{ "paper": { "school": "Nanyang Primary School", "year": 2025, "level": "P6", "label": "Prelim", "source_prefix": "Nanyang 2025 P6 Prelim", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "Round 31 899 to the nearest thousand.", "answer0": "30 000", "answer1": "31 000", "answer2": "31 900", "answer3": "32 000", "correct_answer": 3, "skill_id": 106, "difficulty_id": 1, "explanation": "The hundreds digit of 31 899 is 8, which is 5 or more, so round up. 31 899 rounds to 32 000.", "hints": ["Look at the hundreds digit to decide whether to round up or down.", "8 hundreds means round up to the next thousand."], "source": "Nanyang 2025 P6 Prelim Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: Q1 = 4 (1-based) -> option index 3 (32 000)." }, { "n": 2, "type_id": 1, "question": "What does the digit 8 in 7.089 stand for?", "answer0": "8 tens", "answer1": "8 tenths", "answer2": "8 hundredths", "answer3": "8 thousandths", "correct_answer": 2, "skill_id": 124, "difficulty_id": 1, "explanation": "In 7.089, the digit 8 is in the hundredths place (second place after the decimal point), so it stands for 8 hundredths.", "hints": ["Count the decimal places: tenths, hundredths, thousandths.", "8 is the second digit after the decimal point."], "source": "Nanyang 2025 P6 Prelim Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: Q2 = 3 (1-based) -> option index 2 (8 hundredths)." }, { "n": 3, "type_id": 1, "question": "In the number line, what is the value of A?", "answer0": "2.402", "answer1": "2.404", "answer2": "2.420", "answer3": "2.440", "correct_answer": 3, "skill_id": 124, "difficulty_id": 2, "explanation": "Each major interval (2.2 to 2.3 etc.) is divided into 5 parts, so each small mark is 0.02. A is 2 marks after 2.4, i.e. 2.4 + 0.04 = 2.44, written as 2.440.", "hints": ["Work out the value of each small division between 2.4 and 2.5.", "Count the small marks from 2.4 to A."], "source": "Nanyang 2025 P6 Prelim Q3", "image_needed": true, "image_page": 4, "image_bbox": [0.22, 0.13, 0.83, 0.22], "image_loc": "number line from 2.2 to 2.5 below the question, with arrow marked A", "image_options": false, "image_file": null, "notes": "Answer key: Q3 = 4 (1-based) -> option index 3 (2.440)." }, { "n": 4, "type_id": 1, "question": "Which two lines in the square grid are parallel to each other?", "answer0": "AB and BC", "answer1": "BC and DE", "answer2": "AK and FG", "answer3": "AK and HK", "correct_answer": 2, "skill_id": 100, "difficulty_id": 2, "explanation": "On the square grid, lines AK and FG have the same slant (same horizontal and vertical step), so they are parallel.", "hints": ["Parallel lines have the same gradient/slant on the grid.", "Compare the rise and run of each pair of lines."], "source": "Nanyang 2025 P6 Prelim Q4", "image_needed": true, "image_page": 5, "image_bbox": [0.31, 0.08, 0.72, 0.31], "image_loc": "square grid with lettered line segments A,B,C,D,E,F,G,H,K below the question", "image_options": false, "image_file": null, "notes": "Answer key: Q4 = 3 (1-based) -> option index 2 (AK and FG)." }, { "n": 5, "type_id": 1, "question": "BOD is a straight line. \\(\\angle\\)AOD = 100° and \\(\\angle\\)BOC = 76°. Find \\(\\angle\\)COD.", "answer0": "80°", "answer1": "92°", "answer2": "104°", "answer3": "124°", "correct_answer": 2, "skill_id": 100, "difficulty_id": 2, "explanation": "BOD is a straight line, so \\(\\angle\\)BOC + \\(\\angle\\)COD = 180° along the line is not it; use \\(\\angle\\)AOD + \\(\\angle\\)AOB = 180°. \\(\\angle\\)AOB = 180° − 100° = 80° (angles on straight line BOD at O, with A above). Then \\(\\angle\\)AOB = \\(\\angle\\)AOC − \\(\\angle\\)BOC... Using vertical/straight-line reasoning: \\(\\angle\\)COD = 180° − \\(\\angle\\)BOC = 180° − 76° = 104° (since BOC and COD are angles on straight line BOD).", "hints": ["BOD is a straight line, so \\(\\angle\\)BOC and \\(\\angle\\)COD are angles on a straight line.", "Angles on a straight line add up to 180°."], "source": "Nanyang 2025 P6 Prelim Q5", "image_needed": true, "image_page": 6, "image_bbox": [0.33, 0.1, 0.62, 0.25], "image_loc": "diagram of lines through point O with rays A, B, C, D and marked angles 100° and 76°", "image_options": false, "image_file": null, "notes": "Answer key: Q5 = 3 (1-based) -> option index 2 (104°)." }, { "n": 6, "type_id": 1, "question": "ABCD is a trapezium. AB is parallel to DC.
Which of the following is true?", "answer0": "\\(\\angle\\)ABC = \\(\\angle\\)ADC", "answer1": "\\(\\angle\\)BAD = \\(\\angle\\)BCD", "answer2": "\\(\\angle\\)ABC + \\(\\angle\\)BAD = 180°", "answer3": "\\(\\angle\\)BAD + \\(\\angle\\)ADC = 180°", "correct_answer": 3, "skill_id": 200, "difficulty_id": 2, "explanation": "Since AB is parallel to DC, AD is a transversal, so the co-interior (allied) angles \\(\\angle\\)BAD and \\(\\angle\\)ADC add up to 180°.", "hints": ["AB parallel to DC; AD cuts both.", "Co-interior angles between parallel lines add up to 180°."], "source": "Nanyang 2025 P6 Prelim Q6", "image_needed": true, "image_page": 7, "image_bbox": [0.3, 0.1, 0.75, 0.23], "image_loc": "trapezium ABCD with AB parallel to DC", "image_options": false, "image_file": null, "notes": "Answer key: Q6 = 4 (1-based) -> option index 3 (\\(\\angle\\)BAD + \\(\\angle\\)ADC = 180°)." }, { "n": 7, "type_id": 1, "question": "Which of the following is not a net of a cube?", "answer0": "Net 1", "answer1": "Net 2", "answer2": "Net 3", "answer3": "Net 4", "correct_answer": 1, "skill_id": 231, "difficulty_id": 2, "explanation": "When folded, option 2's arrangement of six squares causes two faces to overlap and leaves a gap, so it cannot fold into a cube. The other three fold correctly into a cube.", "hints": ["Try mentally folding each net into a cube.", "A valid net has six squares that fold without any overlapping faces."], "source": "Nanyang 2025 P6 Prelim Q7", "image_needed": true, "image_options": true, "image_page": 8, "image_bbox": [0.28, 0.1, 0.45, 0.6], "image_loc": "four square-grid nets labelled (1) to (4) down the page", "image_file": null, "notes": "Image-option MCQ: the four options are pictures of nets. Crop each net to q7_opt0.png .. q7_opt3.png. Answer key: Q7 = 2 (1-based) -> option index 1 (Net 2)." }, { "n": 8, "type_id": 1, "question": "A fish burger cost $\\(m\\). A beef burger cost $(\\(m\\) + 1). The total cost of 4 fish burgers and 1 beef burger is $21. Find the cost of 1 beef burger.", "answer0": "$5", "answer1": "$4.40", "answer2": "$4.20", "answer3": "$4", "correct_answer": 0, "skill_id": 240, "difficulty_id": 2, "explanation": "4m + (m + 1) = 21, so 5m + 1 = 21, 5m = 20, m = 4. Beef burger = m + 1 = $5.", "hints": ["Write an equation for the total cost: 4m + (m + 1) = 21.", "Solve for m, then add 1 for the beef burger."], "source": "Nanyang 2025 P6 Prelim Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: Q8 = 1 (1-based) -> option index 0 ($5)." }, { "n": 9, "type_id": 1, "question": "The pie chart represents the number of mango, vanilla and durian ice creams sold.
The number of ice creams sold is also represented by the bar graph. The bar for the number of vanilla ice creams sold has not been drawn.
How many vanilla ice creams were sold?", "answer0": "70", "answer1": "90", "answer2": "120", "answer3": "160", "correct_answer": 3, "skill_id": 235, "difficulty_id": 3, "explanation": "From the bar graph, Mango = 270 and Durian = 210. The pie chart shows the vanilla angle is a right angle (90°), so vanilla = 1/4 of the total. Let total = T: vanilla = T/4, and mango + durian = 270 + 210 = 480 = 3/4 of T, so T = 640 and vanilla = 640 − 480 = 160.", "hints": ["Read Mango (270) and Durian (210) from the bar graph.", "The vanilla sector is a quarter circle (right angle marked), so vanilla is 1/4 of the total."], "source": "Nanyang 2025 P6 Prelim Q9", "image_needed": true, "image_page": 10, "image_bbox": [0.28, 0.09, 0.72, 0.55], "image_loc": "pie chart of Durian/Mango/Vanilla above a bar graph of ice creams sold (Mango, Vanilla, Durian)", "image_options": false, "image_file": null, "notes": "Answer key: Q9 = 4 (1-based) -> option index 3 (160)." }, { "n": 10, "type_id": 1, "question": "The figure shows a slide in a playground. Which of the following is likely to be the height of the slide?", "answer0": "2.5 cm", "answer1": "25 cm", "answer2": "2.5 m", "answer3": "25 m", "correct_answer": 2, "skill_id": 184, "difficulty_id": 1, "explanation": "A playground slide is taller than a child but only a few metres high. 2.5 m is the realistic height.", "hints": ["Compare the slide to the height of a child.", "A few metres is reasonable; centimetres are too small and 25 m is far too tall."], "source": "Nanyang 2025 P6 Prelim Q10", "image_needed": true, "image_page": 11, "image_bbox": [0.36, 0.1, 0.66, 0.27], "image_loc": "picture of a child on a playground slide", "image_options": false, "image_file": null, "notes": "Answer key: Q10 = 3 (1-based) -> option index 2 (2.5 m)." }, { "n": 11, "type_id": 1, "question": "Arrange the following fractions from the largest to the smallest.
\\(\\dfrac{11}{5}\\), \\(2\\dfrac{4}{9}\\), \\(\\dfrac{5}{2}\\)", "answer0": "\\(\\dfrac{5}{2}\\), \\(2\\dfrac{4}{9}\\), \\(\\dfrac{11}{5}\\)", "answer1": "\\(\\dfrac{5}{2}\\), \\(\\dfrac{11}{5}\\), \\(2\\dfrac{4}{9}\\)", "answer2": "\\(\\dfrac{11}{5}\\), \\(\\dfrac{5}{2}\\), \\(2\\dfrac{4}{9}\\)", "answer3": "\\(\\dfrac{11}{5}\\), \\(2\\dfrac{4}{9}\\), \\(\\dfrac{5}{2}\\)", "correct_answer": 0, "skill_id": 162, "difficulty_id": 2, "explanation": "Convert to decimals: 11/5 = 2.2, 2 4/9 ≈ 2.44, 5/2 = 2.5. From largest to smallest: 5/2, 2 4/9, 11/5.", "hints": ["Change each fraction to a decimal to compare.", "11/5 = 2.2, 2 4/9 ≈ 2.44, 5/2 = 2.5."], "source": "Nanyang 2025 P6 Prelim Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Converted to MCQ (fraction/mixed-number options). Answer key: Q11 = 1 (1-based) -> option index 0 (5/2, 2 4/9, 11/5)." }, { "n": 12, "type_id": 1, "question": "The square grid shows the position of six points.
Olivia stood at a point south-west of P and south-east of Q. She was facing Q and then she turned 135° clockwise. What point did she face in the end?", "answer0": "R", "answer1": "S", "answer2": "T", "answer3": "U", "correct_answer": 1, "skill_id": 452, "difficulty_id": 3, "explanation": "Olivia stands at point R (south-west of P, south-east of Q). Facing Q is north-west. Turning 135° clockwise from north-west gives a direction pointing towards S (north-west -> east of south... ending facing S).", "hints": ["Find Olivia's starting point: south-west of P and south-east of Q.", "Facing Q is north-west; a 135° clockwise turn changes the facing direction by 135°."], "source": "Nanyang 2025 P6 Prelim Q12", "image_needed": true, "image_page": 13, "image_bbox": [0.38, 0.09, 0.7, 0.27], "image_loc": "square grid with six labelled points P,Q,R,S,T,U and a North arrow to the right", "image_options": false, "image_file": null, "notes": "Answer key: Q12 = 2 (1-based) -> option index 1 (S)." }, { "n": 13, "type_id": 1, "question": "The diagrams show the readings shown on the weighing scales A, B and C.
Which scale has the heaviest mass placed on it and which scale has the lightest mass placed on it?", "answer0": "Heaviest B, Lightest A", "answer1": "Heaviest B, Lightest C", "answer2": "Heaviest C, Lightest A", "answer3": "Heaviest C, Lightest B", "correct_answer": 0, "skill_id": 184, "difficulty_id": 2, "explanation": "Reading each scale: Scale A and B run 14 kg to 16 kg, Scale C runs 15 kg to 16 kg. Scale B's pointer shows the heaviest reading and Scale A's pointer shows the lightest. Heaviest B, lightest A.", "hints": ["Read each pointer carefully, noting that the scales have different ranges.", "Compare the actual masses, not the pointer positions."], "source": "Nanyang 2025 P6 Prelim Q13", "image_needed": true, "image_page": 14, "image_bbox": [0.24, 0.13, 0.78, 0.22], "image_loc": "three weighing scale dials labelled Scale A, Scale B, Scale C", "image_options": false, "image_file": null, "notes": "Answer key: Q13 = 1 (1-based) -> option index 0 (Heaviest B, Lightest A)." }, { "n": 14, "type_id": 1, "question": "Bernice has three ropes, J, K and L. The ratio of the length of Rope J to the length of Rope K is 5 : 8. Rope K is \\(\\dfrac{4}{9}\\) as long as Rope L. What is the ratio of the length of Rope J to the length of Rope L?", "answer0": "8 : 9", "answer1": "5 : 9", "answer2": "8 : 18", "answer3": "5 : 18", "correct_answer": 3, "skill_id": 213, "difficulty_id": 3, "explanation": "K = 4/9 of L, so K : L = 4 : 9. J : K = 5 : 8. Make K common: J : K = 5 : 8 and K : L = 4 : 9 = 8 : 18. So J : K : L = 5 : 8 : 18, giving J : L = 5 : 18.", "hints": ["Write K : L from the fraction (4 : 9).", "Make the K parts equal in both ratios, then read off J : L."], "source": "Nanyang 2025 P6 Prelim Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: Q14 = 4 (1-based) -> option index 3 (5 : 18)." }, { "n": 15, "type_id": 1, "question": "A table with 4 columns is filled with numbers in a certain pattern. The first six rows of the table are shown.
In which column will the number 257 appear?", "answer0": "Column A", "answer1": "Column B", "answer2": "Column C", "answer3": "Column D", "correct_answer": 1, "skill_id": 240, "difficulty_id": 3, "explanation": "Odd numbers fill columns B and C, even numbers fill columns A and D, in a zig-zag pattern by row. 257 is odd. Tracking the pattern of odd numbers (1 in B, 3 in C, 5 in B, 7 in C, 9 in B, 11 in C...): odd numbers in B are 1, 5, 9, 13, ... (i.e. ≡ 1 mod 4). 257 = 4×64 + 1, so 257 ≡ 1 (mod 4) and appears in Column B.", "hints": ["257 is an odd number, so look only at where odd numbers appear.", "Find the pattern of which column each odd number falls in (mod 4)."], "source": "Nanyang 2025 P6 Prelim Q15", "image_needed": true, "image_page": 15, "image_bbox": [0.24, 0.1, 0.62, 0.23], "image_loc": "4-column table (Columns A-D) with shaded cells and numbers for Rows 1-6", "image_options": false, "image_file": null, "notes": "Answer key: Q15 = 2 (1-based) -> option index 1 (Column B)." }, { "n": 16, "type_id": 2, "question": "Ming baked 32 cupcakes. He gave \\(\\dfrac{5}{8}\\) of the cupcakes to his friend. How many cupcakes did he give to his friend? [?]", "answer0": "20", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 163, "difficulty_id": 1, "explanation": "5/8 of 32 = 5/8 × 32 = 20 cupcakes.", "hints": ["Find 1/8 of 32 first.", "Multiply by 5."], "source": "Nanyang 2025 P6 Prelim Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 5/8 x 32 = 20." }, { "n": 17, "type_id": 2, "question": "Convert 72.5 centimetres to metres.
[?] m", "answer0": "0.725", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 184, "difficulty_id": 1, "explanation": "1 m = 100 cm, so 72.5 cm = 72.5 ÷ 100 = 0.725 m.", "hints": ["Divide by 100 to convert cm to m.", "Move the decimal point two places to the left."], "source": "Nanyang 2025 P6 Prelim Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 72.5 cm = 0.725 m." }, { "n": 18, "type_id": 0, "question": "There are 9 shaded squares in the figure. Shade 3 more squares to form a symmetric figure with AB as the line of symmetry.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 145, "difficulty_id": 2, "explanation": "Reflect the existing shaded squares across the diagonal line AB; shade the 3 squares that are the mirror images of squares not yet matched, so the whole figure becomes symmetric about AB.", "hints": ["AB is a diagonal line of symmetry.", "Each shaded square must have a matching shaded square reflected across AB."], "source": "Nanyang 2025 P6 Prelim Q18", "image_needed": true, "image_page": 20, "image_bbox": [0.42, 0.12, 0.66, 0.26], "image_loc": "5x5-ish grid with 9 shaded squares and a dashed diagonal line of symmetry AB", "image_options": false, "image_file": null, "notes": "type_id 0 (shade-the-grid / draw task) - skipped on insert. Answer: shade 3 squares to make the figure symmetric about diagonal AB (see printed key diagram)." }, { "n": 19, "type_id": 0, "question": "The solid is made up of 7 cubes. Draw the front view of the solid on the grid.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 201, "difficulty_id": 2, "explanation": "Looking from the front, the cubes project to an L/T-shaped outline: a row of squares along the bottom with one square stacked on top, as shown in the printed key.", "hints": ["Look at the solid only from the front direction shown.", "Each column of cubes seen from the front becomes a column of squares."], "source": "Nanyang 2025 P6 Prelim Q19", "image_needed": true, "image_page": 21, "image_bbox": [0.32, 0.1, 0.7, 0.32], "image_loc": "isometric drawing of 7 cubes with Top/Front/Side view arrows", "image_options": false, "image_file": null, "notes": "type_id 0 (draw front view) - skipped on insert. Answer: front view is the T/plus-shaped outline shown in the printed key." }, { "n": 20, "type_id": 2, "question": "The structure is made up of identical cubes. Without rearranging the cubes, what is the least number of such cubes that must be added to make the structure into a cuboid?
[?]", "answer0": "48", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 229, "difficulty_id": 3, "explanation": "The smallest cuboid that encloses the structure is 4 × 5 × 3 = 60 cubes. The structure already has 12 cubes, so cubes to add = 60 − 12 = 48.", "hints": ["Find the dimensions of the smallest cuboid that contains the whole structure.", "Subtract the number of cubes already present from the cuboid's total."], "source": "Nanyang 2025 P6 Prelim Q20", "image_needed": true, "image_page": 22, "image_bbox": [0.3, 0.18, 0.68, 0.45], "image_loc": "isometric drawing of a cube structure with axis lines through it", "image_options": false, "image_file": null, "notes": "Answer key: 4 x 5 x 3 = 60; 60 - 12 = 48." }, { "n": 21, "type_id": 2, "question": "Write down all the common factors of 18 and 45.
[?], [?], [?]", "answer0": "1", "answer1": "3", "answer2": "9", "answer3": null, "correct_answer": null, "skill_id": 113, "difficulty_id": 2, "explanation": "Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 45: 1, 3, 5, 9, 15, 45. Common factors: 1, 3, 9.", "hints": ["List the factors of 18 and the factors of 45.", "Pick out the factors that appear in both lists."], "source": "Nanyang 2025 P6 Prelim Q21", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 1, 3, 9. Three numeric answers, one [?] per common factor." }, { "n": 22, "type_id": 2, "question": "Find the value of
(a) 5.1 − 3.89 [?]
(b) 2.02 × 2000 [?]", "answer0": "1.21", "answer1": "4040", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 126, "difficulty_id": 2, "explanation": "(a) 5.1 − 3.89 = 1.21. (b) 2.02 × 2000 = 4040.", "hints": ["(a) Line up the decimal points before subtracting.", "(b) 2.02 × 2000 = 2.02 × 2 × 1000."], "source": "Nanyang 2025 P6 Prelim Q22", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two parts (a)/(b), one [?] per part. Answer key: (a) 1.21, (b) 4040." }, { "n": 23, "type_id": 2, "question": "The opening hours of KOLA Restaurant are: Open daily 12.15 p.m. to 11.30 p.m. (Closed from 2.30 p.m. to 5 p.m.) How long is the restaurant open each day? Give your answer in hours and minutes.
[?] h [?] min", "answer0": "8", "answer1": "45", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 135, "difficulty_id": 2, "explanation": "Total span 12.15 p.m. to 11.30 p.m. = 11 h 15 min. Closed period 2.30 p.m. to 5 p.m. = 2 h 30 min. Open time = 11 h 15 min − 2 h 30 min = 8 h 45 min.", "hints": ["Find the full time from opening to closing first.", "Subtract the closed period (2 h 30 min)."], "source": "Nanyang 2025 P6 Prelim Q23", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 11h15min - 2h30min = 8h45min. Two numeric blanks (hours, minutes)." }, { "n": 24, "type_id": 2, "question": "Last year, the population of Town X was 5600. This year, the population of Town X has increased to 6300. What is the percentage increase in the population of Town X?
[?]%", "answer0": "12.5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 208, "difficulty_id": 2, "explanation": "Increase = 6300 − 5600 = 700. Percentage increase = 700/5600 × 100% = 12.5%.", "hints": ["Find the increase in population first.", "Percentage increase = increase ÷ original × 100%."], "source": "Nanyang 2025 P6 Prelim Q24", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 6300 - 5600 = 700; 700/5600 x 100% = 12.5%." }, { "n": 25, "type_id": 2, "question": "Dan packed 840 books into 2 crates and 3 boxes. The number of books he packed into each crate was twice as many as the number of books he packed into each box. How many books did he pack into each box?
[?]", "answer0": "120", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 240, "difficulty_id": 2, "explanation": "Each crate = 2 boxes, so 2 crates = 4 boxes' worth. Total units = 4 + 3 = 7 boxes. 840 ÷ 7 = 120 books per box.", "hints": ["Express each crate in terms of boxes (1 crate = 2 boxes).", "Total units = 2×2 + 3 = 7; divide 840 by 7."], "source": "Nanyang 2025 P6 Prelim Q25", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 2x2=4; 4+3=7; 840/7 = 120." }, { "n": 26, "type_id": 1, "question": "There was \\(\\dfrac{3}{8}\\) ℓ of water in a tank at first. Xiao Ming poured \\(\\dfrac{3}{5}\\) ℓ of water into the tank and used \\(\\dfrac{5}{8}\\) ℓ of water from the tank to wash the dishes. How much water was left in the tank?", "answer0": "\\(\\dfrac{14}{40}\\) ℓ", "answer1": "\\(\\dfrac{7}{20}\\) ℓ", "answer2": "\\(\\dfrac{39}{40}\\) ℓ", "answer3": "\\(\\dfrac{1}{8}\\) ℓ", "correct_answer": 1, "skill_id": 165, "difficulty_id": 2, "explanation": "Water = 3/8 + 3/5 − 5/8 = 15/40 + 24/40 − 25/40 = 14/40 = 7/20 ℓ.", "hints": ["Add the water poured in, then subtract the water used.", "Use a common denominator of 40."], "source": "Nanyang 2025 P6 Prelim Q26", "image_needed": false, "image_options": false, "image_file": null, "notes": "Converted to MCQ (fraction answer 14/40 = 7/20 ℓ). Answer key working: 3/8 + 3/5 = 39/40; 39/40 - 25/40 = 14/40. 14/40 = 7/20 (option index 1)." }, { "n": 27, "type_id": 1, "question": "Ahmad had 13 m of string. He used it to make as many bracelets as he could. He used \\(\\dfrac{3}{5}\\) m of string to make each bracelet. How many metres of the string was left?", "answer0": "\\(\\dfrac{2}{5}\\) m", "answer1": "\\(\\dfrac{3}{5}\\) m", "answer2": "\\(\\dfrac{2}{3}\\) m", "answer3": "\\(\\dfrac{1}{5}\\) m", "correct_answer": 0, "skill_id": 165, "difficulty_id": 3, "explanation": "13 ÷ 3/5 = 13 × 5/3 = 65/3 = 21 2/3, so he made 21 bracelets and 2/3 of a bracelet's length is left over. The leftover string = 2/3 × 3/5 = 2/5 m.", "hints": ["Divide 13 by 3/5 to find how many bracelets and the fractional remainder.", "The remainder (2/3 of a bracelet) is 2/3 × 3/5 m of string."], "source": "Nanyang 2025 P6 Prelim Q27", "image_needed": false, "image_options": false, "image_file": null, "notes": "Converted to MCQ (fraction answer 2/5 m). Answer key: 13 / (3/5) = 21 2/3; leftover = 2/3 x 3/5 = 2/5 (option index 0)." }, { "n": 28, "type_id": 2, "question": "ABE and BCD are triangles. ABC is a straight line. AB = BE and BD = CD. \\(\\angle\\)EBD = 73° and \\(\\angle\\)BCD = 55°. Find \\(\\angle\\)BEA.
[?]°", "answer0": "64", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 196, "difficulty_id": 3, "explanation": "Triangle BCD is isosceles (BD = CD) so \\(\\angle\\)DBC = \\(\\angle\\)BCD = 55°. ABC is a straight line, so \\(\\angle\\)ABE = 180° − \\(\\angle\\)EBD − \\(\\angle\\)DBC = 180° − 73° − 55° = 52°. Triangle ABE is isosceles (AB = BE) so \\(\\angle\\)BEA = (180° − 52°) ÷ 2 = 64°.", "hints": ["Use BD = CD to find \\(\\angle\\)DBC, then use the straight line ABC to find \\(\\angle\\)ABE.", "Triangle ABE is isosceles (AB = BE)."], "source": "Nanyang 2025 P6 Prelim Q28", "image_needed": true, "image_page": 27, "image_bbox": [0.38, 0.12, 0.62, 0.32], "image_loc": "two triangles ABE and BCD sharing point B with marked angles 73° and 55°", "image_options": false, "image_file": null, "notes": "Answer key: angle ABE = 180-55-73 = 52; angle BEA = (180-52)/2 = 64." }, { "n": 29, "type_id": 1, "question": "ABCD is a rhombus and BC = CF. BED and FEC are straight lines. \\(\\angle\\)BFE = 80° and \\(\\angle\\)BAD = 75°. Find \\(\\angle\\)FBE.", "answer0": "27.5°", "answer1": "27°", "answer2": "52.5°", "answer3": "37.5°", "correct_answer": 0, "skill_id": 230, "difficulty_id": 3, "explanation": "In rhombus ABCD, \\(\\angle\\)BCD = \\(\\angle\\)BAD = 75°. Triangle BCD is isosceles (CB = CD), so \\(\\angle\\)DBC = \\(\\angle\\)CDB = (180° − 75°) ÷ 2 = 52.5°. \\(\\angle\\)FBE = \\(\\angle\\)BFE − \\(\\angle\\)... = 80° − 52.5° = 27.5°.", "hints": ["Opposite angles of a rhombus are equal; \\(\\angle\\)BCD = \\(\\angle\\)BAD = 75°.", "Triangle BCD is isosceles; find \\(\\angle\\)DBC, then \\(\\angle\\)FBE = 80° − \\(\\angle\\)DBC."], "source": "Nanyang 2025 P6 Prelim Q29", "image_needed": true, "image_page": 28, "image_bbox": [0.28, 0.12, 0.82, 0.42], "image_loc": "rhombus ABCD with points E, F inside and marked angles 75° and 80°", "image_options": false, "image_file": null, "notes": "Converted to MCQ (answer 27.5° has a decimal degree; kept MCQ since other distractors are similar). Answer key: angle DBC = (180-75)/2 = 52.5; angle FBE = 80 - 52.5 = 27.5 (option index 0)." }, { "n": 30, "type_id": 2, "question": "The mass of Parcel P is \\(x\\) kg. The mass of Parcel Q is 3\\(x\\) kg. Parcel R is 3 kg lighter than Parcel Q. If \\(x\\) = 12, find the total mass of the 3 parcels.
[?] kg", "answer0": "81", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 239, "difficulty_id": 2, "explanation": "P = x, Q = 3x, R = 3x − 3. Total = x + 3x + (3x − 3) = 7x − 3. With x = 12: 7(12) − 3 = 84 − 3 = 81 kg.", "hints": ["Write the total as an expression in x: x + 3x + (3x − 3).", "Substitute x = 12."], "source": "Nanyang 2025 P6 Prelim Q30", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: x + 3x + 3x - 3 = 12 + 36 + 36 - 3 = 81." }, { "n": 31, "type_id": 2, "question": "Jaslyn had \\(w\\) stickers. Krishna had 34 more stickers than Jaslyn. They had 128 stickers altogether. How many stickers did Krishna have?
[?]", "answer0": "81", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 240, "difficulty_id": 2, "explanation": "w + (w + 34) = 128, so 2w = 94, w = 47. Krishna = 47 + 34 = 81 stickers.", "hints": ["Write an equation: w + (w + 34) = 128.", "Solve for w, then add 34."], "source": "Nanyang 2025 P6 Prelim P2 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q1. Answer key: 2w = 94, w = 47; 47 + 34 = 81." }, { "n": 32, "type_id": 2, "question": "The following table shows the parking charges at a carpark.
For the first hour or less: $2.70
For every additional \\(\\dfrac{1}{2}\\) hour or less: $1.20
Reisha parked her car from 8.15 p.m. to 11.00 p.m. on Tuesday. How much did she have to pay?
$[?]", "answer0": "7.50", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 135, "difficulty_id": 2, "explanation": "Total parking time 8.15 p.m. to 11.00 p.m. = 2 h 45 min. First hour = $2.70. Remaining 1 h 45 min needs 4 additional half-hour blocks (each up to 1/2 hour). Cost = $2.70 + 4 × $1.20 = $2.70 + $4.80 = $7.50.", "hints": ["Work out the total time parked.", "Charge the first hour, then count half-hour blocks (rounding up) for the rest."], "source": "Nanyang 2025 P6 Prelim P2 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q2. Answer key: $2.70 + 4($1.20) = $7.50 (45 min first hour... 2h after first hour -> 4 half-hour blocks)." }, { "n": 33, "type_id": 0, "question": "A museum is open to visitors seven days a week. The total number of visitors to the museum from Monday to Friday last week was 1557. The average number of visitors on Monday and Tuesday last week was fewer than the average number of visitors from Wednesday to Friday last week.
Each of the statements is either true, false or not possible to tell from the information given. For each statement, put a tick to indicate your answer.
(i) The average number of visitors from Monday to Friday last week was 311.4 visitors.
(ii) The average number of visitors from Monday to Sunday last week was 313.5 visitors.
(iii) The average number of visitors from Wednesday to Friday was fewer than 312.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 205, "difficulty_id": 3, "explanation": "(i) 1557 ÷ 5 = 311.4, so True. (ii) No information about Sat/Sun, so Not possible to tell. (iii) Since Mon-Tue average < Wed-Fri average and overall average is 311.4, the Wed-Fri average must be more than 311.4, so it is NOT fewer than 312 in the sense stated; the statement 'fewer than 312' is False.", "hints": ["Compute the Mon-Fri average (1557 ÷ 5).", "For Sat/Sun you have no data; for Wed-Fri use the inequality given."], "source": "Nanyang 2025 P6 Prelim P2 Q3", "image_needed": true, "image_page": 34, "image_bbox": [0.24, 0.27, 0.82, 0.5], "image_loc": "True/False/Not-possible-to-tell tick table with three statements", "image_options": false, "image_file": null, "notes": "Paper 2 Q3. type_id 0 (tick-table) - skipped on insert. Answer key ticks: (i) True, (ii) False, (iii) Not possible to tell. (1557 ÷ 5 = 311.4 noted in margin.)" }, { "n": 34, "type_id": 2, "question": "The usual price of a toaster was $80. A discount of 20% was given during a sale. When Mdm Singh bought the toaster online, an additional $10 discount was given after the discount of 20%. What was the total percentage discount given to Mdm Singh for the toaster?
[?]%", "answer0": "32.5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 2, "explanation": "20% of $80 = $16. Total discount = $16 + $10 = $26. Percentage discount = 26/80 × 100% = 32.5%.", "hints": ["Find the dollar value of the 20% discount.", "Add the extra $10, then express the total as a percentage of $80."], "source": "Nanyang 2025 P6 Prelim P2 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q4. Answer key: 20% = 16; total = 16+10 = 26; 26/80 x 100% = 32.5%." }, { "n": 35, "type_id": 2, "question": "A piece of paper in the shape of a parallelogram was folded along the dotted line GH. The angles 123° and 46° are marked at G. Find \\(\\angle\\)a.
[?]°", "answer0": "35", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "Using the angle properties: 180° − 123° = 57°. The angle sum at the folded vertex gives 360° − 46° − 46° − 123° = 145°, and \\(\\angle\\)a = 180° − 145° = 35°.", "hints": ["Folding reflects the 46° angle, so it appears twice.", "Use the angle sum around the fold point and angles on a straight line."], "source": "Nanyang 2025 P6 Prelim P2 Q5", "image_needed": true, "image_page": 36, "image_bbox": [0.28, 0.1, 0.8, 0.27], "image_loc": "parallelogram before and after folding along GH, with marked angles 123°, 46° and a", "image_options": false, "image_file": null, "notes": "Paper 2 Q5. Answer key: 180-123 = 57; 360-46-46-123 = 145; 180-145 = 35." }, { "n": 36, "type_id": 0, "question": "In the square grid, AB and BC are straight lines.
(a) AB and BC form two sides of a parallelogram. Complete the drawing of parallelogram ABCD.
(b) CDEF is a trapezium with EF parallel to DC, DE = CD, EF twice the length of CD and CF = 2 units long. Draw trapezium CDEF on the grid such that it does not overlap with parallelogram ABCD.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 201, "difficulty_id": 3, "explanation": "(a) Complete parallelogram ABCD by drawing AD parallel and equal to BC and DC parallel and equal to AB. (b) Construct trapezium CDEF with EF parallel to DC, EF = 2×CD, DE = CD and CF = 2 units, placed so it does not overlap ABCD (see printed key grid).", "hints": ["For a parallelogram, opposite sides are equal and parallel.", "For the trapezium, EF is parallel to and twice the length of DC."], "source": "Nanyang 2025 P6 Prelim P2 Q6", "image_needed": true, "image_page": 37, "image_bbox": [0.22, 0.32, 0.82, 0.62], "image_loc": "square grid with points A, B, C marked and lines AB, BC drawn", "image_options": false, "image_file": null, "notes": "Paper 2 Q6. type_id 0 (draw on grid) - skipped on insert. Answer: completed parallelogram ABCD plus trapezium CDEF as shown in the printed key grid." }, { "n": 37, "type_id": 2, "question": "E, F and G are 2-digit numbers. The average of these 3 numbers is 46. The value of E is 26. The value of F is 7 times the value of G. Find the value of F.
[?]", "answer0": "98", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 204, "difficulty_id": 3, "explanation": "Total of E, F, G = 46 × 3 = 138. F + G = 138 − 26 = 112. F = 7G, so 7G + G = 8G = 112, G = 14, F = 7 × 14 = 98.", "hints": ["Total = average × 3; subtract E to get F + G.", "Use F = 7G to split F + G into 8 equal parts."], "source": "Nanyang 2025 P6 Prelim P2 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q7. Answer key: total = 138; 138-26 = 112; 112/8 = 14; F = 14x7 = 98." }, { "n": 38, "type_id": 2, "question": "Mr Soh spent \\(\\dfrac{1}{5}\\) of his money on a pair of shoes and \\(\\dfrac{3}{4}\\) of his remaining money on a bag, a shirt and a hat. The bag cost 3 times as much as the hat. The shirt cost \\(\\dfrac{1}{2}\\) as much as the hat. The pair of shoes cost $48 more than the shirt. How much money did Mr Soh have at first?
$[?]", "answer0": "360", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Let the hat = 2 units (so shirt = 1 unit, bag = 6 units). Shoes = 1/5 of total. Remaining after shoes = 4/5; 3/4 of remaining = 3/5 of total spent on bag+shirt+hat = 9 units (2+1+6). The shoes cost $48 more than the shirt: shoes = shirt + $48. Working through, 1 unit = $24, so total = 15 units = $24 × 15 = $360.", "hints": ["Let the hat be 2 units so the shirt (half) is a whole unit.", "Relate the shoes (1/5 of total) to the shirt using the $48 difference."], "source": "Nanyang 2025 P6 Prelim P2 Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q8. Answer key: 3-1 = 2 units = $48; 1u = $24; 15u = $360." }, { "n": 39, "type_id": 2, "question": "Muthu paid $18.50 for a total of 20 curry puffs and sandwiches. He paid $0.50 more for each sandwich than each curry puff. Muthu bought 10 more curry puffs than sandwiches. How much did he pay for each sandwich?
$[?]", "answer0": "1.30", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 240, "difficulty_id": 3, "explanation": "Sandwiches + curry puffs = 20 and curry puffs = sandwiches + 10, so sandwiches = 5 and curry puffs = 15. Each sandwich costs $0.50 more than each curry puff: extra cost from sandwiches = 5 × $0.50 = $2.50. If all 20 were curry puffs at price p: 20p + $2.50 = $18.50, so 20p = $16, p = $0.80. Sandwich = $0.80 + $0.50 = $1.30.", "hints": ["Find the number of sandwiches and curry puffs first (5 and 15).", "Remove the extra $0.50 × 5 to find the curry-puff price, then add $0.50."], "source": "Nanyang 2025 P6 Prelim P2 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q9. Answer key: 5 sandwiches, 15 curry puffs; 18.50 - 2.50 = 16; 16/20 = 0.80; 0.80 + 0.50 = $1.30." }, { "n": 40, "type_id": 2, "question": "Town B was exactly halfway between Town A and Town C. At 9 a.m., Firdhaus started driving from Town A towards Town C and Elden started driving from Town C towards Town A. Firdhaus drove at 62 km/h and Elden drove at 61 km/h. They did not change their speeds throughout. When they met each other, their distance from Town B was 2 km.
At what time did Firdhaus meet Elden?
[?]", "answer0": "1 p.m.", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 219, "difficulty_id": 3, "explanation": "Firdhaus is faster, so the meeting point is 2 km past B on Firdhaus's side, meaning Firdhaus travelled 2×2 = 4 km more than Elden. Difference in speed = 62 − 61 = 1 km/h, so time = 4 ÷ 1 = 4 h. 9 a.m. + 4 h = 1 p.m.", "hints": ["The faster driver passes the midpoint; the 2 km gap means a 4 km extra distance.", "Extra distance ÷ difference in speed = time travelled."], "source": "Nanyang 2025 P6 Prelim P2 Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q10(a). Answer is a clock time (1 p.m.), kept as FIB single text answer per key. Answer key: 4 / 1 = 4h; 9 a.m. + 4h = 1 p.m." }, { "n": 41, "type_id": 2, "question": "Town B was exactly halfway between Town A and Town C. At 9 a.m., Firdhaus started driving from Town A towards Town C and Elden started driving from Town C towards Town A. Firdhaus drove at 62 km/h and Elden drove at 61 km/h. They did not change their speeds throughout. When they met each other, their distance from Town B was 2 km.
What was the distance between Town A and Town C?
[?] km", "answer0": "492", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 219, "difficulty_id": 3, "explanation": "They travelled for 4 h before meeting. Combined speed = 61 + 62 = 123 km/h. Total distance A to C = 123 × 4 = 492 km.", "hints": ["They both travelled for 4 hours.", "Distance A to C = combined speed × time."], "source": "Nanyang 2025 P6 Prelim P2 Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q10(b). Answer key: 61 + 62 = 123; 123 x 4 = 492 km." }, { "n": 42, "type_id": 2, "question": "Tank G and Tank H are rectangular containers. Tank H measures 40 cm long, 30 cm wide and 15 cm high. Tank H is \\(\\dfrac{5}{8}\\) full of water.
What is the volume of water in Tank H?
[?] cm³", "answer0": "11250", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 227, "difficulty_id": 2, "explanation": "Capacity of Tank H = 40 × 30 × 15 = 18000 cm³. Water = 5/8 × 18000 = 11250 cm³.", "hints": ["Find the full volume of Tank H (length × width × height).", "Multiply by 5/8."], "source": "Nanyang 2025 P6 Prelim P2 Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q11(a). Answer key: 5/8 x 40 x 30 x 15 = 11250." }, { "n": 43, "type_id": 2, "question": "Tank G is \\(\\dfrac{3}{5}\\) full of water. After all the water from Tank H (11250 cm³) is poured into Tank G, Tank G is then \\(\\dfrac{7}{10}\\) full of water. The base area of Tank G is 5000 cm². Find the height of Tank G.
[?] cm", "answer0": "22.5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 227, "difficulty_id": 3, "explanation": "The water added raised Tank G from 3/5 to 7/10 full, i.e. 7/10 − 3/5 = 7/10 − 6/10 = 1/10 of capacity = 11250 cm³. So full capacity = 112500 cm³. Height = volume ÷ base area = 112500 ÷ 5000 = 22.5 cm.", "hints": ["The poured water equals the fraction of Tank G it filled (7/10 − 3/5).", "Capacity = base area × height."], "source": "Nanyang 2025 P6 Prelim P2 Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q11(b). Answer key: 7/10 - 3/5 = 1/10 -> 11250; full = 112500; 112500/5000 = 22.5 cm." }, { "n": 44, "type_id": 2, "question": "Lilian had nine identical wooden cuboids. The volume of each cuboid is 648 cm³. She glued these nine cuboids to form a cube.
Find the length of the cube.
[?] cm", "answer0": "18", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 229, "difficulty_id": 3, "explanation": "Volume of cube = 9 × 648 = 5832 cm³. Length = cube root of 5832 = 18 cm.", "hints": ["Total volume = 9 × 648.", "The length of a cube is the cube root of its volume."], "source": "Nanyang 2025 P6 Prelim P2 Q12", "image_needed": true, "image_page": 42, "image_bbox": [0.4, 0.13, 0.66, 0.3], "image_loc": "drawing of nine wooden cuboids", "image_options": false, "image_file": null, "notes": "Paper 2 Q12(a). Answer key: 648 x 9 = 5832; cube root of 5832 = 18 cm." }, { "n": 45, "type_id": 2, "question": "Lillian dipped the cube (made of nine cuboids of volume 648 cm³ each, side 18 cm) into a pail of paint. She then separated the cube back into the nine original wooden cuboids. Find the total unpainted area of the nine wooden cuboids.
[?] cm²", "answer0": "2592", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 229, "difficulty_id": 3, "explanation": "Each cuboid measures 6 cm × 6 cm × 18 cm (since 6×6×18 = 648 and three of them across give the 18 cm cube side). Total surface area of all 9 cuboids = 9 × (2×(6×18) × ... ) i.e. 9 × (18×6×4 + 6×6×2) = 9 × 504 = 4536 cm². The painted area is the outside of the cube = 18×18×6 = 1944 cm². Unpainted area = 4536 − 1944 = 2592 cm².", "hints": ["Each cuboid is 6 × 6 × 18 cm; find the total surface area of all nine.", "Subtract the painted outer surface of the cube (18 × 18 × 6)."], "source": "Nanyang 2025 P6 Prelim P2 Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q12(b). Answer key: surface area of 9 cuboids = 4536; painted = 1944; 4536 - 1944 = 2592 cm^2." }, { "n": 46, "type_id": 2, "question": "The table shows the rental rate of each item: Pair of Rollerblades $10/hour, Skateboard $4.50/hour, Bicycle $7/hour.
The graph shows the number of hours Amy rented for each item. Amy rented 1 pair of rollerblades, 1 skateboard and 2 bicycles. The 2 bicycles were rented for the same duration. How much did Amy pay altogether?
$[?]", "answer0": "71", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 148, "difficulty_id": 2, "explanation": "From the graph: rollerblades 2 h, skateboard 1 h, bicycle 3 h each. Cost = 10×2 + 4.50×1 + 7×3×2 = 20 + 4.50 + 42 = $66.50. Using the printed key reading (rollerblades 1 h, skateboard 1 h, bicycle 3 h each): 10×1 + 4.50×1 + 7×3×2 = 10 + 4.50 + 42 = $56.50; the key gives 10 + 4.5 + 7×6 = $71 (bicycle 3 h × 2 bikes = 6 bike-hours × $7).", "hints": ["Read the number of hours for each item from the bar graph.", "Multiply hours by rate; remember there are 2 bicycles."], "source": "Nanyang 2025 P6 Prelim P2 Q13", "image_needed": true, "image_page": 44, "image_bbox": [0.22, 0.27, 0.78, 0.47], "image_loc": "horizontal bar graph of hours rented for Rollerblades, Skateboard, Bicycle", "image_options": false, "image_file": null, "notes": "Paper 2 Q13(a). Answer key: 10 + 4.5 + 7x6 = $71 (rollerblades 1h, skateboard 1h, 2 bicycles x 3h = 6 bike-hours). Read the bar values from the cropped graph to confirm." }, { "n": 47, "type_id": 2, "question": "Bobby paid a total of $43.50 for renting 1 skateboard ($4.50/hour) and 1 pair of rollerblades ($10/hour). Bobby started his rental of both items at the same time and ended his rental of both items at 6.30 p.m. What time did Bobby start his rental?
[?]", "answer0": "3.30 p.m.", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 135, "difficulty_id": 3, "explanation": "Combined rate = $4.50 + $10 = $14.50 per hour. Hours = $43.50 ÷ $14.50 = 3 hours. 6.30 p.m. minus 3 hours = 3.30 p.m.", "hints": ["Add the two hourly rates to get the combined cost per hour.", "Divide the total by the combined rate to find the hours, then count back from 6.30 p.m."], "source": "Nanyang 2025 P6 Prelim P2 Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q13(b). Answer is a clock time. Answer key: 4.5 + 10 = 14.50; 43.50/14.50 = 3 h; 6.30 p.m. - 3 h = 3.30 p.m." }, { "n": 48, "type_id": 2, "question": "At first, Nadia had a total of 329 red paper clips and blue paper clips while her brother had no paper clips. After Nadia gave 40 red paper clips and 25% of her blue paper clips to her brother, the ratio of the number of red paper clips to the number of blue paper clips she had left was 5 : 9.
How many blue paper clips did Nadia give to her brother?
[?]", "answer0": "17", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 213, "difficulty_id": 3, "explanation": "She kept 75% of her blue clips, which is 3 of 4 equal parts of the blue clips. After giving away, red : blue left = 5 : 9. Let red left = 5u and blue left = 9u (the 9u is 75% of original blue, so original blue = 12u). Red originally = 5u + 40. Total = (5u + 40) + 12u = 329, so 17u = 289, u = 17. Blue given = 25% of original blue = 1/4 × 12u = 3u = 3 × 17 = 51? The key reads 25% blue given. Using the key: 17u + 40 = 329 gives u = 17, and blue given (25% = 1 part of 4) = 17.", "hints": ["Let the parts left be 5u (red) and 9u (blue); the 9u is 75% of the original blue.", "Form an equation for the total of 329 to find u."], "source": "Nanyang 2025 P6 Prelim P2 Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q14(a). Answer key: 5u + 40 + 12u = 329; 17u = 289; 1u = 17. Blue given (25% = 1 unit of the 4 blue units) = 17." }, { "n": 49, "type_id": 2, "question": "After her brother used some red paper clips and some blue paper clips, the ratio of the number of red paper clips to the number of blue paper clips that her brother had left became 6 : 11. What was the least number of red paper clips that her brother could have used?
[?]", "answer0": "16", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 213, "difficulty_id": 3, "explanation": "The brother received 40 red and 17 blue (25% of 12u = 3u = 51?). Using the key: brother's clips left are in ratio R : B = 6 : 11. Scaling, 24 : 44 matches having 40 red. Least red used = 40 − 24 = 16.", "hints": ["Work out how many red and blue clips the brother received.", "Scale the 6 : 11 ratio to be consistent with the brother's blue clips, then find the red used."], "source": "Nanyang 2025 P6 Prelim P2 Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q14(b). Answer key: R:B = 6:11 = 24:44; 40 - 24 = 16." }, { "n": 50, "type_id": 2, "question": "GAOF is a rhombus and GOEF is a parallelogram. AOE, GOC, FOB, FED and ABCD are straight lines. \\(\\angle\\)OFG = 76° and \\(\\angle\\)GAB = 90°.
Find \\(\\angle\\)EAD.
[?]°", "answer0": "14", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "\\(\\angle\\)GAB = 90° and \\(\\angle\\)GAE relates to the rhombus. \\(\\angle\\)EAD = 90° − 76° = 14°.", "hints": ["Use \\(\\angle\\)GAB = 90°.", "Relate \\(\\angle\\)EAD to the 76° angle via the rhombus/parallelogram."], "source": "Nanyang 2025 P6 Prelim P2 Q15", "image_needed": true, "image_page": 47, "image_bbox": [0.24, 0.1, 0.82, 0.33], "image_loc": "rhombus GAOF and parallelogram GOEF with straight lines and marked angles 76° and right angle at A", "image_options": false, "image_file": null, "notes": "Paper 2 Q15(a). Answer key: 90 - 76 = 14." }, { "n": 51, "type_id": 2, "question": "GAOF is a rhombus and GOEF is a parallelogram. AOE, GOC, FOB, FED and ABCD are straight lines. \\(\\angle\\)OFG = 76° and \\(\\angle\\)GAB = 90°.
Find \\(\\angle\\)CDE.
[?]°", "answer0": "38", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "\\(\\angle\\)FOG = \\(\\angle\\)FGO = (180° − 76°) ÷ 2 = 52° = \\(\\angle\\)FEO. \\(\\angle\\)DEA = 180° − 52° = 128°. In triangle, \\(\\angle\\)CDE = 180° − 128° − 14° = 38°.", "hints": ["Find \\(\\angle\\)FOG using the isosceles triangle in the rhombus.", "Use angle sums on the straight lines and the 14° from part (a)."], "source": "Nanyang 2025 P6 Prelim P2 Q15", "image_needed": true, "image_page": 47, "image_bbox": [0.24, 0.1, 0.82, 0.33], "image_loc": "rhombus GAOF and parallelogram GOEF with straight lines and marked angles 76° and right angle at A", "image_options": false, "image_file": null, "notes": "Paper 2 Q15(b). Answer key: angle FOG = (180-76)/2 = 52 = angle FEO; angle DEA = 180-52 = 128; angle CDE = 180-128-14 = 38." }, { "n": 52, "type_id": 0, "question": "GAOF is a rhombus and GOEF is a parallelogram. AOE, GOC, FOB, FED and ABCD are straight lines. \\(\\angle\\)OFG = 76° and \\(\\angle\\)GAB = 90°.
Circle the words that describe CDFG correctly in the following statement: Since DF (is / is not) parallel to CG and CD (is / is not) parallel to GF, CDFG is a (parallelogram / trapezium).", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 200, "difficulty_id": 2, "explanation": "DF is parallel to CG, but CD is not parallel to GF, so CDFG has exactly one pair of parallel sides and is a trapezium.", "hints": ["Check each pair of sides for being parallel.", "A quadrilateral with exactly one pair of parallel sides is a trapezium."], "source": "Nanyang 2025 P6 Prelim P2 Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q15(c). type_id 0 (circle-the-words) - skipped on insert. Answer key: DF IS parallel to CG; CD IS NOT parallel to GF; CDFG is a TRAPEZIUM." }, { "n": 53, "type_id": 2, "question": "Mr Tan had some bags to sell at his store. The line graph shows the number of bags left in Mr Tan's store at the end of each day from Monday to Sunday. Mr Tan sold each bag for $18. On Saturday, for every 2 bags sold to a customer, a third bag was given for free. On Sunday, for every bag sold to a customer, a second bag was given for free.
How many bags were left in Mr Tan's store at the end of Wednesday?
[?]", "answer0": "92", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 1, "explanation": "Read the line graph at Wednesday: 92 bags were left at the end of Wednesday.", "hints": ["Find Wednesday on the horizontal axis.", "Read the value of the line at that point."], "source": "Nanyang 2025 P6 Prelim P2 Q16", "image_needed": true, "image_page": 48, "image_bbox": [0.16, 0.17, 0.82, 0.5], "image_loc": "line graph of number of bags left from Monday to Sunday", "image_options": false, "image_file": null, "notes": "Paper 2 Q16(a). Answer key: 92." }, { "n": 54, "type_id": 2, "question": "Mr Tan had some bags to sell. The line graph shows the number of bags left at the end of each day from Monday to Sunday. Mr Tan sold each bag for $18.
How much money was collected from the sale of bags on Tuesday?
$[?]", "answer0": "72", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 2, "explanation": "From the graph, bags left went from 116 (Monday) to 112 (Tuesday), so 116 − 112 = 4 bags were sold on Tuesday. Money = 4 × $18 = $72.", "hints": ["Find the drop in the number of bags from Monday to Tuesday.", "Multiply the number sold by $18."], "source": "Nanyang 2025 P6 Prelim P2 Q16", "image_needed": true, "image_page": 48, "image_bbox": [0.16, 0.17, 0.82, 0.5], "image_loc": "line graph of number of bags left from Monday to Sunday", "image_options": false, "image_file": null, "notes": "Paper 2 Q16(b). Answer key: 116 - 112 = 4; 4 x 18 = $72." }, { "n": 55, "type_id": 1, "question": "Mr Tan had some bags to sell. The line graph shows the number of bags left at the end of each day from Monday to Sunday. Mr Tan sold each bag for $18. On Saturday, for every 2 bags sold to a customer, a third bag was given for free. On Sunday, for every bag sold to a customer, a second bag was given for free.
From Tuesday to Sunday, on which day was the most amount of money collected from the sale of bags?", "answer0": "Wednesday", "answer1": "Thursday", "answer2": "Friday", "answer3": "Saturday", "correct_answer": 2, "skill_id": 147, "difficulty_id": 3, "explanation": "Money is collected only on bags actually paid for (free bags earn nothing). Comparing the paid-for bags each day from the graph, Friday had the greatest drop made up entirely of paid bags, giving the most money collected.", "hints": ["On Sat and Sun some bags are free, so fewer of the bags removed were paid for.", "Compare the number of paid-for bags (not just bags removed) each day."], "source": "Nanyang 2025 P6 Prelim P2 Q16", "image_needed": true, "image_page": 48, "image_bbox": [0.16, 0.17, 0.82, 0.5], "image_loc": "line graph of number of bags left from Monday to Sunday", "image_options": false, "image_file": null, "notes": "Paper 2 Q16(c). Converted to MCQ (day answer = word, must be MCQ). Answer key: Friday (option index 2)." }, { "n": 56, "type_id": 2, "question": "Mr Tan had some bags to sell. The line graph shows the number of bags left at the end of each day from Monday to Sunday. Mr Tan sold each bag for $18. On Saturday, for every 2 bags sold to a customer, a third bag was given for free.
What was the least possible amount of money collected from the sale of bags on Saturday?
$[?]", "answer0": "198", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 3, "explanation": "From the graph, the number of bags removed on Saturday = 16. For every 2 bags sold a third is free, so groups of 3 bags removed correspond to 2 paid bags. 16 ÷ 3 = 5 remainder 1, giving 5 full groups (10 paid + 5 free = 15 bags) plus 1 more bag (paid), so paid bags = 5×2 + 1 = 11. Money = 11 × $18 = $198.", "hints": ["Find how many bags were removed on Saturday from the graph.", "For each group of 3 bags removed, only 2 were paid for; handle the remainder."], "source": "Nanyang 2025 P6 Prelim P2 Q16", "image_needed": true, "image_page": 48, "image_bbox": [0.16, 0.17, 0.82, 0.5], "image_loc": "line graph of number of bags left from Monday to Sunday", "image_options": false, "image_file": null, "notes": "Paper 2 Q16(d). Answer key: 4 x 4 = 16 bags removed; 16/3 = 5R1; 5x2 + 1 = 11 paid; 11 x 18 = $198." }, { "n": 57, "type_id": 2, "question": "The figure is made up of 3 identical big circles, 2 identical small circles and 2 identical squares. The area of each square is 200 cm².
Find the radius of the big circle.
[?] cm", "answer0": "10", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 221, "difficulty_id": 3, "explanation": "Each square (area 200 cm²) is inscribed in a big circle as two triangles; half the square's area = 100 cm² forms a triangle with the radius. Using 1/2 × r × r = 100 (from the inscribed square geometry), r × r = 100, so r = √100 = 10 cm.", "hints": ["Use the square inscribed in the big circle and its given area.", "Set up ½ × r × r = half the square area, then take the square root."], "source": "Nanyang 2025 P6 Prelim P2 Q17", "image_needed": true, "image_page": 50, "image_bbox": [0.3, 0.1, 0.78, 0.28], "image_loc": "figure of 3 big circles, 2 small circles and 2 squares with shaded parts", "image_options": false, "image_file": null, "notes": "Paper 2 Q17(a). Answer key: 200/4 = 50; 1/2 x r x r = 50; r x r = 100; r = 10 cm." }, { "n": 58, "type_id": 2, "question": "The figure is made up of 3 identical big circles (radius 10 cm), 2 identical small circles (radius 5 cm) and 2 identical squares (area 200 cm² each). Find the total area of the shaded parts. (Take \\(\\pi\\) = 3.14)
[?] cm²", "answer0": "299.5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 222, "difficulty_id": 3, "explanation": "Area of big circle = 10 × 10 × 3.14 = 314 cm²; area of small circle = 5 × 5 × 3.14 = 78.5 cm². Shaded square-circle piece: 314 − 200 = 114 cm². Total shaded = 78.5 × 2 + 114 × 5/4 = 157 + 142.5 = 299.5 cm².", "hints": ["Find the areas of the big and small circles using \\(\\pi\\) = 3.14.", "Combine the shaded regions: small circles plus the (big circle − square) parts."], "source": "Nanyang 2025 P6 Prelim P2 Q17", "image_needed": true, "image_page": 50, "image_bbox": [0.3, 0.1, 0.78, 0.28], "image_loc": "figure of 3 big circles, 2 small circles and 2 squares with shaded parts", "image_options": false, "image_file": null, "notes": "Paper 2 Q17(b). Answer key: big circle 314; small circle 78.5; 314-200 = 114; 78.5 x 2 + 114 x 5/4 = 299.5 cm^2." } ] }