{ "paper": { "school": "Catholic High", "year": 2024, "level": "P5", "label": "End-of-Year Exam", "source_prefix": "Catholic High 2024 P5 End-of-Year Exam", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "100 000 + 6 000 + 50 + 3 =", "answer0": "106 053", "answer1": "106 503", "answer2": "160 053", "answer3": "160 503", "correct_answer": 0, "skill_id": 149, "difficulty_id": 1, "explanation": "Expanded form: 100 000 + 6 000 + 50 + 3 = 106 053. There are no thousands beyond the 6 thousands and no hundreds, so the answer is 106 053.", "hints": ["Line up each part by its place value.", "There are 0 hundreds, so the hundreds digit is 0."], "source": "Catholic High 2024 P5 End-of-Year Exam Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 1 (0-based 0)." }, { "n": 2, "type_id": 1, "question": "Express 20 400 mℓ in ℓ.", "answer0": "0.204 ℓ", "answer1": "2.04 ℓ", "answer2": "20.4 ℓ", "answer3": "204 ℓ", "correct_answer": 2, "skill_id": 192, "difficulty_id": 1, "explanation": "1 ℓ = 1000 mℓ. So 20 400 mℓ = 20 400 ÷ 1000 = 20.4 ℓ.", "hints": ["Divide millilitres by 1000 to get litres.", "Move the decimal point 3 places left."], "source": "Catholic High 2024 P5 End-of-Year Exam Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3 (0-based 2)." }, { "n": 3, "type_id": 1, "question": "Which line in the square grid is parallel to DC?", "answer0": "AB", "answer1": "BC", "answer2": "DE", "answer3": "AE", "correct_answer": 0, "skill_id": 194, "difficulty_id": 2, "explanation": "On the square grid, line DC runs at a particular slant. The line that goes in the same direction (never meeting DC) is AB. Hence AB is parallel to DC.", "hints": ["Parallel lines have the same slant and never meet.", "Compare the grid direction of each option to DC."], "source": "Catholic High 2024 P5 End-of-Year Exam Q3", "image_needed": true, "image_options": false, "image_file": "q3.png", "image_page": 3, "image_bbox": [0.40, 0.49, 0.74, 0.66], "image_loc": "square grid with points A,B,C,D,E in middle of page below the question", "notes": "Key: option 1 (0-based 0)." }, { "n": 4, "type_id": 1, "question": "What is the value of 57 − 5 × 3 + 2?", "answer0": "40", "answer1": "44", "answer2": "158", "answer3": "260", "correct_answer": 1, "skill_id": 155, "difficulty_id": 1, "explanation": "Do multiplication first: 5 × 3 = 15. Then 57 − 15 + 2 = 42 + 2 = 44.", "hints": ["Multiply before adding or subtracting.", "57 − 15 = 42, then add 2."], "source": "Catholic High 2024 P5 End-of-Year Exam Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 (0-based 1)." }, { "n": 5, "type_id": 1, "question": "In 3.421, which digit is in the tenths place?", "answer0": "1", "answer1": "2", "answer2": "3", "answer3": "4", "correct_answer": 3, "skill_id": 123, "difficulty_id": 1, "explanation": "The first digit after the decimal point is the tenths place. In 3.421 that digit is 4.", "hints": ["Tenths is the first place after the decimal point.", "Ones . tenths hundredths thousandths."], "source": "Catholic High 2024 P5 End-of-Year Exam Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 4 (0-based 3)." }, { "n": 6, "type_id": 1, "question": "Which of the following has the same value as 2400 ÷ 30?", "answer0": "2400 × 10 × 3", "answer1": "2400 × 10 ÷ 3", "answer2": "2400 ÷ 10 ÷ 3", "answer3": "2400 ÷ 10 × 3", "correct_answer": 2, "skill_id": 151, "difficulty_id": 2, "explanation": "Dividing by 30 is the same as dividing by 10 and then dividing by 3: 2400 ÷ 30 = 2400 ÷ 10 ÷ 3 = 240 ÷ 3 = 80.", "hints": ["30 = 10 × 3, so dividing by 30 means dividing by 10 then by 3.", "Check: 2400 ÷ 30 = 80."], "source": "Catholic High 2024 P5 End-of-Year Exam Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3 (0-based 2)." }, { "n": 7, "type_id": 1, "question": "Which of the following shows \\(\\dfrac{3}{5}\\) of the figure shaded?", "answer0": "Figure 1", "answer1": "Figure 2", "answer2": "Figure 3", "answer3": "Figure 4", "correct_answer": 0, "skill_id": 41, "difficulty_id": 2, "explanation": "A figure shows 3/5 shaded when it is divided into 5 equal parts with 3 shaded. Figure 1 is divided into equal parts with exactly 3 of every 5 shaded, so it shows 3/5.", "hints": ["The figure must be in 5 equal parts.", "Count shaded parts out of total equal parts: needs to equal 3 out of 5."], "source": "Catholic High 2024 P5 End-of-Year Exam Q7", "image_needed": true, "image_options": true, "image_file": null, "image_page": 4, "image_bbox": [0.28, 0.56, 0.86, 0.68], "image_loc": "four shaded shape figures in a row below the question, labelled (1)-(4)", "notes": "Key: option 1 (0-based 0). image_options: crop each option to q7_opt0.png..q7_opt3.png (octagon, pentagon, concentric circles, cross)." }, { "n": 8, "type_id": 1, "question": "Find the value of \\(\\dfrac{2}{3} \\times 8\\).", "answer0": "\\(\\dfrac{2}{11}\\)", "answer1": "\\(\\dfrac{2}{38}\\)", "answer2": "\\(3\\dfrac{1}{3}\\)", "answer3": "\\(5\\dfrac{1}{3}\\)", "correct_answer": 3, "skill_id": 163, "difficulty_id": 1, "explanation": "2/3 × 8 = 16/3 = 5 1/3.", "hints": ["Multiply the numerator by 8: 2 × 8 = 16, keep denominator 3.", "Convert 16/3 to a mixed number: 16 ÷ 3 = 5 r 1."], "source": "Catholic High 2024 P5 End-of-Year Exam Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 4 (0-based 3). Mixed-number options -> MCQ." }, { "n": 9, "type_id": 1, "question": "EF and GH are straight lines. Which of the following is true?", "answer0": "∠a = ∠c", "answer1": "∠b = ∠d", "answer2": "∠a + ∠c = 180°", "answer3": "∠b + ∠d = 180°", "correct_answer": 1, "skill_id": 194, "difficulty_id": 2, "explanation": "∠b and ∠d are vertically opposite angles (formed by the two straight lines EF and GH crossing), so ∠b = ∠d.", "hints": ["Two straight lines crossing make vertically opposite angles equal.", "∠b and ∠d are on opposite sides of the crossing point."], "source": "Catholic High 2024 P5 End-of-Year Exam Q9", "image_needed": true, "image_options": false, "image_file": "q9.png", "image_page": 5, "image_bbox": [0.38, 0.37, 0.70, 0.48], "image_loc": "intersecting straight lines EF and GH with angles a,b,c,d labelled, centre of page", "notes": "Key: option 2 (0-based 1)." }, { "n": 10, "type_id": 1, "question": "When QR is the base of triangle QRS, which is the height of triangle QRS?", "answer0": "SR", "answer1": "SV", "answer2": "RT", "answer3": "RW", "correct_answer": 3, "skill_id": 186, "difficulty_id": 2, "explanation": "The height must be perpendicular to the base QR and drawn from the opposite vertex. RW is perpendicular to QR (the right-angle mark at W), so RW is the height.", "hints": ["The height is perpendicular (90°) to the chosen base.", "Look for the right-angle mark on the base QR."], "source": "Catholic High 2024 P5 End-of-Year Exam Q10", "image_needed": true, "image_options": false, "image_file": "q10.png", "image_page": 6, "image_bbox": [0.38, 0.14, 0.70, 0.27], "image_loc": "triangle QRS with points T,V,W and perpendicular marks, top of page", "notes": "Key: option 4 (0-based 3)." }, { "n": 11, "type_id": 1, "question": "Three containers with some water are shown. Which container has the most water and which container has the least?", "answer0": "Most Z, Least X", "answer1": "Most Z, Least Y", "answer2": "Most X, Least Z", "answer3": "Most X, Least Y", "correct_answer": 3, "skill_id": 191, "difficulty_id": 2, "explanation": "Container X reads to about 0.5 ℓ on the 1 ℓ scale (≈500 mℓ). Y reads less than 500 mℓ and Z reads almost full to 500 mℓ. Comparing actual volumes, X has the most water and Y has the least.", "hints": ["Read each scale (X is in litres, Y and Z in mℓ) to find the actual volume.", "Compare the three real volumes, not just the heights."], "source": "Catholic High 2024 P5 End-of-Year Exam Q11", "image_needed": true, "image_options": false, "image_file": "q11.png", "image_page": 6, "image_bbox": [0.28, 0.45, 0.80, 0.59], "image_loc": "three measuring beakers X (1 l scale), Y and Z (500 ml scale) with water levels, middle of page", "notes": "Key: option 4 (0-based 3). Diagram needed to read water levels." }, { "n": 12, "type_id": 1, "question": "The solid shown is formed using unit cubes. What is the least number of unit cubes needed to be added to the solid to form a cuboid?", "answer0": "12", "answer1": "24", "answer2": "36", "answer3": "52", "correct_answer": 1, "skill_id": 188, "difficulty_id": 2, "explanation": "The solid fits inside a 4 × 3 × ... bounding cuboid. The smallest cuboid that contains the staircase solid holds 36 cubes; the solid already has 12, so 36 − 12 = 24 cubes must be added.", "hints": ["Find the smallest cuboid that can completely enclose the solid.", "Subtract the cubes already present from the cuboid's total."], "source": "Catholic High 2024 P5 End-of-Year Exam Q12", "image_needed": true, "image_options": false, "image_file": "q12.png", "image_page": 7, "image_bbox": [0.38, 0.14, 0.66, 0.27], "image_loc": "isometric drawing of a unit-cube staircase solid, top of page", "notes": "Key: option 2 (0-based 1). Need diagram to count visible cubes." }, { "n": 13, "type_id": 1, "question": "Mila baked 120 brownies. She sold 45% of them. How many brownies had she left?", "answer0": "54", "answer1": "65", "answer2": "66", "answer3": "75", "correct_answer": 2, "skill_id": 175, "difficulty_id": 2, "explanation": "Brownies left = 100% − 45% = 55% of 120 = 55/100 × 120 = 66.", "hints": ["She kept 100% − 45% = 55%.", "55% of 120 = 0.55 × 120."], "source": "Catholic High 2024 P5 End-of-Year Exam Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3 (0-based 2)." }, { "n": 14, "type_id": 1, "question": "Asher had \\(\\dfrac{5}{6}\\) kg of clay. He used \\(\\dfrac{1}{3}\\) of it to make some mugs. How much clay had he left?", "answer0": "\\(\\dfrac{5}{9}\\) kg", "answer1": "\\(\\dfrac{5}{18}\\) kg", "answer2": "\\(\\dfrac{1}{2}\\) kg", "answer3": "\\(\\dfrac{1}{6}\\) kg", "correct_answer": 0, "skill_id": 161, "difficulty_id": 2, "explanation": "Used = 1/3 × 5/6 = 5/18 kg. Left = 5/6 − 5/18 = 15/18 − 5/18 = 10/18 = 5/9 kg.", "hints": ["Clay left is 2/3 of the original (since 1/3 was used).", "2/3 × 5/6 = 10/18 = 5/9."], "source": "Catholic High 2024 P5 End-of-Year Exam Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 1 (0-based 0). Fraction options -> MCQ." }, { "n": 15, "type_id": 1, "question": "Helen, Indra and Jack were each given an identical chocolate bar. Helen ate \\(\\dfrac{7}{12}\\) of hers and Jack ate \\(\\dfrac{1}{4}\\) of his. Indra ate more than Jack but less than Helen. What fraction of a chocolate bar could Indra have possibly eaten?", "answer0": "\\(\\dfrac{1}{6}\\)", "answer1": "\\(\\dfrac{5}{6}\\)", "answer2": "\\(\\dfrac{1}{3}\\)", "answer3": "\\(\\dfrac{2}{3}\\)", "correct_answer": 2, "skill_id": 159, "difficulty_id": 3, "explanation": "Jack ate 1/4 = 3/12, Helen ate 7/12. Indra ate between 3/12 and 7/12. Converting options to twelfths: 1/6 = 2/12 (too small), 5/6 = 10/12 (too big), 1/3 = 4/12 (between 3/12 and 7/12), 2/3 = 8/12 (too big). So Indra could have eaten 1/3.", "hints": ["Convert all fractions to twelfths to compare.", "Indra's amount must lie strictly between 3/12 and 7/12."], "source": "Catholic High 2024 P5 End-of-Year Exam Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3 (0-based 2). Fraction options -> MCQ." }, { "n": 16, "type_id": 2, "question": "Write thirteen thousand and eleven in numerals. [?]", "answer0": "13011", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 149, "difficulty_id": 1, "explanation": "Thirteen thousand = 13 000; and eleven = 11. Together 13 000 + 11 = 13011.", "hints": ["Thirteen thousand is 13 000.", "Add eleven: 13 000 + 11."], "source": "Catholic High 2024 P5 End-of-Year Exam Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 13011." }, { "n": 17, "type_id": 2, "question": "Find the value of 7.5 × 500. [?]", "answer0": "3750", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 166, "difficulty_id": 1, "explanation": "7.5 × 500 = 7.5 × 5 × 100 = 37.5 × 100 = 3750.", "hints": ["7.5 × 5 = 37.5.", "Then multiply by 100."], "source": "Catholic High 2024 P5 End-of-Year Exam Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 3750." }, { "n": 18, "type_id": 1, "question": "Find the value of \\(1 - \\dfrac{2}{5} - \\dfrac{1}{2}\\).", "answer0": "\\(\\dfrac{1}{10}\\)", "answer1": "\\(\\dfrac{1}{5}\\)", "answer2": "\\(\\dfrac{3}{10}\\)", "answer3": "\\(\\dfrac{1}{3}\\)", "correct_answer": 0, "skill_id": 159, "difficulty_id": 2, "explanation": "Use tenths: 1 = 10/10, 2/5 = 4/10, 1/2 = 5/10. 10/10 − 4/10 − 5/10 = 1/10.", "hints": ["Convert all to tenths (common denominator 10).", "10/10 − 4/10 − 5/10 = 1/10."], "source": "Catholic High 2024 P5 End-of-Year Exam Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 1/10. Fraction answer -> MCQ (distractors generated)." }, { "n": 19, "type_id": 2, "question": "Calvin has a book with 205 pages. He reads an average of 5 pages of the book every day. How many days will he take to finish reading the book? [?]", "answer0": "41", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 1, "explanation": "Number of days = total pages ÷ pages per day = 205 ÷ 5 = 41 days.", "hints": ["Divide total pages by pages read each day.", "205 ÷ 5 = 41."], "source": "Catholic High 2024 P5 End-of-Year Exam Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 41." }, { "n": 20, "type_id": 1, "question": "Find the value of 26 ÷ 4. Give your answer as a mixed number in the simplest form.", "answer0": "\\(6\\dfrac{1}{2}\\)", "answer1": "\\(6\\dfrac{2}{4}\\)", "answer2": "\\(6\\dfrac{1}{4}\\)", "answer3": "\\(5\\dfrac{1}{2}\\)", "correct_answer": 0, "skill_id": 157, "difficulty_id": 1, "explanation": "26 ÷ 4 = 26/4 = 6 remainder 2 = 6 2/4 = 6 1/2 in simplest form.", "hints": ["26 ÷ 4 = 6 remainder 2.", "Remainder over divisor: 2/4 simplifies to 1/2."], "source": "Catholic High 2024 P5 End-of-Year Exam Q20", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 6 1/2. Mixed-number answer -> MCQ (distractors generated)." }, { "n": 21, "type_id": 2, "question": "Express \\(\\dfrac{48}{7}\\) as a decimal. Correct your answer to 2 decimal places. [?]", "answer0": "6.86", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 158, "difficulty_id": 2, "explanation": "48 ÷ 7 = 6.857... Rounded to 2 decimal places, 6.857 ≈ 6.86.", "hints": ["Divide 48 by 7.", "Look at the third decimal (7) to round the second decimal up."], "source": "Catholic High 2024 P5 End-of-Year Exam Q21", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 6.86." }, { "n": 22, "type_id": 2, "question": "A machine takes 2 minutes to print 10 posters. At the same rate, how long will it take to print 145 posters? [?] min", "answer0": "29", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 2, "explanation": "1 poster takes 2 ÷ 10 = 0.2 min. 145 posters take 145 × 0.2 = 29 min. (Or 145 ÷ 10 = 14.5 groups × 2 min = 29 min.)", "hints": ["Find the time for 1 poster: 2 ÷ 10 min.", "Multiply by 145."], "source": "Catholic High 2024 P5 End-of-Year Exam Q22", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 29 mins." }, { "n": 23, "type_id": 2, "question": "A string of length 8.1 m was cut into three pieces. The first piece was 3 times as long as the second piece. The second piece was twice as long as the third piece. How long was the first piece? [?] m", "answer0": "5.4", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 183, "difficulty_id": 3, "explanation": "Let the third piece = 1 unit. Second = 2 units. First = 3 × 2 = 6 units. Total = 6 + 2 + 1 = 9 units = 8.1 m, so 1 unit = 0.9 m. First piece = 6 × 0.9 = 5.4 m.", "hints": ["Let the third piece be 1 unit and express the others in units.", "Total units = 9; 9 units = 8.1 m, so 1 unit = 0.9 m."], "source": "Catholic High 2024 P5 End-of-Year Exam Q23", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 5.4 m." }, { "n": 24, "type_id": 1, "question": "Rama had some erasers in box A and B at first. After he transferred \\(\\dfrac{1}{7}\\) of the erasers in box A to box B, the ratio of the number of erasers in box A to the number of erasers in box B became 2 : 1. What was the ratio of the number of erasers in box A to the total number of erasers in box A and B at first?", "answer0": "7 : 9", "answer1": "6 : 7", "answer2": "2 : 3", "answer3": "7 : 16", "correct_answer": 0, "skill_id": 183, "difficulty_id": 3, "explanation": "Let A at first = 7 units. He transferred 1/7 of A = 1 unit to B, leaving A with 6 units. After transfer A : B = 2 : 1, so B after = 3 units. B at first = 3 − 1 = 2 units. Total at first = 7 + 2 = 9 units. So A : total = 7 : 9.", "hints": ["Let A at first be 7 units so that 1/7 of A is a whole unit.", "After transfer A = 6 units = 2 parts, so 1 part = 3 units = B after; work back to B at first."], "source": "Catholic High 2024 P5 End-of-Year Exam Q24", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 7 : 9. Ratio answer -> MCQ (distractors generated)." }, { "n": 25, "type_id": 2, "question": "The base of a cuboid is a square of side 2 cm. The height of the cuboid is 8 cm. Find its volume. [?] cm³", "answer0": "32", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 190, "difficulty_id": 1, "explanation": "Volume = length × breadth × height = 2 × 2 × 8 = 32 cm³.", "hints": ["The square base has area 2 × 2 = 4 cm².", "Multiply base area by height: 4 × 8."], "source": "Catholic High 2024 P5 End-of-Year Exam Q25", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 32 cm³." }, { "n": 26, "type_id": 2, "question": "ADE and BCD are equilateral triangles. EDC is a straight line. ∠DAB is 32°. Find ∠ABD. [?]°", "answer0": "88", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 3, "explanation": "Triangle ADE is equilateral so ∠ADE = 60°. Triangle BCD is equilateral so ∠BDC = 60°. EDC is a straight line (180°), so ∠ADB = 180° − 60° − 60° = 60°. In triangle ABD: ∠ABD = 180° − ∠DAB − ∠ADB = 180° − 32° − 60° = 88°.", "hints": ["Each angle of an equilateral triangle is 60°.", "Angles on the straight line EDC at D sum to 180°; then use the angle sum of triangle ABD."], "source": "Catholic High 2024 P5 End-of-Year Exam Q26", "image_needed": true, "image_options": false, "image_file": "q26.png", "image_page": 14, "image_bbox": [0.32, 0.48, 0.70, 0.63], "image_loc": "two equilateral triangles ADE and BCD sharing straight line EDC, with 32° marked at A, middle of page", "notes": "Key: 88°." }, { "n": 27, "type_id": 2, "question": "Triangles K, L, M are drawn in a square grid. Arrange triangles K, L, M from the smallest area to the largest area. [?] , [?] , [?]", "answer0": "L", "answer1": "M", "answer2": "K", "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 2, "explanation": "Using area = 1/2 × base × height counted in grid squares, the triangles' areas order from smallest to largest is L, M, K.", "hints": ["Area of a triangle = 1/2 × base × height; count grid squares.", "Compare the three computed areas and list smallest first."], "source": "Catholic High 2024 P5 End-of-Year Exam Q27", "image_needed": true, "image_options": false, "image_file": "q27.png", "image_page": 15, "image_bbox": [0.26, 0.14, 0.83, 0.28], "image_loc": "square grid showing three triangles labelled K, L, M, top of page", "notes": "Key order smallest->largest: L, M, K. Three ordered blanks. Need grid figure to read base/height." }, { "n": 28, "type_id": 2, "question": "The figure shows a rectangle EFHJ and a triangle EGJ. The area of rectangle EFHJ is 215 cm². Find the area of triangle EGJ. [?] cm²", "answer0": "107.3", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 3, "explanation": "Triangle EGJ has base EJ (a side of the rectangle) and its height equals the full width of the rectangle, so its area is exactly half the rectangle's area: 215 ÷ 2 = 107.5 cm². The printed answer key states 107.3 cm².", "hints": ["The triangle shares base EJ with the rectangle and its height is the rectangle's width.", "Area of triangle = 1/2 × area of rectangle."], "source": "Catholic High 2024 P5 End-of-Year Exam Q28", "image_needed": true, "image_options": false, "image_file": "q28.png", "image_page": 15, "image_bbox": [0.30, 0.48, 0.52, 0.66], "image_loc": "rectangle EFHJ with diagonal triangle EGJ, vertices E,F (top) J,H (bottom), G on side FH, left of page", "notes": "Key: 107.3 cm². NOTE: mathematically 215 ÷ 2 = 107.5; printed key says 107.3 (likely typo). Used printed key value 107.3 per spec; flag for review." }, { "n": 29, "type_id": 2, "question": "The average mass of Ahmad, Ben and Carl is 40 kg. Ahmad and Ben are of the same mass and Carl is 6 kg heavier than Ben. Find Ahmad's mass. [?] kg", "answer0": "38", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 205, "difficulty_id": 3, "explanation": "Total mass = 40 × 3 = 120 kg. Let Ahmad = Ben = x. Carl = x + 6. So x + x + (x + 6) = 120, 3x + 6 = 120, 3x = 114, x = 38. Ahmad's mass = 38 kg.", "hints": ["Total mass = average × number of people = 40 × 3.", "Let Ahmad = Ben = x, Carl = x + 6; solve 3x + 6 = 120."], "source": "Catholic High 2024 P5 End-of-Year Exam Q29", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 38 kg." }, { "n": 30, "type_id": 2, "question": "Figure 1 shows an equilateral triangle which has a perimeter of 33 cm. Three such triangles are joined to form Figure 2. What is the perimeter of Figure 2? [?] cm", "answer0": "77", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "Each side of one triangle = 33 ÷ 3 = 11 cm. Three triangles together have 9 sides, total 9 × 11 = 99 cm. When joined, 2 pairs of sides become shared internal edges (2 × 11 × 2 = removed from perimeter). The outline of Figure 2 has 7 exposed sides = 7 × 11 = 77 cm.", "hints": ["One side = 33 ÷ 3 = 11 cm.", "Count only the sides on the outside of Figure 2: 7 sides remain exposed."], "source": "Catholic High 2024 P5 End-of-Year Exam Q30", "image_needed": true, "image_options": false, "image_file": "q30.png", "image_page": 16, "image_bbox": [0.30, 0.46, 0.83, 0.57], "image_loc": "Figure 1 (single triangle) and Figure 2 (three triangles joined) side by side, middle of page", "notes": "Key: 77 cm. Three joined triangles leave 7 exposed sides (2 shared edges, each shared by 2 sides)." }, { "n": 31, "type_id": 2, "question": "Tickets for a theme park were sold at 20% discount. The price of 4 tickets before discount was $196. What was the discount for one ticket? $[?]", "answer0": "9.80", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 176, "difficulty_id": 2, "explanation": "Price of 1 ticket before discount = 196 ÷ 4 = $49. Discount for one ticket = 20% of $49 = 20/100 × 49 = $9.80.", "hints": ["Find the price of one ticket: 196 ÷ 4.", "Discount = 20% of one ticket's price."], "source": "Catholic High 2024 P5 End-of-Year Exam Q31", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q1. Key: $9.80." }, { "n": 32, "type_id": 0, "question": "The table shows the number of sports played by each pupil in a group. Part of the table is covered by an ink blot. There were 157 pupils who played at least 2 sports. Number of sports: 0,1,2,3,4 with number of pupils 12,71,112,?,?. Each statement is either true, false or not possible to tell. (a) There were 240 pupils in the group. (b) The number of pupils who played 3 sports was equal to the number of pupils who played 4 sports.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 3, "explanation": "Pupils playing at least 2 sports = 157, and 112 played exactly 2, so pupils playing 3 or 4 sports = 157 − 112 = 45 (hidden by ink blot). (a) Total = 12 + 71 + 157 = 240. The statement says 240 — TRUE. (b) We only know 3-sport + 4-sport = 45; we cannot split them, so equality cannot be confirmed from the data — FALSE is the key's answer (the split is not equal / not determinable as equal).", "hints": ["At least 2 sports (157) = (2 sports) + (3 sports) + (4 sports).", "Total pupils = 12 + 71 + 157."], "source": "Catholic High 2024 P5 End-of-Year Exam Q32", "image_needed": true, "image_options": false, "image_file": "q32.png", "image_page": 18, "image_bbox": [0.20, 0.50, 0.80, 0.78], "image_loc": "two tables: sports-vs-pupils data table with ink blot, and a True/False/Not-possible tick table, lower half of page", "notes": "Paper 2 Q2. Key: (a) True, (b) False. Interactive tick-the-box format -> type_id 0 (SKIPPED on insert)." }, { "n": 33, "type_id": 2, "question": "The graph shows the amount of money John saved every month from January to May. What was the average amount of money John saved from January to May? $[?]", "answer0": "48", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 203, "difficulty_id": 2, "explanation": "From the bar graph: Jan = 50, Feb = 95, Mar = 0, Apr = 75, May = 20. Total = 50 + 95 + 0 + 75 + 20 = 240. Average = 240 ÷ 5 = $48.", "hints": ["Read each month's bar (note Mar = 0).", "Average = total ÷ number of months (5)."], "source": "Catholic High 2024 P5 End-of-Year Exam Q33", "image_needed": true, "image_options": false, "image_file": "q33.png", "image_page": 19, "image_bbox": [0.26, 0.16, 0.82, 0.45], "image_loc": "bar graph of money saved (Jan-May) on y-axis $0-100, upper-middle of page", "notes": "Paper 2 Q3. Key: $48 (bar values 50,95,0,75,20)." }, { "n": 34, "type_id": 1, "question": "Mr Ng bought three types of stationery. Pens cost $1.20 each (8 bought), Notepads cost 90¢ each (14 bought), Erasers cost 55¢ each (18 bought). Which type of stationery did Mr Ng spend the most on?", "answer0": "Pens", "answer1": "Notepads", "answer2": "Erasers", "answer3": "All the same", "correct_answer": 1, "skill_id": 167, "difficulty_id": 2, "explanation": "Pens: $1.20 × 8 = $9.60. Notepads: $0.90 × 14 = $12.60. Erasers: $0.55 × 18 = $9.90. The largest is Notepads ($12.60).", "hints": ["Multiply each price by the number bought.", "Compare the three totals."], "source": "Catholic High 2024 P5 End-of-Year Exam Q34", "image_needed": true, "image_options": false, "image_file": "q34.png", "image_page": 20, "image_bbox": [0.22, 0.14, 0.78, 0.28], "image_loc": "stationery price/quantity table (Pens, Notepads, Erasers), top of page", "notes": "Paper 2 Q4a. Key: Notepad. Word answer -> MCQ. Table data also given in stem." }, { "n": 35, "type_id": 2, "question": "Mr Ng bought Pens at $1.20 each (8 bought), Notepads at 90¢ each (14 bought) and Erasers at 55¢ each (18 bought). How much did he spend on all the stationery in total? $[?]", "answer0": "32.10", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 2, "explanation": "Pens: $9.60, Notepads: $12.60, Erasers: $9.90. Total = 9.60 + 12.60 + 9.90 = $32.10.", "hints": ["Find each subtotal: price × quantity.", "Add the three subtotals."], "source": "Catholic High 2024 P5 End-of-Year Exam Q35", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q4b. Key: $32.10. Data restated in stem (table on p20)." }, { "n": 36, "type_id": 0, "question": "The following solid is made up of 9 unit cubes. Draw the top view and the side view of the solid.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 188, "difficulty_id": 2, "explanation": "Top view: a plus/cross shape of cubes plus the one stacked cube square in the centre. Side view: an L/step outline as drawn in the answer key (page 36, Q5).", "hints": ["The top view shows how many cubes you see looking down.", "The side view shows the height profile from the side."], "source": "Catholic High 2024 P5 End-of-Year Exam Q36", "image_needed": true, "image_options": false, "image_file": "q36.png", "image_page": 21, "image_bbox": [0.36, 0.16, 0.62, 0.36], "image_loc": "isometric drawing of 9-unit-cube solid with Top/Front/Side view arrows, upper-middle of page", "notes": "Paper 2 Q5. Drawing task (draw top & side views) -> type_id 0 (SKIPPED on insert). Answer drawings on p36." }, { "n": 37, "type_id": 2, "question": "2 soccer balls cost as much as 3 volleyballs. Mr Lim bought 2 soccer balls and 4 volleyballs for $266. Find the total cost of 2 such soccer balls. $[?]", "answer0": "114", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 183, "difficulty_id": 3, "explanation": "2 soccer balls = 3 volleyballs in cost. So 2 soccer + 4 volleyballs = 3 volleyballs + 4 volleyballs = 7 volleyballs = $266. 1 volleyball = 266 ÷ 7 = $38. 2 soccer balls = 3 volleyballs = 3 × 38 = $114.", "hints": ["Replace 2 soccer balls by 3 volleyballs, so everything is in volleyballs.", "7 volleyballs = $266; find 1, then 3 volleyballs."], "source": "Catholic High 2024 P5 End-of-Year Exam Q37", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q6. Key: $114." }, { "n": 38, "type_id": 2, "question": "A rectangular tank 70 cm long by 35 cm wide by 30 cm high is filled up with water up to \\(\\dfrac{3}{5}\\) of its height. Water is then poured into the tank until it is filled with 58 ℓ of water. Find the amount of water that was poured into the tank. Give your answer in litres. [?] ℓ", "answer0": "13.9", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 193, "difficulty_id": 3, "explanation": "Water height at first = 3/5 × 30 = 18 cm. Initial volume = 70 × 35 × 18 = 44 100 cm³ = 44.1 ℓ. Water poured in = 58 − 44.1 = 13.9 ℓ.", "hints": ["Initial water height = 3/5 of 30 cm.", "Initial volume in cm³ ÷ 1000 = litres; subtract from 58 ℓ."], "source": "Catholic High 2024 P5 End-of-Year Exam Q38", "image_needed": true, "image_options": false, "image_file": "q38.png", "image_page": 23, "image_bbox": [0.28, 0.20, 0.72, 0.36], "image_loc": "3D rectangular tank with dimensions 70 cm, 35 cm, 30 cm and water shaded, upper-middle of page", "notes": "Paper 2 Q7. Key: 13.9 ℓ." }, { "n": 39, "type_id": 2, "question": "The total amount of money that Alan, Betty and Kalen has is $34.20. The ratio of the amount of money Alan has to the amount of money Betty has is 2 : 3. Kalen has $10.60 less than Betty. How much money does Kalen have? $[?]", "answer0": "6.20", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 183, "difficulty_id": 3, "explanation": "Total = $34.20. Kalen = Betty − 10.60. Add 10.60 to make Kalen equal Betty: 34.20 + 10.60 = 44.80 represents Alan + Betty + Betty = 2 + 3 + 3 = 8 units. 1 unit = 44.80 ÷ 8 = 5.60. Betty = 3 units = 16.80. Kalen = 16.80 − 10.60 = $6.20.", "hints": ["Alan : Betty = 2 : 3; treat Kalen as 'Betty − $10.60'.", "Add $10.60 to the total so Kalen becomes a 3-unit amount, giving 8 equal units."], "source": "Catholic High 2024 P5 End-of-Year Exam Q39", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q8. Key: $6.20." }, { "n": 40, "type_id": 2, "question": "In the square grid, PQ and QR are straight lines. Measure and write down the size of ∠PQR. [?]°", "answer0": "70", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 140, "difficulty_id": 2, "explanation": "Measuring ∠PQR with a protractor gives 70° (per the answer key).", "hints": ["Place the protractor centre at Q.", "Read the angle between arm QP and arm QR."], "source": "Catholic High 2024 P5 End-of-Year Exam Q40", "image_needed": true, "image_options": false, "image_file": "q40.png", "image_page": 25, "image_bbox": [0.28, 0.20, 0.74, 0.50], "image_loc": "square grid with points P, Q, R and lines PQ, QR drawn, middle of page", "notes": "Paper 2 Q9a only (the (b) part is a draw-the-parallelogram task and is omitted as non-servable). Key: 70°." }, { "n": 41, "type_id": 2, "question": "PQR and SRU are triangles. ∠RPQ is 40°, ∠PQR is 102° and ∠TSQ is 18°. Find ∠PUT. [?]°", "answer0": "56", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 3, "explanation": "In triangle PQR: ∠PRQ = 180° − 102° − 40° = 38°... Using the answer key working: 180° − 102° = 78° (∠TQ along the line); ∠STQ region gives 180° − 78° − 18° = 84°; then ∠PUT = 180° − 84° − 40° = 56°.", "hints": ["Use the angle sum of a triangle (180°) and angles on a straight line.", "Work through triangle by triangle to reach ∠PUT."], "source": "Catholic High 2024 P5 End-of-Year Exam Q41", "image_needed": true, "image_options": false, "image_file": "q41.png", "image_page": 26, "image_bbox": [0.30, 0.13, 0.72, 0.37], "image_loc": "two overlapping triangles PQR and SRU with angles 18°, 102°, 40° marked and points T, U, upper-left of page", "notes": "Paper 2 Q10. Key: 56°." }, { "n": 42, "type_id": 2, "question": "A tank was completely filled with water. A pump was turned on for some time to drain water out of the tank. The line graph shows the volume of water in the tank over 40 minutes. How much water was drained out of the tank in one minute? [?] ℓ", "answer0": "10", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 2, "explanation": "From the line graph the water fell from 700 ℓ to about 300 ℓ over... reading the key: 10 min corresponds to 100 ℓ drained, so 1 min = 100 ÷ 10 = 10 ℓ drained per minute.", "hints": ["Pick two points on the line and find the drop in volume over the time taken.", "Drained per minute = total drained ÷ number of minutes."], "source": "Catholic High 2024 P5 End-of-Year Exam Q42", "image_needed": true, "image_options": false, "image_file": "q42.png", "image_page": 27, "image_bbox": [0.30, 0.14, 0.78, 0.38], "image_loc": "line graph of volume of water (litres) vs time (minutes 0-40), upper-middle of page", "notes": "Paper 2 Q11a. Key: 10 ℓ/min." }, { "n": 43, "type_id": 2, "question": "A tank was completely filled with water. A pump drains it at a steady rate of 10 ℓ per minute; over the first 40 minutes the volume fell from the full amount to 300 ℓ. At the same rate, how long would it take for the water to be completely drained out of the tank after the 40 minutes? [?] min", "answer0": "30", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 2, "explanation": "After 40 minutes, 300 ℓ remain. At 10 ℓ per minute, time to drain the rest = 300 ÷ 10 = 30 minutes.", "hints": ["Read the volume left after 40 minutes (300 ℓ).", "Divide by the rate of 10 ℓ per minute."], "source": "Catholic High 2024 P5 End-of-Year Exam Q43", "image_needed": true, "image_options": false, "image_file": "q43.png", "image_page": 27, "image_bbox": [0.30, 0.14, 0.78, 0.38], "image_loc": "same line graph as Q42 (volume vs time), upper-middle of page", "notes": "Paper 2 Q11b. Key: 30 mins (300 ℓ ÷ 10 ℓ/min). Uses same graph as Q42." }, { "n": 44, "type_id": 2, "question": "ABCD is a rhombus and DCEF is a parallelogram. DGC is a straight line. ∠BCD is 100°, ∠BGD is 128° and ∠DFE (reflex) is 230°. Find ∠CEF. [?]°", "answer0": "50", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 200, "difficulty_id": 3, "explanation": "The interior ∠DFE = 360° − 230° = 130°. In parallelogram DCEF, ∠CEF and ∠DFE are co-interior (sum to 180°), so ∠CEF = 180° − 130° = 50°.", "hints": ["The reflex angle 230° means the interior angle at F is 360° − 230°.", "In a parallelogram, adjacent angles add up to 180°."], "source": "Catholic High 2024 P5 End-of-Year Exam Q44", "image_needed": true, "image_options": false, "image_file": "q44.png", "image_page": 28, "image_bbox": [0.26, 0.10, 0.78, 0.34], "image_loc": "rhombus ABCD joined to parallelogram DCEF with angles 100°, 128°, 230° marked, top of page", "notes": "Paper 2 Q12a. Key: 50°." }, { "n": 45, "type_id": 2, "question": "ABCD is a rhombus and DCEF is a parallelogram. DGC is a straight line. ∠BCD is 100° and ∠BGD is 128°. Find ∠DBG. [?]°", "answer0": "12", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 200, "difficulty_id": 3, "explanation": "In triangle BGC, ∠BGC = 180° − 128° = 52° (angles on straight line DGC). ∠BCG = ∠BCD = 100°... using the key working: ∠GBC = 180° − 100° − 52° = 28°. In the rhombus, ∠DBC = 80° − 40°... finally ∠DBG = 80° − 40° − 28° = 12°.", "hints": ["Use angles on the straight line DGC at G.", "Use the rhombus property (diagonal bisects the angle) and the triangle angle sum."], "source": "Catholic High 2024 P5 End-of-Year Exam Q45", "image_needed": true, "image_options": false, "image_file": "q45.png", "image_page": 28, "image_bbox": [0.26, 0.10, 0.78, 0.34], "image_loc": "same rhombus+parallelogram figure as Q44, top of page", "notes": "Paper 2 Q12b. Key: 12°. Uses same figure as Q44." }, { "n": 46, "type_id": 1, "question": "At a charity bake sale, each person bought either 2 muffins, 5 muffins or 7 muffins. \\(\\dfrac{3}{10}\\) of the people bought 2 muffins, \\(\\dfrac{11}{20}\\) of the people bought 5 muffins and the rest bought 7 muffins. What was the ratio of the number of people who bought 2 muffins to the number of people who bought 5 muffins to the number of people who bought 7 muffins?", "answer0": "6 : 11 : 3", "answer1": "3 : 11 : 6", "answer2": "3 : 11 : 20", "answer3": "6 : 11 : 20", "correct_answer": 0, "skill_id": 180, "difficulty_id": 3, "explanation": "Rest (7 muffins) = 1 − 3/10 − 11/20 = 20/20 − 6/20 − 11/20 = 3/20. As twentieths: 2-muffin = 6/20, 5-muffin = 11/20, 7-muffin = 3/20. Ratio = 6 : 11 : 3.", "hints": ["Find the fraction who bought 7 muffins: 1 − 3/10 − 11/20.", "Put all fractions over 20 and read off the numerators as the ratio."], "source": "Catholic High 2024 P5 End-of-Year Exam Q46", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q13a. Key: 6 : 11 : 3. Ratio answer -> MCQ (distractors generated)." }, { "n": 47, "type_id": 2, "question": "At a charity bake sale, \\(\\dfrac{3}{10}\\) of the people bought 2 muffins, \\(\\dfrac{11}{20}\\) bought 5 muffins and the rest (\\(\\dfrac{3}{20}\\)) bought 7 muffins. The number of people who bought 2 muffins were 147 more than those who bought 7 muffins. Each muffin was sold at $1.50. How much money was collected from the people who only bought 2 muffins? $[?]", "answer0": "882", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 180, "difficulty_id": 3, "explanation": "In twentieths the ratio is 6 : 11 : 3. Difference between 2-muffin (6 units) and 7-muffin (3 units) = 3 units = 147 people, so 1 unit = 49. People who bought 2 muffins = 6 units = 294. Muffins = 294 × 2 = 588. Money = 588 × $1.50 = $882.", "hints": ["The difference 6 units − 3 units = 3 units = 147 people.", "Find the number of 2-muffin buyers, then muffins, then money at $1.50 each."], "source": "Catholic High 2024 P5 End-of-Year Exam Q47", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q13b. Key: $882." }, { "n": 48, "type_id": 2, "question": "Ali received $500 as a prize. He gave $225 to his parents. He saved $123 and used the remaining amount of prize money to pay for a total of 24 cupcakes and tarts. What percentage of the prize money did Ali give to his parents? [?]%", "answer0": "45", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 171, "difficulty_id": 2, "explanation": "Percentage = amount given ÷ total prize × 100% = 225/500 × 100% = 45%.", "hints": ["Percentage = part ÷ whole × 100%.", "225 ÷ 500 × 100%."], "source": "Catholic High 2024 P5 End-of-Year Exam Q48", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q14a. Key: 45%." }, { "n": 49, "type_id": 2, "question": "Ali received $500 as a prize. He gave $225 to his parents and saved $123. He used the remaining money to pay for a total of 24 cupcakes and tarts. Cupcakes were sold at $5 each and tarts were sold at $7 each. How many tarts did Ali buy? [?]", "answer0": "16", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "Remaining money = 500 − 225 − 123 = $152. If all 24 were cupcakes: 24 × 5 = $120. Extra = 152 − 120 = $32. Each tart costs $7 − $5 = $2 more than a cupcake, so number of tarts = 32 ÷ 2 = 16.", "hints": ["Money for cakes/tarts = 500 − 225 − 123 = $152.", "Assume all 24 are cupcakes ($120); each tart adds $2, so 32 ÷ 2 tarts."], "source": "Catholic High 2024 P5 End-of-Year Exam Q49", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q14b. Key: 16 tarts." }, { "n": 50, "type_id": 2, "question": "A company ordered an equal number of large tubs and small tubs of ice-cream. 1 large tub costs $5; 3 small tubs cost $8. They paid a total of $112 more for the large tubs of ice-cream. How many tubs of ice-cream did the company order altogether? [?]", "answer0": "96", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "Cost of 1 large tub = $5. Cost of 1 small tub = $8 ÷ 3. For 3 tubs of each type: large = 3 × 5 = $15, small = $8; difference per 3 = $7... Per the key: large − small per tub difference 5(3) − 8 = $7 for every 3 of each. 112 ÷ 7 = 16 sets, each set has 3 large + 3 small. Large tubs = 16 × 3 = 48, small = 48, total = 96.", "hints": ["Compare cost of 3 large ($15) with 3 small ($8): difference $7 per 3 of each.", "112 ÷ 7 = 16 sets of (3 large + 3 small); total tubs = 16 × 6."], "source": "Catholic High 2024 P5 End-of-Year Exam Q50", "image_needed": true, "image_options": false, "image_file": "q50.png", "image_page": 31, "image_bbox": [0.34, 0.13, 0.68, 0.30], "image_loc": "drawing of 1 large tub ($5) and 3 small tubs ($8) of ice-cream, top-middle of page", "notes": "Paper 2 Q15a. Key: 96 tubs." }, { "n": 51, "type_id": 2, "question": "A company ordered an equal number of large tubs and small tubs of ice-cream. 1 large tub costs $5; 3 small tubs cost $8. They paid $112 more for the large tubs. The company ordered 48 large tubs and 48 small tubs. How much did the company pay for all the small tubs of ice-cream? $[?]", "answer0": "128", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "There are 48 small tubs. 3 small tubs cost $8, so 48 small tubs = 48 ÷ 3 = 16 sets, 16 × $8 = $128.", "hints": ["48 small tubs = 16 groups of 3.", "Each group of 3 costs $8: 16 × 8 = $128."], "source": "Catholic High 2024 P5 End-of-Year Exam Q51", "image_needed": true, "image_options": false, "image_file": "q51.png", "image_page": 31, "image_bbox": [0.34, 0.13, 0.68, 0.30], "image_loc": "same ice-cream tub drawing as Q50, top-middle of page", "notes": "Paper 2 Q15b. Key: $128. 48 small tubs (from part a) × cost." }, { "n": 52, "type_id": 1, "question": "Mrs Lee bought some star-shaped keychains, square-shaped keychains and pens. Mrs Lee spent \\(\\dfrac{3}{7}\\) of her money on the star-shaped keychains and \\(\\dfrac{5}{12}\\) of her remaining money on 15 square-shaped keychains. The rest of her money was spent on the pens. What fraction of her money did she spend on the pens?", "answer0": "\\(\\dfrac{1}{3}\\)", "answer1": "\\(\\dfrac{5}{12}\\)", "answer2": "\\(\\dfrac{4}{7}\\)", "answer3": "\\(\\dfrac{5}{21}\\)", "correct_answer": 0, "skill_id": 165, "difficulty_id": 3, "explanation": "Remaining after stars = 1 − 3/7 = 4/7. Spent on squares = 5/12 of 4/7 = 5/21. Spent on pens = 4/7 − 5/21 = 12/21 − 5/21 = 7/21 = 1/3.", "hints": ["Money left after star keychains = 4/7 of total.", "Squares took 5/12 of that 4/7; pens take the rest of the 4/7."], "source": "Catholic High 2024 P5 End-of-Year Exam Q52", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q16a. Key: 1/3 (= 7/21). Fraction answer -> MCQ (distractors generated)." }, { "n": 53, "type_id": 2, "question": "Mrs Lee spent \\(\\dfrac{3}{7}\\) of her money on star-shaped keychains and \\(\\dfrac{5}{12}\\) of her remaining money on 15 square-shaped keychains. Each square-shaped keychain costs the same and each star-shaped keychain costs the same; the money per keychain is equal across the two shapes. How many keychains did she buy altogether? [?]", "answer0": "42", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Squares took 5/21 of the money for 15 keychains; stars took 3/7 = 9/21 of the money. Since each keychain costs the same, money is proportional to count: 5/21 ↔ 15 keychains means 1/21 ↔ 3 keychains. Stars = 9/21 → 9 × 3 = 27 keychains. Total keychains = 27 + 15 = 42.", "hints": ["From part (a): squares = 5/21 of money buys 15 keychains, so 1/21 buys 3.", "Stars take 3/7 = 9/21; find star keychains then add the 15 squares."], "source": "Catholic High 2024 P5 End-of-Year Exam Q53", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q16b. Key: 42. (Key working: 15 ÷ 5 = 3; 14 × 3 = 42 — the key treats 4/7 = ? Using 14 units × 3.) Answer 42 confirmed by printed key." }, { "n": 54, "type_id": 2, "question": "The first three figures of a pattern have shaded and unshaded squares as: Figure 1 = 4 shaded, 5 unshaded; Figure 2 = 7 shaded, 8 unshaded; Figure 3 = 10 shaded, 11 unshaded. Complete the table for Figure 4: number of shaded squares = [?] , number of unshaded squares = [?].", "answer0": "13", "answer1": "14", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 108, "difficulty_id": 2, "explanation": "Shaded squares increase by 3 each figure: 4, 7, 10, 13. Unshaded squares increase by 3 each figure: 5, 8, 11, 14. So Figure 4 has 13 shaded and 14 unshaded.", "hints": ["Each figure adds 3 to the previous count.", "Figure 4 shaded = 10 + 3; unshaded = 11 + 3."], "source": "Catholic High 2024 P5 End-of-Year Exam Q54", "image_needed": true, "image_options": false, "image_file": "q54.png", "image_page": 33, "image_bbox": [0.20, 0.13, 0.78, 0.21], "image_loc": "three checkerboard pattern figures (Figure 1-3) in a row, top of page", "notes": "Paper 2 Q17a. Key: 13, 14. Two ordered blanks (shaded, unshaded)." }, { "n": 55, "type_id": 2, "question": "In a pattern, Figure 1 has 5 unshaded squares and the number of unshaded squares increases by 3 for each later figure (Figure 1 = 5, Figure 2 = 8, Figure 3 = 11). Find the total number of unshaded squares for Figure 47. [?]", "answer0": "143", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 108, "difficulty_id": 2, "explanation": "Unshaded squares = 5 + 3 × (figure number − 1) = 3 × figure number + 2. For Figure 47: 47 × 3 + 2 = 141 + 2 = 143.", "hints": ["Unshaded for Figure n = 3n + 2 (since 5, 8, 11, ...).", "Substitute n = 47: 47 × 3 + 2."], "source": "Catholic High 2024 P5 End-of-Year Exam Q55", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q17b. Key: 143 (= 47 × 3 + 2)." } ] }