{
"paper": {
"school": "Ai Tong",
"year": 2022,
"level": "P5",
"label": "Semestral Assessment 2",
"source_prefix": "Ai Tong 2022 P5 Semestral Assessment 2",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "Find the value of \\((100 + 250 \\div 10) \\times 3\\).",
"answer0": "105",
"answer1": "175",
"answer2": "325",
"answer3": "375",
"correct_answer": 3,
"skill_id": 155,
"difficulty_id": 1,
"explanation": "Order of operations: divide first, then add, then multiply. \\(250 \\div 10 = 25\\); \\(100 + 25 = 125\\); \\(125 \\times 3 = 375\\). Answer: 375.",
"hints": ["Do the division inside the brackets first.", "Then add, then multiply by 3."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (4) = 375."
},
{
"n": 2,
"type_id": 1,
"question": "Which of the following numbers when rounded to the nearest hundred becomes 61 400?",
"answer0": "61 349",
"answer1": "61 449",
"answer2": "61 450",
"answer3": "61 495",
"correct_answer": 1,
"skill_id": 150,
"difficulty_id": 2,
"explanation": "Numbers rounding to 61 400 lie from 61 350 to 61 449. 61 349 rounds to 61 300; 61 450 rounds to 61 500; 61 495 rounds to 61 500. Only 61 449 rounds to 61 400. Answer: 61 449.",
"hints": ["Rounding to the nearest hundred: look at the tens digit.", "The range that rounds to 61 400 is 61 350 to 61 449."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (2) = 61 449."
},
{
"n": 3,
"type_id": 1,
"question": "How many sixths are there in \\(4\\dfrac{5}{6}\\)?",
"answer0": "29",
"answer1": "26",
"answer2": "15",
"answer3": "5",
"correct_answer": 0,
"skill_id": 157,
"difficulty_id": 1,
"explanation": "Convert the mixed number to sixths: \\(4\\dfrac{5}{6} = \\dfrac{4 \\times 6 + 5}{6} = \\dfrac{29}{6}\\). So there are 29 sixths. Answer: 29.",
"hints": ["Convert the mixed number to an improper fraction with denominator 6.", "The numerator is the number of sixths."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (1) = 29."
},
{
"n": 4,
"type_id": 1,
"question": "Which of the following is not equal to \\(\\dfrac{1}{2}\\)?",
"answer0": "\\(\\dfrac{1}{3} + \\dfrac{1}{6}\\)",
"answer1": "\\(\\dfrac{1}{4} + \\dfrac{3}{8}\\)",
"answer2": "\\(\\dfrac{1}{5} + \\dfrac{3}{10}\\)",
"answer3": "\\(\\dfrac{3}{7} + \\dfrac{1}{14}\\)",
"correct_answer": 1,
"skill_id": 159,
"difficulty_id": 2,
"explanation": "Evaluate each sum. \\(\\dfrac{1}{3}+\\dfrac{1}{6}=\\dfrac{2}{6}+\\dfrac{1}{6}=\\dfrac{1}{2}\\). \\(\\dfrac{1}{4}+\\dfrac{3}{8}=\\dfrac{2}{8}+\\dfrac{3}{8}=\\dfrac{5}{8}\\ne\\dfrac{1}{2}\\). \\(\\dfrac{1}{5}+\\dfrac{3}{10}=\\dfrac{2}{10}+\\dfrac{3}{10}=\\dfrac{1}{2}\\). \\(\\dfrac{3}{7}+\\dfrac{1}{14}=\\dfrac{6}{14}+\\dfrac{1}{14}=\\dfrac{1}{2}\\). The odd one out is option (2). Answer: \\(\\dfrac{1}{4}+\\dfrac{3}{8}\\).",
"hints": ["Add each pair using a common denominator.", "Find the one that does not simplify to one half."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q4",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (2)."
},
{
"n": 5,
"type_id": 1,
"question": "What is the value of X on the scale?",
"answer0": "5.04",
"answer1": "5.02",
"answer2": "5.2",
"answer3": "5.4",
"correct_answer": 0,
"skill_id": 124,
"difficulty_id": 2,
"explanation": "From 4.8 to 4.9 to 5.0 the scale moves in steps of 0.1, divided into smaller marks. Each small interval is 0.02. X sits two small marks past 5.0, giving \\(5.0 + 0.04 = 5.04\\). Answer: 5.04.",
"hints": ["Work out the value of each small interval between the labelled marks.", "Count the small marks from 5.0 to X."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q5",
"image_needed": true,
"image_options": false,
"image_file": "q5.png",
"image_page": 4,
"image_bbox": [0.18, 0.40, 0.88, 0.50],
"image_loc": "number-line scale below the question, marks at 4.8, 4.9, 5.0 and X to the right",
"notes": "Key: option (1) = 5.04."
},
{
"n": 6,
"type_id": 1,
"question": "A typist can type 160 words in 5 minutes. At this rate, how long does the typist take to type 320 words?",
"answer0": "10 minutes",
"answer1": "2 minutes",
"answer2": "32 minutes",
"answer3": "64 minutes",
"correct_answer": 0,
"skill_id": 152,
"difficulty_id": 1,
"explanation": "320 words is twice 160 words, so it takes twice as long: \\(5 \\times 2 = 10\\) minutes. Answer: 10 minutes.",
"hints": ["320 is double 160.", "Double the time as well."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (1) = 10 minutes."
},
{
"n": 7,
"type_id": 1,
"question": "What is the missing number in the box?
\\(7 : [\\;] = 3 : 15\\)",
"answer0": "19",
"answer1": "21",
"answer2": "24",
"answer3": "35",
"correct_answer": 3,
"skill_id": 181,
"difficulty_id": 2,
"explanation": "The ratio 3 : 15 simplifies to 1 : 5, so the second term is 5 times the first. \\(7 \\times 5 = 35\\). Answer: 35.",
"hints": ["Simplify 3 : 15.", "Apply the same multiplier to 7."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (4) = 35. Box is a display blank in a ratio, not an answer-entry blank."
},
{
"n": 8,
"type_id": 1,
"question": "Four letters P, E, A and R are shown. How many of the letters has/have a line of symmetry?",
"answer0": "1",
"answer1": "2",
"answer2": "3",
"answer3": "4",
"correct_answer": 1,
"skill_id": 144,
"difficulty_id": 2,
"explanation": "P has no line of symmetry. E has a horizontal line of symmetry. A has a vertical line of symmetry. R has no line of symmetry. So 2 letters (E and A) have a line of symmetry. Answer: 2.",
"hints": ["Check each letter for a fold line that gives matching halves.", "E and A are symmetric; P and R are not."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q8",
"image_needed": true,
"image_options": false,
"image_file": "q8.png",
"image_page": 5,
"image_bbox": [0.30, 0.40, 0.82, 0.52],
"image_loc": "outlined letters P E A R shown across the middle of the page",
"notes": "Key: option (2) = 2 (E and A)."
},
{
"n": 9,
"type_id": 1,
"question": "AF, BD and CE are straight lines. \\(\\angle\\)AFE = 43°. \\(\\angle\\)AFB is a right angle. Find \\(\\angle\\)CFD.",
"answer0": "141°",
"answer1": "137°",
"answer2": "133°",
"answer3": "129°",
"correct_answer": 2,
"skill_id": 194,
"difficulty_id": 2,
"explanation": "\\(\\angle\\)CFD is vertically opposite \\(\\angle\\)AFB plus \\(\\angle\\)AFE? Use angles on a straight line. \\(\\angle\\)EFB = \\(\\angle\\)AFB − \\(\\angle\\)AFE = 90° − 43° = 47°. \\(\\angle\\)CFD is vertically opposite \\(\\angle\\)EFB measured as the reflex split: \\(\\angle\\)BFD and \\(\\angle\\)AFC are straight-line continuations. \\(\\angle\\)DFC = 180° − \\(\\angle\\)AFE = 180° − 47° = 133°. Answer: 133°.",
"hints": ["Find \\(\\angle\\)EFB = 90° − 43° first.", "\\(\\angle\\)CFD is the angle on the opposite side; use the straight line and vertically opposite angles."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q9",
"image_needed": true,
"image_options": false,
"image_file": "q9.png",
"image_page": 6,
"image_bbox": [0.30, 0.17, 0.66, 0.42],
"image_loc": "angle diagram with lines AF, BD, CE crossing at F, 43 degrees and right-angle mark shown",
"notes": "Key: option (3) = 133°."
},
{
"n": 10,
"type_id": 1,
"question": "What is the area of triangle ABC?",
"answer0": "90 cm²",
"answer1": "108 cm²",
"answer2": "120 cm²",
"answer3": "240 cm²",
"correct_answer": 0,
"skill_id": 186,
"difficulty_id": 2,
"explanation": "Use base BC = 20 cm with its perpendicular height 9 cm (or base AB = 24 cm with height 10 cm — not matching). Taking base 20 cm and height 9 cm: area = \\(\\dfrac{1}{2} \\times 20 \\times 9 = 90\\) cm². Answer: 90 cm².",
"hints": ["Area of a triangle = \\(\\dfrac{1}{2} \\times\\) base \\(\\times\\) height.", "Pair base 20 cm with the perpendicular height 9 cm."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q10",
"image_needed": true,
"image_options": false,
"image_file": "q10.png",
"image_page": 7,
"image_bbox": [0.28, 0.18, 0.78, 0.38],
"image_loc": "right-angled triangle ABC with 9 cm vertical, 20 cm base, 24 cm hypotenuse and 10 cm perpendicular shown",
"notes": "Key: option (1) = 90 cm²."
},
{
"n": 11,
"type_id": 1,
"question": "The ratio of the cost of an eraser to the cost of a pen is 2 : 5. A ruler costs twice as much as the eraser. What is the ratio of the cost of the ruler to the cost of the eraser to the total cost of the three items?",
"answer0": "2 : 4 : 5",
"answer1": "4 : 2 : 5",
"answer2": "2 : 4 : 11",
"answer3": "4 : 2 : 11",
"correct_answer": 3,
"skill_id": 180,
"difficulty_id": 2,
"explanation": "Let eraser = 2 units, pen = 5 units. Ruler = twice eraser = 4 units. Total = 2 + 5 + 4 = 11 units. Ruler : eraser : total = 4 : 2 : 11. Answer: 4 : 2 : 11.",
"hints": ["Set eraser = 2 units, pen = 5 units, then ruler = 4 units.", "Add all three for the total, then write ruler : eraser : total."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q11",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (4) = 4 : 2 : 11."
},
{
"n": 12,
"type_id": 1,
"question": "The average mass of four boys is 52 kg. The masses of Cameron and James are 42 kg and 56 kg. Leon and Zach are of the same mass each. What is the total mass of Zach and Cameron?",
"answer0": "55 kg",
"answer1": "92 kg",
"answer2": "97 kg",
"answer3": "110 kg",
"correct_answer": 0,
"skill_id": 203,
"difficulty_id": 2,
"explanation": "Total mass of 4 boys = \\(52 \\times 4 = 208\\) kg. Leon + Zach = \\(208 - 42 - 56 = 110\\) kg. Since equal, Zach = \\(110 \\div 2 = 55\\) kg. Zach + Cameron = \\(55 + 42 = 97\\)... recheck: actually Zach + Cameron = 55 + 42 = 97 kg, matching option (3). Key states option (1). Per key option (1) = 55 kg, but mathematically Zach + Cameron = 97 kg. Using printed key answer (1) = 55 kg.",
"hints": ["Total of 4 boys = average × 4.", "Find Leon + Zach, halve it for Zach, then add Cameron."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q12",
"image_needed": true,
"image_options": false,
"image_file": "q12.png",
"image_page": 8,
"image_bbox": [0.26, 0.18, 0.74, 0.30],
"image_loc": "table with columns Cameron 42 kg, James 56 kg, Leon ?, Zach ?",
"notes": "Printed key gives option (1) = 55 kg, but the worked total mass of Zach + Cameron computes to 97 kg (option 3). Key appears inconsistent; following the printed key (1). FLAG for review."
},
{
"n": 13,
"type_id": 1,
"question": "Jovan had a piece of rectangular paper and folded it along the dotted line. Find \\(\\angle\\)y.",
"answer0": "117°",
"answer1": "126°",
"answer2": "144°",
"answer3": "153°",
"correct_answer": 1,
"skill_id": 197,
"difficulty_id": 3,
"explanation": "When the corner is folded, the fold preserves the 90° corner split. The top angle shown is 63°. The folded angle y relates to the right angle: \\(\\angle y = 180° - (90° - 63°) \\times ... \\) Using the fold, the marked angle 63° reflects so y = \\(180° - 2 \\times 27° = 126°\\), where \\(27° = 90° - 63°\\). Answer: 126°.",
"hints": ["A fold creates two equal angles (reflection).", "Use the 90° corner of the rectangle and the 63° angle."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q13",
"image_needed": true,
"image_options": false,
"image_file": "q13.png",
"image_page": 8,
"image_bbox": [0.16, 0.50, 0.86, 0.76],
"image_loc": "two diagrams: rectangle with dotted fold line and arrow, then folded result showing 63 degrees at top and angle y at lower right",
"notes": "Key: option (2) = 126°."
},
{
"n": 14,
"type_id": 1,
"question": "Which one of the figures shows that 40% of the figure is shaded?",
"answer0": "Figure A",
"answer1": "Figure B",
"answer2": "Figure C",
"answer3": "Figure D",
"correct_answer": 2,
"skill_id": 171,
"difficulty_id": 2,
"explanation": "40% means 40 out of 100, i.e. 2 out of every 5 cells shaded. Each figure is a 5×4 = 20-cell grid, so 40% = 8 shaded cells. Figure C has exactly 8 of the 20 squares shaded. Answer: Figure C.",
"hints": ["40% of a 20-cell grid = 8 cells.", "Count the shaded cells in each figure."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q14",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 9,
"image_bbox": [0.18, 0.16, 0.82, 0.42],
"image_loc": "four 5x4 grids labelled Figure A, B, C, D with various cells shaded",
"notes": "Key: option (3) = Figure C. Options are picture grids; crop each to q14_opt0..3.png."
},
{
"n": 15,
"type_id": 1,
"question": "A rectangular glass box is filled with some 1-cm cubes. What is the volume of the rectangular glass box?",
"answer0": "8 cm³",
"answer1": "12 cm³",
"answer2": "33 cm³",
"answer3": "45 cm³",
"correct_answer": 3,
"skill_id": 190,
"difficulty_id": 2,
"explanation": "The box dimensions can be read from the cube arrangement: it is a cuboid measuring 5 cm long by 3 cm wide by 3 cm high, giving volume \\(5 \\times 3 \\times 3 = 45\\) cm³. Answer: 45 cm³.",
"hints": ["The box is a cuboid; find length, width and height in cm from the cubes.", "Volume = length × width × height."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q15",
"image_needed": true,
"image_options": false,
"image_file": "q15.png",
"image_page": 9,
"image_bbox": [0.30, 0.56, 0.66, 0.78],
"image_loc": "3-D rectangular glass box partly filled with 1-cm unit cubes",
"notes": "Key: option (4) = 45 cm³."
},
{
"n": 16,
"type_id": 2,
"question": "Express 1.3 ℓ in litres and millilitres.
[?] ℓ [?] mℓ",
"answer0": "1",
"answer1": "300",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 192,
"difficulty_id": 1,
"explanation": "1.3 ℓ = 1 ℓ and 0.3 ℓ. Since 1 ℓ = 1000 mℓ, 0.3 ℓ = 300 mℓ. So 1.3 ℓ = 1 ℓ 300 mℓ. Answer: 1 ℓ 300 mℓ.",
"hints": ["The whole-number part is the litres.", "Multiply the decimal part (0.3) by 1000 to get millilitres."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q16",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 1ℓ 300mℓ. Two blanks: litres then millilitres."
},
{
"n": 17,
"type_id": 2,
"question": "Find the value of \\(0.32 \\times 40\\).
[?]",
"answer0": "12.8",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 166,
"difficulty_id": 1,
"explanation": "\\(0.32 \\times 40 = 0.32 \\times 4 \\times 10 = 1.28 \\times 10 = 12.8\\). Answer: 12.8.",
"hints": ["Multiply 0.32 by 4 first.", "Then multiply by 10."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q17",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 12.8."
},
{
"n": 18,
"type_id": 1,
"question": "Find the value of \\(\\dfrac{5}{6} - \\dfrac{4}{9}\\). Give your answer in the simplest form.",
"answer0": "\\(\\dfrac{7}{18}\\)",
"answer1": "\\(\\dfrac{1}{3}\\)",
"answer2": "\\(\\dfrac{9}{15}\\)",
"answer3": "\\(\\dfrac{1}{18}\\)",
"correct_answer": 0,
"skill_id": 159,
"difficulty_id": 2,
"explanation": "Common denominator 18: \\(\\dfrac{5}{6} = \\dfrac{15}{18}\\), \\(\\dfrac{4}{9} = \\dfrac{8}{18}\\). \\(\\dfrac{15}{18} - \\dfrac{8}{18} = \\dfrac{7}{18}\\), already in simplest form. Answer: \\(\\dfrac{7}{18}\\).",
"hints": ["Use a common denominator of 18.", "Subtract the numerators and simplify."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q18",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 7/18. Converted to MCQ because the answer is a fraction (FIB allows integers/decimals only)."
},
{
"n": 19,
"type_id": 2,
"question": "Mr Muthu bought 1 plush toy at 1 for $20. He had to pay 7% GST. How much did Mr Muthu pay for the plush toy inclusive of GST?
Ans: $[?]",
"answer0": "21.40",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 176,
"difficulty_id": 2,
"explanation": "GST = 7% of $20 = \\(\\dfrac{7}{100} \\times 20 = \\$1.40\\). Total = \\(\\$20 + \\$1.40 = \\$21.40\\). Answer: $21.40.",
"hints": ["Find 7% of $20.", "Add the GST to the original price."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q19",
"image_needed": true,
"image_options": false,
"image_file": "q19.png",
"image_page": 11,
"image_bbox": [0.18, 0.18, 0.62, 0.36],
"image_loc": "plush-toy picture with a price tag flag reading '1 for $20'",
"notes": "Key: $21.40. Price '1 for $20' is in the figure; kept in stem for clarity."
},
{
"n": 20,
"type_id": 2,
"question": "Express \\(\\dfrac{3}{8}\\) as a decimal.
[?]",
"answer0": "0.375",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 158,
"difficulty_id": 1,
"explanation": "\\(\\dfrac{3}{8} = 3 \\div 8 = 0.375\\). (Equivalently \\(\\dfrac{1}{8} = 0.125\\), so \\(0.125 \\times 3 = 0.375\\).) Answer: 0.375.",
"hints": ["Divide 3 by 8.", "Or use \\(\\dfrac{1}{8} = 0.125\\)."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q20",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working: 125 x 3 = 0.375, i.e. 0.375. Answer is a decimal, FIB valid."
},
{
"n": 21,
"type_id": 2,
"question": "The figure is made up of 3 identical rectangles. The area of the figure is 24 cm². What is the perimeter of the figure?
Ans: [?] cm",
"answer0": "20",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 2,
"explanation": "3 identical rectangles have total area 24 cm², so each rectangle = \\(24 \\div 3 = 8\\) cm². Each small rectangle is 2 cm by 4 cm. Tracing the outline of the figure gives a perimeter of \\(4 + 4 + 4 + 4 + 2 + 2 = 20\\) cm. Answer: 20 cm.",
"hints": ["Each rectangle has area \\(24 \\div 3 = 8\\) cm².", "Work out the rectangle dimensions (2 cm by 4 cm), then trace the outline."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q21",
"image_needed": true,
"image_options": false,
"image_file": "q21.png",
"image_page": 12,
"image_bbox": [0.16, 0.18, 0.40, 0.32],
"image_loc": "L-shaped figure made of 3 identical rectangles (one tall on the left, two stacked on the right)",
"notes": "Key working: 24/3=8 then 4+4+4+4+2+2=20cm."
},
{
"n": 22,
"type_id": 2,
"question": "Theo is making some cookies based on a recipe that makes 8 cookies each time: 90 g flour, 100 g sugar, 40 g cocoa powder. He has 600 g of flour, 420 g of sugar and 280 g of cocoa powder. How many cookies can Theo make at most?
Ans: [?]",
"answer0": "32",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "Per batch (8 cookies): 90 g flour, 100 g sugar, 40 g cocoa. Batches possible: flour 600÷90 = 6 (rem); sugar 420÷100 = 4 (rem); cocoa 280÷40 = 7. The cocoa is the printed limiting working: \\(280 \\div 40 = 7\\) batches, \\(7 \\times 8 = ...\\) The key uses cocoa as binding but the limiting ingredient is sugar (4 batches). Printed key: \\(280 \\div 40 = 7\\), \\(4 \\times 8 = 32\\) — i.e. 4 full batches (limited by sugar) × 8 = 32 cookies. Answer: 32 cookies.",
"hints": ["Find how many full recipe batches each ingredient allows.", "The smallest number of batches is the limit; multiply by 8."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q22",
"image_needed": true,
"image_options": false,
"image_file": "q22.png",
"image_page": 12,
"image_bbox": [0.28, 0.52, 0.66, 0.66],
"image_loc": "recipe card 'Mini chocolate cookies (Makes 8 cookies)' with cookie picture",
"notes": "Key: 4x8=32. Recipe amounts kept in stem. Limiting ingredient is sugar (4 batches)."
},
{
"n": 23,
"type_id": 0,
"question": "Joash stacked 12 unit cubes to form the solid. Draw the front view and the top view of the solid on the grids.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 188,
"difficulty_id": 3,
"explanation": "Front view and top view must be drawn on the grids — see answer key page (Pg1, Q23) for the correct front-view and top-view sketches of the 12-cube solid.",
"hints": ["The front view is what you see looking along the 'Front view' arrow.", "The top view is what you see looking straight down."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q23",
"image_needed": true,
"image_options": false,
"image_file": "q23.png",
"image_page": 13,
"image_bbox": [0.28, 0.16, 0.72, 0.40],
"image_loc": "3-D drawing of 12 stacked unit cubes with Top view, Front view and Side view arrows",
"notes": "Drawing task (draw front & top views) — no app question type, set type_id 0. Answer is a sketch shown in the key. SKIPPED on insert."
},
{
"n": 24,
"type_id": 1,
"question": "The time Janet spends on her piano, dance and swimming lessons is in the ratio 5 : 4 : 3. She spends 8 hours on all these enrichment lessons. How much time does she spend on her dance lesson? Leave your answer as a mixed number.",
"answer0": "\\(2\\dfrac{2}{3}\\) h",
"answer1": "\\(3\\dfrac{1}{3}\\) h",
"answer2": "\\(2\\dfrac{1}{3}\\) h",
"answer3": "2 h",
"correct_answer": 0,
"skill_id": 182,
"difficulty_id": 2,
"explanation": "Total ratio units = 5 + 4 + 3 = 12. Dance = 4 units. 1 unit = \\(8 \\div 12 = \\dfrac{8}{12} = \\dfrac{2}{3}\\) h. Dance = \\(4 \\times \\dfrac{2}{3} = \\dfrac{8}{3} = 2\\dfrac{2}{3}\\) h. Answer: \\(2\\dfrac{2}{3}\\) h.",
"hints": ["Total units = 5 + 4 + 3 = 12; find the value of 1 unit.", "Dance = 4 units; express as a mixed number."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q24",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working: 8÷12=... 4 units = 160min = 2⅔ h. Converted to MCQ because answer is a mixed number (FIB allows integers/decimals only)."
},
{
"n": 25,
"type_id": 2,
"question": "PQRS is a rhombus. Find \\(\\angle\\)y.
Ans: [?]°",
"answer0": "22",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 200,
"difficulty_id": 3,
"explanation": "In rhombus PQRS, triangle PQR has \\(\\angle\\)QPR-related angles. Using the key: \\(\\angle\\)PRS-type calc: 180 − 120 = 60; the marked 120° and 104° give: 180 − 104 − 60 = 16; 180 − 104 = 76; \\(76 \\div 2 = 38\\); \\(38 - 16 = 22\\). So \\(\\angle\\)y = 22°. Answer: 22°.",
"hints": ["Use the angle sum of a triangle (180°) and properties of a rhombus.", "Rhombus diagonals create isosceles triangles with equal base angles."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q25",
"image_needed": true,
"image_options": false,
"image_file": "q25.png",
"image_page": 14,
"image_bbox": [0.14, 0.42, 0.46, 0.62],
"image_loc": "rhombus PQRS with diagonal PR, angles 120 degrees and 104 degrees marked at top and angle y near R",
"notes": "Key working final answer 22°."
},
{
"n": 26,
"type_id": 1,
"question": "Mrs Tan baked a cake. She gave \\(\\dfrac{1}{3}\\) of the cake to Shirley. Then she gave \\(\\dfrac{1}{6}\\) of the remaining cake to Peter. What fraction of the cake was Mrs Tan left with?",
"answer0": "\\(\\dfrac{5}{9}\\)",
"answer1": "\\(\\dfrac{1}{2}\\)",
"answer2": "\\(\\dfrac{5}{18}\\)",
"answer3": "\\(\\dfrac{2}{3}\\)",
"correct_answer": 0,
"skill_id": 165,
"difficulty_id": 2,
"explanation": "After Shirley: remaining = \\(1 - \\dfrac{1}{3} = \\dfrac{2}{3}\\). Peter gets \\(\\dfrac{1}{6}\\) of \\(\\dfrac{2}{3} = \\dfrac{2}{18} = \\dfrac{1}{9}\\). Left = \\(\\dfrac{2}{3} - \\dfrac{1}{9} = \\dfrac{6}{9} - \\dfrac{1}{9} = \\dfrac{5}{9}\\). Answer: \\(\\dfrac{5}{9}\\).",
"hints": ["Find the remaining cake after Shirley (\\(\\dfrac{2}{3}\\)).", "Peter's share is \\(\\dfrac{1}{6}\\) of that remainder; subtract."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q26",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 5/9. Converted to MCQ because answer is a fraction (FIB allows integers/decimals only)."
},
{
"n": 27,
"type_id": 2,
"question": "An inline skates rental shop charges $4 for the first 30 minutes and $2.50 for every subsequent \\(\\dfrac{1}{2}\\) hour or part thereof. Elaine and Alicia each rented a pair of inline skates for 3.5 hours. How much did they have to pay altogether?
Ans: $[?]",
"answer0": "38",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 2,
"explanation": "3.5 hours = 7 half-hour blocks. First half hour = $4. Remaining 6 blocks at $2.50 = \\(6 \\times 2.50 = \\$15\\). Cost per person = \\(4 + 15 = \\$19\\). Two people = \\(19 \\times 2 = \\$38\\). Answer: $38.",
"hints": ["3.5 hours is 7 half-hour blocks; the first is $4.", "Charge the other 6 blocks at $2.50, then double for two people."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q27",
"image_needed": true,
"image_options": false,
"image_file": "q27.png",
"image_page": 15,
"image_bbox": [0.18, 0.46, 0.66, 0.56],
"image_loc": "RENTAL CHARGES table: first 30 minutes $4, every subsequent half hour or part thereof $2.50",
"notes": "Key: 19x2=$38. Charge table kept in stem."
},
{
"n": 28,
"type_id": 2,
"question": "Deena had 20 fewer stamps than Joey at first. Deena gave 12 of her stamps to Joey. Joey now has 3 times as many stamps as Deena. How many stamps did Deena have at first?
Ans: [?]",
"answer0": "34",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "After Deena gives 12 to Joey, the gap between them becomes \\(20 + 12 + 12 = 44\\) stamps. Joey is 3 times Deena, so the difference is 2 'units' = 44, giving 1 unit = 22 = Deena's stamps now. Deena at first = \\(22 + 12 = 34\\). Answer: 34.",
"hints": ["Giving away stamps widens the difference: \\(20 + 12 + 12 = 44\\).", "Joey = 3 × Deena means difference = 2 units; find Deena now, then add back 12."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q28",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working: 12+12+20=44, 44÷2=22, 22+12=34."
},
{
"n": 29,
"type_id": 2,
"question": "ABC is a straight line. \\(\\angle\\)ABD is 149° and \\(\\angle\\)EBC is 118°. Find \\(\\angle\\)EBD.
Ans: [?]°",
"answer0": "87",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 194,
"difficulty_id": 2,
"explanation": "\\(\\angle\\)DBC = 180° − \\(\\angle\\)ABD = 180° − 149° = 31°. \\(\\angle\\)EBD = \\(\\angle\\)EBC − \\(\\angle\\)DBC = 118° − 31° = 87°. Answer: 87°.",
"hints": ["Find \\(\\angle\\)DBC using angles on a straight line (180° − 149°).", "Subtract \\(\\angle\\)DBC from \\(\\angle\\)EBC."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q29",
"image_needed": true,
"image_options": false,
"image_file": "q29.png",
"image_page": 16,
"image_bbox": [0.22, 0.42, 0.72, 0.62],
"image_loc": "straight line ABC with rays BE and BD above, angle marked at B",
"notes": "Key working: 149→... 118−31=87°."
},
{
"n": 30,
"type_id": 0,
"question": "Triangle A is drawn on a 1-cm grid. Draw a right-angled triangle with the same area as triangle A on the second grid.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 186,
"difficulty_id": 2,
"explanation": "Triangle A has base 4 cm and height 3 cm, area = \\(\\dfrac{1}{2} \\times 4 \\times 3 = 6\\) cm². Any right-angled triangle with the same area (e.g. base 4 cm, height 3 cm with a right angle, or base 3 cm, height 4 cm) is acceptable — see answer-key sketch on Pg2.",
"hints": ["Find the area of triangle A first (\\(\\dfrac{1}{2} ×\\) base × height).", "Draw a right-angled triangle whose legs give the same area."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P1Q30",
"image_needed": true,
"image_options": false,
"image_file": "q30.png",
"image_page": 17,
"image_bbox": [0.26, 0.22, 0.70, 0.46],
"image_loc": "first 1-cm grid showing triangle A (isosceles, base 4 cm, height 3 cm)",
"notes": "Drawing task (draw a triangle on a grid) — no app question type, set type_id 0. Answer is a sketch in the key. SKIPPED on insert."
},
{
"n": 31,
"type_id": 2,
"question": "Patricia has 0.35 kg of flour. Mary has 0.68 kg more flour than Patricia. How much flour do they have altogether?
Ans: [?] kg",
"answer0": "1.38",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 167,
"difficulty_id": 1,
"explanation": "Patricia = 0.35 kg. Mary = \\(0.35 + 0.68 = 1.03\\) kg. Altogether = \\(0.35 + 1.03 = 1.38\\) kg. (Key: \\(0.35 + 0.35 + 0.68 = 1.38\\) kg.) Answer: 1.38 kg.",
"hints": ["Find Mary's flour first (Patricia + 0.68).", "Add Patricia's and Mary's amounts."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 0.35+0.35+0.68=1.38kg."
},
{
"n": 32,
"type_id": 2,
"question": "After Patrick spent $6 on a meal, he had $24 left. What percentage of his money did he spend?
Ans: [?]%",
"answer0": "20",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 171,
"difficulty_id": 2,
"explanation": "Total money = \\(6 + 24 = \\$30\\). Fraction spent = \\(\\dfrac{6}{30} = \\dfrac{1}{5} = \\dfrac{20}{100} = 20\\%\\). Answer: 20%.",
"hints": ["Total = amount spent + amount left.", "Percentage spent = \\(\\dfrac{6}{30} \\times 100\\%\\)."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 6/30=1/5=20%."
},
{
"n": 33,
"type_id": 2,
"question": "Mdm Koh paid $266 for 8 swimming lessons. She paid the same amount for each lesson. At this rate, how much would she need to pay for 6 lessons only?
Ans: $[?]",
"answer0": "199.50",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 167,
"difficulty_id": 2,
"explanation": "Cost per lesson = \\(266 \\div 8 = \\$33.25\\). For 6 lessons = \\(33.25 \\times 6 = \\$199.50\\). Answer: $199.50.",
"hints": ["Find the cost of 1 lesson (\\(266 \\div 8\\)).", "Multiply by 6."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 266÷8=33.25, x6=$199.50."
},
{
"n": 34,
"type_id": 2,
"question": "A shop opens daily for the times shown: 8.30 am to 12.30 pm, 2 pm to 4.45 pm, and 5.30 pm to 9 pm. How many hours and minutes is the shop open each day?
Ans: [?] h [?] min",
"answer0": "10",
"answer1": "15",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 135,
"difficulty_id": 2,
"explanation": "8.30 am to 12.30 pm = 4 h. 2 pm to 4.45 pm = 2 h 45 min. 5.30 pm to 9 pm = 3 h 30 min. Total = \\(4 + 2 + 3 = 9\\) h and \\(45 + 30 = 75\\) min = 1 h 15 min. Total = \\(9 + 1 = 10\\) h 15 min. Answer: 10 h 15 min.",
"hints": ["Work out each opening period separately.", "Add the hours and minutes, converting 60 min to 1 h."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q4",
"image_needed": true,
"image_options": false,
"image_file": "q34.png",
"image_page": 22,
"image_bbox": [0.24, 0.14, 0.64, 0.32],
"image_loc": "Opening hours table: 8.30 am to 12.30 pm, 2 pm to 4.45 pm, 5.30 pm to 9 pm",
"notes": "Key: 10h15min. Two blanks: hours then minutes. Table content kept in stem."
},
{
"n": 35,
"type_id": 2,
"question": "In the figure, all lines meet at right angles. What is the perimeter of the figure?
Ans: [?] m",
"answer0": "82",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 2,
"explanation": "For a rectilinear (staircase) figure with all right angles, the total horizontal segments add to the full width (21 m on each of top and bottom) and the vertical segments add to the full height (20 m on each side). Perimeter = \\(20 + 20 + 21 + 21 = 82\\) m. Answer: 82 m.",
"hints": ["The step lengths add up to the overall width and height.", "Perimeter = 2 × (overall width + overall height)."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q5",
"image_needed": true,
"image_options": false,
"image_file": "q35.png",
"image_page": 22,
"image_bbox": [0.50, 0.52, 0.82, 0.74],
"image_loc": "staircase-shaped rectilinear figure, overall height 20 m, overall width 21 m",
"notes": "Key: 20+20+21+21=82m."
},
{
"n": 36,
"type_id": 2,
"question": "ABCD is a trapezium and BCDE is a rhombus. AE = ED. \\(\\angle\\)AED = 128°. Find \\(\\angle\\)ADC.
Ans: [?]°",
"answer0": "154",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "Triangle AED is isosceles (AE = ED) with apex \\(\\angle\\)AED = 128°, so base angles \\(\\angle\\)EAD = \\(\\angle\\)EDA = \\((180 - 128) \\div 2 = 26°\\). \\(\\angle\\)DEB (rhombus angle) = 180 − 128 = 52°... Using the key: \\(180 - 128 = 52\\); \\(52 \\div 2 = 26\\); \\(360 - 128 - 128 = 104\\); \\(104 \\div 2 = 52\\); \\(\\angle\\)ADC = \\(128 + 26 = 154°\\). Answer: 154°.",
"hints": ["Triangle AED is isosceles; find its base angles.", "Use rhombus angle properties and add to find \\(\\angle\\)ADC."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q6",
"image_needed": true,
"image_options": false,
"image_file": "q36.png",
"image_page": 23,
"image_bbox": [0.38, 0.18, 0.86, 0.36],
"image_loc": "trapezium ABCD with rhombus BCDE attached, angle AED = 128 degrees marked at E",
"notes": "Key working final answer 154°. [3 marks]"
},
{
"n": 37,
"type_id": 2,
"question": "A wooden plank is sawed into two parts. The first part is 3.75 m long. It is 1.38 m longer than the second part. How long was the wooden plank before it was sawed?
Ans: [?] m",
"answer0": "6.12",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 167,
"difficulty_id": 2,
"explanation": "Second part = \\(3.75 - 1.38 = 2.37\\) m. Whole plank = \\(3.75 + 2.37 = 6.12\\) m. Answer: 6.12 m.",
"hints": ["Find the second part: first part − 1.38.", "Add both parts for the original length."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 3.75−1.38=2.37; 2.37+3.75=6.12m. [3 marks]"
},
{
"n": 38,
"type_id": 2,
"question": "There were 147 children and some adults at a carnival. \\(\\dfrac{2}{3}\\) of the adults were men and the rest were women. \\(\\dfrac{2}{9}\\) of the people at the carnival were women. How many people were at the carnival?
Ans: [?]",
"answer0": "441",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "Women = \\(\\dfrac{1}{3}\\) of adults (since \\(\\dfrac{2}{3}\\) are men). Let adults = A. Women = \\(\\dfrac{1}{3}A\\). Total people = 147 + A, and women = \\(\\dfrac{2}{9}\\) of total. So \\(\\dfrac{1}{3}A = \\dfrac{2}{9}(147 + A)\\). Key approach: \\(9u - 2u = 7u\\) (children), \\(2u + 2u = 4u\\)... children = 7u of 9u total? Key: \\(147 \\div 3 = 49\\), \\(49 \\times 9 = 441\\). Total people = 441. Answer: 441.",
"hints": ["Women are \\(\\dfrac{1}{3}\\) of adults and \\(\\dfrac{2}{9}\\) of everyone.", "Express the total in units; children (147) fill the remaining units."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working: 9u−2u=7u, 2u+2u=4u, 147÷3=49, 49x9=441. [3 marks]"
},
{
"n": 39,
"type_id": 0,
"question": "RSTU is a parallelogram. RS = RV and \\(\\angle\\)SRV = 46°. (a) Name an angle that has the same size as \\(\\angle\\)STU.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 199,
"difficulty_id": 2,
"explanation": "In parallelogram RSTU, opposite angles are equal, so \\(\\angle\\)STU = \\(\\angle\\)SRU. Therefore the angle equal in size to \\(\\angle\\)STU is \\(\\angle\\)SRU. Answer: \\(\\angle\\)SRU.",
"hints": ["Opposite angles of a parallelogram are equal.", "\\(\\angle\\)STU is opposite \\(\\angle\\)SRU."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q9a",
"image_needed": true,
"image_options": false,
"image_file": "q39.png",
"image_page": 25,
"image_bbox": [0.28, 0.16, 0.66, 0.46],
"image_loc": "parallelogram RSTU with point V on SU, RV drawn, angle SRV = 46 degrees marked at R",
"notes": "Part (a): answer is an angle name (∠SRU). Naming an angle is a word/label answer with no numeric value, so type_id 0 (skipped on insert). Key: ∠SRU. [1 mark]"
},
{
"n": 40,
"type_id": 2,
"question": "RSTU is a parallelogram. RS = RV and \\(\\angle\\)SRV = 46°. Find \\(\\angle\\)RVU.
Ans: [?]°",
"answer0": "113",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 199,
"difficulty_id": 3,
"explanation": "Triangle RSV is isosceles (RS = RV) with apex \\(\\angle\\)SRV = 46°, so base angles = \\((180 - 46) \\div 2 = 67°\\). \\(\\angle\\)RVS = 67°, and \\(\\angle\\)RVU is on the straight line SU: \\(\\angle\\)RVU = 180° − 67° = 113°. Answer: 113°.",
"hints": ["Triangle RSV is isosceles; find \\(\\angle\\)RVS = \\((180 - 46) \\div 2\\).", "\\(\\angle\\)RVU and \\(\\angle\\)RVS are angles on a straight line (SVU)."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q9b",
"image_needed": true,
"image_options": false,
"image_file": "q40.png",
"image_page": 25,
"image_bbox": [0.28, 0.16, 0.66, 0.46],
"image_loc": "parallelogram RSTU with point V on SU, RV drawn, angle SRV = 46 degrees marked at R (same figure as part a)",
"notes": "Key working: 180−46=134, 134÷2=67, 180−67=113°. [2 marks]. Same figure as Q39."
},
{
"n": 41,
"type_id": 1,
"question": "David used 60 blue tiles, 48 red tiles and 24 green tiles to design a project. Find the ratio of the number of blue tiles to the number of red tiles to the total number of tiles that he used for the project. Give your answer in its simplest form.",
"answer0": "5 : 4 : 11",
"answer1": "5 : 4 : 2",
"answer2": "60 : 48 : 132",
"answer3": "10 : 8 : 22",
"correct_answer": 0,
"skill_id": 180,
"difficulty_id": 2,
"explanation": "Total tiles = \\(60 + 48 + 24 = 132\\). Ratio blue : red : total = 60 : 48 : 132. Divide by 12: 5 : 4 : 11. Answer: 5 : 4 : 11.",
"hints": ["Total = 60 + 48 + 24.", "Write blue : red : total, then divide by the common factor (12)."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q10a",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 5:4:11. Made MCQ as the answer is a ratio (sequence with colons), not a single integer/decimal. [1 mark]"
},
{
"n": 42,
"type_id": 2,
"question": "David used blue, red and green tiles in the ratio 5 : 4 : 2 (blue : red : green). He designed another project using the same ratio with a total of 792 tiles. How many green tiles did he use?
Ans: [?]",
"answer0": "144",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 182,
"difficulty_id": 2,
"explanation": "Blue : red : green = 60 : 48 : 24 = 5 : 4 : 2. Total units = 5 + 4 + 2 = 11. 1 unit = \\(792 \\div 11 = 72\\). Green = 2 units = \\(72 \\times 2 = 144\\) tiles. Answer: 144.",
"hints": ["Simplify the tile ratio to 5 : 4 : 2 (total 11 units).", "1 unit = \\(792 \\div 11\\); green = 2 units."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q10b",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working: 5:4:2, 5+4+2=11, 792÷11=72, 72x2=144. The blue:red:green ratio is restated in the stem since part (a)'s ratio differs (it included the total). [2 marks]"
},
{
"n": 43,
"type_id": 2,
"question": "Aisha, Belle and Carl baked an average of 128 cupcakes. Aisha and Belle baked an average of 126 cupcakes. Belle and Carl baked an average of 115 cupcakes. How many cupcakes did Belle bake?
Ans: [?]",
"answer0": "98",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 205,
"difficulty_id": 3,
"explanation": "Total of all three = \\(128 \\times 3 = 384\\). Aisha + Belle = \\(126 \\times 2 = 252\\). Belle + Carl = \\(115 \\times 2 = 230\\). (Aisha + Belle) + (Belle + Carl) = \\(252 + 230 = 482\\) = (Aisha + Belle + Carl) + Belle = \\(384 + \\)Belle. So Belle = \\(482 - 384 = 98\\). Answer: 98.",
"hints": ["Total of all three = 128 × 3.", "Add the two pair totals; the overlap counts Belle twice."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q11",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working: 128x3=384, 126x2=252, 115x2=230, 252+230=482, 482−384=98. [4 marks]"
},
{
"n": 44,
"type_id": 0,
"question": "At a Sports carnival, cups of Milo were distributed from a Milo van to students. The line graph shows the volume of Milo left in the Milo van at different times of the day. (a) During which two-hour interval was the decrease in the volume of Milo the greatest?",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 147,
"difficulty_id": 2,
"explanation": "From the line graph, the steepest downward segment is between 11 00 and 13 00, where the volume drops from about 280 ℓ to 120 ℓ (a fall of about 160 ℓ), the greatest two-hour decrease. Answer: 11 00 to 13 00.",
"hints": ["The greatest decrease is the steepest downward part of the graph.", "Compare the drop over each two-hour interval."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q12a",
"image_needed": true,
"image_options": false,
"image_file": "q44.png",
"image_page": 28,
"image_bbox": [0.10, 0.16, 0.82, 0.40],
"image_loc": "line graph of Volume of Milo left (litres) versus Time from 09 00 to 17 00",
"notes": "Part (a): answer is a time interval '11 00 to 13 00' (two values forming an interval, not a single numeric blank), so type_id 0 (skipped on insert). Key: 1100 to 1300. [1 mark]. Graph shared by Q44/45/46."
},
{
"n": 45,
"type_id": 2,
"question": "The line graph shows the volume of Milo left in a Milo van at different times of the day. How many litres of Milo was distributed from 09 00 to 17 00?
Ans: [?] ℓ",
"answer0": "300",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 148,
"difficulty_id": 2,
"explanation": "At 09 00 the van held about 360 ℓ; at 17 00 about 60 ℓ remained. Milo distributed = \\(360 - 60 = 300\\) ℓ. Answer: 300 ℓ.",
"hints": ["Read the volume at 09 00 and at 17 00 from the graph.", "Distributed = starting volume − ending volume."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q12b",
"image_needed": true,
"image_options": false,
"image_file": "q45.png",
"image_page": 28,
"image_bbox": [0.10, 0.16, 0.82, 0.40],
"image_loc": "line graph of Volume of Milo left (litres) versus Time from 09 00 to 17 00 (same graph as part a)",
"notes": "Key working: 360−60=300ℓ. [2 marks]. Same graph as Q44."
},
{
"n": 46,
"type_id": 2,
"question": "The volume of Milo left in a Milo van is shown on the line graph. 300 ℓ of Milo was distributed from 09 00 to 17 00. The volume of each cup of Milo distributed was 120 mℓ. How many cups of Milo were distributed from 09 00 to 17 00?
Ans: [?]",
"answer0": "2500",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 192,
"difficulty_id": 2,
"explanation": "300 ℓ = \\(300 \\times 1000 = 300000\\) mℓ. Number of cups = \\(300000 \\div 120 = 2500\\) cups. Answer: 2500.",
"hints": ["Convert 300 ℓ to millilitres (×1000).", "Divide by the cup size 120 mℓ."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q12c",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working: 300x1000=300000, 300000÷120=2500. The 300 ℓ result from part (b) is restated in the stem. [1 mark]"
},
{
"n": 47,
"type_id": 2,
"question": "In the diagram, UVW is a triangle. VYX and UYZ are straight lines. Y is the mid-point of UZ and Z is the mid-point of VW. WX is twice as long as UX. UZ is 48 cm and VW is 52 cm. What is the area of the shaded part WXYZ?
Ans: [?] cm²",
"answer0": "520",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 186,
"difficulty_id": 3,
"explanation": "Area of triangle UVW: using the printed working, \\(\\dfrac{1}{2} \\times 48 \\times 52 = 1248\\) cm². Triangle with \\(\\dfrac{1}{2} \\times 26 \\times 24 = 312\\) cm² (using half-lengths from the midpoints). Shaded WXYZ = \\(\\dfrac{2}{3} \\times 1248 - 312 = 832 - 312 = 520\\) cm². Answer: 520 cm².",
"hints": ["Find the area of the whole triangle (\\(\\dfrac{1}{2} \\times 48 \\times 52\\)).", "Use the midpoints and the WX = 2×UX ratio to subtract the unshaded triangle."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q13",
"image_needed": true,
"image_options": false,
"image_file": "q47.png",
"image_page": 29,
"image_bbox": [0.22, 0.18, 0.78, 0.42],
"image_loc": "triangle UVW with cevians, shaded quadrilateral WXYZ, 48 cm height and 52 cm base marked",
"notes": "Key working: ½×48×52=1248, ½×26×24=312, ⅔×1248=832, 832−312=520cm². [4 marks]"
},
{
"n": 48,
"type_id": 2,
"question": "Alice, Brenda, Charles and David shared a box of cards. David took \\(\\dfrac{2}{5}\\) of the cards from the box. Charles took \\(\\dfrac{3}{10}\\) of the remaining cards. Brenda took 18 more cards than Charles and Alice took the rest of the cards. Alice had 54 cards. How many cards were there in the box at first?
Ans: [?]",
"answer0": "180",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "Let the box have N cards. David took \\(\\dfrac{2}{5}N\\), leaving \\(\\dfrac{3}{5}N\\). Charles took \\(\\dfrac{3}{10} \\times \\dfrac{3}{5}N = \\dfrac{9}{50}N\\). Remaining after Charles = \\(\\dfrac{3}{5}N - \\dfrac{9}{50}N = \\dfrac{21}{50}N\\), shared by Brenda and Alice. Brenda = Charles + 18 = \\(\\dfrac{9}{50}N + 18\\); Alice = remaining − Brenda = \\(\\dfrac{21}{50}N - (\\dfrac{9}{50}N + 18) = \\dfrac{12}{50}N - 18 = 54\\). So \\(\\dfrac{12}{50}N = 72\\), \\(N = 72 \\times \\dfrac{50}{12} = 300\\)... Note: this differs from the printed key (180). Following printed answer key = 180. FLAG for review.",
"hints": ["Work in units of the box; David leaves \\(\\dfrac{3}{5}\\).", "Set up Alice's count = 54 and solve for the box total."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q14",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Printed answer key gives 180 but no worked solution is shown for Q14 in the key, and an independent recompute gives 300. FLAG for review; using printed key value 180. [5 marks]"
},
{
"n": 49,
"type_id": 2,
"question": "Lines are drawn to form figures that follow a pattern. Figure 1 has 2 squares and 7 lines; Figure 2 has 4 squares and 12 lines; Figure 3 has 6 squares and 17 lines; Figure 4 has 8 squares. How many lines are needed to form Figure 4?
Ans: [?]",
"answer0": "22",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 108,
"difficulty_id": 2,
"explanation": "Lines increase by 5 each figure: 7, 12, 17, ... Figure 4 = \\(17 + 5 = 22\\) lines. (Key: \\(17 + 5 = 22\\).) Answer: 22.",
"hints": ["Find the difference in the number of lines between figures.", "Add that difference to Figure 3's line count."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q15a",
"image_needed": true,
"image_options": false,
"image_file": "q49.png",
"image_page": 31,
"image_bbox": [0.16, 0.14, 0.78, 0.34],
"image_loc": "pattern of Figures 1-3 (grids of squares) with Figure 4 shown as a question mark, plus the figure/squares/lines table",
"notes": "Key: 17+5=22. Table and figure pattern kept; figure-bearing. [1 mark]. Figure shared by Q49/50/51."
},
{
"n": 50,
"type_id": 2,
"question": "Lines are drawn to form figures that follow a pattern. The number of squares is 2, 4, 6, 8, ... for Figures 1, 2, 3, 4. How many squares are there in Figure 36?
Ans: [?]",
"answer0": "72",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 108,
"difficulty_id": 2,
"explanation": "The number of squares = \\(2 \\times\\) figure number. Figure 36 = \\(36 \\times 2 = 72\\) squares. Answer: 72.",
"hints": ["Squares go 2, 4, 6, 8 — twice the figure number.", "Multiply 36 by 2."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q15b",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 36x2=72. [1 mark]"
},
{
"n": 51,
"type_id": 2,
"question": "Lines are drawn to form figures that follow a pattern. The number of lines is 7, 12, 17, ... for Figures 1, 2, 3 (increasing by 5 each time). Which Figure is drawn with 62 lines?
Ans: Figure [?]",
"answer0": "12",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 108,
"difficulty_id": 3,
"explanation": "Lines for Figure n = \\(7 + 5(n-1) = 5n + 2\\). Set \\(5n + 2 = 62\\): \\(5n = 60\\), \\(n = 12\\). (Key: \\(62 - 7 = 55\\); \\(55 \\div 5 = 11\\); \\(11 + 1 = 12\\).) Answer: Figure 12.",
"hints": ["Number of lines = \\(5 \\times\\) figure number + 2.", "Solve \\(5n + 2 = 62\\)."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q15c",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working: 62−7=55, 55÷5=11, 11+1=12. Answer is Figure 12. [2 marks]"
},
{
"n": 52,
"type_id": 2,
"question": "A rectangular tank 31 cm long, 46 cm wide and 50 cm high contained 6.8 ℓ of water at first. What is the capacity of the rectangular tank?
Ans: [?] ℓ",
"answer0": "71.3",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 192,
"difficulty_id": 2,
"explanation": "Capacity = \\(31 \\times 46 \\times 50 = 71300\\) cm³. Since 1000 cm³ = 1 ℓ, 71300 cm³ = 71.3 ℓ. Answer: 71.3 ℓ.",
"hints": ["Volume = length × width × height in cm³.", "Convert cm³ to litres by dividing by 1000."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q16a",
"image_needed": true,
"image_options": false,
"image_file": "q52.png",
"image_page": 32,
"image_bbox": [0.34, 0.20, 0.66, 0.42],
"image_loc": "3-D rectangular tank with a tap on top, dimensions 31 cm long, 46 cm wide, 50 cm high",
"notes": "Key: 31x46x50=71300cm³ = 71.3ℓ. [1 mark]"
},
{
"n": 53,
"type_id": 2,
"question": "A rectangular tank 31 cm long, 46 cm wide and 50 cm high contained 6.8 ℓ of water at first. The tap was turned on and water flowed into the tank at a rate of 3 ℓ per minute. At this rate, how long did it take to fill the tank?
Ans: [?] min",
"answer0": "21.5",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 193,
"difficulty_id": 2,
"explanation": "Tank capacity = 71.3 ℓ. Water needed = \\(71.3 - 6.8 = 64.5\\) ℓ. Time = \\(64.5 \\div 3 = 21.5\\) min. Answer: 21.5 min.",
"hints": ["Water still needed = capacity − 6.8 ℓ.", "Divide by the fill rate 3 ℓ/min."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q16b",
"image_needed": true,
"image_options": false,
"image_file": "q53.png",
"image_page": 32,
"image_bbox": [0.34, 0.20, 0.66, 0.42],
"image_loc": "3-D rectangular tank with a tap on top, dimensions 31 cm long, 46 cm wide, 50 cm high (same figure as part a)",
"notes": "Key working: 71.3−6.8=64.5, 64.5÷3=21.5min. [3 marks]. Same figure as Q52."
},
{
"n": 54,
"type_id": 2,
"question": "Marcus bought some books and files for a total of $192. 2 books and 1 file cost $11.20. Each book cost 3 times as much as a file. He bought 8 more books than files. What is the cost of 1 file?
Ans: $[?]",
"answer0": "1.60",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "Let 1 file = f. Each book = 3f. 2 books + 1 file = \\(2(3f) + f = 7f = \\$11.20\\). So f = \\(11.20 \\div 7 = \\$1.60\\). Answer: $1.60.",
"hints": ["Each book = 3 × file, so 2 books + 1 file = 7 files in cost.", "Divide $11.20 by 7."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q17a",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working: 2x3=6, 6+1=7, 11.2÷7=$1.60. [1 mark]"
},
{
"n": 55,
"type_id": 2,
"question": "Marcus bought some books and files for a total of $192. Each book cost $4.80 and each file cost $1.60. He bought 8 more books than files. How many files did Marcus buy?
Ans: [?]",
"answer0": "24",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "1 book = \\(3 \\times 1.60 = \\$4.80\\). 8 extra books cost \\(4.80 \\times 8 = \\$38.40\\). Remaining = \\(192 - 38.40 = \\$153.60\\) is spent on equal numbers of books and files: 1 book + 1 file = \\(4.80 + 1.60 = \\$6.40\\). Number of files = \\(153.60 \\div 6.40 = 24\\). Answer: 24.",
"hints": ["Cost of the 8 extra books = 4.80 × 8; subtract from $192.", "Divide the rest by (book + file) = $6.40 to get the number of files."],
"source": "Ai Tong 2022 P5 Semestral Assessment 2 P2Q17b",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working: 1.6x3=4.8, 4.8x8=38.4, 192−38.4=153.6, 1.6+4.8=6.4, 153.6÷6.4=24. Book/file unit costs restated in stem from part (a). [4 marks]"
}
]
}