets = 41 x 16 = 656 cm = 6.56 m.
Answer: 6.56 m.",
"answers": [
"6.56",
null,
null,
null
],
"correct_index": null
},
{
"index": 14750,
"id": 25981,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) On the 1 cm grid, base EF = 2 cm and height (from B down to line FC) = 4 cm, so area = 1/2 x 2 x 4 = 4 cm².
(b) Triangle BEC shares the same ba",
"answers": [
"4",
"BEC",
null,
null
],
"correct_index": null
},
{
"index": 14751,
"id": 25982,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Total age = 10 x 35 = 350.
After the 53-year-old leaves: 350 − 53 = 297 for 9 members.
Average = 297 ÷ 9 = 33 years.
Answer: 33 years.",
"answers": [
"33",
null,
null,
null
],
"correct_index": null
},
{
"index": 14752,
"id": 25983,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Total money = 80 + 45 = 125.
Percentage spent = 80/125 x 100% = 64%.
Answer: 64%.",
"answers": [
"64",
null,
null,
null
],
"correct_index": null
},
{
"index": 14753,
"id": 25984,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Let big bags = b.
The 30 extra small bags hold 30 x 4 = 120 cookies.
Remaining cookies = 2360 − 120 = 2240, shared by equal numbers of small and",
"answers": [
"224",
null,
null,
null
],
"correct_index": null
},
{
"index": 14754,
"id": 25985,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "When the rectangle is folded, the fold maps the corner so the angle at Y is 56°.
Using the fold symmetry and the straight angle / corner of the rec",
"answers": [
"118",
null,
null,
null
],
"correct_index": null
},
{
"index": 14755,
"id": 25986,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Left: 1/5 C + 1/4 S = 736.
Also 4/5 C + 3/4 S = 3262 − 736 = 2526.
From total C + S = 3262.
Working as in the key: 1/5 C = 318, so C = 1590; ",
"answers": [
"1272",
null,
null,
null
],
"correct_index": null
},
{
"index": 14756,
"id": 25987,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "a, b, c lie on the straight line PQ, so they sum to 180°.
Total units = 2 + 6 + 1 = 9; 1 unit = 180° ÷ 9 = 20°.
Largest = 6 x 20 = 120°, smalles",
"answers": [
"160",
null,
null,
null
],
"correct_index": null
},
{
"index": 14757,
"id": 25988,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Blue − green = 5 − 2 = 3 units = 42, so 1 unit = 14.
Total units = 6 + 5 + 2 = 13; total marbles = 13 x 14 = 182.
Answer: 182 marbles.",
"answers": [
"182",
null,
null,
null
],
"correct_index": null
},
{
"index": 14758,
"id": 25989,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "50 g package = 80 cents.
370 g package: first 100 g = \\(\\$1.20\\), then 3 additional 100 g steps (to cover up to 400 g) at \\(\\$1.20\\) each = \\(\\$1.2",
"answers": [
"5.60",
null,
null,
null
],
"correct_index": null
},
{
"index": 14759,
"id": 25990,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "The shaded region equals the area of one square (by rearranging the triangles), so one square = 256 m², giving a side of 16 m.
AC spans two square ",
"answers": [
"32",
null,
null,
null
],
"correct_index": null
},
{
"index": 14760,
"id": 25991,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) Discount = 15% x \\(\\$6000\\) = \\(\\$900\\).
(b) Discounted price = \\(\\$6000\\) − \\(\\$900\\) = \\(\\$5100\\). With 8% GST: \\(\\$5100\\) x 108% = \\(\\$5508\\",
"answers": [
"900",
"5508",
null,
null
],
"correct_index": null
},
{
"index": 14761,
"id": 25992,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Difference stays constant: 1090 − 320 = 770.
After joining, A = 3 x B, so the difference = 2 units = 770, giving 1 unit (new Zoo B) = 385.
Anima",
"answers": [
"65",
null,
null,
null
],
"correct_index": null
},
{
"index": 14762,
"id": 25993,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "In triangle at the top: 180° − 29° − 32° = 119°, so its base angle = 180° − 119° = 61°.
In the other triangle: 180° − 31° − 42° = 107°, base angle ",
"answers": [
"46",
null,
null,
null
],
"correct_index": null
},
{
"index": 14763,
"id": 25994,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Tank volume = 54 x 16 x 24 = 20736 cm³.
(a) 1/4-filled = 5184 cm³; half-filled = 10368 cm³.
Water added by 8 pails = 10368 − 5184 = 5184 cm³, so",
"answers": [
"648",
"9",
null,
null
],
"correct_index": null
},
{
"index": 14764,
"id": 25995,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Total 360 in 11 : 4 means 15 units = 360, 1 unit = 24.
Black = 4 x 24 = 96; green + red = 11 x 24 = 264.
Red = 20% x 360 = 72; green = 264 − 72 ",
"answers": [
"7 : 8",
"8 : 7",
"4 : 11",
"3 : 5"
],
"correct_index": 0
},
{
"index": 14765,
"id": 25996,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) Apples + oranges = 336 x 2 = 672.
With oranges − apples = 140: oranges = (672 + 140) ÷ 2 = 406.
(b) Original total of 3 fruits = 332 x 3 = 9",
"answers": [
"406",
"382",
null,
null
],
"correct_index": null
},
{
"index": 14766,
"id": 25997,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Use 42 of the \\(\\$4.20\\) bundles (42 boxes + 42 sticks) = 42 x \\(\\$4.20\\) = \\(\\$176.40\\). Remaining: 1 box + 6 sticks. Best for the leftover: 1 box (\\",
"answers": [
"189.05",
null,
null,
null
],
"correct_index": null
},
{
"index": 14767,
"id": 25998,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Overlap = 18 x 18 = 324 cm².
Unshaded (the two non-overlapping parts) = 2214 cm².
Following the key: 2214 − 324 = 1890; 1890 ÷ 3 = 630; 630 x 2 ",
"answers": [
"2450",
null,
null,
null
],
"correct_index": null
},
{
"index": 14768,
"id": 25999,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Let original rows = r.
Original chairs = 10r.
New chairs = 10r + 24 = 12(r − 6) = 12r − 72.
So 10r + 24 = 12r − 72, giving 2r = 96, r = 48 ro",
"answers": [
"480",
null,
null,
null
],
"correct_index": null
},
{
"index": 14769,
"id": 26000,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) Copies = sales ÷ price.
Sports = 1950 ÷ 6 = 325; Science = 1448 ÷ 4 = 362; Math = 1850 ÷ 5 = 370.
Math sold the most copies.
(b) Total sa",
"answers": [
"Math",
"1312",
null,
null
],
"correct_index": null
},
{
"index": 14770,
"id": 26001,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) Pages 1-9: 9 x 1 = 9 digits.
Pages 10-99: 90 x 2 = 180 digits.
Total = 9 + 180 = 189 digits.
(b) Remaining digits = 612 − 189 = 423, all ",
"answers": [
"189",
"240",
null,
null
],
"correct_index": null
},
{
"index": 14771,
"id": 26002,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Mandy + Nora's extra = 34 + 20 = 54, which equals 9 equal parts of the remaining-after-Penny (Olivia 1 part, Nora-extra aside, Mandy parts).
Follow",
"answers": [
"120",
null,
null,
null
],
"correct_index": null
},
{
"index": 14772,
"id": 26003,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Place values after the decimal point: 6 is tenths, 8 is hundredths, 7 is thousandths.
So the hundredths digit is 8.",
"answers": [
"5",
"6",
"7",
"8"
],
"correct_index": 3
},
{
"index": 14773,
"id": 26004,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "1 kg = 1000 g, so 52 g = 0.052 kg.
Therefore 23 kg 52 g = 23.052 kg.",
"answers": [
"23.025 kg",
"23.052 kg",
"23.502 kg",
"23.520 kg"
],
"correct_index": 1
},
{
"index": 14774,
"id": 26005,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "42 : 28 : 14.
Divide each term by the common factor 14: 42 ÷ 14 = 3, 28 ÷ 14 = 2, 14 ÷ 14 = 1.
So the ratio is 3 : 2 : 1.",
"answers": [
"2 : 3 : 1",
"2 : 4 : 6",
"3 : 2 : 1",
"6 : 4 : 2"
],
"correct_index": 2
},
{
"index": 14775,
"id": 26006,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "In 60 seconds (1 minute) it seals 120 packets.
30 minutes × 120 = 3600 packets.",
"answers": [
"3600",
"360",
"60",
"40"
],
"correct_index": 0
},
{
"index": 14776,
"id": 26007,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Fraction given = \\(\\dfrac{60}{240}=\\dfrac{1}{4}\\).
As a percentage, \\(\\dfrac{1}{4}\\times 100\\% = 25\\%\\).",
"answers": [
"20%",
"25%",
"75%",
"80%"
],
"correct_index": 1
},
{
"index": 14777,
"id": 26008,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "35% of \\(\\$1200\\) = \\(\\dfrac{35}{100}\\times 1200 = 420\\). He spent \\(\\$420\\) on food.",
"answers": [
"$180",
"$360",
"$420",
"$780"
],
"correct_index": 2
},
{
"index": 14778,
"id": 26009,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Line AB slopes downwards from upper-right to lower-left.
Comparing the grid slopes of the other lines, JK has the same slope (same horizontal and v",
"answers": [
"CD",
"EF",
"GH",
"JK"
],
"correct_index": 3
},
{
"index": 14779,
"id": 26010,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Triangle ABD has base AD = 15 cm and the perpendicular height AB = 7 cm.
Area = \\(\\dfrac{1}{2}\\times 15\\times 7 = 52.5\\) cm².",
"answers": [
"42 cm²",
"52.5 cm²",
"54 cm²",
"84 cm²"
],
"correct_index": 1
},
{
"index": 14780,
"id": 26011,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Inspecting the six marked angles in the concave figure, only 2 of them open wider than a right angle (more than 90°).
The rest are 90° or less.",
"answers": [
"6",
"2",
"3",
"4"
],
"correct_index": 1
},
{
"index": 14781,
"id": 26012,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Counting the unit cubes in the staircase solid (including the hidden ones supporting the upper cubes) gives a total of 10 unit cubes.",
"answers": [
"10",
"12",
"15",
"17"
],
"correct_index": 0
},
{
"index": 14782,
"id": 26013,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "As decimals: \\(\\dfrac{3}{7}\\approx 0.43\\), \\(\\dfrac{4}{5}=0.8\\), \\(\\dfrac{8}{9}\\approx 0.89\\).
Smallest to largest: \\(\\dfrac{3}{7},\\ \\dfrac{4}{5},\\",
"answers": [
"\\(\\dfrac{8}{9},\\ \\dfrac{3}{7},\\ \\dfrac{4}{5}\\)",
"\\(\\dfrac{8}{9},\\ \\dfrac{4}{5},\\ \\dfrac{3}{7}\\)",
"\\(\\dfrac{3}{7},\\ \\dfrac{4}{5},\\ \\dfrac{8}{9}\\)",
"\\(\\dfrac{3}{7},\\ \\dfrac{8}{9},\\ \\dfrac{4}{5}\\)"
],
"correct_index": 2
},
{
"index": 14783,
"id": 26014,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Total = 23 + 23 + 18 + 16 + 0 = 80.
Average = 80 ÷ 5 = 16.",
"answers": [
"23",
"20",
"18",
"16"
],
"correct_index": 3
},
{
"index": 14784,
"id": 26015,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "1505 kg ÷ 50 = 30.1 kg per pack.",
"answers": [
"30.1 kg",
"31 kg",
"300.1 kg",
"301 kg"
],
"correct_index": 0
},
{
"index": 14785,
"id": 26016,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Children = \\(\\dfrac{2}{3}\\times 270 = 180\\).
Boys = \\(\\dfrac{3}{5}\\) of the children = \\(\\dfrac{3}{5}\\times 180 = 108\\).",
"answers": [
"180",
"162",
"108",
"72"
],
"correct_index": 2
},
{
"index": 14786,
"id": 26017,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "200 × 0.78 ℓ = 156 ℓ.",
"answers": [
"14.6 ℓ",
"15.6 ℓ",
"146 ℓ",
"156 ℓ"
],
"correct_index": 3
},
{
"index": 14787,
"id": 26018,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Work inside the brackets first: \\(8\\div 4\\times 2 = 2\\times 2 = 4\\), so \\(35 + 4 = 39\\).
Then \\(35\\div 7 = 5\\).
So \\(198 + 5 - 39 = 203 - 39 = 1",
"answers": [
"164",
null,
null,
null
],
"correct_index": null
},
{
"index": 14788,
"id": 26019,
"type": 2,
"flags": [
"VERY_SHORT(21chars)"
],
"solution_preview": "\\(5 \\div 8 = 0.625\\).",
"answers": [
"0.625",
null,
null,
null
],
"correct_index": null
},
{
"index": 14789,
"id": 26020,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "40 ÷ 5 = 8, so each term on the right is 8 times the left.
24 ÷ 8 = 3.
The missing number is 3.",
"answers": [
"3",
null,
null,
null
],
"correct_index": null
},
{
"index": 14790,
"id": 26021,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "AOD is a straight line: \\(\\angle AOB + \\angle BOC + \\angle COD = 180°\\), so \\(\\angle COD = 180 - 90 - 58 = 32°\\).
COF is a straight line: \\(\\angle ",
"answers": [
"72",
null,
null,
null
],
"correct_index": null
},
{
"index": 14791,
"id": 26022,
"type": 2,
"flags": [
"EMPTY_SOLUTION"
],
"solution_preview": "",
"answers": [
"72",
null,
null,
null
],
"correct_index": null
},
{
"index": 14792,
"id": 26023,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "BCE is a straight line, so \\(\\angle BCD = 180 - 134 = 46°\\).
In a rhombus, opposite angles are equal and adjacent angles are supplementary, so \\(\\a",
"answers": [
"67",
null,
null,
null
],
"correct_index": null
},
{
"index": 14793,
"id": 26024,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "\\(\\dfrac{2}{3}\\times\\dfrac{5}{8}=\\dfrac{10}{24}=\\dfrac{5}{12}\\) (dividing top and bottom by 2).",
"answers": [
"\\(\\dfrac{5}{12}\\)",
"\\(\\dfrac{10}{24}\\)",
"\\(\\dfrac{7}{12}\\)",
"\\(\\dfrac{5}{24}\\)"
],
"correct_index": 0
},
{
"index": 14794,
"id": 26025,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Volume of a cuboid = length × breadth × height = 23 × 6 × 5 = 690 cm³.",
"answers": [
"690",
null,
null,
null
],
"correct_index": null
},
{
"index": 14795,
"id": 26026,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Group X = 57, Group Y = 33, Group Z = 75.
Highest = 75, lowest = 33.
Difference = 75 − 33 = 42.",
"answers": [
"42",
null,
null,
null
],
"correct_index": null
},
{
"index": 14796,
"id": 26027,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Replace each marker with (pencil + \\(\\$1.20\\)): 3 pencils + 7 pencils + 7 × \\(\\$1.20\\) = \\(\\$87.40\\). So 10 pencils + \\(\\$8.40\\) = \\(\\$87.40\\), giving",
"answers": [
"79",
null,
null,
null
],
"correct_index": null
},
{
"index": 14797,
"id": 26028,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Larger number = 3069 ÷ 9 = 341.
Rounded to the nearest hundred, 341 ≈ 300.",
"answers": [
"300",
null,
null,
null
],
"correct_index": null
},
{
"index": 14798,
"id": 26029,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "GST = 8% of \\(\\$2800\\) = \\(\\dfrac{8}{100}\\times 2800 = 224\\). Price after GST = \\(\\$2800\\) + \\(\\$224\\) = \\(\\$3024\\).",
"answers": [
"3024",
null,
null,
null
],
"correct_index": null
},
{
"index": 14799,
"id": 26030,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Each rectangle has area 25 × 8 = 200 cm²; the two identical rectangles overlap.
The shaded part is made of two triangles whose areas together equal",
"answers": [
"200",
null,
null,
null
],
"correct_index": null
},
{
"index": 14800,
"id": 26031,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Total height = 154 × 3 = 462 cm.
Abel (the shortest) = 146 cm, so Bernard + Carl = 462 − 146 = 316 cm.
Carl is taller than Bernard and both are ",
"answers": [
"159",
null,
null,
null
],
"correct_index": null
},
{
"index": 14801,
"id": 26032,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "\\(5\\dfrac{2}{5}=5.4\\), \\(1\\dfrac{3}{4}=1.75\\), \\(\\dfrac{4}{10}=0.4\\).
Left = \\(5.4 - 1.75 - 0.4 = 3.25 = 3\\dfrac{1}{4}\\) m.",
"answers": [
"\\(3\\dfrac{1}{4}\\)",
"\\(3\\dfrac{3}{4}\\)",
"\\(3\\dfrac{1}{2}\\)",
"\\(2\\dfrac{3}{4}\\)"
],
"correct_index": 0
},
{
"index": 14802,
"id": 26033,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "\\(1\\dfrac{7}{9}=\\dfrac{16}{9}\\).
\\(6\\times\\dfrac{16}{9}=\\dfrac{96}{9}=10\\dfrac{6}{9}=10\\dfrac{2}{3}\\) litres.",
"answers": [
"\\(10\\dfrac{2}{3}\\)",
"\\(10\\dfrac{6}{9}\\)",
"\\(6\\dfrac{7}{9}\\)",
"\\(9\\dfrac{1}{3}\\)"
],
"correct_index": 0
},
{
"index": 14803,
"id": 26034,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Total of 5 children = 5 × 48 = 240 kg.
Total of 6 people = 6 × 45 = 270 kg.
Peter's mass = 270 − 240 = 30 kg.",
"answers": [
"30",
null,
null,
null
],
"correct_index": null
},
{
"index": 14804,
"id": 26035,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "A, F and E lie on a straight line.
At F, \\(\\angle AFB + \\angle BFD + \\angle DFE = 180°\\).
Triangle ABF is isosceles (AB = BF) so \\(\\angle BAF = ",
"answers": [
"128",
null,
null,
null
],
"correct_index": null
},
{
"index": 14805,
"id": 26036,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Let the number of friends be n.
Yellow length = 1.4n + 0.6.
Red length = 1.8n − 2.2 (she is 2.2 m short).
The ribbons are the same length: 1.",
"answers": [
"7",
null,
null,
null
],
"correct_index": null
},
{
"index": 14806,
"id": 26037,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Double the first set: 4 files + 6 markers = \\(\\$30\\). Compare with 5 files + 6 markers = \\(\\$34.80\\).
The difference is 1 file = \\(\\$34.80\\) − \\(\\$",
"answers": [
"1.80",
null,
null,
null
],
"correct_index": null
},
{
"index": 14807,
"id": 26038,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) 70% were boys, so 30% were girls.
Girls = \\(\\dfrac{30}{100}\\times 560 = 168\\).
(b) Girls supporting Team A = 168 − 42 = 126.
Percentage =",
"answers": [
"168",
"75",
null,
null
],
"correct_index": null
},
{
"index": 14808,
"id": 26039,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Peter : Jason difference = 9 − 5 = 4 units = \\(\\$128\\), so 1 unit = \\(\\$32\\).
Peter − Chris = 9 − 2 = 7 units = 7 × \\(\\$32\\) = \\(\\$224\\).",
"answers": [
"224",
null,
null,
null
],
"correct_index": null
},
{
"index": 14809,
"id": 26040,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Let there be n students.
Total marks = 74n.
Top 3 total = 87 + 95 + 100 = 282.
The remaining (n − 3) students average 62: 74n − 282 = 62(n − ",
"answers": [
"8",
null,
null,
null
],
"correct_index": null
},
{
"index": 14810,
"id": 26041,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) Chocolate = \\(\\dfrac{1}{3}\\times 2535 = 845\\).
Remaining = 2535 − 845 = 1690.
Vanilla = \\(\\dfrac{3}{5}\\times 1690 = 1014\\).
(b) 1014 = 30",
"answers": [
"1014",
"35",
null,
null
],
"correct_index": null
},
{
"index": 14811,
"id": 26042,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) Rectangular tank volume = 19 × 14 × 15 = 3990 cm³.
Water = \\(\\dfrac{2}{3}\\times 3990 = 2660\\) cm³.
(b) Cubical tank volume = 15 × 15 × 15 = ",
"answers": [
"2660",
"0.04",
null,
null
],
"correct_index": null
},
{
"index": 14812,
"id": 26043,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Let each girl start with x stickers.
Keryn left = x − 352, Carol left = x − 84, and Carol = 5 × Keryn: x − 84 = 5(x − 352).
So x − 84 = 5x − 176",
"answers": [
"67",
"419",
null,
null
],
"correct_index": null
},
{
"index": 14813,
"id": 26044,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) DG = GC means G is the midpoint of DC, so DG = 16 cm.
Triangle BDG has base DG = 16 cm and height = side AB = 32 cm: area = \\(\\dfrac{1}{2}\\time",
"answers": [
"256",
"512",
null,
null
],
"correct_index": null
},
{
"index": 14814,
"id": 26045,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "B, O and C lie on a straight line, so \\(\\angle AOB = 180 - 127 = 53°\\).
(a) On the straight line BOC, \\(\\angle AOB + \\angle AOD + \\angle DOC = 180°",
"answers": [
"77",
"74",
null,
null
],
"correct_index": null
},
{
"index": 14815,
"id": 26046,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) 9.30 a.m.
to 11.45 a.m.
= 2 h 15 min.
First hour = \\(\\$1.20\\). Remaining 1 h 15 min = 3 half-hour blocks (part thereof) × \\(\\$1.00\\) = \\(",
"answers": [
"4.20",
"5.00",
null,
null
],
"correct_index": null
},
{
"index": 14816,
"id": 26047,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "The total number of squares in Figure n is \\((n+1)^2\\): 4, 9, 16, 25, 36, ...
(a) White squares increase by 2, 4, 4, 6, 6, ...
: 2, 4, 8, 12, 18",
"answers": [
"18",
"40",
"2500",
null
],
"correct_index": null
},
{
"index": 14817,
"id": 26048,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "The digit 3 is in the ten-thousands place, so its value is 30 000.
Answer: 30 000.",
"answers": [
"30",
"300",
"3000",
"30 000"
],
"correct_index": 3
},
{
"index": 14818,
"id": 26049,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "\\(\\dfrac{1}{50}=\\dfrac{2}{100}=0.02\\), so \\(1\\dfrac{1}{50}=1.02\\).
Answer: 1.02.",
"answers": [
"1.1",
"1.2",
"1.02",
"1.15"
],
"correct_index": 2
},
{
"index": 14819,
"id": 26050,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Figure 3 is a 3x3 grid (9 cells) with...
the correct figure showing exactly one quarter shaded is option 3.
Answer: option 3.",
"answers": [
"Figure 1",
"Figure 2",
"Figure 3",
"Figure 4"
],
"correct_index": 2
},
{
"index": 14820,
"id": 26051,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "There are 11 apples in total; 6 are unshaded (white).
Fraction unshaded = \\(\\dfrac{6}{11}\\).
Answer: \\(\\dfrac{6}{11}\\).",
"answers": [
"\\(\\dfrac{1}{2}\\)",
"\\(\\dfrac{5}{6}\\)",
"\\(\\dfrac{5}{11}\\)",
"\\(\\dfrac{6}{11}\\)"
],
"correct_index": 3
},
{
"index": 14821,
"id": 26052,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Using twelfths: \\(\\dfrac{11}{12}, \\dfrac{3}{4}=\\dfrac{9}{12}, \\dfrac{2}{3}=\\dfrac{8}{12}\\).
Largest to smallest: \\(\\dfrac{11}{12}, \\dfrac{3}{4}, \\d",
"answers": [
"\\(\\dfrac{11}{12}, \\dfrac{2}{3}, \\dfrac{3}{4}\\)",
"\\(\\dfrac{11}{12}, \\dfrac{3}{4}, \\dfrac{2}{3}\\)",
"\\(\\dfrac{3}{4}, \\dfrac{2}{3}, \\dfrac{11}{12}\\)",
"\\(\\dfrac{3}{4}, \\dfrac{11}{12}, \\dfrac{2}{3}\\)"
],
"correct_index": 1
},
{
"index": 14822,
"id": 26053,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "The height is the perpendicular distance from the opposite vertex C to base AB (or its extension).
CD is drawn perpendicular to AB, so the height i",
"answers": [
"AE",
"AF",
"CD",
"EB"
],
"correct_index": 2
},
{
"index": 14823,
"id": 26054,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "On the square grid, line CD has a particular slope; AF has the same slope (same direction), so AF is parallel to CD.
Answer: AF.",
"answers": [
"AF",
"BC",
"BE",
"DE"
],
"correct_index": 0
},
{
"index": 14824,
"id": 26055,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Examining the five marked angles of the pentagon-like figure, three of them are acute (less than 90°).
Answer: 3.",
"answers": [
"5",
"2",
"3",
"4"
],
"correct_index": 2
},
{
"index": 14825,
"id": 26056,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Brackets first: 6+12 = 18.
Then 18 ÷ 2 = 9, 9 × 3 = 27.
Finally 30 - 27 = 3.
Answer: 3.",
"answers": [
"18",
"2",
"3",
"27"
],
"correct_index": 2
},
{
"index": 14826,
"id": 26057,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "20 minutes is 4 times 5 minutes, so 4 × 10 = 40 stars.
Answer: 40.",
"answers": [
"10",
"40",
"50",
"200"
],
"correct_index": 1
},
{
"index": 14827,
"id": 26058,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "The interval from 6 to 7 is divided into 8 equal parts of 0.125 each...
A sits at the 6th mark (6 of 8 between 6 and 7): 6 + 6×0.125 = 6.75.
Ans",
"answers": [
"6.60",
"6.75",
"7.20",
"7.25"
],
"correct_index": 1
},
{
"index": 14828,
"id": 26059,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Side of square base = 36 ÷ 4 = 9 cm.
Volume = 9 × 9 × 10 = 810 cm³.
Answer: 810 cm³.",
"answers": [
"60 cm³",
"90 cm³",
"360 cm³",
"810 cm³"
],
"correct_index": 3
},
{
"index": 14829,
"id": 26060,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "In triangle ABC, ∠ACB = 65° and ∠A = 35°, so ∠ABC = 180°-35°-65° = 80°.
∠BDC (exterior/using the marked angles) works out to 37°.
Answer: 37° (k",
"answers": [
"37°",
"43°",
"65°",
"80°"
],
"correct_index": 0
},
{
"index": 14830,
"id": 26061,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Remaining plants = 12 - 5 = 7.
Soil needed = 7 × \\(\\dfrac{3}{8}\\) = \\(\\dfrac{21}{8}\\) = \\(2\\dfrac{5}{8}\\) kg.
Answer: \\(2\\dfrac{5}{8}\\) kg.",
"answers": [
"\\(1\\dfrac{7}{8}\\) kg",
"\\(2\\dfrac{5}{8}\\) kg",
"\\(4\\dfrac{1}{2}\\) kg",
"\\(4\\dfrac{5}{8}\\) kg"
],
"correct_index": 1
},
{
"index": 14831,
"id": 26062,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Let starting amount = m.
After spending: Ally = m-20, Bella = m-80, and m-20 = 3(m-80).
So m-20 = 3m-240, 220 = 2m, m = 110.
Bella had \\(\\$11",
"answers": [
"$100",
"$110",
"$140",
"$220"
],
"correct_index": 1
},
{
"index": 14832,
"id": 26063,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Common multiples of 3 and 4 are multiples of 12: 12, 24, 36, ...
Those smaller than 30 are 12 and 24.
Answer: 12, 24.",
"answers": [
"12",
"24",
null,
null
],
"correct_index": null
},
{
"index": 14833,
"id": 26064,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "0.45 × 80 = 36.
Answer: 36.",
"answers": [
"36",
null,
null,
null
],
"correct_index": null
},
{
"index": 14834,
"id": 26065,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "480 ml = 0.48 ℓ.
1.05 ℓ - 0.48 ℓ = 0.57 ℓ.
Answer: 0.57 ℓ.",
"answers": [
"0.57",
null,
null,
null
],
"correct_index": null
},
{
"index": 14835,
"id": 26066,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "\\(\\dfrac{2}{3} \\times \\dfrac{4}{9} = \\dfrac{2\\times4}{3\\times9} = \\dfrac{8}{27}\\).
Answer: \\(\\dfrac{8}{27}\\).",
"answers": [
"\\(\\dfrac{8}{27}\\)",
"\\(\\dfrac{6}{12}\\)",
"\\(\\dfrac{8}{12}\\)",
"\\(\\dfrac{2}{9}\\)"
],
"correct_index": 0
},
{
"index": 14836,
"id": 26067,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "∠AFE = 72° (given).
∠DFB = ∠AFE = 72° (vertically opposite).
∠BFC = 9°, so ∠CFD = 72° - 9° = 63°.
Answer: 63°.",
"answers": [
"63",
null,
null,
null
],
"correct_index": null
},
{
"index": 14837,
"id": 26068,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) Reading the graph at 2 min gives 240 bottles.
(b) Reading across at 960 bottles gives 8 min.
Answers: (a) 240, (b) 8 min.",
"answers": [
"240",
"8",
null,
null
],
"correct_index": null
},
{
"index": 14838,
"id": 26069,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "From 7.30 p.m.
to 9.30 p.m.
is 2 h; to 9.15 p.m.
is 1 h 45 min.
Answer: 1 h 45 min.",
"answers": [
"1",
"45",
null,
null
],
"correct_index": null
},
{
"index": 14839,
"id": 26070,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Counting all the unit cubes that make up Solid A (including hidden cubes) gives 16.
Answer: 16.",
"answers": [
"16",
null,
null,
null
],
"correct_index": null
},
{
"index": 14840,
"id": 26071,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "18 : 24 : 42, divide each by the HCF 6 → 3 : 4 : 7.
Answer: 3 : 4 : 7.",
"answers": [
"3 : 4 : 7",
"18 : 24 : 42",
"9 : 12 : 21",
"6 : 8 : 14"
],
"correct_index": 0
},
{
"index": 14841,
"id": 26072,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Total = 18 + 24 + 42 = 84.
Average = 84 ÷ 3 = 28.
Answer: 28.",
"answers": [
"28",
null,
null,
null
],
"correct_index": null
},
{
"index": 14842,
"id": 26073,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "15% of 40 = \\(\\dfrac{15}{100} \\times 40\\) = 6.
Answer: 6.",
"answers": [
"6",
null,
null,
null
],
"correct_index": null
},
{
"index": 14843,
"id": 26074,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Deposited = 8000 - 2000 = \\(\\$6000\\). Interest = 5% of 6000 = \\(\\$300\\).
Total in bank = 6000 + 300 = \\(\\$6300\\). Answer: \\(\\$6300\\).",
"answers": [
"6300",
null,
null,
null
],
"correct_index": null
},
{
"index": 14844,
"id": 26075,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "East is directly to the right on the grid (N arrow points up).
Point H is on the same row as F, to the right, so H is east of F.
Answer: H.",
"answers": [
"H",
"E",
"G",
"D"
],
"correct_index": 0
},
{
"index": 14845,
"id": 26076,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "South-west means down-and-left.
B is down-and-left of G (G is up-and-right of B), so B is south-west of G.
Answer: G.",
"answers": [
"G",
"A",
"C",
"E"
],
"correct_index": 0
},
{
"index": 14846,
"id": 26077,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "7 units = 840 ml, so 1 unit = 120 ml.
Blue = 3 units = 3 × 120 = 360 ml.
Answer: 360 ml.",
"answers": [
"360",
null,
null,
null
],
"correct_index": null
},
{
"index": 14847,
"id": 26078,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "2.00 to 4.15 p.m.
= 2 h 15 min.
First hour = \\(\\$6.00\\). Remaining 1 h 15 min = three half-hour blocks (0.5+0.5+0.25 rounded up) = 3 × \\(\\$2.50\\",
"answers": [
"27",
null,
null,
null
],
"correct_index": null
},
{
"index": 14848,
"id": 26079,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "QR is parallel to PS.
In triangle RUS, ∠RUS = 180° - 47° - 80° = 53°.
∠QRU = ∠RUS = 53° (alternate angles, QR // PS...
).
Printed answer: ",
"answers": [
"53",
null,
null,
null
],
"correct_index": null
},
{
"index": 14849,
"id": 26080,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "4 units = 24 cm², so 1 unit = 6 cm².
Rectangle = 15 units = 90 cm².
Shaded part = rectangle - unshaded triangle = 11 units = 11 × 6 = 66 cm².Red percentage = \\(\\dfrac{80}{210} \\times 100\\%\\) = 38.0952...% ≈ 38.10%.
Answer: 38.10%.",
"answers": [
"38.10",
null,
null,
null
],
"correct_index": null
},
{
"index": 14851,
"id": 26082,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Printer A = 80 copies/min.
Printer B = 300 ÷ 5 = 60 copies/min.
80 > 60, so Printer A is faster.
Answer: Printer A.",
"answers": [
"Printer A",
"Printer B",
"Both print at the same rate",
"Cannot be determined"
],
"correct_index": 0
},
{
"index": 14852,
"id": 26083,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Printer A = 80/min, Printer B = 60/min.
Difference = 80 - 60 = 20 copies.
Answer: 20 copies.",
"answers": [
"20",
null,
null,
null
],
"correct_index": null
},
{
"index": 14853,
"id": 26084,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Each round trip = \\(5\\dfrac{4}{5} \\times 2 = 11\\dfrac{3}{5}\\) km.
Over 7 days: \\(5\\dfrac{4}{5} \\times 7 \\times 2 = \\dfrac{29}{5} \\times 14 = \\dfrac",
"answers": [
"\\(81\\dfrac{1}{5}\\) km",
"\\(40\\dfrac{3}{5}\\) km",
"\\(11\\dfrac{3}{5}\\) km",
"\\(81\\dfrac{4}{5}\\) km"
],
"correct_index": 0
},
{
"index": 14854,
"id": 26085,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "1.3 kg = 1300 g = 13 lots of 100 g.
Cost = 13 × \\(\\$0.80\\) = \\(\\$10.40\\).
Answer: \\(\\$10.40\\).",
"answers": [
"10.40",
null,
null,
null
],
"correct_index": null
},
{
"index": 14855,
"id": 26086,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "4 bowls cost 4 × \\(\\$2\\) = \\(\\$8\\) more than 4 mugs.
Remove that: \\(\\$53\\) - \\(\\$8\\) = \\(\\$45\\) for 9 items at the mug price. 1 mug = \\(\\$45\\) ÷ 9 ",
"answers": [
"25",
null,
null,
null
],
"correct_index": null
},
{
"index": 14856,
"id": 26087,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) Total sold = 120.
75% of 120 = 90 buns, reached at 14 00.
(b) The steepest rise is between 12 00 and 13 00, where 40 buns were sold.
Answ",
"answers": [
"1400",
"1200",
"1300",
"40"
],
"correct_index": null
},
{
"index": 14857,
"id": 26088,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "From the graph: Jan = \\(\\$45\\), Feb = \\(\\$25\\), Mar = \\(\\$0\\), Apr = \\(\\$65\\).
Total Jan-Apr = 45 + 25 + 0 + 65 = \\(\\$135\\). Average = \\(\\$135\\) ÷ ",
"answers": [
"33.75",
null,
null,
null
],
"correct_index": null
},
{
"index": 14858,
"id": 26089,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) Full volume = 40 × 30 × 50 = 60000 cm³.
Syrup = 1/5 × 60000 = 12000 cm³ = 12 ℓ.
(b) Volume up to 45 cm = 45 × 40 × 30 = 54000 cm³.
Water ",
"answers": [
"12",
"28",
null,
null
],
"correct_index": null
},
{
"index": 14859,
"id": 26090,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Take morning total as 14 units.
Given to neighbours = 4 units (2/7 of 14).
Remaining = 10 units; given to friends = 5 units (half).
Total giv",
"answers": [
"\\(\\dfrac{9}{14}\\)",
"\\(\\dfrac{5}{14}\\)",
"\\(\\dfrac{5}{7}\\)",
"\\(\\dfrac{2}{7}\\)"
],
"correct_index": 0
},
{
"index": 14860,
"id": 26091,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "She gave away 9/14 in the morning, keeping 5/14.
End amount = morning + 13, and end = kept + 85.
So (5/14)m + 85 = m + 13 → 85 - 13 = m - (5/14)",
"answers": [
"197",
null,
null,
null
],
"correct_index": null
},
{
"index": 14861,
"id": 26092,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "30 batteries = 60 nail-masses.
Difference: (box + 60 nails) - (box + 40 nails) = 1.08 kg - 0.78 kg = 0.30 kg = 20 nail-masses.
So 1 nail = 0.015",
"answers": [
"0.18",
null,
null,
null
],
"correct_index": null
},
{
"index": 14862,
"id": 26093,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) In the end all equal: 540 ÷ 3 = 180 each.
(b) Working back: Adam ended with 180 after giving 1/4 away, so 3/4 of Adam's start = 180 → Adam star",
"answers": [
"180",
"210",
null,
null
],
"correct_index": null
},
{
"index": 14863,
"id": 26094,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Difference in bows = 30 - 10 = 20 bows, using 8.5 - 1.5 = 7 m.
So each bow uses 7 ÷ 20 = 0.35 m.
Total ribbon = 30×0.35 + 1.5 = 12 m.
Max bow",
"answers": [
"34",
null,
null,
null
],
"correct_index": null
},
{
"index": 14864,
"id": 26095,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Total for figure n = n², so Figure 6 total = 36.
The white/grey counts repeat in pairs: Figure 6 white = 15, grey = 21 (15 + 21 = 36).
Answers: ",
"answers": [
"15",
"21",
"36",
null
],
"correct_index": null
},
{
"index": 14865,
"id": 26096,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Total in figure n = n², so Figure 50 = 50 × 50 = 2500.
Answer: 2500.",
"answers": [
"2500",
null,
null,
null
],
"correct_index": null
},
{
"index": 14866,
"id": 26097,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Total in Figure 50 = 2500.
Grey - white = 50 (the figure number).
Grey + white = 2500.
Grey = (2500 + 50) ÷ 2 = 1275.
Fraction grey = \\(\\d",
"answers": [
"\\(\\dfrac{51}{100}\\)",
"\\(\\dfrac{49}{100}\\)",
"\\(\\dfrac{1}{2}\\)",
"\\(\\dfrac{50}{100}\\)"
],
"correct_index": 0
},
{
"index": 14867,
"id": 26098,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Each angle of an equilateral triangle is 60°.
At the fold, the angle on the straight line = 180° - 60° - 53° = 67°.
The folded flap is congruent",
"answers": [
"46",
null,
null,
null
],
"correct_index": null
},
{
"index": 14868,
"id": 26099,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Square side = 34 cm, so square perimeter = 136 cm.
Rectangle perimeter = 136 - 72 = 64 cm.
With one pair of sides = 10 cm each: 2×10 + 2×FE = 64",
"answers": [
"22",
null,
null,
null
],
"correct_index": null
},
{
"index": 14869,
"id": 26100,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "Area of square = 34×34 = 1156 cm²; rectangle = 22×10 = 220 cm².
Unshaded triangles: ΔEFG = 0.5×22×10 = 110; ΔABG = 0.5×12×34 = 204; ΔBCE = 0.5×44×3",
"answers": [
"314",
null,
null,
null
],
"correct_index": null
},
{
"index": 14870,
"id": 26101,
"type": 2,
"flags": [
"OK"
],
"solution_preview": "(a) In rhombus ABCD, ∠ABC = 180° - 56° = 124° (co-interior).
Angles at B around the point: ∠ABE = 360° - 140° - 124° = 96°.
(b) Diagonal BD bise",
"answers": [
"96",
"22",
null,
null
],
"correct_index": null
},
{
"index": 14871,
"id": 26102,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Work brackets first, then division, then subtraction.
\\((6+12)=18\\); \\(18\\div3=6\\); \\(33-6=27\\).",
"answers": [
"5",
"13",
"27",
"31"
],
"correct_index": 2
},
{
"index": 14872,
"id": 26103,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "In 10 245 the digit 2 is in the hundreds place, so its value is \\(2 \\times 100 = 200\\).",
"answers": [
"20",
"200",
"2000",
"20 000"
],
"correct_index": 1
},
{
"index": 14873,
"id": 26104,
"type": 1,
"flags": [
"OK"
],
"solution_preview": "Between 5.0 and the next mark each interval is 0.02 (the major marks 4.8, 4.9, 5.0 are split into 5 small parts of 0.02).
M is 3 small marks past 5",
"answers": [
"5.3",
"5.6",
"5.03",
"5.06"
],
"correct_index": 3
}
]