{
"paper": {
"school": "SCGS",
"year": 2024,
"level": "P6",
"label": "Prelim",
"source_prefix": "SCGS 2024 P6 Prelim",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "3 hundreds, 2 tenths and 7 hundredths is ____.",
"answer0": "300.027",
"answer1": "300.270",
"answer2": "300.720",
"answer3": "320.070",
"correct_answer": 1,
"skill_id": 149,
"difficulty_id": 1,
"explanation": "3 hundreds = 300, 2 tenths = 0.2, 7 hundredths = 0.07. Sum = 300 + 0.2 + 0.07 = 300.27, option (2).",
"hints": ["Tenths are the first place after the decimal point; hundredths are the second.", "300 + 0.2 + 0.07 = 300.27."],
"source": "SCGS 2024 P6 Prelim Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key (option 2) verified against printed answer table."
},
{
"n": 2,
"type_id": 1,
"question": "Round 467 583 to the nearest thousand.",
"answer0": "467 000",
"answer1": "467 600",
"answer2": "468 000",
"answer3": "470 000",
"correct_answer": 2,
"skill_id": 150,
"difficulty_id": 1,
"explanation": "To round to the nearest thousand, look at the hundreds digit (5). Since 583 is 500 or more, round up: 467 583 rounds to 468 000, option (3).",
"hints": ["Look at the hundreds digit to decide whether to round up or down.", "583 is more than 500, so round the thousands up."],
"source": "SCGS 2024 P6 Prelim Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key (option 3) verified against printed answer table."
},
{
"n": 3,
"type_id": 1,
"question": "Which of the following fractions is the largest?",
"answer0": "\\(\\dfrac{2}{3}\\)",
"answer1": "\\(\\dfrac{3}{5}\\)",
"answer2": "\\(\\dfrac{5}{9}\\)",
"answer3": "\\(\\dfrac{6}{11}\\)",
"correct_answer": 0,
"skill_id": 158,
"difficulty_id": 2,
"explanation": "Convert to decimals: \\(\\dfrac{2}{3} \\approx 0.667\\), \\(\\dfrac{3}{5} = 0.6\\), \\(\\dfrac{5}{9} \\approx 0.556\\), \\(\\dfrac{6}{11} \\approx 0.545\\). The largest is \\(\\dfrac{2}{3}\\), option (1).",
"hints": ["Convert each fraction to a decimal to compare them.", "2/3 is about 0.67, the biggest of the four."],
"source": "SCGS 2024 P6 Prelim Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key (option 1) verified against printed answer table."
},
{
"n": 4,
"type_id": 1,
"question": "How many eighths are there in \\(2\\dfrac{3}{4}\\)?",
"answer0": "11",
"answer1": "19",
"answer2": "22",
"answer3": "23",
"correct_answer": 2,
"skill_id": 158,
"difficulty_id": 2,
"explanation": "\\(2\\dfrac{3}{4} = \\dfrac{11}{4} = \\dfrac{22}{8}\\). So there are 22 eighths, option (3).",
"hints": ["Convert the mixed number to a fraction with denominator 8.", "2 3/4 = 11/4 = 22/8."],
"source": "SCGS 2024 P6 Prelim Q4",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key (option 3) verified against printed answer table."
},
{
"n": 5,
"type_id": 1,
"question": "The figure shows an 8-point compass. Judy was facing north-west (NW) after she had turned 135° clockwise. Which direction was Judy facing at first?",
"answer0": "North",
"answer1": "South",
"answer2": "East",
"answer3": "West",
"correct_answer": 1,
"skill_id": 452,
"difficulty_id": 2,
"explanation": "She ended facing NW after turning 135° clockwise. Turning back 135° anticlockwise from NW: each 8-point step is 45°, so 135° = 3 steps. Going back 3 steps anticlockwise from NW (NW → W → SW → S) gives South, option (2).",
"hints": ["Each step on an 8-point compass is 45°; 135° is 3 steps.", "Turn back 3 steps anticlockwise from NW to find the starting direction."],
"source": "SCGS 2024 P6 Prelim Q5",
"image_needed": true,
"image_options": false,
"image_file": "q5.png",
"image_page": 3,
"image_bbox": [0.33, 0.34, 0.66, 0.52],
"image_loc": "centre of page, the 8-point compass rose (N/NE/E/SE/S/SW/W/NW with arrows)",
"notes": "Key (option 2, South) verified against printed answer table. 8-point compass topic (removed from 2026 syllabus, skill 452)."
},
{
"n": 6,
"type_id": 1,
"question": "There were 80 children in a school hall. 24 children were boys. What percentage of the children were girls?",
"answer0": "24%",
"answer1": "30%",
"answer2": "56%",
"answer3": "70%",
"correct_answer": 3,
"skill_id": 171,
"difficulty_id": 1,
"explanation": "Girls = 80 − 24 = 56. Percentage of girls = \\(\\dfrac{56}{80} \\times 100\\% = 70\\%\\), option (4).",
"hints": ["First find the number of girls: 80 − 24.", "Percentage = (girls ÷ total) × 100%."],
"source": "SCGS 2024 P6 Prelim Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key (option 4) verified against printed answer table."
},
{
"n": 7,
"type_id": 1,
"question": "Wenling had $20. After buying 4 identical plates, she had $z left. Express the cost of 1 plate in terms of z.",
"answer0": "\\($(20 - 4z)\\)",
"answer1": "\\($\\left(20 - \\dfrac{z}{4}\\right)\\)",
"answer2": "\\($\\left(\\dfrac{20z}{4}\\right)\\)",
"answer3": "\\($\\left(\\dfrac{20 - z}{4}\\right)\\)",
"correct_answer": 3,
"skill_id": 241,
"difficulty_id": 2,
"explanation": "Total spent on plates = $(20 − z). This was for 4 plates, so cost of 1 plate = \\($\\left(\\dfrac{20 - z}{4}\\right)\\), option (4).",
"hints": ["Money spent on plates = 20 − z.", "Divide the amount spent by 4 to get the cost of one plate."],
"source": "SCGS 2024 P6 Prelim Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key (option 4) verified against printed answer table."
},
{
"n": 8,
"type_id": 1,
"question": "The table shows the number of cars and motorcycles in a carpark over the weekend.
Saturday: 240 cars, ? motorcycles
Sunday: 128 cars, 72 motorcycles
20% of the vehicles in the carpark on Saturday were motorcycles. How many motorcycles were there in the carpark on Saturday?",
"answer0": "48",
"answer1": "60",
"answer2": "88",
"answer3": "110",
"correct_answer": 1,
"skill_id": 175,
"difficulty_id": 2,
"explanation": "On Saturday, motorcycles = 20% of total, so cars = 80% of total. Cars = 240 = 80%, so 1% = 3, and total = 300. Motorcycles = 20% × 300 = 60, option (2).",
"hints": ["Cars are 80% of the Saturday total; use this to find the total.", "240 cars = 80%, so 100% = 300, then motorcycles = 20% of 300."],
"source": "SCGS 2024 P6 Prelim Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Small 2x2 vehicle table transcribed inline. Key (option 2) verified against printed answer table."
},
{
"n": 9,
"type_id": 1,
"question": "The figure is made up of 5 identical squares, each of side 4 cm. Find the perimeter of the figure.",
"answer0": "40 cm",
"answer1": "48 cm",
"answer2": "56 cm",
"answer3": "80 cm",
"correct_answer": 2,
"skill_id": 223,
"difficulty_id": 2,
"explanation": "Counting the outer edges of the figure (two squares on the left, two on the right, joined by one connecting square between them), the total perimeter works out to 56 cm, option (3).",
"hints": ["Each square has side 4 cm; trace the outer boundary of the whole figure.", "Count how many 4 cm edges lie on the outside."],
"source": "SCGS 2024 P6 Prelim Q9",
"image_needed": true,
"image_options": false,
"image_file": "q9.png",
"image_page": 5,
"image_bbox": [0.42, 0.13, 0.68, 0.27],
"image_loc": "top centre of page, figure of 5 identical squares (two pairs joined by a connector) with the 4 cm side marked",
"notes": "Key (option 3, 56 cm) verified against printed answer table. Figure required to count the boundary."
},
{
"n": 10,
"type_id": 1,
"question": "Which of the following is not the net of a cube?",
"answer0": "Net (1)",
"answer1": "Net (2)",
"answer2": "Net (3)",
"answer3": "Net (4)",
"correct_answer": 2,
"skill_id": 233,
"difficulty_id": 2,
"explanation": "Mentally fold each net of 6 squares. Three of them fold into a cube without overlap; net (3) has two faces that overlap when folded, so it is not a valid cube net, option (3).",
"hints": ["A cube net has 6 squares that fold without any two faces overlapping.", "Fold each net in your mind and find the one where faces clash."],
"source": "SCGS 2024 P6 Prelim Q10",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 5,
"image_bbox": [0.13, 0.46, 0.85, 0.85],
"image_loc": "lower half of page, four labelled square-nets (1)-(4) arranged in two rows",
"notes": "Key (option 3) verified against printed answer table. image_options true: each option is a net diagram; crop each to q10_opt0..3. type_id 1 retained (image-option MCQ)."
},
{
"n": 11,
"type_id": 1,
"question": "ABCD is a rhombus. ADE is a straight line and ∠CAD is 36°. Find ∠CDE.",
"answer0": "36°",
"answer1": "72°",
"answer2": "108°",
"answer3": "144°",
"correct_answer": 1,
"skill_id": 230,
"difficulty_id": 2,
"explanation": "In a rhombus the diagonal AC bisects the angles, and triangle ACD is isosceles (AD = CD). With ∠CAD = 36°, ∠ACD = 36° too, so ∠ADC = 180 − 36 − 36 = 108°. ∠CDE is the angle on the straight line ADE: ∠CDE = 180 − 108 = 72°, option (2).",
"hints": ["Triangle ACD is isosceles with AD = CD, so ∠CAD = ∠ACD = 36°.", "∠ADC = 108°; ∠CDE is its supplement on the straight line ADE."],
"source": "SCGS 2024 P6 Prelim Q11",
"image_needed": true,
"image_options": false,
"image_file": "q11.png",
"image_page": 6,
"image_bbox": [0.18, 0.11, 0.55, 0.24],
"image_loc": "upper left of page, rhombus ABCD with diagonal AC, the 36° angle at A, and straight line A-D-E with the angle at D",
"notes": "Key (option 2, 72°) verified against printed answer table. Figure required."
},
{
"n": 12,
"type_id": 1,
"question": "A group of children were asked to name their favourite ice cream flavours. The pie chart shows their choices. How many children chose chocolate ice cream as their favourite?",
"answer0": "160",
"answer1": "170",
"answer2": "240",
"answer3": "400",
"correct_answer": 0,
"skill_id": 235,
"difficulty_id": 2,
"explanation": "Strawberry (70), Vanilla (120) and Mint (50) account for 70 + 120 + 50 = 240 children, which is 60% (since Chocolate is 40%). So 60% = 240, 1% = 4, and Chocolate = 40% × 4 = 160 children, option (1).",
"hints": ["The three numbered sectors make up 100% − 40% = 60% of the children.", "70 + 120 + 50 = 240 is 60%; scale up to find 40%."],
"source": "SCGS 2024 P6 Prelim Q12",
"image_needed": true,
"image_options": false,
"image_file": "q12.png",
"image_page": 6,
"image_bbox": [0.38, 0.52, 0.66, 0.72],
"image_loc": "centre of page, pie chart with sectors Chocolate 40%, Strawberry 70, Vanilla 120, Mint 50",
"notes": "Key (option 1, 160) verified against printed answer table. Pie chart required."
},
{
"n": 13,
"type_id": 1,
"question": "Alison and Betty had 200 picture cards. After Alison gave Betty 20 picture cards, Alison still had 40 cards more than Betty. How many cards did Betty have at first?",
"answer0": "60",
"answer1": "70",
"answer2": "80",
"answer3": "140",
"correct_answer": 0,
"skill_id": 152,
"difficulty_id": 2,
"explanation": "After the transfer the total is still 200, with Alison 40 more than Betty. So after: Betty = (200 − 40) ÷ 2 = 80, Alison = 120. Before, Alison had given away 20, so Betty originally had 80 − 20 = 60 cards, option (1).",
"hints": ["The total stays 200; after the move Alison has 40 more than Betty.", "Find Betty's amount after the move, then subtract the 20 she received."],
"source": "SCGS 2024 P6 Prelim Q13",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key (option 1, 60) verified against printed answer table."
},
{
"n": 14,
"type_id": 1,
"question": "The price of a handbag was reduced from $150 to $120. What was the percentage decrease in price of the handbag?",
"answer0": "20%",
"answer1": "25%",
"answer2": "30%",
"answer3": "80%",
"correct_answer": 0,
"skill_id": 208,
"difficulty_id": 1,
"explanation": "Decrease = 150 − 120 = $30. Percentage decrease = \\(\\dfrac{30}{150} \\times 100\\% = 20\\%\\), option (1).",
"hints": ["Percentage decrease is based on the original price ($150).", "30 ÷ 150 × 100% = 20%."],
"source": "SCGS 2024 P6 Prelim Q14",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key (option 1) verified against printed answer table."
},
{
"n": 15,
"type_id": 1,
"question": "A table with 4 columns is filled with numbers in a certain pattern.
Row 1: A 57, B 58, C 59, D 60
Row 2: A 61, B 62, C 63, D 64
Row 3: A 65, B 66, C 67, D 68
Row 4: A 69, B 70, C 71, D 72
In which column will the number 350 appear?",
"answer0": "Column A",
"answer1": "Column B",
"answer2": "Column C",
"answer3": "Column D",
"correct_answer": 1,
"skill_id": 108,
"difficulty_id": 2,
"explanation": "Column A holds 57, 61, 65, ... (remainder 1 when ÷4 starting pattern). Each entry is the previous +1 across a row and +4 down a column. 350 = 57 + 293; checking the column pattern, 350 lands in Column B, option (2).",
"hints": ["Each row increases by 4 from the previous row in the same column.", "Track which column the running value 350 falls into."],
"source": "SCGS 2024 P6 Prelim Q15",
"image_needed": true,
"image_options": false,
"image_file": "q15.png",
"image_page": 7,
"image_bbox": [0.16, 0.58, 0.85, 0.72],
"image_loc": "centre of page, the 4-column number pattern table (Columns A-D, Rows 1-4) with dotted continuation rows",
"notes": "Key (option 2, Column B) verified against printed answer table. The full pattern table is transcribed inline but the figure aids reading."
},
{
"n": 16,
"type_id": 2,
"question": "What is the length of the nail shown in the figure? [?]",
"answer0": "1.6",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 184,
"difficulty_id": 1,
"explanation": "The nail spans from the 2 cm mark to the 3.6 cm mark on the ruler. Length = 3.6 − 2 = 1.6 cm.",
"hints": ["Read the ruler positions of both ends of the nail.", "Length = right reading − left reading."],
"source": "SCGS 2024 P6 Prelim Q16",
"image_needed": true,
"image_options": false,
"image_file": "q16.png",
"image_page": 9,
"image_bbox": [0.22, 0.24, 0.62, 0.36],
"image_loc": "upper left of page, a nail lying along a ruler scale marked 2 cm, 3 cm, 4 cm",
"notes": "Printed answer 1.6 cm verified. Answer unit is cm; FIB numeric answer = 1.6. Ruler image required."
},
{
"n": 17,
"type_id": 2,
"question": "Find the value of \\(8 + 32 \\div 4 - 3 \\times 2\\). [?]",
"answer0": "10",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 155,
"difficulty_id": 1,
"explanation": "Order of operations: \\(32 \\div 4 = 8\\) and \\(3 \\times 2 = 6\\). So \\(8 + 8 - 6 = 10\\).",
"hints": ["Do division and multiplication before addition and subtraction.", "8 + 8 − 6 = 10."],
"source": "SCGS 2024 P6 Prelim Q17",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Printed answer 10 verified."
},
{
"n": 18,
"type_id": 2,
"question": "Find the value of \\(24.12 - 6.75\\). [?]",
"answer0": "17.37",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 167,
"difficulty_id": 1,
"explanation": "\\(24.12 - 6.75 = 17.37\\).",
"hints": ["Line up the decimal points and subtract.", "24.12 − 6.75 = 17.37."],
"source": "SCGS 2024 P6 Prelim Q18",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Printed answer 17.37 verified."
},
{
"n": 19,
"type_id": 1,
"question": "Find the value of \\(\\dfrac{3}{10} \\div 12\\).",
"answer0": "\\(\\dfrac{3}{120}\\)",
"answer1": "\\(\\dfrac{1}{40}\\)",
"answer2": "\\(\\dfrac{36}{10}\\)",
"answer3": "\\(\\dfrac{12}{10}\\)",
"correct_answer": 0,
"skill_id": 164,
"difficulty_id": 2,
"explanation": "\\(\\dfrac{3}{10} \\div 12 = \\dfrac{3}{10} \\times \\dfrac{1}{12} = \\dfrac{3}{120}\\) (which simplifies to \\(\\dfrac{1}{40}\\)).",
"hints": ["Dividing by 12 is the same as multiplying by 1/12.", "3/10 × 1/12 = 3/120."],
"source": "SCGS 2024 P6 Prelim Q19",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Printed answer 3/120 (= 1/40). Fraction answer → converted to MCQ per spec (FIB answers must be integers/decimals). Distractors include the simplest-form value."
},
{
"n": 20,
"type_id": 0,
"question": "Shade 2 more unit squares so that AB is the line of symmetry for the figure.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 144,
"difficulty_id": 2,
"explanation": "Reflect the existing shaded squares across the diagonal line AB; the two squares whose mirror images are not yet shaded must be shaded to complete the symmetry (see printed key figure).",
"hints": ["Each shaded square should have a mirror-image shaded square across line AB.", "Find the squares whose reflections are currently blank and shade them."],
"source": "SCGS 2024 P6 Prelim Q20",
"image_needed": true,
"image_options": false,
"image_file": null,
"image_page": 10,
"image_bbox": [0.18, 0.45, 0.62, 0.74],
"image_loc": "centre of page, grid with diagonal line A (top-left) to B (bottom-right) and several pre-shaded unit squares",
"notes": "Interactive shade-the-grid task → type_id 0 (skipped on insert). Answer per printed key: shade the 2 squares completing reflection symmetry across AB."
},
{
"n": 21,
"type_id": 2,
"question": "Find the perimeter of the quadrant of radius 7 cm. \\(\\left(\\text{Take } \\pi = \\dfrac{22}{7}\\right)\\) [?]",
"answer0": "25",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 221,
"difficulty_id": 2,
"explanation": "Arc of quadrant = \\(\\dfrac{1}{4} \\times 2 \\times \\dfrac{22}{7} \\times 7 = 11\\) cm. Perimeter = arc + 2 radii = 11 + 7 + 7 = 25 cm.",
"hints": ["Quadrant arc = 1/4 of the full circumference.", "Add the two straight radii (7 cm each) to the arc."],
"source": "SCGS 2024 P6 Prelim Q21",
"image_needed": true,
"image_options": false,
"image_file": "q21.png",
"image_page": 11,
"image_bbox": [0.15, 0.22, 0.30, 0.33],
"image_loc": "upper left of page, a shaded quarter-circle (quadrant)",
"notes": "Printed answer: 44÷4 = 11, 11 + 14 = 25 cm verified. Answer unit cm; FIB numeric answer = 25."
},
{
"n": 22,
"type_id": 2,
"question": "The table shows the charges to post a parcel.
First 3 kg: $1 per kg
Each additional kg: $2 per kg
Mrs Tan posted 2 parcels. One weighs 2 kg and the other weighs 5 kg. How much did Mrs Tan pay? [?]",
"answer0": "9",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 2,
"explanation": "2 kg parcel: within first 3 kg, so 2 × $1 = $2. 5 kg parcel: first 3 kg at $1 = $3, plus 2 extra kg at $2 = $4, total $7. Overall = $2 + $7 = $9.",
"hints": ["The 2 kg parcel is all charged at $1 per kg.", "For the 5 kg parcel, charge the first 3 kg at $1 and the extra 2 kg at $2."],
"source": "SCGS 2024 P6 Prelim Q22",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Small charges table transcribed inline. Printed answer: 2kg = $2, 5kg = $7, total = $9 verified. Answer is money $9; FIB numeric = 9."
},
{
"n": 23,
"type_id": 0,
"question": "A triangle ABC is drawn on a square grid inside a box. By joining dots on the grid with straight lines, (a) draw ABD such that ABD is a right-angled triangle with the same perimeter as triangle ABC, ABD should not overlap with ABC; (b) draw ABE such that ABE is an obtuse triangle with the same area as triangle ABC.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 195,
"difficulty_id": 3,
"explanation": "(a) Draw a right-angled triangle sharing AB with the same total perimeter as ABC by choosing grid points so its three side lengths sum to ABC's perimeter. (b) Draw an obtuse triangle on the same base AB with the same height (hence same area) as ABC, positioned so one angle exceeds 90°. (Printed key: drawing only.)",
"hints": ["Same perimeter means equal total side length; same area means equal base × height ÷ 2.", "Use the grid to keep base AB fixed and pick the third vertex to satisfy each condition."],
"source": "SCGS 2024 P6 Prelim Q23",
"image_needed": true,
"image_options": false,
"image_file": null,
"image_page": 12,
"image_bbox": [0.20, 0.13, 0.70, 0.46],
"image_loc": "upper area of page, square dot-grid box with triangle ABC drawn (vertices A, B, C marked)",
"notes": "Interactive draw-on-grid task → type_id 0 (skipped on insert). Printed key: a) DRAWING, b) DRAWING."
},
{
"n": 24,
"type_id": 2,
"question": "The average height of 5 boys is 146 cm. Sundra whose height is 158 cm left the group. What is the average height of the remaining boys? [?]",
"answer0": "143",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 205,
"difficulty_id": 2,
"explanation": "Total height of 5 boys = 146 × 5 = 730 cm. After Sundra (158 cm) leaves: 730 − 158 = 572 cm for 4 boys. New average = 572 ÷ 4 = 143 cm.",
"hints": ["Total = average × number of boys.", "Remove Sundra's height, then divide by the 4 remaining boys."],
"source": "SCGS 2024 P6 Prelim Q24",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Printed answer: 146×5 = 730, 730−158 = 572, 572÷4 = 143 cm verified. Answer unit cm; FIB numeric = 143."
},
{
"n": 25,
"type_id": 1,
"question": "Mrs Teo had \\(\\dfrac{5}{6}\\) kg of sugar. She used \\(\\dfrac{1}{2}\\) of it and gave \\(\\dfrac{1}{4}\\) kg of sugar away. How much sugar did she have left?",
"answer0": "\\(\\dfrac{1}{6}\\) kg",
"answer1": "\\(\\dfrac{5}{12}\\) kg",
"answer2": "\\(\\dfrac{1}{12}\\) kg",
"answer3": "\\(\\dfrac{1}{4}\\) kg",
"correct_answer": 0,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "Sugar used = \\(\\dfrac{1}{2} \\times \\dfrac{5}{6} = \\dfrac{5}{12}\\) kg. After using: \\(\\dfrac{5}{6} - \\dfrac{5}{12} = \\dfrac{10}{12} - \\dfrac{5}{12} = \\dfrac{5}{12}\\) kg. After giving away \\(\\dfrac{1}{4} = \\dfrac{3}{12}\\) kg: \\(\\dfrac{5}{12} - \\dfrac{3}{12} = \\dfrac{2}{12} = \\dfrac{1}{6}\\) kg.",
"hints": ["'Used 1/2 of it' means 1/2 × 5/6, not 1/2 kg.", "Subtract the used amount and then the 1/4 kg given away, using a common denominator of 12."],
"source": "SCGS 2024 P6 Prelim Q25",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Printed key works to 1/6 kg. Fraction answer → converted to MCQ per spec (FIB answers must be integers/decimals)."
},
{
"n": 26,
"type_id": 2,
"question": "A tank with a square base has a volume of 16 \\(l\\). Given that the height of the tank is 40 cm, find the length of the square base. [?]",
"answer0": "20",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 224,
"difficulty_id": 3,
"explanation": "16 \\(l\\) = 16 000 cm³. Base area = volume ÷ height = 16 000 ÷ 40 = 400 cm². For a square base, length = \\(\\sqrt{400}\\) = 20 cm.",
"hints": ["Convert 16 litres to 16 000 cm³.", "Base area = volume ÷ height; the base is square, so take the square root."],
"source": "SCGS 2024 P6 Prelim Q26",
"image_needed": true,
"image_options": false,
"image_file": "q26.png",
"image_page": 13,
"image_bbox": [0.18, 0.53, 0.40, 0.70],
"image_loc": "left of page, a tall cuboid (square-base tank) with the 40 cm height marked",
"notes": "Printed answer: 16000÷40 = 400, √400 = 20 cm verified. Answer unit cm; FIB numeric = 20."
},
{
"n": 27,
"type_id": 2,
"question": "AEB and CED are straight lines. ∠AEC = 100° and ∠DEF = 68°. Find ∠p. [?]",
"answer0": "32",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 194,
"difficulty_id": 2,
"explanation": "∠AEC = 100°, so its vertically opposite angle ∠BED = 100°. ∠DEF = 68° is part of ∠BED, so ∠p (= ∠FEB) = 100 − 68 = 32°. (Equivalently 180 − 100 − 68 = 12... using straight line; the printed key gives ∠p = 180 − 80 − 68 = 32°.)",
"hints": ["Use vertically opposite angles and angles on a straight line at point E.", "∠p = 180 − 100 − 68 = 32°."],
"source": "SCGS 2024 P6 Prelim Q27",
"image_needed": true,
"image_options": false,
"image_file": "q27.png",
"image_page": 14,
"image_bbox": [0.18, 0.13, 0.52, 0.30],
"image_loc": "upper left of page, intersecting straight lines AEB and CED with ray EF, angles 100°, 68° and p marked at E",
"notes": "Printed answer: 180 − 80 − 68 = 32° verified. Answer in degrees; FIB numeric = 32. Figure required."
},
{
"n": 28,
"type_id": 2,
"question": "Mrs Raju had 120 apples and pears at her stall. She sold \\(\\dfrac{1}{2}\\) of the apples and \\(\\dfrac{1}{4}\\) of the pears and had an equal number of apples and pears left. How many apples did Mrs Raju sell? [?]",
"answer0": "36",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "Apples left = \\(\\dfrac{1}{2}\\) of apples; pears left = \\(\\dfrac{3}{4}\\) of pears. These are equal: \\(\\dfrac{1}{2}A = \\dfrac{3}{4}P\\). From the printed key, this gives A = 72 and P = 48 (total 120), so apples sold = \\(\\dfrac{1}{2} \\times 72 = 36\\).",
"hints": ["Apples left = 1/2 of apples; pears left = 3/4 of pears; set them equal.", "With apples + pears = 120, solve to get apples = 72, then sell half."],
"source": "SCGS 2024 P6 Prelim Q28",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Printed key: 1/2 = 3/6 units relation, 120 ÷ 10 = 12, apples sold = 12 × 3 = 36 verified. FIB numeric = 36."
},
{
"n": 29,
"type_id": 2,
"question": "Mrs Wong gave her students some pencils. If she gave each student 11 pencils each, she would have 5 pencils left. If she gave each student 8 pencils each, there would be 32 pencils left. How many pencils did she have altogether? [?]",
"answer0": "104",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "The difference in pencils given out = (11 − 8) per student = 3 per student, and this equals the difference in leftovers = 32 − 5 = 27. So number of students = 27 ÷ 3 = 9. Total pencils = 11 × 9 + 5 = 99 + 5 = 104.",
"hints": ["The extra 3 pencils per student account for the 27 fewer left over.", "Students = 27 ÷ 3 = 9; total = 11 × 9 + 5."],
"source": "SCGS 2024 P6 Prelim Q29",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Printed key: 11x + 5 = 8x + 32, x = 9, N = 104 verified. FIB numeric = 104."
},
{
"n": 30,
"type_id": 2,
"question": "Alex and Meng took part in a race. Both of them ran at constant speeds. Alex ran 50 m/min faster than Meng. When Meng had run \\(\\dfrac{1}{4}\\) of the race, Alex was 600 m ahead of him. How long did Meng take to complete the race? Express your answer in minutes. [?]",
"answer0": "48",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 219,
"difficulty_id": 3,
"explanation": "Alex is 50 m/min faster, so in the time elapsed the 600 m lead means 600 ÷ 50 = 12 minutes have passed. That 12 minutes is the time for Meng to run 1/4 of the race. So the whole race takes Meng 12 × 4 = 48 minutes.",
"hints": ["The 600 m gap grows at 50 m per minute, so it took 600 ÷ 50 = 12 min.", "That 12 min covers 1/4 of Meng's race, so the full race is 12 × 4 min."],
"source": "SCGS 2024 P6 Prelim Q30",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Printed answer: 12 min × 4 = 48 mins verified. Answer in minutes; FIB numeric = 48. Speed topic (skill 219, moved to Sec 1 in 2026)."
},
{
"n": 31,
"type_id": 2,
"question": "The market is 7.5 km away from Siva's house. Siva took 10 minutes to drive to the market. Find Siva's average speed for the journey. [?]",
"answer0": "45",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 217,
"difficulty_id": 2,
"explanation": "10 minutes = \\(\\dfrac{10}{60} = \\dfrac{1}{6}\\) hour. Average speed = distance ÷ time = 7.5 ÷ \\(\\dfrac{1}{6}\\) = 7.5 × 6 = 45 km/h.",
"hints": ["Convert 10 minutes to a fraction of an hour: 1/6 h.", "Speed = distance ÷ time = 7.5 ÷ 1/6."],
"source": "SCGS 2024 P6 Prelim Q31",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q1. Printed answer 45 km/h verified. Answer unit km/h; FIB numeric = 45. Speed topic (skill 217)."
},
{
"n": 32,
"type_id": 2,
"question": "Farah and Sue shared the cost of an oven. Farah paid $30 more than \\(\\dfrac{5}{8}\\) of the cost of the oven. Sue paid $90. How much did the oven cost? [?]",
"answer0": "320",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "Let the oven cost u. Farah paid \\(\\dfrac{5}{8}u + 30\\), Sue paid the rest = \\(u - \\dfrac{5}{8}u - 30 = \\dfrac{3}{8}u - 30 = 90\\). So \\(\\dfrac{3}{8}u = 120\\), \\(u = 120 \\times \\dfrac{8}{3} = 320\\). The oven cost $320.",
"hints": ["Sue's payment = total − Farah's payment.", "Set 3/8 of the cost minus 30 equal to 90 and solve."],
"source": "SCGS 2024 P6 Prelim Q32",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q2. Printed key: 3/8 u − 30 = 90, u = $320 verified (the printed 'Ans: 45 km per hr' label is a copy-paste typo on the key; the working clearly gives $320). FIB numeric = 320."
},
{
"n": 33,
"type_id": 1,
"question": "Kelly had \\(2\\dfrac{4}{5}\\) \\(l\\) of juice. She used it to fill as many identical glasses as she could to the brim. Each glass holds \\(\\dfrac{1}{4}\\) \\(l\\) of juice. How much juice did she have left?",
"answer0": "\\(\\dfrac{1}{20}\\) \\(l\\)",
"answer1": "\\(\\dfrac{1}{5}\\) \\(l\\)",
"answer2": "\\(\\dfrac{3}{4}\\) \\(l\\)",
"answer3": "\\(\\dfrac{1}{10}\\) \\(l\\)",
"correct_answer": 0,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "\\(2\\dfrac{4}{5} = \\dfrac{14}{5}\\) \\(l\\). Number of \\(\\dfrac{1}{4}\\) \\(l\\) glasses = \\(\\dfrac{14}{5} \\div \\dfrac{1}{4} = \\dfrac{56}{5} = 11\\dfrac{1}{5}\\), so 11 full glasses. Juice used = 11 × \\(\\dfrac{1}{4} = \\dfrac{11}{4} = \\dfrac{55}{20}\\) \\(l\\). Left = \\(\\dfrac{14}{5} - \\dfrac{11}{4} = \\dfrac{56}{20} - \\dfrac{55}{20} = \\dfrac{1}{20}\\) \\(l\\).",
"hints": ["Only whole glasses count; find how many 1/4 l glasses fit.", "Left = total − (number of whole glasses × 1/4 l)."],
"source": "SCGS 2024 P6 Prelim Q33",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q3. Printed key works to 1/20 l. Fraction answer → converted to MCQ per spec."
},
{
"n": 34,
"type_id": 2,
"question": "In the figure, ABC is a right-angled triangle and BCD is an isosceles triangle. BC = CD. ∠AED = 76° and ∠BDC = 58°. Find ∠BAC. [?]",
"answer0": "44",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 197,
"difficulty_id": 3,
"explanation": "Triangle BCD is isosceles with BC = CD, so ∠DBC = ∠BDC = 58°. In right-angled triangle ABC, ∠ABC = 90°, so ∠ABE = 90 − 58 = 32°. ∠AEB = 180 − 76 = 104° (angles on a straight line at E). In triangle ABE, ∠BAC = 180 − 32 − 104 = 44°.",
"hints": ["Use the isosceles triangle BCD to find ∠DBC = 58°.", "Then work through triangle ABE: ∠BAC = 180 − ∠ABE − ∠AEB."],
"source": "SCGS 2024 P6 Prelim Q34",
"image_needed": true,
"image_options": false,
"image_file": "q34.png",
"image_page": 18,
"image_bbox": [0.16, 0.16, 0.42, 0.40],
"image_loc": "upper left of page, right-angled triangle ABC with isosceles triangle BCD, intersection point E, angles 76° and 58° marked",
"notes": "Paper 2 Q4. Printed answer 44° verified. Answer in degrees; FIB numeric = 44. Figure required."
},
{
"n": 35,
"type_id": 2,
"question": "The figure is made up of 2 identical triangles, Triangle AGH and Triangle BGH, drawn within Square ABCD. EF is \\(\\dfrac{2}{5}\\) of BC. The area of the shaded parts is 36 cm². Find the area of Triangle AGH. [?]",
"answer0": "22.5",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 186,
"difficulty_id": 3,
"explanation": "Let GH = u and BC = v. Shaded area = area of two triangles minus the overlapping middle = \\(\\dfrac{1}{2}uv + \\dfrac{1}{2}uv - \\dfrac{1}{2}u \\times \\dfrac{2}{5}v = \\dfrac{4}{5}uv = 36\\), so \\(uv = 36 \\times \\dfrac{5}{4} = 45\\). Area of triangle AGH = \\(\\dfrac{1}{2}uv = \\dfrac{1}{2} \\times 45 = 22.5\\) cm².",
"hints": ["Set GH = u and BC = v; express the shaded area in terms of u and v.", "Shaded = 4/5 uv = 36, so uv = 45, then triangle AGH = 1/2 uv."],
"source": "SCGS 2024 P6 Prelim Q35",
"image_needed": true,
"image_options": false,
"image_file": "q35.png",
"image_page": 18,
"image_bbox": [0.16, 0.62, 0.40, 0.84],
"image_loc": "lower left of page, square ABCD with two shaded triangles AGH and BGH meeting at E above the base DC (points D, G, F, H, C along the base)",
"notes": "Paper 2 Q5. Printed answer 22.5 cm² verified (printed 'Ans: 44°' label is a copy-paste typo; working gives 22.5 cm²). Answer unit cm²; FIB numeric = 22.5. Figure required."
},
{
"n": 36,
"type_id": 2,
"question": "The table shows the number of magazines sold in a book store last week.
Monday to Friday: 3y per day
Saturday: 2y + 10
Sunday: 4y − 2
If y = 15, what was the total number of magazines sold on Saturday and Sunday? [?]",
"answer0": "98",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 240,
"difficulty_id": 2,
"explanation": "Magazines on Saturday and Sunday = (2y + 10) + (4y − 2) = 6y + 8. When y = 15: 6 × 15 + 8 = 90 + 8 = 98.",
"hints": ["Add the Saturday and Sunday expressions: (2y + 10) + (4y − 2).", "Substitute y = 15 into 6y + 8."],
"source": "SCGS 2024 P6 Prelim Q36",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q6. Part (a) of the original asks for the simplified expression 21y + 8 (an algebraic answer, not a value); only part (b) gives a numeric answer (98), so this question records part (b). Printed answer b) 98 verified. FIB numeric = 98."
},
{
"n": 37,
"type_id": 2,
"question": "A shopkeeper has some red and blue pens. After he sells 240 red pens, the percentage of pens he has that are red will decrease from 40% to 20%. How many red pens does he have at first? [?]",
"answer0": "384",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 209,
"difficulty_id": 3,
"explanation": "The number of blue pens does not change. At first red = 40% so blue = 60% of the total. After selling 240 red, red = 20% so blue = 80% of the new total. Since blue is constant: 60% of the old total = 80% of the new total. Solving (printed key) gives old total = 960, blue = 576, so red at first = 960 − 576 = 384.",
"hints": ["Blue pens stay the same; express blue as a percentage before and after.", "60% × (old total) = 80% × (old total − 240); solve for the totals."],
"source": "SCGS 2024 P6 Prelim Q37",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q7. Printed answer 384 verified (total at first 960, blue 576, red 384). FIB numeric = 384."
},
{
"n": 38,
"type_id": 2,
"question": "A shop sells identical rolls of coloured wire of length 40 cm. Alice needs 120 pieces of wire, each of length 7 cm, to complete an art project. What is the least number of rolls of coloured wire that Alice needs to buy from the shop to complete her project? [?]",
"answer0": "24",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 2,
"explanation": "From each 40 cm roll, the number of 7 cm pieces = 40 ÷ 7 = 5 remainder 5, so 5 pieces per roll (the 5 cm offcut is wasted). Least number of rolls = 120 ÷ 5 = 24 rolls.",
"hints": ["Each roll gives only whole 7 cm pieces: 40 ÷ 7 = 5 pieces (5 cm wasted).", "Rolls needed = 120 pieces ÷ 5 pieces per roll."],
"source": "SCGS 2024 P6 Prelim Q38",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q8. Printed answer 24 verified. FIB numeric = 24."
},
{
"n": 39,
"type_id": 2,
"question": "The solid is made up of 8 identical unit cubes. What is the greatest number of unit cubes that can be added to the solid without changing the front view and side view? [?]",
"answer0": "3",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 188,
"difficulty_id": 3,
"explanation": "Filling in the hidden positions that do not alter the front and side silhouettes, the greatest number of unit cubes that can be added is 3 (printed key).",
"hints": ["You may add cubes only where they stay hidden behind the existing front and side outlines.", "Count the empty interior positions that keep both views unchanged."],
"source": "SCGS 2024 P6 Prelim Q39",
"image_needed": true,
"image_options": false,
"image_file": "q39.png",
"image_page": 21,
"image_bbox": [0.30, 0.13, 0.66, 0.32],
"image_loc": "upper centre of page, isometric drawing of the 8-unit-cube solid with Top View / Front View / Side View arrows",
"notes": "Paper 2 Q9. Part (a) is a draw-the-views task (interactive); part (b) gives the numeric answer 3. This question records part (b). Printed answer b) 3 verified. FIB numeric = 3."
},
{
"n": 40,
"type_id": 2,
"question": "The line graph shows the total volume of water collected in a tank from 12 00 to 17 00. What was the average volume of water collected per hour? Express your answer in litres. [?]",
"answer0": "16",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 205,
"difficulty_id": 2,
"explanation": "Total water collected from 12 00 to 17 00 = 80 \\(l\\) (final reading). Number of hours = 17 − 12 = 5. Average per hour = 80 ÷ 5 = 16 \\(l\\) per hour.",
"hints": ["Read the total volume at 17 00 from the graph (80 l).", "Average = total volume ÷ number of hours (5 hours)."],
"source": "SCGS 2024 P6 Prelim Q40",
"image_needed": true,
"image_options": false,
"image_file": "q40.png",
"image_page": 22,
"image_bbox": [0.20, 0.16, 0.80, 0.40],
"image_loc": "upper area of page, line graph 'Total volume of water collected in litres' against time 12 00 to 17 00",
"notes": "Paper 2 Q10. Parts (a) (15 00 to 16 00) and (b) (16 l) are short sub-answers; this question records part (c), the average (16 l per hr). Printed answer c) 16 l per hr verified. Answer unit litres; FIB numeric = 16. Graph required."
},
{
"n": 41,
"type_id": 2,
"question": "Julia went shopping. After spending \\(\\dfrac{3}{8}\\) of her money on a bag, she bought a wallet which cost $60 less than the bag. Finally, with the remaining money, she bought a dress which was \\(\\dfrac{1}{2}\\) of the total cost of the bag and wallet. How much did Julia pay for the wallet? [?]",
"answer0": "210",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 209,
"difficulty_id": 3,
"explanation": "Let u be her money. Bag = \\(\\dfrac{3}{8}u\\), wallet = \\(\\dfrac{3}{8}u - 60\\), dress = \\(\\dfrac{1}{2}\\left(\\dfrac{3}{8}u + \\dfrac{3}{8}u - 60\\right) = \\dfrac{3}{8}u - 30\\). The dress equals the remaining money = \\(u - \\dfrac{3}{8}u - \\left(\\dfrac{3}{8}u - 60\\right) = \\dfrac{1}{4}u + 60\\). Setting equal: \\(\\dfrac{3}{8}u - 30 = \\dfrac{1}{4}u + 60\\) gives \\(\\dfrac{1}{8}u = 90\\), so u = $720. Wallet = \\(\\dfrac{3}{8} \\times 720 - 60 = 270 - 60 = $210\\).",
"hints": ["Express bag, wallet and dress in terms of her total money u.", "The dress cost = remaining money; set up and solve, then compute the wallet."],
"source": "SCGS 2024 P6 Prelim Q41",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q11. Printed answer $210 verified (u = $720, wallet = $210). FIB numeric = 210."
},
{
"n": 42,
"type_id": 2,
"question": "9 identical small rectangles are combined to form a large rectangle ABCD. The perimeter of Rectangle ABCD is 138 cm. Find the area of rectangle ABCD. [?]",
"answer0": "1134",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Let the small rectangle have width u and length 3.5u (from the arrangement). The perimeter of ABCD in terms of u is 23u = 138, so u = 6 cm and length of small rectangle = 3.5 × 6 = 21 cm. Area of ABCD = (6 × 7) × (6 + 21) = 42 × 27 = 1134 cm².",
"hints": ["Express the big rectangle's perimeter in terms of one small-rectangle width u.", "23u = 138 → u = 6; then compute the big rectangle's dimensions and area."],
"source": "SCGS 2024 P6 Prelim Q42",
"image_needed": true,
"image_options": false,
"image_file": "q42.png",
"image_page": 24,
"image_bbox": [0.30, 0.18, 0.60, 0.32],
"image_loc": "upper centre of page, large rectangle ABCD divided into 9 identical small rectangles (one row across the top, vertical strips below)",
"notes": "Paper 2 Q12. Printed answer 1134 cm² verified (u = 6, length 21, area 1134). Answer unit cm²; FIB numeric = 1134. Figure required."
},
{
"n": 43,
"type_id": 2,
"question": "The bar graph shows the number of electronic devices owned by 200 employees in a company. What is the total number of electronic devices owned by all the employees in the company? [?]",
"answer0": "450",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 104,
"difficulty_id": 2,
"explanation": "From the bar graph: 10 own 0 devices, 30 own 1, 80 own 2, 60 own 3, 20 own 4. Total devices = 30 × 1 + 80 × 2 + 60 × 3 + 20 × 4 = 30 + 160 + 180 + 80 = 450.",
"hints": ["Multiply the number of employees in each bar by the number of devices.", "30(1) + 80(2) + 60(3) + 20(4) = 450."],
"source": "SCGS 2024 P6 Prelim Q43",
"image_needed": true,
"image_options": false,
"image_file": "q43.png",
"image_page": 25,
"image_bbox": [0.20, 0.16, 0.80, 0.40],
"image_loc": "upper area of page, bar graph 'Number of employees' against 'Number of electronic devices' (0 to 4)",
"notes": "Paper 2 Q13. Parts (a) (1/20) and (b) (160) are sub-answers; this question records part (c), the total (450). Printed answer c) 450 verified. FIB numeric = 450. Bar graph required."
},
{
"n": 44,
"type_id": 2,
"question": "The figure shows 2 identical semi-circles within a quadrant. The radius of the quadrant is 28 cm. Find the perimeter of the shaded part. \\(\\left(\\text{Take } \\pi = \\dfrac{22}{7}\\right)\\) [?]",
"answer0": "116",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 222,
"difficulty_id": 3,
"explanation": "Quadrant arc = \\(\\dfrac{1}{4} \\times 2 \\times \\dfrac{22}{7} \\times 28 = 44\\) cm. The two semicircles each have radius 7 cm; their arcs total \\(2 \\times \\dfrac{22}{7} \\times 7 = 44\\) cm. Perimeter of shaded part = quadrant arc + two semicircle arcs + one straight radius = 44 + 44 + 28 = 116 cm.",
"hints": ["Find the quadrant arc and the two semicircle arcs separately.", "Add the one straight side (28 cm): 44 + 44 + 28 = 116 cm."],
"source": "SCGS 2024 P6 Prelim Q44",
"image_needed": true,
"image_options": false,
"image_file": "q44.png",
"image_page": 26,
"image_bbox": [0.17, 0.16, 0.36, 0.30],
"image_loc": "upper left of page, shaded quadrant of radius 28 cm with two small semicircles cut out along the top edge",
"notes": "Paper 2 Q14(a). Printed answer 116 cm verified. Answer unit cm; FIB numeric = 116. Figure required. (Q14(b) is a separate question, recorded next.)"
},
{
"n": 45,
"type_id": 2,
"question": "The figure shows a circle with centre O and a trapezium OABC. The radius of the circle is 6 cm and AB is 9 cm. Find the area of the shaded part. (Take π = 3.14) [?]",
"answer0": "16.74",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 223,
"difficulty_id": 3,
"explanation": "Following the printed key: Area of the square (side 6) = 36 cm². Area of quadrant = 3.14 × 6 × 6 × \\(\\dfrac{1}{4}\\) = 28.26 cm². Area of triangle = \\(\\dfrac{1}{2} \\times 3 \\times 6 = 9\\) cm². Shaded area = 36 − 28.26 + 9 = 16.74 cm².",
"hints": ["Break the shaded region into a square/triangle minus a quadrant of the circle.", "36 − 28.26 + 9 = 16.74 cm²."],
"source": "SCGS 2024 P6 Prelim Q45",
"image_needed": true,
"image_options": false,
"image_file": "q45.png",
"image_page": 26,
"image_bbox": [0.55, 0.52, 0.80, 0.70],
"image_loc": "centre-right of page, circle with centre O and trapezium OABC, AB = 9 cm marked, shaded region near A-B-C",
"notes": "Paper 2 Q14(b). Printed answer 16.74 cm² verified. Answer unit cm²; FIB numeric = 16.74. Figure required."
},
{
"n": 46,
"type_id": 2,
"question": "PQRS is a parallelogram, and PQT and PVU are straight lines. ∠QWV = 50°, ∠WQV = 38°, ∠WSR = 29°, ∠QPW = 21° and ∠QTU = 67°. Find ∠SPW. [?]",
"answer0": "92",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "In triangle QRS, ∠QRS = 180 − 38 − 29 = 113°. In a parallelogram, ∠QPS = ∠QRS = 113°. ∠SPW = ∠QPS − ∠QPW = 113 − 21 = 92°.",
"hints": ["Find ∠QRS using the angle sum of a triangle, then use parallelogram opposite angles.", "∠SPW = ∠QPS − ∠QPW = 113 − 21."],
"source": "SCGS 2024 P6 Prelim Q46",
"image_needed": true,
"image_options": false,
"image_file": "q46.png",
"image_page": 27,
"image_bbox": [0.20, 0.15, 0.66, 0.32],
"image_loc": "upper area of page, parallelogram PQRS with straight lines PQT and PVU and interior points W, V; angles 21°, 38°, 50°, 29°, 67° marked",
"notes": "Paper 2 Q15(a). Printed answer 92° verified. Answer in degrees; FIB numeric = 92. Part (b) is a true/false/not-possible tick table (interactive, recorded next as type_id 0). Figure required."
},
{
"n": 47,
"type_id": 0,
"question": "PQRS is a parallelogram, and PQT and PVU are straight lines. ∠QWV = 50°, ∠WQV = 38°, ∠WSR = 29°, ∠QPW = 21° and ∠QTU = 67°. Each statement is either true, false or not possible to tell. State your answer for each: (i) ∠SPW = ∠RVU; (ii) TU is parallel to QV.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "(i) ∠SPW = ∠RVU is True (corresponding angles). (ii) ∠QWP = 180 − 50 = 130°, so ∠PQW = 180 − 21 − 130 = 29°, giving ∠PQV = 38 + 29 = 67° = ∠PTU, therefore TU is parallel to QV — True. Both statements are True.",
"hints": ["For (i) look for corresponding angles formed by the straight lines.", "For (ii) compute ∠PQV and compare with ∠QTU = 67° to test for parallel lines."],
"source": "SCGS 2024 P6 Prelim Q47",
"image_needed": true,
"image_options": false,
"image_file": null,
"image_page": 27,
"image_bbox": [0.20, 0.15, 0.66, 0.32],
"image_loc": "upper area of page (same figure as Q46), parallelogram PQRS with straight lines and interior points W, V",
"notes": "Paper 2 Q15(b). Tick-the-box true/false/not-possible table → type_id 0 (skipped on insert). Printed key: both statements True (T, T)."
}
]
}