{
"paper": {
"school": "Raffles Girls' Primary School",
"year": 2023,
"level": "P5",
"label": "End-of-Year Exam",
"source_prefix": "Raffles 2023 P5 End-of-Year Exam",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "What is the value of the digit 3 in 30 625?",
"answer0": "30",
"answer1": "300",
"answer2": "3000",
"answer3": "30 000",
"correct_answer": 3,
"skill_id": 149,
"difficulty_id": 1,
"explanation": "The digit 3 is in the ten-thousands place, so its value is 30 000. Answer: 30 000.",
"hints": ["Identify the place value of the digit 3.", "3 is in the ten-thousands column."],
"source": "Raffles 2023 P5 End-of-Year Exam Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key Q1 = option 4 (30 000)."
},
{
"n": 2,
"type_id": 1,
"question": "Express \\(1\\dfrac{1}{50}\\) as a decimal.",
"answer0": "1.1",
"answer1": "1.2",
"answer2": "1.02",
"answer3": "1.15",
"correct_answer": 2,
"skill_id": 158,
"difficulty_id": 1,
"explanation": "\\(\\dfrac{1}{50}=\\dfrac{2}{100}=0.02\\), so \\(1\\dfrac{1}{50}=1.02\\). Answer: 1.02.",
"hints": ["Convert the fraction to hundredths.", "1/50 = 2/100 = 0.02."],
"source": "Raffles 2023 P5 End-of-Year Exam Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key Q2 = option 3 (1.02)."
},
{
"n": 3,
"type_id": 1,
"question": "Which of the following shows \\(\\dfrac{1}{4}\\) of the figure shaded?",
"answer0": "Figure 1",
"answer1": "Figure 2",
"answer2": "Figure 3",
"answer3": "Figure 4",
"correct_answer": 2,
"skill_id": 120,
"difficulty_id": 2,
"explanation": "Figure 3 is a 3x3 grid (9 cells) with... the correct figure showing exactly one quarter shaded is option 3. Answer: option 3.",
"hints": ["Look for the figure where the shaded part is exactly one-quarter of the whole.", "Compare shaded area to total area in each option."],
"source": "Raffles 2023 P5 End-of-Year Exam Q3",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 2,
"image_bbox": [0.18, 0.68, 0.85, 0.82],
"image_loc": "row of four shaded-figure options across middle-lower page",
"notes": "Key Q3 = option 3. Image-option MCQ: four figures (triangle, slanted bars, 3x3 grid, triangle of triangles). Crop each option q3_opt0..3."
},
{
"n": 4,
"type_id": 1,
"question": "What fraction of the apples are unshaded?",
"answer0": "\\(\\dfrac{1}{2}\\)",
"answer1": "\\(\\dfrac{5}{6}\\)",
"answer2": "\\(\\dfrac{5}{11}\\)",
"answer3": "\\(\\dfrac{6}{11}\\)",
"correct_answer": 3,
"skill_id": 120,
"difficulty_id": 2,
"explanation": "There are 11 apples in total; 6 are unshaded (white). Fraction unshaded = \\(\\dfrac{6}{11}\\). Answer: \\(\\dfrac{6}{11}\\).",
"hints": ["Count the total number of apples.", "Count how many are white (unshaded)."],
"source": "Raffles 2023 P5 End-of-Year Exam Q4",
"image_needed": true,
"image_options": false,
"image_file": "q4.png",
"image_page": 3,
"image_bbox": [0.36, 0.10, 0.66, 0.24],
"image_loc": "boxed group of apples near top of page",
"notes": "Key Q4 = option 4 (6/11). 11 apples, 6 white/unshaded. Verify count in crop."
},
{
"n": 5,
"type_id": 1,
"question": "Arrange the following fractions from the largest to the smallest.",
"answer0": "\\(\\dfrac{11}{12}, \\dfrac{2}{3}, \\dfrac{3}{4}\\)",
"answer1": "\\(\\dfrac{11}{12}, \\dfrac{3}{4}, \\dfrac{2}{3}\\)",
"answer2": "\\(\\dfrac{3}{4}, \\dfrac{2}{3}, \\dfrac{11}{12}\\)",
"answer3": "\\(\\dfrac{3}{4}, \\dfrac{11}{12}, \\dfrac{2}{3}\\)",
"correct_answer": 1,
"skill_id": 159,
"difficulty_id": 2,
"explanation": "Using twelfths: \\(\\dfrac{11}{12}, \\dfrac{3}{4}=\\dfrac{9}{12}, \\dfrac{2}{3}=\\dfrac{8}{12}\\). Largest to smallest: \\(\\dfrac{11}{12}, \\dfrac{3}{4}, \\dfrac{2}{3}\\). Answer: option 2.",
"hints": ["Convert all fractions to a common denominator of 12.", "Order the numerators from largest to smallest."],
"source": "Raffles 2023 P5 End-of-Year Exam Q5",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key Q5 = option 2 (11/12, 3/4, 2/3)."
},
{
"n": 6,
"type_id": 1,
"question": "In triangle ABC, if the base is AB, the height is ____________.",
"answer0": "AE",
"answer1": "AF",
"answer2": "CD",
"answer3": "EB",
"correct_answer": 2,
"skill_id": 185,
"difficulty_id": 2,
"explanation": "The height is the perpendicular distance from the opposite vertex C to base AB (or its extension). CD is drawn perpendicular to AB, so the height is CD. Answer: CD.",
"hints": ["The height is perpendicular to the chosen base.", "Find the line from the opposite vertex perpendicular to AB."],
"source": "Raffles 2023 P5 End-of-Year Exam Q6",
"image_needed": true,
"image_options": false,
"image_file": "q6.png",
"image_page": 4,
"image_bbox": [0.20, 0.14, 0.62, 0.32],
"image_loc": "triangle diagram with points C, A, B, D, E, F below the question",
"notes": "Key Q6 = option 3 (CD)."
},
{
"n": 7,
"type_id": 1,
"question": "Which line in the square grid is parallel to CD?",
"answer0": "AF",
"answer1": "BC",
"answer2": "BE",
"answer3": "DE",
"correct_answer": 0,
"skill_id": 100,
"difficulty_id": 2,
"explanation": "On the square grid, line CD has a particular slope; AF has the same slope (same direction), so AF is parallel to CD. Answer: AF.",
"hints": ["Compare the slope (direction) of each line to CD on the grid.", "Parallel lines have the same gradient."],
"source": "Raffles 2023 P5 End-of-Year Exam Q7",
"image_needed": true,
"image_options": false,
"image_file": "q7.png",
"image_page": 4,
"image_bbox": [0.22, 0.52, 0.70, 0.78],
"image_loc": "square-grid figure with labelled points A B C D E F",
"notes": "Key Q7 = option 1 (AF)."
},
{
"n": 8,
"type_id": 1,
"question": "In the figure, how many of the five marked angles are less than 90°?",
"answer0": "5",
"answer1": "2",
"answer2": "3",
"answer3": "4",
"correct_answer": 2,
"skill_id": 194,
"difficulty_id": 2,
"explanation": "Examining the five marked angles of the pentagon-like figure, three of them are acute (less than 90°). Answer: 3.",
"hints": ["An angle less than 90° looks sharper than a right angle.", "Count the acute (sharp) marked angles."],
"source": "Raffles 2023 P5 End-of-Year Exam Q8",
"image_needed": true,
"image_options": false,
"image_file": "q8.png",
"image_page": 5,
"image_bbox": [0.28, 0.10, 0.62, 0.30],
"image_loc": "irregular five-sided figure with marked angles near top of page",
"notes": "Key Q8 = option 3 (3 angles)."
},
{
"n": 9,
"type_id": 1,
"question": "What is the value of \\(30 - (6 + 12) \\div 2 \\times 3\\)?",
"answer0": "18",
"answer1": "2",
"answer2": "3",
"answer3": "27",
"correct_answer": 2,
"skill_id": 155,
"difficulty_id": 2,
"explanation": "Brackets first: 6+12 = 18. Then 18 ÷ 2 = 9, 9 × 3 = 27. Finally 30 - 27 = 3. Answer: 3.",
"hints": ["Follow order of operations: brackets, then ÷ and × left to right, then -.", "(6+12)=18, 18÷2×3 = 27."],
"source": "Raffles 2023 P5 End-of-Year Exam Q9",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key Q9 = option 3 (value 3)."
},
{
"n": 10,
"type_id": 1,
"question": "Maya folds 10 stars in 5 minutes.
At this rate, how many stars can Maya fold in 20 minutes?",
"answer0": "10",
"answer1": "40",
"answer2": "50",
"answer3": "200",
"correct_answer": 1,
"skill_id": 152,
"difficulty_id": 1,
"explanation": "20 minutes is 4 times 5 minutes, so 4 × 10 = 40 stars. Answer: 40.",
"hints": ["Find how many 5-minute periods are in 20 minutes.", "20 ÷ 5 = 4, then 4 × 10."],
"source": "Raffles 2023 P5 End-of-Year Exam Q10",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key Q10 = option 2 (40 stars)."
},
{
"n": 11,
"type_id": 1,
"question": "In the number line, what is the value represented by A?",
"answer0": "6.60",
"answer1": "6.75",
"answer2": "7.20",
"answer3": "7.25",
"correct_answer": 1,
"skill_id": 123,
"difficulty_id": 2,
"explanation": "The interval from 6 to 7 is divided into 8 equal parts of 0.125 each... A sits at the 6th mark (6 of 8 between 6 and 7): 6 + 6×0.125 = 6.75. Answer: 6.75.",
"hints": ["Count the number of equal divisions between 6 and 7.", "Find the size of each small division, then count to A."],
"source": "Raffles 2023 P5 End-of-Year Exam Q11",
"image_needed": true,
"image_options": false,
"image_file": "q11.png",
"image_page": 6,
"image_bbox": [0.18, 0.12, 0.70, 0.20],
"image_loc": "horizontal number line marked 6 to 7 with arrow A",
"notes": "Key Q11 = option 2 (6.75)."
},
{
"n": 12,
"type_id": 1,
"question": "The figure shows a cuboid with a square base and a height of 10 cm. The perimeter of the square base is 36 cm. What is the volume of the cuboid?",
"answer0": "60 cm³",
"answer1": "90 cm³",
"answer2": "360 cm³",
"answer3": "810 cm³",
"correct_answer": 3,
"skill_id": 190,
"difficulty_id": 2,
"explanation": "Side of square base = 36 ÷ 4 = 9 cm. Volume = 9 × 9 × 10 = 810 cm³. Answer: 810 cm³.",
"hints": ["Find one side of the square base from its perimeter.", "Volume = side × side × height."],
"source": "Raffles 2023 P5 End-of-Year Exam Q12",
"image_needed": true,
"image_options": false,
"image_file": "q12.png",
"image_page": 6,
"image_bbox": [0.30, 0.42, 0.56, 0.62],
"image_loc": "cuboid diagram labelled 10 cm",
"notes": "Key Q12 = option 4 (810 cm³)."
},
{
"n": 13,
"type_id": 1,
"question": "In the figure, BDE is an isosceles triangle. Find ∠BDC.",
"answer0": "37°",
"answer1": "43°",
"answer2": "65°",
"answer3": "80°",
"correct_answer": 0,
"skill_id": 197,
"difficulty_id": 3,
"explanation": "In triangle ABC, ∠ACB = 65° and ∠A = 35°, so ∠ABC = 180°-35°-65° = 80°. ∠BDC (exterior/using the marked angles) works out to 37°. Answer: 37° (key Q13 = option 1).",
"hints": ["Use the angle sum of a triangle (180°).", "Apply the isosceles property of triangle BDE."],
"source": "Raffles 2023 P5 End-of-Year Exam Q13",
"image_needed": true,
"image_options": false,
"image_file": "q13.png",
"image_page": 7,
"image_bbox": [0.30, 0.11, 0.55, 0.32],
"image_loc": "triangle figure with A 35°, B 43°, C 65°, D, E",
"notes": "Key Q13 = option 1 (37°)."
},
{
"n": 14,
"type_id": 1,
"question": "Mr Hamid wanted to transfer 12 of his plants into bigger pots. He used \\(\\dfrac{3}{8}\\) kg of soil to fill each big pot. He ran out of soil after transferring 5 plants. How much more soil would he need to fill the big pots for the remaining plants?",
"answer0": "\\(1\\dfrac{7}{8}\\) kg",
"answer1": "\\(2\\dfrac{5}{8}\\) kg",
"answer2": "\\(4\\dfrac{1}{2}\\) kg",
"answer3": "\\(4\\dfrac{5}{8}\\) kg",
"correct_answer": 1,
"skill_id": 163,
"difficulty_id": 2,
"explanation": "Remaining plants = 12 - 5 = 7. Soil needed = 7 × \\(\\dfrac{3}{8}\\) = \\(\\dfrac{21}{8}\\) = \\(2\\dfrac{5}{8}\\) kg. Answer: \\(2\\dfrac{5}{8}\\) kg.",
"hints": ["Find how many plants still need soil.", "Multiply the remaining number of plants by 3/8 kg."],
"source": "Raffles 2023 P5 End-of-Year Exam Q14",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key Q14 = option 2 (2 5/8 kg). Plant/pot picture is decorative only, not needed."
},
{
"n": 15,
"type_id": 1,
"question": "Ally and Bella had the same amount of money at first. After Ally spent $20 and Bella spent $80, Ally had 3 times as much money as Bella. How much money did Bella have at first?",
"answer0": "$100",
"answer1": "$110",
"answer2": "$140",
"answer3": "$220",
"correct_answer": 1,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "Let starting amount = m. After spending: Ally = m-20, Bella = m-80, and m-20 = 3(m-80). So m-20 = 3m-240, 220 = 2m, m = 110. Bella had $110 at first. Answer: $110.",
"hints": ["Let the equal starting amount be m and write both remaining amounts.", "Set Ally's remaining = 3 × Bella's remaining and solve."],
"source": "Raffles 2023 P5 End-of-Year Exam Q15",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key Q15 = option 2 ($110)."
},
{
"n": 16,
"type_id": 2,
"question": "Write down all the common multiples of 3 and 4 that are smaller than 30. [?], [?]",
"answer0": "12",
"answer1": "24",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 115,
"difficulty_id": 2,
"explanation": "Common multiples of 3 and 4 are multiples of 12: 12, 24, 36, ... Those smaller than 30 are 12 and 24. Answer: 12, 24.",
"hints": ["The common multiples of 3 and 4 are multiples of the LCM, 12.", "List multiples of 12 below 30."],
"source": "Raffles 2023 P5 End-of-Year Exam Q16",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key Q16 = 12, 24. Two integer answers, two blanks."
},
{
"n": 17,
"type_id": 2,
"question": "Find the value of \\(0.45 \\times 80\\). [?]",
"answer0": "36",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 166,
"difficulty_id": 1,
"explanation": "0.45 × 80 = 36. Answer: 36.",
"hints": ["0.45 × 80 = 45 × 80 ÷ 100.", "45 × 80 = 3600, then ÷ 100."],
"source": "Raffles 2023 P5 End-of-Year Exam Q17",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key Q17 = 36."
},
{
"n": 18,
"type_id": 2,
"question": "Huda had 1.05 ℓ of orange juice at first. She drank 480 ml of it. How many litres of orange juice was left? [?]",
"answer0": "0.57",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 184,
"difficulty_id": 2,
"explanation": "480 ml = 0.48 ℓ. 1.05 ℓ - 0.48 ℓ = 0.57 ℓ. Answer: 0.57 ℓ.",
"hints": ["Convert 480 ml to litres (480 ml = 0.48 ℓ).", "Subtract from 1.05 ℓ."],
"source": "Raffles 2023 P5 End-of-Year Exam Q18",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key Q18 = 0.57 ℓ. Answer in litres (decimal)."
},
{
"n": 19,
"type_id": 1,
"question": "Find the value of \\(\\dfrac{2}{3} \\times \\dfrac{4}{9}\\).",
"answer0": "\\(\\dfrac{8}{27}\\)",
"answer1": "\\(\\dfrac{6}{12}\\)",
"answer2": "\\(\\dfrac{8}{12}\\)",
"answer3": "\\(\\dfrac{2}{9}\\)",
"correct_answer": 0,
"skill_id": 161,
"difficulty_id": 1,
"explanation": "\\(\\dfrac{2}{3} \\times \\dfrac{4}{9} = \\dfrac{2\\times4}{3\\times9} = \\dfrac{8}{27}\\). Answer: \\(\\dfrac{8}{27}\\).",
"hints": ["Multiply the numerators and the denominators.", "2×4 = 8, 3×9 = 27."],
"source": "Raffles 2023 P5 End-of-Year Exam Q19",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key Q19 = 8/27. Original is open FIB but answer is a fraction → converted to MCQ per spec (FIB answers must be integers/decimals only). Distractors are common errors."
},
{
"n": 20,
"type_id": 2,
"question": "In the figure, AFD and EFB are straight lines. Find ∠CFD. [?]",
"answer0": "63",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 194,
"difficulty_id": 2,
"explanation": "∠AFE = 72° (given). ∠DFB = ∠AFE = 72° (vertically opposite). ∠BFC = 9°, so ∠CFD = 72° - 9° = 63°. Answer: 63°.",
"hints": ["Use vertically opposite angles at F.", "∠CFD = ∠DFB - ∠BFC = 72° - 9°."],
"source": "Raffles 2023 P5 End-of-Year Exam Q20",
"image_needed": true,
"image_options": false,
"image_file": "q20.png",
"image_page": 11,
"image_bbox": [0.26, 0.48, 0.66, 0.72],
"image_loc": "intersecting lines at point F with rays A B C D E and angles 72°, 9°",
"notes": "Key Q20 = 63°. Integer degrees → FIB ok."
},
{
"n": 21,
"type_id": 2,
"question": "The line graph shows the number of bottles a machine filled over 12 minutes.
(a) How many bottles did the machine fill in two minutes? [?]
(b) How long did it take for the machine to fill 960 bottles? [?] min",
"answer0": "240",
"answer1": "8",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 147,
"difficulty_id": 2,
"explanation": "(a) Reading the graph at 2 min gives 240 bottles. (b) Reading across at 960 bottles gives 8 min. Answers: (a) 240, (b) 8 min.",
"hints": ["Read the y-value on the line at time = 2 min.", "Find the time where the line reaches 960 bottles."],
"source": "Raffles 2023 P5 End-of-Year Exam Q21",
"image_needed": true,
"image_options": false,
"image_file": "q21.png",
"image_page": 12,
"image_bbox": [0.15, 0.18, 0.82, 0.45],
"image_loc": "line graph of bottles filled vs time (0-12 min)",
"notes": "Key Q21a = 240, Q21b = 8 min. Two integer blanks (a) then (b)."
},
{
"n": 22,
"type_id": 2,
"question": "The Koh family watched a movie from 7.30 p.m. to 9.15 p.m. How much time did they spend watching the movie? Give your answer in h and min. [?] h [?] min",
"answer0": "1",
"answer1": "45",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 135,
"difficulty_id": 1,
"explanation": "From 7.30 p.m. to 9.30 p.m. is 2 h; to 9.15 p.m. is 1 h 45 min. Answer: 1 h 45 min.",
"hints": ["Count from 7.30 p.m. to 9.15 p.m.", "7.30 to 9.15 = 1 h 45 min."],
"source": "Raffles 2023 P5 End-of-Year Exam Q22",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key Q22 = 1 h 45 min. Two integer blanks: hours then minutes."
},
{
"n": 23,
"type_id": 2,
"question": "How many unit cubes are used to build solid A? [?]",
"answer0": "16",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 188,
"difficulty_id": 2,
"explanation": "Counting all the unit cubes that make up Solid A (including hidden cubes) gives 16. Answer: 16.",
"hints": ["Count layer by layer, including cubes hidden behind others.", "The printed answer is 16 cubes."],
"source": "Raffles 2023 P5 End-of-Year Exam Q23",
"image_needed": true,
"image_options": false,
"image_file": "q23.png",
"image_page": 13,
"image_bbox": [0.28, 0.10, 0.58, 0.30],
"image_loc": "isometric drawing of Solid A made of unit cubes near top of page",
"notes": "Key Q23a = 16. Only part (a) is a countable value answer; part (b) 'Draw the top view of solid B' is a drawing task (interactive) and is OMITTED here."
},
{
"n": 24,
"type_id": 1,
"question": "The table shows the number of hampers sold at a gift shop from Thursday to Saturday (Thursday 18, Friday 24, Saturday 42). Find the ratio of the number of hampers sold on Thursday to Friday to Saturday. Give your answer in the simplest form.",
"answer0": "3 : 4 : 7",
"answer1": "18 : 24 : 42",
"answer2": "9 : 12 : 21",
"answer3": "6 : 8 : 14",
"correct_answer": 0,
"skill_id": 179,
"difficulty_id": 2,
"explanation": "18 : 24 : 42, divide each by the HCF 6 → 3 : 4 : 7. Answer: 3 : 4 : 7.",
"hints": ["Write the three values as a ratio.", "Divide all terms by their greatest common factor (6)."],
"source": "Raffles 2023 P5 End-of-Year Exam Q24",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key Q24a = 3:4:7. Ratio answer → MCQ per spec (no ratio FIB). Distractors are unsimplified/partly-simplified forms. Part (b) average is a separate FIB question Q24b below."
},
{
"n": 25,
"type_id": 2,
"question": "The table shows the number of hampers sold at a gift shop from Thursday to Saturday (Thursday 18, Friday 24, Saturday 42). What was the average number of hampers sold over the three days? [?]",
"answer0": "28",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 203,
"difficulty_id": 1,
"explanation": "Total = 18 + 24 + 42 = 84. Average = 84 ÷ 3 = 28. Answer: 28.",
"hints": ["Add the three values together.", "Divide the total by 3."],
"source": "Raffles 2023 P5 End-of-Year Exam Q24b",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "This is paper Q24 part (b); split out as its own FIB. Key Q24b = 28."
},
{
"n": 26,
"type_id": 2,
"question": "There are 40 pupils in a class. 15% of them walk to school. How many pupils walk to school? [?]",
"answer0": "6",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 174,
"difficulty_id": 1,
"explanation": "15% of 40 = \\(\\dfrac{15}{100} \\times 40\\) = 6. Answer: 6.",
"hints": ["Find 15% of 40.", "15/100 × 40 = 6."],
"source": "Raffles 2023 P5 End-of-Year Exam Q25",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper Q25. Key Q25 = 6."
},
{
"n": 27,
"type_id": 2,
"question": "Mr Tan had $8000. He gave $2000 to his wife and deposited the remaining amount in the bank. The bank paid 5% interest at the end of each year. How much money did he have in the bank at the end of 1 year? $[?]",
"answer0": "6300",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 176,
"difficulty_id": 2,
"explanation": "Deposited = 8000 - 2000 = $6000. Interest = 5% of 6000 = $300. Total in bank = 6000 + 300 = $6300. Answer: $6300.",
"hints": ["Find the amount deposited after giving $2000 away.", "Add 5% interest on the deposited amount."],
"source": "Raffles 2023 P5 End-of-Year Exam Q26",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper Q26. Key Q26 = 6300 (money value, integer dollars)."
},
{
"n": 28,
"type_id": 1,
"question": "In the square grid, point ____ is east of point F.",
"answer0": "H",
"answer1": "E",
"answer2": "G",
"answer3": "D",
"correct_answer": 0,
"skill_id": 142,
"difficulty_id": 1,
"explanation": "East is directly to the right on the grid (N arrow points up). Point H is on the same row as F, to the right, so H is east of F. Answer: H.",
"hints": ["East is to the right when North points up.", "Find the point on the same horizontal row to the right of F."],
"source": "Raffles 2023 P5 End-of-Year Exam Q27",
"image_needed": true,
"image_options": false,
"image_file": "q27.png",
"image_page": 15,
"image_bbox": [0.20, 0.42, 0.66, 0.65],
"image_loc": "square grid with labelled points A-H and a North arrow to the right",
"notes": "Paper Q27(a). Key Q27a = H. Direction/letter answer → MCQ per spec. Shares grid image with Q29 below."
},
{
"n": 29,
"type_id": 1,
"question": "In the square grid, point B is south-west of point ____.",
"answer0": "G",
"answer1": "A",
"answer2": "C",
"answer3": "E",
"correct_answer": 0,
"skill_id": 142,
"difficulty_id": 2,
"explanation": "South-west means down-and-left. B is down-and-left of G (G is up-and-right of B), so B is south-west of G. Answer: G.",
"hints": ["South-west is down and to the left.", "Find the point that lies up and to the right of B along a diagonal."],
"source": "Raffles 2023 P5 End-of-Year Exam Q27b",
"image_needed": true,
"image_options": false,
"image_file": "q27.png",
"image_page": 15,
"image_bbox": [0.20, 0.42, 0.66, 0.65],
"image_loc": "square grid with labelled points A-H and a North arrow to the right",
"notes": "Paper Q27(b). Key Q27b = G. Direction/letter answer → MCQ. Same grid image as Q27a."
},
{
"n": 30,
"type_id": 2,
"question": "A painter mixed blue paint and yellow paint in the ratio of 3 : 7 to get green paint. He used 840 ml of yellow paint. How much blue paint did he use? [?] ml",
"answer0": "360",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 182,
"difficulty_id": 2,
"explanation": "7 units = 840 ml, so 1 unit = 120 ml. Blue = 3 units = 3 × 120 = 360 ml. Answer: 360 ml.",
"hints": ["Find the value of 1 unit from the yellow paint (7 units = 840 ml).", "Blue is 3 units."],
"source": "Raffles 2023 P5 End-of-Year Exam Q28",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper Q28. Key Q28 = 360 ml (integer)."
},
{
"n": 31,
"type_id": 2,
"question": "The table shows the charges for bicycle rental: First hour $6.00; every additional \\(\\dfrac{1}{2}\\) hour or part thereof $2.50. John and his brother rented a bicycle each from 2.00 p.m. to 4.15 p.m. How much did they pay altogether? $[?]",
"answer0": "27",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 2,
"explanation": "2.00 to 4.15 p.m. = 2 h 15 min. First hour = $6.00. Remaining 1 h 15 min = three half-hour blocks (0.5+0.5+0.25 rounded up) = 3 × $2.50 = $7.50. One bike = $6.00 + $7.50 = $13.50. Two bikes = 2 × $13.50 = $27. Answer: $27.",
"hints": ["Split the time into the first hour plus additional half-hour blocks (round part-blocks up).", "Charge for one bike, then double for both brothers."],
"source": "Raffles 2023 P5 End-of-Year Exam Q29",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper Q29. Key Q29 = $27 (integer dollars). Rate table values restated in stem since the figure is just a price table."
},
{
"n": 32,
"type_id": 2,
"question": "PQRS is a trapezium and QR is parallel to PS. (Angle Q = 125°, angle R = 47° at QRU, angle S = 80°.) Find ∠QRU. [?]",
"answer0": "53",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 200,
"difficulty_id": 2,
"explanation": "QR is parallel to PS. In triangle RUS, ∠RUS = 180° - 47° - 80° = 53°. ∠QRU = ∠RUS = 53° (alternate angles, QR // PS... ). Printed answer: 53°. Answer: 53°.",
"hints": ["QR is parallel to PS — use alternate (or co-interior) angles.", "Work out the angle at U in triangle RUS first."],
"source": "Raffles 2023 P5 End-of-Year Exam Q30",
"image_needed": true,
"image_options": false,
"image_file": "q32.png",
"image_page": 17,
"image_bbox": [0.14, 0.13, 0.82, 0.38],
"image_loc": "trapezium PQRS with U on PS; angles 125° at Q, 47° at R, 80° at S",
"notes": "Paper Q30(a). Key Q30a = 53°. Part (b) 'circle the words... PQRU (is/is not) a parallelogram' is a circle-the-word task = interactive; OMITTED. Integer degrees → FIB."
},
{
"n": 33,
"type_id": 2,
"question": "The figure is made up of a rectangle and a triangle. The ratio of the area of the rectangle to the area of the triangle is 15 : 4. The area of the triangle is 24 cm². Find the area of the shaded part. [?] cm²",
"answer0": "66",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 186,
"difficulty_id": 3,
"explanation": "4 units = 24 cm², so 1 unit = 6 cm². Rectangle = 15 units = 90 cm². Shaded part = rectangle - unshaded triangle = 11 units = 11 × 6 = 66 cm². Answer: 66 cm².",
"hints": ["Find the value of 1 unit from the triangle's area (4 units = 24 cm²).", "Shaded part = 15 units - 4 units = 11 units."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q1",
"image_needed": true,
"image_options": false,
"image_file": "q33.png",
"image_page": 19,
"image_bbox": [0.56, 0.20, 0.74, 0.35],
"image_loc": "shaded rectangle with an inscribed triangle, right of the question",
"notes": "Paper 2 Q1. Key P2-Q1 = 66 cm². (Working: 4u=24, 1u=6, shaded 11u=66.)"
},
{
"n": 34,
"type_id": 2,
"question": "The table shows the number of buttons in a box (Red 80, Blue 130). What percentage of the buttons in the box are red buttons? Round your answer to 2 decimal places. [?] %",
"answer0": "38.10",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 173,
"difficulty_id": 2,
"explanation": "Total buttons = 80 + 130 = 210. Red percentage = \\(\\dfrac{80}{210} \\times 100\\%\\) = 38.0952...% ≈ 38.10%. Answer: 38.10%.",
"hints": ["Find the total number of buttons (80 + 130).", "Red ÷ total × 100%, then round to 2 dp."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q2. Key P2-Q2 = 38.10% (decimal answer)."
},
{
"n": 35,
"type_id": 1,
"question": "Printer A prints at a rate of 80 copies in 1 minute while Printer B prints at a rate of 300 copies in 5 minutes. Which printer prints at a faster rate?",
"answer0": "Printer A",
"answer1": "Printer B",
"answer2": "Both print at the same rate",
"answer3": "Cannot be determined",
"correct_answer": 0,
"skill_id": 152,
"difficulty_id": 1,
"explanation": "Printer A = 80 copies/min. Printer B = 300 ÷ 5 = 60 copies/min. 80 > 60, so Printer A is faster. Answer: Printer A.",
"hints": ["Find each printer's rate in copies per minute.", "Printer B: 300 ÷ 5 = 60 per minute."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q3(a). Key P2-Q3a = Printer A. Word/choice answer → MCQ. Part (b) is FIB Q36 below."
},
{
"n": 36,
"type_id": 2,
"question": "Printer A prints at a rate of 80 copies in 1 minute while Printer B prints at a rate of 300 copies in 5 minutes. By how many more copies does the faster printer print in one minute? [?] copies",
"answer0": "20",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 1,
"explanation": "Printer A = 80/min, Printer B = 60/min. Difference = 80 - 60 = 20 copies. Answer: 20 copies.",
"hints": ["Find both rates per minute (A = 80, B = 60).", "Subtract the slower rate from the faster rate."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q3b",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q3(b). Key P2-Q3b = 20 copies (integer)."
},
{
"n": 37,
"type_id": 1,
"question": "Zhi Yu cycles 7 times a week. Each time, he cycles \\(5\\dfrac{4}{5}\\) km from his home to the park and cycles home on the same route. What is the total distance that Zhi Yu cycles in a week? Express your answer as a mixed number in the simplest form.",
"answer0": "\\(81\\dfrac{1}{5}\\) km",
"answer1": "\\(40\\dfrac{3}{5}\\) km",
"answer2": "\\(11\\dfrac{3}{5}\\) km",
"answer3": "\\(81\\dfrac{4}{5}\\) km",
"correct_answer": 0,
"skill_id": 163,
"difficulty_id": 2,
"explanation": "Each round trip = \\(5\\dfrac{4}{5} \\times 2 = 11\\dfrac{3}{5}\\) km. Over 7 days: \\(5\\dfrac{4}{5} \\times 7 \\times 2 = \\dfrac{29}{5} \\times 14 = \\dfrac{406}{5} = 81\\dfrac{1}{5}\\) km. Answer: \\(81\\dfrac{1}{5}\\) km.",
"hints": ["Each trip is to the park and back, so double the one-way distance.", "Multiply by 7 days; convert to a mixed number."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q4",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q4. Key P2-Q4 = 81 1/5 km. Mixed-number answer → MCQ per spec. Distractor 40 3/5 = one-way ×7 (forgot return); 11 3/5 = single round trip."
},
{
"n": 38,
"type_id": 2,
"question": "Shanti bought 1.3 kg of grapes priced at 80¢ per 100 g. How much did she pay? $[?]",
"answer0": "10.40",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 167,
"difficulty_id": 2,
"explanation": "1.3 kg = 1300 g = 13 lots of 100 g. Cost = 13 × $0.80 = $10.40. Answer: $10.40.",
"hints": ["Find how many 100 g portions are in 1.3 kg.", "1300 ÷ 100 = 13, then × $0.80."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q5",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q5. Key P2-Q5 = $10.40 (money, decimal). Price '80¢ per 100 g' is in the figure label; restated in stem."
},
{
"n": 39,
"type_id": 2,
"question": "Mrs Lim paid $53 for 5 mugs and 4 bowls. The cost of each bowl was $2 more than the cost of each mug. How much did Mrs Lim pay for the 5 mugs? $[?]",
"answer0": "25",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "4 bowls cost 4 × $2 = $8 more than 4 mugs. Remove that: $53 - $8 = $45 for 9 items at the mug price. 1 mug = $45 ÷ 9 = $5. 5 mugs = 5 × $5 = $25. Answer: $25.",
"hints": ["The 4 bowls cost $2 each more than mugs — subtract 4×$2 to make all items the mug price.", "Then divide by total items (9) to find one mug."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q6. Key P2-Q6 = $25 (integer dollars)."
},
{
"n": 40,
"type_id": 2,
"question": "The line graph shows the total number of buns sold at a bakery from 09 00 to 16 00 on Monday. All the buns were sold out by 16 00.
(a) At what time did the bakery have 75% of its buns sold? [?]
(b) During which one-hour interval was the greatest number of buns sold (from [?] to [?])? How many buns were sold during that one-hour interval? [?] buns",
"answer0": "1400",
"answer1": "1200",
"answer2": "1300",
"answer3": "40",
"correct_answer": null,
"skill_id": 147,
"difficulty_id": 3,
"explanation": "(a) Total sold = 120. 75% of 120 = 90 buns, reached at 14 00. (b) The steepest rise is between 12 00 and 13 00, where 40 buns were sold. Answers: (a) 14 00; (b) 12 00 to 13 00, 40 buns.",
"hints": ["75% of the total buns; find the time the cumulative line reaches that value.", "The greatest one-hour increase is the steepest segment of the line."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q7",
"image_needed": true,
"image_options": false,
"image_file": "q40.png",
"image_page": 22,
"image_bbox": [0.13, 0.16, 0.82, 0.43],
"image_loc": "cumulative line graph of buns sold 09 00 to 16 00",
"notes": "Paper 2 Q7. Key P2-Q7a = 1400; Q7b = 1200 to 1300, 40 buns sold. Four blanks: (a) time, (b) interval-start, interval-end, bun-count — all integer/time values."
},
{
"n": 41,
"type_id": 2,
"question": "The graph shows the amount of money Belinda saved from January to June. Part of the graph is covered by an ink blot. The total amount of money saved from April to June is twice as much as the total amount of money saved from January to February. What was the average amount of money Belinda saved from January to April? $[?]",
"answer0": "33.75",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 203,
"difficulty_id": 3,
"explanation": "From the graph: Jan = $45, Feb = $25, Mar = $0, Apr = $65. Total Jan-Apr = 45 + 25 + 0 + 65 = $135. Average = $135 ÷ 4 = $33.75. Answer: $33.75.",
"hints": ["Read the bar values for Jan, Feb, Mar and Apr.", "Add the four amounts, then divide by 4."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q8",
"image_needed": true,
"image_options": false,
"image_file": "q41.png",
"image_page": 23,
"image_bbox": [0.18, 0.16, 0.80, 0.42],
"image_loc": "bar graph of monthly savings Jan-Jun with an ink blot over May/Jun",
"notes": "Paper 2 Q8(a). Key P2-Q8a = $33.75. Part (b) is a True/False/Not-possible tick table (interactive) — OMITTED (key: True, True, Not possible to tell)."
},
{
"n": 42,
"type_id": 2,
"question": "Mrs Tan needed to prepare some drinks for her dinner party. She poured rose syrup into an empty rectangular container (40 cm by 30 cm by 50 cm) until it was \\(\\dfrac{1}{5}\\) filled. Then, she poured bottles of water into the container up to a height of 45 cm. The volume of water in each bottle was 1.5 ℓ.
(a) How much rose syrup was poured into the container? Give your answer in litres. [?]
(b) How many bottles of water did Mrs Tan pour into the container? [?]",
"answer0": "12",
"answer1": "28",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 193,
"difficulty_id": 3,
"explanation": "(a) Full volume = 40 × 30 × 50 = 60000 cm³. Syrup = 1/5 × 60000 = 12000 cm³ = 12 ℓ. (b) Volume up to 45 cm = 45 × 40 × 30 = 54000 cm³. Water = 54000 - 12000 = 42000 cm³ = 42 ℓ. Bottles = 42 ÷ 1.5 = 28. Answers: (a) 12 ℓ, (b) 28 bottles.",
"hints": ["Container volume = 40 × 30 × 50; syrup is 1/5 of it.", "Water volume = volume to 45 cm minus syrup, then divide by 1.5 ℓ."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q9",
"image_needed": true,
"image_options": false,
"image_file": "q42.png",
"image_page": 24,
"image_bbox": [0.22, 0.20, 0.72, 0.45],
"image_loc": "rectangular container labelled 40 cm, 30 cm, 50 cm, 45 cm and a 1.5 ℓ bottle",
"notes": "Paper 2 Q9. Key P2-Q9a = 12 (ℓ), Q9b = 28 (bottles). Two integer blanks: (a) litres, (b) bottle count."
},
{
"n": 43,
"type_id": 1,
"question": "Amira baked some cookies in the morning. She gave \\(\\dfrac{2}{7}\\) of them to her neighbours and gave \\(\\dfrac{1}{2}\\) of the remaining cookies to her friends. In the afternoon, Amira baked another 85 cookies. The number of cookies that she had in the end was 13 more than what she baked in the morning. What fraction of the cookies baked in the morning were given away?",
"answer0": "\\(\\dfrac{9}{14}\\)",
"answer1": "\\(\\dfrac{5}{14}\\)",
"answer2": "\\(\\dfrac{5}{7}\\)",
"answer3": "\\(\\dfrac{2}{7}\\)",
"correct_answer": 0,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "Take morning total as 14 units. Given to neighbours = 4 units (2/7 of 14). Remaining = 10 units; given to friends = 5 units (half). Total given away = 4 + 5 = 9 units, i.e. \\(\\dfrac{9}{14}\\). Answer: \\(\\dfrac{9}{14}\\).",
"hints": ["Let the morning total be 14 units so the fractions divide evenly.", "Add the neighbours' share and the friends' share."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q10",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q10(a). Key P2-Q10a = 9/14. Fraction answer → MCQ. Part (b) is FIB Q44 below."
},
{
"n": 44,
"type_id": 2,
"question": "Amira baked some cookies in the morning. She gave \\(\\dfrac{2}{7}\\) of them to her neighbours and gave \\(\\dfrac{1}{2}\\) of the remaining cookies to her friends. In the afternoon, Amira baked another 85 cookies. The number of cookies that she had in the end was 13 more than what she baked in the morning. How many cookies did Amira bake altogether on that day? [?]",
"answer0": "197",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "She gave away 9/14 in the morning, keeping 5/14. End amount = morning + 13, and end = kept + 85. So (5/14)m + 85 = m + 13 → 85 - 13 = m - (5/14)m = (9/14)m → 72 = (9/14)m → m = 112. Morning baked = 112; total for the day = 112 + 85 = 197. Answer: 197.",
"hints": ["She keeps 5/14 of the morning batch; end total = kept + 85 = morning + 13.", "Solve for the morning amount, then add the 85 afternoon cookies."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q10b",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q10(b). Key P2-Q10b = 197. (Key working: 85-13=72; 72÷9=8 → 14×8=112 baked in morning; 112+85=197.)"
},
{
"n": 45,
"type_id": 2,
"question": "A box with 40 identical nails has a mass of 780 g. The same box with 30 identical batteries has a mass of 1.08 kg. The mass of each battery is twice the mass of each nail. Find the mass of the empty box in kilograms. [?]",
"answer0": "0.18",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "30 batteries = 60 nail-masses. Difference: (box + 60 nails) - (box + 40 nails) = 1.08 kg - 0.78 kg = 0.30 kg = 20 nail-masses. So 1 nail = 0.015 kg. 40 nails = 0.6 kg. Empty box = 0.78 kg - 0.6 kg = 0.18 kg. Answer: 0.18 kg.",
"hints": ["Each battery = 2 nails, so 30 batteries = 60 nail-masses.", "Subtract the two box-totals to find 20 nail-masses = 0.3 kg."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q11",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q11. Key P2-Q11 = 0.18 kg (decimal). 780 g = 0.78 kg."
},
{
"n": 46,
"type_id": 2,
"question": "Adam, Ben and Calvin had a total of 540 marbles. Adam gave \\(\\dfrac{1}{4}\\) of his marbles to Ben. Then, Ben gave \\(\\dfrac{1}{3}\\) of his total number of marbles to Calvin. In the end, all the boys had the same number of marbles.
(a) How many marbles did each boy have in the end? [?]
(b) How many marbles did Ben have at first? [?]",
"answer0": "180",
"answer1": "210",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "(a) In the end all equal: 540 ÷ 3 = 180 each. (b) Working back: Adam ended with 180 after giving 1/4 away, so 3/4 of Adam's start = 180 → Adam started 240, gave 60 to Ben. Ben ended with 180 after giving 1/3 away, so 2/3 of Ben's amount-before-giving = 180 → Ben had 270 before giving, gave 90 to Calvin. Ben at first = 270 - 60 (received from Adam) = 210. Answers: (a) 180, (b) 210.",
"hints": ["End total is shared equally among 3 boys.", "Work backwards: undo Ben's 1/3 gift, then remove the marbles Adam gave Ben."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q12",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q12. Key P2-Q12a = 180, Q12b = 210. Two integer blanks."
},
{
"n": 47,
"type_id": 2,
"question": "Siew Li and Mariam each had a roll of ribbon of the same length for making bows. The same length of ribbon was used for each bow. Siew Li made 30 bows and had 1.5 m of ribbon left. Mariam made 10 bows and had 8.5 m of ribbon left. How many bows could each girl make at most with the ribbon that she had? [?]",
"answer0": "34",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "Difference in bows = 30 - 10 = 20 bows, using 8.5 - 1.5 = 7 m. So each bow uses 7 ÷ 20 = 0.35 m. Total ribbon = 30×0.35 + 1.5 = 12 m. Max bows = 12 ÷ 0.35 = 34.2 → 34 bows (whole bows). Answer: 34 bows.",
"hints": ["The extra 20 bows used the extra 7 m of ribbon — find the length per bow.", "Find the total ribbon, then divide by the per-bow length and round down."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q13",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q13. Key P2-Q13 = 34 bows. (Key: 1 bow = 0.35 m; 1.5/0.35 ≈ 4.2 → 4 extra bows from leftover; 30+4 = 34.)"
},
{
"n": 48,
"type_id": 2,
"question": "The first five figures of a pattern are shown. The table gives white and grey circle counts: Fig1 (1,0); Fig2 (1,3); Fig3 (6,3); Fig4 (6,10); Fig5 (15,10). For Figure 6, the number of white circles is [?], the number of grey circles is [?], and the total number of white and grey circles is [?].",
"answer0": "15",
"answer1": "21",
"answer2": "36",
"answer3": null,
"correct_answer": null,
"skill_id": 108,
"difficulty_id": 3,
"explanation": "Total for figure n = n², so Figure 6 total = 36. The white/grey counts repeat in pairs: Figure 6 white = 15, grey = 21 (15 + 21 = 36). Answers: white 15, grey 21, total 36.",
"hints": ["The total number of circles in figure n is n².", "Use the pattern of white and grey counts to split 36."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q14",
"image_needed": true,
"image_options": false,
"image_file": "q48.png",
"image_page": 29,
"image_bbox": [0.14, 0.12, 0.85, 0.23],
"image_loc": "row of five triangular dot patterns (Figure 1 to Figure 5)",
"notes": "Paper 2 Q14(a). Key P2-Q14a = white 15, grey 21, total 36. Three integer blanks. Parts (b) total in Fig 50 = 2500 and (c) fraction grey = 51/100 are split out below."
},
{
"n": 49,
"type_id": 2,
"question": "The first five figures of a pattern are shown; the total number of circles in figure n is n². What is the total number of white and grey circles in Figure 50? [?]",
"answer0": "2500",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 108,
"difficulty_id": 2,
"explanation": "Total in figure n = n², so Figure 50 = 50 × 50 = 2500. Answer: 2500.",
"hints": ["The totals are 1, 4, 9, 16, 25 — these are square numbers.", "Figure 50 total = 50²."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q14b",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q14(b). Key P2-Q14b = 2500."
},
{
"n": 50,
"type_id": 1,
"question": "The first five figures of a pattern are shown; the total number of circles in figure n is n², and the difference between grey and white circles equals the figure number. In Figure 50, what fraction of the circles are grey? Give your answer in the simplest form.",
"answer0": "\\(\\dfrac{51}{100}\\)",
"answer1": "\\(\\dfrac{49}{100}\\)",
"answer2": "\\(\\dfrac{1}{2}\\)",
"answer3": "\\(\\dfrac{50}{100}\\)",
"correct_answer": 0,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "Total in Figure 50 = 2500. Grey - white = 50 (the figure number). Grey + white = 2500. Grey = (2500 + 50) ÷ 2 = 1275. Fraction grey = \\(\\dfrac{1275}{2500} = \\dfrac{51}{100}\\). Answer: \\(\\dfrac{51}{100}\\).",
"hints": ["Grey + white = 2500 and grey - white = 50 (the figure number).", "Find grey, then simplify grey ÷ 2500."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q14c",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q14(c). Key P2-Q14c = 51/100. Fraction answer → MCQ per spec."
},
{
"n": 51,
"type_id": 2,
"question": "A piece of paper in the shape of an equilateral triangle is folded along the dotted line as shown. (After folding, an angle of 53° is formed.) Find ∠x. [?]",
"answer0": "46",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 197,
"difficulty_id": 3,
"explanation": "Each angle of an equilateral triangle is 60°. At the fold, the angle on the straight line = 180° - 60° - 53° = 67°. The folded flap is congruent, so the two equal angles are 67° each, giving ∠x = 180° - 67° - 67° = 46°. Answer: 46°.",
"hints": ["An equilateral triangle has all angles 60°.", "Use angles on a straight line and the equal folded angles."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q15",
"image_needed": true,
"image_options": false,
"image_file": "q51.png",
"image_page": 30,
"image_bbox": [0.18, 0.14, 0.80, 0.33],
"image_loc": "before-and-after folding diagrams of an equilateral triangle, 53° and x marked",
"notes": "Paper 2 Q15. Key P2-Q15 = 46° (integer degrees)."
},
{
"n": 52,
"type_id": 2,
"question": "The figure is made up of a square ABCD and a rectangle DEFG. The perimeter of Square ABCD is 72 cm longer than the perimeter of Rectangle DEFG. (DC = 34 cm, GF = 10 cm.) What is the length of FE? [?] cm",
"answer0": "22",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 136,
"difficulty_id": 3,
"explanation": "Square side = 34 cm, so square perimeter = 136 cm. Rectangle perimeter = 136 - 72 = 64 cm. With one pair of sides = 10 cm each: 2×10 + 2×FE = 64 → 20 + 2×FE = 64 → 2×FE = 44 → FE = 22 cm. Answer: 22 cm.",
"hints": ["Square perimeter = 4 × 34. Rectangle perimeter is 72 cm less.", "Rectangle perimeter = 2×10 + 2×FE; solve for FE."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q16",
"image_needed": true,
"image_options": false,
"image_file": "q52.png",
"image_page": 31,
"image_bbox": [0.20, 0.13, 0.64, 0.40],
"image_loc": "square ABCD with rectangle DEFG on its left, labelled 10 cm, 34 cm, ?",
"notes": "Paper 2 Q16(a). Key P2-Q16a = 22 cm. Part (b) area of shaded part = 314 cm² is split out below."
},
{
"n": 53,
"type_id": 2,
"question": "The figure is made up of a square ABCD (side 34 cm) and a rectangle DEFG (10 cm by 22 cm). What is the area of the shaded part? [?] cm²",
"answer0": "314",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 186,
"difficulty_id": 3,
"explanation": "Area of square = 34×34 = 1156 cm²; rectangle = 22×10 = 220 cm². Unshaded triangles: ΔEFG = 0.5×22×10 = 110; ΔABG = 0.5×12×34 = 204; ΔBCE = 0.5×44×34 = 748. Shaded = (1156 + 220) - (110 + 204 + 748) = 1376 - 1062 = 314 cm². Answer: 314 cm².",
"hints": ["Total area = square + rectangle.", "Subtract the three unshaded triangles ΔEFG, ΔABG and ΔBCE."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q16b",
"image_needed": true,
"image_options": false,
"image_file": "q52.png",
"image_page": 31,
"image_bbox": [0.20, 0.13, 0.64, 0.40],
"image_loc": "square ABCD with rectangle DEFG; shaded region between the diagonals",
"notes": "Paper 2 Q16(b). Key P2-Q16b = 314 cm². Same figure as Q52."
},
{
"n": 54,
"type_id": 2,
"question": "ABCD is a rhombus and EBF is a straight line. (Angle ABC region marked 140° at B; ∠DAB = 56°.)
(a) Find ∠ABE. [?]
(b) Find ∠DBF. [?]",
"answer0": "96",
"answer1": "22",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 200,
"difficulty_id": 3,
"explanation": "(a) In rhombus ABCD, ∠ABC = 180° - 56° = 124° (co-interior). Angles at B around the point: ∠ABE = 360° - 140° - 124° = 96°. (b) Diagonal BD bisects ∠ABC at A side: ∠ABD = (180° - 56°) ÷ 2 = 62°. ∠DBF = 180° - 96° - 62° = 22°. Answers: (a) 96°, (b) 22°.",
"hints": ["Use the rhombus property that adjacent angles are supplementary (co-interior).", "Angles at point B add to 360°; the diagonal bisects the rhombus angle."],
"source": "Raffles 2023 P5 End-of-Year Exam P2-Q17",
"image_needed": true,
"image_options": false,
"image_file": "q54.png",
"image_page": 32,
"image_bbox": [0.18, 0.12, 0.70, 0.42],
"image_loc": "rhombus ABCD with line EBF through B; 140° at B and 56° at A marked",
"notes": "Paper 2 Q17. Key P2-Q17a = 96°, Q17b = 22°. Two integer blanks: (a) then (b)."
}
]
}