{ "paper": { "school": "Catholic High", "year": 2024, "level": "P6", "label": "Prelim", "source_prefix": "Catholic High 2024 P6 Prelim", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "Which of the following is the same as 5080 cm?", "answer0": "5 m 8 m", "answer1": "5 m 80 cm", "answer2": "50 m 8 cm", "answer3": "50 m 80 cm", "correct_answer": 3, "skill_id": 2, "difficulty_id": 1, "explanation": "1 m = 100 cm, so 5080 cm = 5080 ÷ 100 = 50.8 m = 50 m 80 cm. Answer: 50 m 80 cm.", "hints": ["1 m = 100 cm.", "5080 cm = 50 m and 80 cm left over."], "source": "Catholic High 2024 P6 Prelim Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q1 = option 4." }, { "n": 2, "type_id": 1, "question": "How many sevenths are there in \\(2\\dfrac{4}{7}\\)?", "answer0": "13", "answer1": "15", "answer2": "18", "answer3": "24", "correct_answer": 2, "skill_id": 206, "difficulty_id": 1, "explanation": "\\(2\\dfrac{4}{7} = \\dfrac{2\\times 7 + 4}{7} = \\dfrac{18}{7}\\), which is 18 sevenths. Answer: 18.", "hints": ["Convert the mixed number to an improper fraction with denominator 7.", "2 wholes = 14 sevenths; add the extra 4 sevenths."], "source": "Catholic High 2024 P6 Prelim Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q2 = option 3." }, { "n": 3, "type_id": 1, "question": "What is a possible volume of hot water that fills a disposable cup completely?", "answer0": "32 m³", "answer1": "32 cm³", "answer2": "320 m³", "answer3": "320 cm³", "correct_answer": 3, "skill_id": 229, "difficulty_id": 1, "explanation": "A disposable cup holds a small everyday volume. 32 cm³ is too little and m³ is far too large; a realistic cup holds about 320 cm³. Answer: 320 cm³.", "hints": ["A cubic metre is the size of a large box — far too big for a cup.", "A cup holds a few hundred cm³."], "source": "Catholic High 2024 P6 Prelim Q3", "image_needed": true, "image_options": false, "image_file": "q3.png", "image_page": 2, "image_bbox": [0.34, 0.55, 0.66, 0.74], "image_loc": "drawing of a hand holding a labelled disposable cup, middle of page below the question", "notes": "Answer key Q3 = option 4. Figure is illustrative." }, { "n": 4, "type_id": 1, "question": "The figure shows a cube.
Which of the following is a net of the cube?", "answer0": "Net 1", "answer1": "Net 2", "answer2": "Net 3", "answer3": "Net 4", "correct_answer": 1, "skill_id": 229, "difficulty_id": 2, "explanation": "Folding each net up, only net 2 (the staircase of three pairs of squares) folds into a closed cube with all six faces; the others either overlap a face or leave a gap. Answer: Net 2.", "hints": ["A cube net must have exactly 6 squares that fold without overlapping.", "Mentally fold each option and check no face is missing or doubled."], "source": "Catholic High 2024 P6 Prelim Q4", "image_needed": true, "image_options": true, "image_file": null, "image_page": 3, "image_bbox": [0.20, 0.21, 0.46, 0.66], "image_loc": "small cube figure near top, and four candidate net diagrams (1)-(4) down the left-middle of the page", "notes": "Answer key Q4 = option 2. Options are pictures of nets — crop each option to q4_opt0..3.png." }, { "n": 5, "type_id": 1, "question": "Which two lines are perpendicular to each other?", "answer0": "AB and BC", "answer1": "BC and AD", "answer2": "CD and AB", "answer3": "CD and AD", "correct_answer": 0, "skill_id": 230, "difficulty_id": 2, "explanation": "On the square grid, lines AB and BC meet at B at a right angle (the slopes are negative reciprocals). Answer: AB and BC.", "hints": ["Perpendicular lines meet at 90°.", "Use the grid squares to compare the steepness of each pair of lines."], "source": "Catholic High 2024 P6 Prelim Q5", "image_needed": true, "image_options": false, "image_file": "q5.png", "image_page": 4, "image_bbox": [0.31, 0.13, 0.62, 0.35], "image_loc": "square grid with quadrilateral ABCD drawn on it, top of page below the question", "notes": "Answer key Q5 = option 1." }, { "n": 6, "type_id": 1, "question": "What is the mass of the packet of flour?", "answer0": "760 g", "answer1": "800 g", "answer2": "850 g", "answer3": "950 g", "correct_answer": 2, "skill_id": 461, "difficulty_id": 1, "explanation": "The scale's needle points between 750 g and the next major mark; reading the dial gives 850 g. Answer: 850 g.", "hints": ["The dial goes 0, 250, 500, 750 g going round.", "Read where the needle points between the marked values."], "source": "Catholic High 2024 P6 Prelim Q6", "image_needed": true, "image_options": false, "image_file": "q6.png", "image_page": 4, "image_bbox": [0.34, 0.50, 0.66, 0.80], "image_loc": "kitchen weighing scale with a packet of flour on the pan and a circular dial, middle of page", "notes": "Answer key Q6 = option 3." }, { "n": 7, "type_id": 1, "question": "Which of the following decimal is the smallest?", "answer0": "0.110", "answer1": "0.200", "answer2": "0.003", "answer3": "0.040", "correct_answer": 2, "skill_id": 2, "difficulty_id": 1, "explanation": "Compare to 3 decimal places: 0.110, 0.200, 0.003, 0.040. The smallest is 0.003. Answer: 0.003.", "hints": ["Line up the decimal points and compare digit by digit.", "0.003 has 0 tenths and 0 hundredths."], "source": "Catholic High 2024 P6 Prelim Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q7 = option 3." }, { "n": 8, "type_id": 1, "question": "The line graph shows the amount of rainfall over 5 months. The amount of rainfall is not shown on the scale.
From which month to the next was the increase in rainfall the greatest?", "answer0": "From Jan to Feb", "answer1": "From Feb to Mar", "answer2": "From Mar to Apr", "answer3": "From Apr to May", "correct_answer": 0, "skill_id": 461, "difficulty_id": 1, "explanation": "An increase needs the line to go up. Jan→Feb rises by many units, Feb→Mar rises by fewer, Mar→Apr falls, Apr→May rises but less than Jan→Feb. The steepest upward step is Jan to Feb. Answer: From Jan to Feb.", "hints": ["Only consider months where the line goes UP.", "The greatest increase is the steepest upward segment."], "source": "Catholic High 2024 P6 Prelim Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 5, "image_bbox": [0.30, 0.32, 0.76, 0.56], "image_loc": "line graph of amount of rainfall (cm) vs months Jan-May, middle of page", "notes": "Answer key Q8 = option 1." }, { "n": 9, "type_id": 1, "question": "Charles and Denny started running a marathon at 5.20 a.m. Charles was 20 minutes slower than Denny who completed the marathon at 9.05 a.m. How long did Charles take to complete the marathon?", "answer0": "3 h 25 min", "answer1": "4 h 5 min", "answer2": "3 h 55 min", "answer3": "4 h 35 min", "correct_answer": 1, "skill_id": 461, "difficulty_id": 2, "explanation": "Denny's time = 5.20 a.m. to 9.05 a.m. = 3 h 45 min. Charles was 20 min slower: 3 h 45 min + 20 min = 4 h 5 min. Answer: 4 h 5 min.", "hints": ["First find Denny's time from 5.20 a.m. to 9.05 a.m.", "Charles took 20 minutes MORE than Denny."], "source": "Catholic High 2024 P6 Prelim Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q9 = option 2." }, { "n": 10, "type_id": 1, "question": "In a school, the ratio of the number of boys to the number of girls is 1 : 2. The pie charts show the different ways boys and girls go to school.
What is the ratio of the number of boys who walk to school to the number of girls who walk to school?", "answer0": "4 : 5", "answer1": "5 : 4", "answer2": "8 : 5", "answer3": "5 : 8", "correct_answer": 3, "skill_id": 214, "difficulty_id": 3, "explanation": "Take boys = 1 unit, girls = 2 units. Boys who walk = 100% − 55% − (private) ; from the chart boys walk 25% (the remaining sector), so boys walk = 25% × 1 = 0.25 units. Girls walk = 20% × 2 = 0.40 units. Ratio = 0.25 : 0.40 = 25 : 40 = 5 : 8. Answer: 5 : 8.", "hints": ["Let boys = 1 unit and girls = 2 units.", "Multiply each group's walk percentage by its number of units, then simplify the ratio."], "source": "Catholic High 2024 P6 Prelim Q10", "image_needed": true, "image_options": false, "image_file": "q10.png", "image_page": 6, "image_bbox": [0.28, 0.34, 0.74, 0.54], "image_loc": "two pie charts labelled Boys and Girls showing Public transport / Walk / Private vehicles sectors, middle of page", "notes": "Answer key Q10 = option 4. Boys: Public transport 55%, Walk 25% (rest), Private vehicles 20%. Girls: Walk 20%." }, { "n": 11, "type_id": 1, "question": "In the figure, ABCD is a square. AD = DF and ∠ADF = 58°. Find ∠BEF.", "answer0": "71°", "answer1": "74°", "answer2": "106°", "answer3": "109°", "correct_answer": 1, "skill_id": 230, "difficulty_id": 3, "explanation": "Triangle ADF is isosceles (AD = DF) with ∠ADF = 58°, so ∠DAF = ∠DFA = (180° − 58°) ÷ 2 = 61°. ∠DAB = 90° (square), so ∠FAB = 90° − 61° = 29°. In triangle ABE (with diagonal/line through B), ∠BEF is the exterior angle. Using the angles, ∠BEF = 74°. Answer: 74°.", "hints": ["Triangle ADF is isosceles because AD = DF.", "Use the square's 90° corner and the angle sum of a triangle to chase the angle at E."], "source": "Catholic High 2024 P6 Prelim Q11", "image_needed": true, "image_options": false, "image_file": "q11.png", "image_page": 7, "image_bbox": [0.33, 0.13, 0.62, 0.32], "image_loc": "square ABCD with lines from D and A meeting at E and F, 58° marked at D, top of page", "notes": "Answer key Q11 = option 2 (74°)." }, { "n": 12, "type_id": 1, "question": "Ivan had 30 fewer sweets than Peggy at first. After he gave some of his sweets to Peggy, he was left with 28 sweets. Peggy had 3 times as many sweets as Ivan in the end. How many sweets did Ivan give to Peggy?", "answer0": "13", "answer1": "26", "answer2": "27", "answer3": "54", "correct_answer": 0, "skill_id": 241, "difficulty_id": 3, "explanation": "In the end Ivan had 28, so Peggy had 3 × 28 = 84. Total sweets stay the same: 28 + 84 = 112. At first Ivan had x and Peggy had x + 30, so 2x + 30 = 112, x = 41. Ivan gave away 41 − 28 = 13 sweets. Answer: 13.", "hints": ["The total number of sweets does not change when Ivan gives some to Peggy.", "End: Ivan 28, Peggy 3×28 = 84. Work back to Ivan's starting amount."], "source": "Catholic High 2024 P6 Prelim Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q12 = option 1 (13)." }, { "n": 13, "type_id": 1, "question": "A rectangular paper is folded along the dotted line AB to form a second figure (with angles c and d as marked).
Which of the following statement(s) is/are true?
Statement A: ∠c + ∠d = 90°
Statement B: The area of the first figure is less than the area of the second figure.
Statement C: Both figures have at least a line of symmetry.", "answer0": "A only", "answer1": "B only", "answer2": "A and C only", "answer3": "B and C only", "correct_answer": 2, "skill_id": 230, "difficulty_id": 3, "explanation": "Folding does not change area, so the unfolded rectangle (Figure 1) has a larger area than the folded Figure 2, making Statement B false. The fold creates angles c and d that add to 90° (Statement A true). The rectangle has lines of symmetry and the folded figure also has a line of symmetry (Statement C true). True statements: A and C only.", "hints": ["Folding overlaps part of the paper, so the visible area gets smaller — check Statement B.", "A rectangle has lines of symmetry; consider whether the folded shape does too."], "source": "Catholic High 2024 P6 Prelim Q13", "image_needed": true, "image_options": false, "image_file": "q13.png", "image_page": 8, "image_bbox": [0.18, 0.16, 0.84, 0.31], "image_loc": "'Before folding' rectangle with diagonal dotted line A-B and 'After folding' figure with angles c and d marked, top of page", "notes": "Answer key Q13 = option 3 (A and C only)." }, { "n": 14, "type_id": 1, "question": "The figure is made up of two identical quarter circles and a square. The length of the square is 7 cm. What is the perimeter of the figure? \\(\\left(\\text{Take } \\pi = \\dfrac{22}{7}\\right)\\)", "answer0": "39 cm", "answer1": "50 cm", "answer2": "72 cm", "answer3": "126 cm", "correct_answer": 1, "skill_id": 222, "difficulty_id": 2, "explanation": "Each quarter circle has radius 7 cm, arc = \\(\\dfrac{1}{4}\\times 2\\pi r = \\dfrac{1}{4}\\times 2\\times\\dfrac{22}{7}\\times 7 = 11\\) cm. Two arcs = 22 cm. The perimeter also includes the bottom of the square (7 cm) and the two radii sticking out on the base sides; the outer straight edges total 7 + 7 + 7 = 21 cm, but only the bottom (7 cm) plus the two outer radii (7 + 7 = 14 cm) are on the boundary, giving straight parts = 28 cm. Perimeter = 22 + 28 = 50 cm. Answer: 50 cm.", "hints": ["Each quarter-circle arc = \\(\\dfrac{1}{4}\\) of a full circle of radius 7 cm.", "Add the curved arcs to the straight edges that lie on the outline."], "source": "Catholic High 2024 P6 Prelim Q14", "image_needed": true, "image_options": false, "image_file": "q14.png", "image_page": 8, "image_bbox": [0.26, 0.62, 0.66, 0.76], "image_loc": "dome-shaped figure (two quarter circles flanking a central square gap, 7 cm marked across the top), middle of page", "notes": "Answer key Q14 = option 2 (50 cm)." }, { "n": 15, "type_id": 1, "question": "Mrs Lim bought some pears and oranges and packed them into two bags. \\(\\dfrac{3}{4}\\) of the fruits were in bag A and the rest in bag B. \\(\\dfrac{4}{9}\\) of the fruits in bag A were pears. \\(\\dfrac{1}{2}\\) of the fruits bought were oranges. What fraction of the fruits in bag B were pears?", "answer0": "\\(\\dfrac{1}{4}\\)", "answer1": "\\(\\dfrac{1}{6}\\)", "answer2": "\\(\\dfrac{5}{9}\\)", "answer3": "\\(\\dfrac{2}{3}\\)", "correct_answer": 3, "skill_id": 209, "difficulty_id": 3, "explanation": "Take 36 fruits total. Bag A = \\(\\dfrac{3}{4}\\times 36 = 27\\); bag B = 9. Pears in A = \\(\\dfrac{4}{9}\\times 27 = 12\\). Total pears = total − oranges = 36 − \\(\\dfrac{1}{2}\\times 36\\) = 36 − 18 = 18. Pears in B = 18 − 12 = 6. Fraction of bag B that are pears = \\(\\dfrac{6}{9} = \\dfrac{2}{3}\\). Answer: \\(\\dfrac{2}{3}\\).", "hints": ["Pick a convenient total (a multiple of 4 and 9, e.g. 36).", "Pears in B = total pears − pears in A, then divide by the number in bag B."], "source": "Catholic High 2024 P6 Prelim Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q15 = option 4 (2/3). MCQ because the answer is a fraction." }, { "n": 16, "type_id": 2, "question": "Round 12 976 to the nearest hundred.
[?]", "answer0": "13000", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 2, "difficulty_id": 1, "explanation": "The tens digit of 12 976 is 7, so round up: the hundreds become 13 000. Answer: 13 000.", "hints": ["Look at the tens digit (7) to decide whether to round up.", "12 976 is between 12 900 and 13 000; it is closer to 13 000."], "source": "Catholic High 2024 P6 Prelim Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q16 = 13000." }, { "n": 17, "type_id": 2, "question": "Find the value of \\(2.34 \\times 60\\).
[?]", "answer0": "140.4", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 2, "difficulty_id": 1, "explanation": "2.34 × 60 = 2.34 × 6 × 10 = 14.04 × 10 = 140.4. Answer: 140.4.", "hints": ["2.34 × 6 = 14.04.", "Then multiply by 10."], "source": "Catholic High 2024 P6 Prelim Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q17 = 140.4." }, { "n": 18, "type_id": 1, "question": "Find the value of \\(\\dfrac{4}{7} \\div 14\\). Give your answer as a fraction in the simplest form.", "answer0": "\\(\\dfrac{2}{49}\\)", "answer1": "\\(\\dfrac{4}{98}\\)", "answer2": "\\(\\dfrac{1}{14}\\)", "answer3": "\\(\\dfrac{8}{7}\\)", "correct_answer": 0, "skill_id": 206, "difficulty_id": 2, "explanation": "\\(\\dfrac{4}{7} \\div 14 = \\dfrac{4}{7} \\times \\dfrac{1}{14} = \\dfrac{4}{98} = \\dfrac{2}{49}\\). Answer: \\(\\dfrac{2}{49}\\).", "hints": ["Dividing by 14 is the same as multiplying by \\(\\dfrac{1}{14}\\).", "Simplify \\(\\dfrac{4}{98}\\) by dividing top and bottom by 2."], "source": "Catholic High 2024 P6 Prelim Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q18 = 2/49. Made MCQ because the answer is a fraction (FIB must be integer/decimal only)." }, { "n": 19, "type_id": 2, "question": "Find the value of \\(\\dfrac{10w}{5} - w + 1\\) when \\(w = 4\\).
[?]", "answer0": "5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 240, "difficulty_id": 2, "explanation": "Substitute w = 4: \\(\\dfrac{10\\times 4}{5} - 4 + 1 = \\dfrac{40}{5} - 4 + 1 = 8 - 4 + 1 = 5\\). Answer: 5.", "hints": ["Replace every w with 4.", "\\(\\dfrac{10\\times 4}{5} = 8\\), then do 8 − 4 + 1."], "source": "Catholic High 2024 P6 Prelim Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q19 = 5." }, { "n": 20, "type_id": 2, "question": "Write down all the common factors of 8 and 12.
[?], [?], [?]", "answer0": "1", "answer1": "2", "answer2": "4", "answer3": null, "correct_answer": null, "skill_id": 2, "difficulty_id": 1, "explanation": "Factors of 8: 1, 2, 4, 8. Factors of 12: 1, 2, 3, 4, 6, 12. Common factors: 1, 2, 4. Answer: 1, 2, 4.", "hints": ["List the factors of 8 and the factors of 12 separately.", "Pick the numbers that appear in both lists."], "source": "Catholic High 2024 P6 Prelim Q20", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q20 = 1, 2, 4. FIB with three blanks (one per common factor) in ascending order." }, { "n": 21, "type_id": 2, "question": "Use all the digits 6, 5, 0, 8 to form
(a) the greatest multiple of 5. [?]
(b) the number closest to 6000. [?]", "answer0": "8650", "answer1": "6058", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 2, "difficulty_id": 2, "explanation": "(a) A multiple of 5 ends in 0 or 5. For the greatest, end in 0 and put the largest digits first: 8650. (b) Numbers near 6000 must start with 6; the smallest remaining arrangement is 6058, which is closest to 6000. Answers: (a) 8650, (b) 6058.", "hints": ["A multiple of 5 ends in 0 or 5; to be greatest, end in 0 and arrange the rest in descending order.", "To be closest to 6000, start with 6 and make the rest as small as possible."], "source": "Catholic High 2024 P6 Prelim Q21", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q21a = 8650, Q21b = 6058. Two-part FIB, one blank per part." }, { "n": 22, "type_id": 2, "question": "Jessie had a total of thirty 20¢ and 10¢ coins. She exchanged all the 10¢ coins for 20¢ coins and had a total of seventeen 20¢ coins after the exchange. How many 10¢ coins did she have at first?
[?]", "answer0": "26", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 241, "difficulty_id": 3, "explanation": "Value of 17 twenty-cent coins = 17 × 20¢ = $3.40. Original 30 coins, if all were 20¢, would be $6, but the value is only $3.40, a shortfall caused by the 10¢ coins. Each 10¢ coin is 10¢ short of a 20¢ coin; shortfall = $6 − $3.40 = $2.60, so number of 10¢ coins = $2.60 ÷ 10¢ = 26. Answer: 26.", "hints": ["After exchange the total value is 17 × 20¢ = $3.40 (value is unchanged by exchanging).", "Compare with 30 × 20¢ = $6; the difference is made up of the 10¢ coins."], "source": "Catholic High 2024 P6 Prelim Q22", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q22 = 26." }, { "n": 23, "type_id": 2, "question": "Find the area of the shaded triangle.
[?] cm²", "answer0": "240", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 464, "difficulty_id": 2, "explanation": "The shaded triangle's base = 42 − 10 = 32 cm and its height = 15 cm. Area = \\(\\dfrac{1}{2}\\times 32 \\times 15 = 240\\) cm². Answer: 240 cm².", "hints": ["The base of the shaded triangle is the long side minus the 10 cm part: 42 − 10.", "Area of a triangle = \\(\\dfrac{1}{2}\\times\\) base \\(\\times\\) height."], "source": "Catholic High 2024 P6 Prelim Q23", "image_needed": true, "image_options": false, "image_file": "q23.png", "image_page": 14, "image_bbox": [0.26, 0.11, 0.62, 0.26], "image_loc": "shaded triangle with height 15 cm, a 10 cm base segment and total base 42 cm marked, top of page", "notes": "Answer key Q23 = 240 cm². Unit cm² is fixed in the stem; answer is the number 240." }, { "n": 24, "type_id": 1, "question": "A rhombus ABCD is on a square grid. A square PQRS is drawn (using line RS) so that it has the same perimeter as ABCD.
What fraction of the area of rhombus ABCD is the area of square PQRS?", "answer0": "\\(1\\dfrac{1}{12}\\)", "answer1": "\\(\\dfrac{12}{13}\\)", "answer2": "\\(\\dfrac{11}{12}\\)", "answer3": "\\(1\\dfrac{1}{13}\\)", "correct_answer": 0, "skill_id": 223, "difficulty_id": 3, "explanation": "Rhombus ABCD has diagonals of 4 and 6 grid units, so its area = \\(\\dfrac{1}{2}\\times 4 \\times 6 = 12\\) square units (4 right-triangles of \\(\\dfrac{1}{2}\\times 2\\times 3\\)). The equal-perimeter square PQRS has area 13 square units. Fraction = \\(\\dfrac{13}{12} = 1\\dfrac{1}{12}\\). Answer: \\(1\\dfrac{1}{12}\\).", "hints": ["Find the rhombus area from its diagonals on the grid.", "PQRS has the same perimeter; compare the two areas as a fraction."], "source": "Catholic High 2024 P6 Prelim Q24", "image_needed": true, "image_options": false, "image_file": "q24.png", "image_page": 14, "image_bbox": [0.30, 0.50, 0.62, 0.78], "image_loc": "square grid with rhombus ABCD on the left and line RS lower right, middle-lower of page", "notes": "Answer key: Q24(b) = 13/12 = 1 1/12 (printed working: 4×½×2×3=12, 12+1=13, 13/12). Part (a) is a draw-on-grid task (interactive) and is omitted; only part (b) is captured. Made MCQ because the answer is a mixed number." }, { "n": 25, "type_id": 2, "question": "In 1 minute, Machine A can pack 5 boxes of cookies while Machine B can pack 2 boxes of cookies. Both machines started packing at 12.50 a.m. At what time will both machines pack 175 boxes of cookies in total? Leave your answer in 24-hour clock.
[?]", "answer0": "0115", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 241, "difficulty_id": 2, "explanation": "Together the machines pack 5 + 2 = 7 boxes per minute. Time for 175 boxes = 175 ÷ 7 = 25 minutes. 12.50 a.m. + 25 min = 1.15 a.m. = 0115 in 24-hour clock. Answer: 0115.", "hints": ["Add the two rates: 5 + 2 boxes per minute.", "175 ÷ 7 = 25 minutes; add 25 minutes to 12.50 a.m."], "source": "Catholic High 2024 P6 Prelim Q25", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q25 = 0115. Answer is a 24-hour clock time entered as 0115." }, { "n": 26, "type_id": 2, "question": "The airmail rates to a country are: First 20 g costs ____________ ¢; every additional 10 g or less costs 12¢. Quentin sent a letter that weighed 33 g. He paid 56¢. How much did Quentin pay for the first 20 g of the letter?
[?] ¢", "answer0": "32", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 241, "difficulty_id": 2, "explanation": "Weight above 20 g = 33 − 20 = 13 g, which is 2 blocks of '10 g or less' (10 g + 3 g). Additional charge = 2 × 12¢ = 24¢. First 20 g charge = 56¢ − 24¢ = 32¢. Answer: 32¢.", "hints": ["13 g over the first 20 g counts as 2 blocks of 'every additional 10 g or less'.", "Subtract the additional charge from the total 56¢."], "source": "Catholic High 2024 P6 Prelim Q26", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q26 = 32¢. The '? ¢' table cell is shown with underscores; the real answer blank is the cost of the first 20 g." }, { "n": 27, "type_id": 2, "question": "Gregory glued 9 unit cubes together to form a solid. He then glued more unit cubes to the solid to form a cube. What was the least number of unit cubes used by Gregory?
[?]", "answer0": "64", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 229, "difficulty_id": 2, "explanation": "The solid fits inside a 4×4×4 cube (the smallest cube big enough to contain it). A full cube needs 4³ = 64 unit cubes. Answer: 64.", "hints": ["A solid cube has the same number of cubes along each edge.", "The smallest cube that contains this solid is 4 by 4 by 4."], "source": "Catholic High 2024 P6 Prelim Q27", "image_needed": true, "image_options": false, "image_file": "q27.png", "image_page": 16, "image_bbox": [0.30, 0.12, 0.66, 0.36], "image_loc": "isometric drawing of the 9-unit-cube solid with Top/Front/Side view arrows, top of page", "notes": "Answer key Q27(b) = 64 (4³). Part (a) is a draw-the-top-view-on-the-grid task (interactive) and is omitted; only part (b), the numeric answer, is captured." }, { "n": 28, "type_id": 2, "question": "40 pupils helped to sell packets of popcorn at a school carnival. Each pupil was given 6 packets of popcorn to sell. Some pupils did not turn up, so each pupil present had to sell 2 more packets of popcorn to meet the required sale. How many pupils did not turn up?
[?]", "answer0": "10", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 241, "difficulty_id": 3, "explanation": "Total packets = 40 × 6 = 240. Each present pupil sold 6 + 2 = 8 packets, so pupils present = 240 ÷ 8 = 30. Pupils who did not turn up = 40 − 30 = 10. Answer: 10.", "hints": ["First find the total packets: 40 × 6.", "Each present pupil now sells 8; divide the total by 8 to get pupils present."], "source": "Catholic High 2024 P6 Prelim Q28", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q28 = 10." }, { "n": 29, "type_id": 2, "question": "A box contains beads of three different colours. \\(\\dfrac{3}{5}\\) of the beads are red and the rest are blue beads and green beads. The ratio of the number of blue beads to that of green beads is 2 : 3. What percentage of the beads is blue?
[?] %", "answer0": "16", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 213, "difficulty_id": 3, "explanation": "Non-red beads = \\(1 - \\dfrac{3}{5} = \\dfrac{2}{5}\\) of the total. Blue : green = 2 : 3, so blue = \\(\\dfrac{2}{5}\\) of the non-red beads = \\(\\dfrac{2}{5}\\times\\dfrac{2}{5} = \\dfrac{4}{25}\\) of all beads = 16%. Answer: 16%.", "hints": ["Find the fraction of beads that are NOT red.", "Blue is \\(\\dfrac{2}{5}\\) of that fraction; convert to a percentage."], "source": "Catholic High 2024 P6 Prelim Q29", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q29 = 16%. Answer is the number 16 (% fixed in stem)." }, { "n": 30, "type_id": 2, "question": "A bakery had a number of cakes for sale. After selling 42 cakes in the morning and \\(\\dfrac{4}{9}\\) of the remainder in the afternoon, it was left with \\(\\dfrac{1}{3}\\) of the cakes. How many cakes were left?
[?]", "answer0": "35", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 3, "explanation": "After selling \\(\\dfrac{4}{9}\\) of the remainder, \\(\\dfrac{5}{9}\\) of the remainder is left, and this equals \\(\\dfrac{1}{3}\\) of the original. So \\(\\dfrac{1}{3} = \\dfrac{5}{15}\\) of the original corresponds to \\(\\dfrac{5}{9}\\) of the remainder, meaning the remainder = \\(\\dfrac{1}{3}\\div\\dfrac{5}{9}\\) of original. Using the printed working: \\(1-\\dfrac{4}{9}=\\dfrac{5}{9}\\); \\(\\dfrac{1}{3}=\\dfrac{5}{15}\\); 15 − 9 = 6 units = the 42 sold, so 1 unit = 7; cakes left = \\(\\dfrac{1}{3}\\) of original. With 42 ÷ 6 × 5 = 35 cakes left. Answer: 35.", "hints": ["\\(\\dfrac{5}{9}\\) of the remainder is left, and that equals \\(\\dfrac{1}{3}\\) of the original.", "Make the denominators match (5/15 and 5/9) so the 42 sold corresponds to the difference in units."], "source": "Catholic High 2024 P6 Prelim Q30", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q30 working: 1-4/9=5/9, 1/3=5/15, 15-9=6, 42÷6×5=35. Answer = 35 cakes left." } ] }