{ "paper": { "school": "Catholic High", "year": 2022, "level": "P6", "label": "Prelim", "source_prefix": "Catholic High 2022 P6 Prelim", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "Which of the following is four hundred thousand and two in numerals?", "answer0": "402", "answer1": "4002", "answer2": "40 002", "answer3": "400 002", "correct_answer": 3, "skill_id": 149, "difficulty_id": 1, "explanation": "Four hundred thousand = 400 000, plus two = 400 002.", "hints": ["Four hundred thousand is 400 000.", "Add the 'and two' as the ones digit."], "source": "Catholic High 2022 P6 Prelim Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 2, "type_id": 1, "question": "What is the value of \\(4 \\div 800\\)?", "answer0": "0.005", "answer1": "0.02", "answer2": "50", "answer3": "200", "correct_answer": 0, "skill_id": 166, "difficulty_id": 2, "explanation": "\\(4 \\div 800 = 4 \\div 8 \\div 100 = 0.5 \\div 100 = 0.005\\).", "hints": ["Split 800 into 8 x 100.", "4 divided by 8 is 0.5, then divide by 100."], "source": "Catholic High 2022 P6 Prelim Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 3, "type_id": 1, "question": "What is the length of the safety pin?", "answer0": "3.1 cm", "answer1": "3.2 cm", "answer2": "4.3 cm", "answer3": "4.6 cm", "correct_answer": 1, "skill_id": 84, "difficulty_id": 1, "explanation": "The safety pin runs from the 0.3 cm mark to about the 3.5 cm mark; reading the pin's full length against the ruler gives 3.2 cm.", "hints": ["Read both ends of the pin against the ruler scale.", "Subtract the start reading from the end reading."], "source": "Catholic High 2022 P6 Prelim Q3", "image_needed": true, "image_options": false, "image_file": "q3.png", "image_page": 3, "image_bbox": [0.28, 0.50, 0.68, 0.62], "image_loc": "centre of page, safety pin lying over a centimetre ruler", "notes": "Key answer: option 2 (3.2 cm)." }, { "n": 4, "type_id": 1, "question": "Which one of the following is likely to be the mass of a scientific calculator?", "answer0": "9 g", "answer1": "90 g", "answer2": "900 g", "answer3": "9000 g", "correct_answer": 1, "skill_id": 84, "difficulty_id": 1, "explanation": "A scientific calculator is a small handheld object weighing roughly 90 g; 9 g is too light, 900 g and 9000 g are far too heavy.", "hints": ["Estimate the mass of an everyday handheld object.", "9000 g is 9 kg — far too heavy for a calculator."], "source": "Catholic High 2022 P6 Prelim Q4", "image_needed": true, "image_options": false, "image_file": "q4.png", "image_page": 4, "image_bbox": [0.40, 0.10, 0.66, 0.26], "image_loc": "top centre, a hand holding a scientific calculator", "notes": "Key answer: option 2 (90 g)." }, { "n": 5, "type_id": 1, "question": "Find the value of \\(\\dfrac{14m}{3} \\div 1\\) when \\(m = 6\\).", "answer0": "\\(5\\dfrac{2}{3}\\)", "answer1": "28", "answer2": "\\(28\\dfrac{1}{3}\\)", "answer3": "29", "correct_answer": 3, "skill_id": 240, "difficulty_id": 2, "explanation": "\\(\\dfrac{14m}{3} = \\dfrac{14 \\times 6}{3} = \\dfrac{84}{3} = 28\\). Then \\(28 + 1 = 29\\).", "hints": ["Substitute m = 6 first.", "84 ÷ 3 = 28, then add 1."], "source": "Catholic High 2022 P6 Prelim Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Stem prints '+ 1'; key (option 4 = 29) confirms the operation is +1, giving 28 + 1 = 29." }, { "n": 6, "type_id": 1, "question": "Which of the following is the same as 70 ℓ 90 ml?", "answer0": "7 090 ml", "answer1": "7 900 ml", "answer2": "70 090 ml", "answer3": "70 900 ml", "correct_answer": 2, "skill_id": 192, "difficulty_id": 2, "explanation": "70 ℓ = 70 000 ml. Adding 90 ml gives 70 090 ml.", "hints": ["1 litre = 1000 ml.", "70 000 ml + 90 ml."], "source": "Catholic High 2022 P6 Prelim Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 7, "type_id": 1, "question": "A square is first divided into two equal halves. The left half is divided into 3 equal parts while the right half is divided into 4 equal parts. What fraction of the square is shaded?", "answer0": "\\(\\dfrac{5}{12}\\)", "answer1": "\\(\\dfrac{5}{11}\\)", "answer2": "\\(\\dfrac{3}{7}\\)", "answer3": "\\(\\dfrac{3}{4}\\)", "correct_answer": 0, "skill_id": 161, "difficulty_id": 3, "explanation": "Left half = 1/2, split into 3 parts; 1 shaded part = 1/3 of 1/2 = 1/6 = 2/12. Right half = 1/2, split into 4 parts; 2 shaded parts (the two opposite triangles) = 2/4 of 1/2 = 1/4 = 3/12. Total shaded = 2/12 + 3/12 = 5/12.", "hints": ["Each half is 1/2 of the square.", "Convert both shaded portions to twelfths and add."], "source": "Catholic High 2022 P6 Prelim Q7", "image_needed": true, "image_options": false, "image_file": "q7.png", "image_page": 5, "image_bbox": [0.38, 0.16, 0.64, 0.31], "image_loc": "top centre, a square divided into a left (3 parts) and right (4 parts) half with shading", "notes": "Key answer: option 1 (5/12)." }, { "n": 8, "type_id": 1, "question": "Shamsul was North-East of Teddy. At first, they were facing each other. Then both boys made the smallest turn to face North. Which of the following represents the turn made by each boy? (Shamsul / Teddy)", "answer0": "135° anti-clockwise / 45° clockwise", "answer1": "135° clockwise / 45° anti-clockwise", "answer2": "45° anti-clockwise / 135° clockwise", "answer3": "45° clockwise / 135° anti-clockwise", "correct_answer": 1, "skill_id": 142, "difficulty_id": 3, "explanation": "Shamsul is NE of Teddy, so Shamsul faces SW and Teddy faces NE. To face North, Shamsul (facing SW) turns 135° clockwise; Teddy (facing NE) turns 45° anti-clockwise.", "hints": ["Work out which direction each boy faces at first.", "Find the smallest turn from each facing direction to North."], "source": "Catholic High 2022 P6 Prelim Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 5, "image_bbox": [0.45, 0.50, 0.57, 0.60], "image_loc": "centre, a North arrow pointing up", "notes": "Key answer: option 2 (Shamsul 135° clockwise, Teddy 45° anti-clockwise)." }, { "n": 9, "type_id": 1, "question": "ABCD is a rectangle. E and F are points on the rectangle. \\(\\angle ADF = 280^\\circ\\) and \\(\\angle EDC = 60^\\circ\\). Find \\(\\angle EDF\\).", "answer0": "20°", "answer1": "30°", "answer2": "45°", "answer3": "50°", "correct_answer": 3, "skill_id": 230, "difficulty_id": 2, "explanation": "The reflex \\(\\angle ADF = 280^\\circ\\), so the interior \\(\\angle ADF = 360^\\circ - 280^\\circ = 80^\\circ\\). \\(\\angle ADC = 90^\\circ\\), so \\(\\angle FDC = 90^\\circ - 80^\\circ = 10^\\circ\\). \\(\\angle EDF = \\angle EDC - \\angle FDC = 60^\\circ - 10^\\circ = 50^\\circ\\).", "hints": ["A full turn is 360°; find the non-reflex angle at D.", "The corner angle ADC of a rectangle is 90°."], "source": "Catholic High 2022 P6 Prelim Q9", "image_needed": true, "image_options": false, "image_file": "q9.png", "image_page": 6, "image_bbox": [0.36, 0.12, 0.78, 0.28], "image_loc": "top centre, rectangle ABCD with points E, F and angles 280° and 60° marked at D", "notes": "Key answer: option 4 (50°)." }, { "n": 10, "type_id": 1, "question": "The line graph shows the number of books sold from Monday to Thursday. Find the total number of books sold on days with the highest and lowest sale of books.", "answer0": "75", "answer1": "55", "answer2": "120", "answer3": "125", "correct_answer": 0, "skill_id": 147, "difficulty_id": 2, "explanation": "Highest sale is Tuesday (70 books) and lowest is Thursday (5 books). Total = 70 + 5 = 75.", "hints": ["Read the highest and lowest points on the graph.", "Add the two values."], "source": "Catholic High 2022 P6 Prelim Q10", "image_needed": true, "image_options": false, "image_file": "q10.png", "image_page": 6, "image_bbox": [0.24, 0.42, 0.78, 0.66], "image_loc": "centre, line graph of books sold Mon-Thu", "notes": "Key answer: option 1 (75). Tuesday ≈ 70 (highest), Thursday ≈ 5 (lowest)." }, { "n": 11, "type_id": 1, "question": "At first, Kairu covered the base of a rectangular box completely with a layer of unit cubes. He then turned the box to rest on the ground. The unit cubes, when re-arranged, covered 50% of its base. How many cubes can fill the box completely without any gap?", "answer0": "144", "answer1": "168", "answer2": "192", "answer3": "384", "correct_answer": 2, "skill_id": 224, "difficulty_id": 3, "explanation": "Before turning, the base is 4 by 6 = 24 cubes (one layer) and the box is 8 cubes tall standing up. After turning, the base becomes 6 by 8 = 48; the 24 cubes cover 50% of this new base (24 = half of 48), confirming the count. The box dimensions are 4 x 6 x 8 = 192 unit cubes to fill completely.", "hints": ["Count the cubes in the single layer shown.", "Use the 50% clue to find the dimension you can't see, then multiply length x width x height."], "source": "Catholic High 2022 P6 Prelim Q11", "image_needed": true, "image_options": false, "image_file": "q11.png", "image_page": 7, "image_bbox": [0.26, 0.16, 0.82, 0.40], "image_loc": "upper area, two boxes 'Before turning' and 'After turning' with a layer of unit cubes", "notes": "Key answer: option 3 (192). Count cubes in figure to verify base layer." }, { "n": 12, "type_id": 1, "question": "Which one of the following fractions is the furthest from \\(\\dfrac{1}{2}\\)?", "answer0": "\\(\\dfrac{1}{8}\\)", "answer1": "\\(\\dfrac{1}{7}\\)", "answer2": "\\(\\dfrac{1}{6}\\)", "answer3": "\\(\\dfrac{1}{5}\\)", "correct_answer": 0, "skill_id": 159, "difficulty_id": 2, "explanation": "The smaller the fraction, the further it is below 1/2. 1/8 is the smallest of the four, so it is furthest from 1/2.", "hints": ["All four fractions are less than 1/2.", "The smallest fraction is furthest away."], "source": "Catholic High 2022 P6 Prelim Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 13, "type_id": 1, "question": "Zephyr bought 4 times as many chocolates as sweets. For every 5 chocolates packed into a party bag, he packed 3 sweets. He had 35 chocolates left when all the sweets were completely packed. How many chocolates did he buy at first?", "answer0": "15", "answer1": "20", "answer2": "25", "answer3": "60", "correct_answer": 3, "skill_id": 214, "difficulty_id": 3, "explanation": "Let sweets = s, chocolates = 4s. Packed in ratio 5 chocolates : 3 sweets. All sweets packed, so packed chocolates = (5/3) x s. Chocolates left = 4s - (5/3)s = (7/3)s = 35, so s = 15. Chocolates bought = 4 x 15 = 60.", "hints": ["Let the number of sweets be one part; chocolates are 4 parts.", "Chocolates packed = (5/3) of the sweets; the rest (35) are left over."], "source": "Catholic High 2022 P6 Prelim Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key answer: option 4 (60)." }, { "n": 14, "type_id": 1, "question": "The figure is formed by a semicircle with centre O and 4 straight lines KL, OL, OM and NM. K, L, M and N lie on either the arc or the diameter of the semicircle. Which of the following statement(s) is/are true?
Statement A: Line NM is equal to the radius of the semicircle.
Statement B: When a straight line is joined from L to M, an isosceles triangle LOM is formed.
Statement C: The area of the shaded part LOM is greater than the area of the unshaded part KLO.", "answer0": "A only", "answer1": "C only", "answer2": "A and B only", "answer3": "B and C only", "correct_answer": 3, "skill_id": 221, "difficulty_id": 3, "explanation": "M and N are on the circle/diameter; OM and OL are radii. Statement A is false (NM is a chord, not equal to the radius in general). Statement B is true: OL = OM (both radii), so triangle LOM is isosceles. Statement C is true: the shaded region LOM is larger than the small right-angled region KLO. So B and C only.", "hints": ["OL and OM are both radii of the semicircle.", "Two equal radii form an isosceles triangle."], "source": "Catholic High 2022 P6 Prelim Q14", "image_needed": true, "image_options": false, "image_file": "q14.png", "image_page": 8, "image_bbox": [0.30, 0.30, 0.72, 0.48], "image_loc": "centre, semicircle with centre O, points K, L, M, N and shaded triangle LOM", "notes": "Key answer: option 4 (B and C only)." }, { "n": 15, "type_id": 1, "question": "James bought a packet of flour to make cakes. He used an equal amount of flour for each cake. After he had used the flour to make 3 cakes, \\(\\dfrac{3}{4}\\) of the packet of flour was left. He went on to bake another 5 cakes and had 1400 g of the flour left. How much flour was used for each cake?", "answer0": "350 g", "answer1": "700 g", "answer2": "2800 g", "answer3": "4200 g", "correct_answer": 3, "skill_id": 165, "difficulty_id": 3, "explanation": "After 3 cakes, 3/4 left means 3 cakes used 1/4 of the packet, so each cake uses 1/12 of the packet. After 5 more cakes (8 total), used 8/12 = 2/3, leaving 1/3 = 1400 g, so the whole packet = 4200 g. Each cake = 1/12 x 4200 = 350 g.", "hints": ["3 cakes used 1/4 of the packet, so 1 cake uses 1/12.", "After 8 cakes, 1/3 of the packet (1400 g) is left; find the whole packet."], "source": "Catholic High 2022 P6 Prelim Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key answer is option 4. NOTE: printed key marks Q15 as 4 (4200 g). Mathematically each cake = 350 g (option 1); 4200 g is the whole packet, not per cake. Following the printed key as instructed; flagged discrepancy." }, { "n": 16, "type_id": 2, "question": "Round 29 947 to the nearest hundred.
Ans: [?]", "answer0": "29900", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 150, "difficulty_id": 1, "explanation": "29 947 → the tens digit is 4 (less than 5), so round down: 29 900.", "hints": ["Look at the tens digit to decide rounding.", "Tens digit 4 means round down."], "source": "Catholic High 2022 P6 Prelim Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 29900." }, { "n": 17, "type_id": 2, "question": "Find the value of \\(6 \\div \\dfrac{3}{5}\\).
Ans: [?]", "answer0": "10", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 206, "difficulty_id": 2, "explanation": "\\(6 \\div \\dfrac{3}{5} = 6 \\times \\dfrac{5}{3} = \\dfrac{30}{3} = 10\\).", "hints": ["Dividing by a fraction means multiply by its reciprocal.", "6 x 5/3 = 30/3."], "source": "Catholic High 2022 P6 Prelim Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 10. Answer is a whole number, so FIB is valid." }, { "n": 18, "type_id": 2, "question": "Measure and write down the size of \\(\\angle m\\) in the figure.
Ans: [?]°", "answer0": "94", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 140, "difficulty_id": 1, "explanation": "Using a protractor, the reflex/marked angle m measures 94°.", "hints": ["Line up the protractor's centre on the vertex.", "Read off the angle along one arm."], "source": "Catholic High 2022 P6 Prelim Q18", "image_needed": true, "image_options": false, "image_file": "q18.png", "image_page": 12, "image_bbox": [0.28, 0.56, 0.55, 0.80], "image_loc": "lower centre, an angle marked m formed by two rays", "notes": "Key: 94 degrees. Answer is a whole number; FIB valid." }, { "n": 19, "type_id": 1, "question": "Find the value of \\(2 - \\dfrac{1}{4} - \\dfrac{1}{3}\\). Leave your answer as a mixed number.", "answer0": "\\(1\\dfrac{5}{12}\\)", "answer1": "\\(1\\dfrac{1}{12}\\)", "answer2": "\\(1\\dfrac{7}{12}\\)", "answer3": "\\(1\\dfrac{1}{2}\\)", "correct_answer": 0, "skill_id": 160, "difficulty_id": 2, "explanation": "\\(2 - \\dfrac{1}{4} - \\dfrac{1}{3} = \\dfrac{24}{12} - \\dfrac{3}{12} - \\dfrac{4}{12} = \\dfrac{17}{12} = 1\\dfrac{5}{12}\\).", "hints": ["Use a common denominator of 12.", "24/12 - 3/12 - 4/12 = 17/12."], "source": "Catholic High 2022 P6 Prelim Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 1 5/12. Answer is a mixed number, so converted to MCQ per spec; distractors are plausible miscalculations." }, { "n": 20, "type_id": 0, "question": "The figure shows half of a symmetric figure. Draw lines to complete the symmetric figure with the dotted line AB as the line of symmetry.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 145, "difficulty_id": 2, "explanation": "Reflect each vertex of the given half-shape across the diagonal line of symmetry AB and join the reflected points to complete the symmetric figure.", "hints": [], "source": "Catholic High 2022 P6 Prelim Q20", "image_needed": true, "image_options": false, "image_file": "q20.png", "image_page": 13, "image_bbox": [0.24, 0.40, 0.70, 0.74], "image_loc": "centre, square grid with half a figure and dotted line of symmetry AB", "notes": "Drawing/construction task — no app question type. Answer: reflect the shape across AB (see key page). type_id 0, skipped on insert." }, { "n": 21, "type_id": 2, "question": "Jai and Kyle entered a gym at 6.30 p.m. Jai left 2 h 30 min later. Kyle left 20 min earlier than Jai. At what time did Kyle leave the gym? Give your answer in 24-hour clock format.
Ans: [?]", "answer0": "2040", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 135, "difficulty_id": 2, "explanation": "Jai left 2 h 30 min after 6.30 p.m. = 9.00 p.m. Kyle left 20 min earlier = 8.40 p.m. = 2040 in 24-hour clock.", "hints": ["Add 2 h 30 min to 6.30 p.m. to get Jai's leaving time.", "Subtract 20 min, then convert to 24-hour format."], "source": "Catholic High 2022 P6 Prelim Q21", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 2040." }, { "n": 22, "type_id": 2, "question": "Molly is 1.74 m tall. She is 7 cm taller than her brother. What is her brother's height in metres?
Ans: [?] m", "answer0": "1.67", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 184, "difficulty_id": 1, "explanation": "1.74 m = 174 cm. Brother = 174 - 7 = 167 cm = 1.67 m.", "hints": ["Convert 1.74 m to centimetres.", "Subtract 7 cm, then convert back to metres."], "source": "Catholic High 2022 P6 Prelim Q22", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 1.67 m." }, { "n": 23, "type_id": 2, "question": "What is the price of the tennis racket after discount? Usual Price: $89.
Ans: $[?]", "answer0": "80.10", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 176, "difficulty_id": 2, "explanation": "A 10% discount means the racket costs 90% of $89: \\(\\dfrac{89}{100} \\times 90 = 8.9 \\times 9 = 80.10\\), so $80.10.", "hints": ["The sign shows a 10% discount.", "Pay 90% of $89."], "source": "Catholic High 2022 P6 Prelim Q23", "image_needed": true, "image_options": false, "image_file": "q23.png", "image_page": 15, "image_bbox": [0.26, 0.10, 0.64, 0.27], "image_loc": "top, tennis racket with a 'discount SALE' banner and 'Usual Price: $89'", "notes": "Key: $80.10 (working uses 89/100 x 90, i.e. 10% discount shown on the banner). Discount % is in the figure." }, { "n": 24, "type_id": 2, "question": "The figure shows a semicircle of diameter 14 cm. What is the area of the figure? Take \\(\\pi = \\dfrac{22}{7}\\).
Ans: [?] cm²", "answer0": "77", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 221, "difficulty_id": 2, "explanation": "Radius = 7 cm. Area of semicircle = \\(\\dfrac{1}{2} \\times \\dfrac{22}{7} \\times 7 \\times 7 = 77\\) cm².", "hints": ["The radius is half of 14 cm.", "Area = 1/2 x π x r x r."], "source": "Catholic High 2022 P6 Prelim Q24", "image_needed": true, "image_options": false, "image_file": "q24.png", "image_page": 15, "image_bbox": [0.28, 0.50, 0.52, 0.62], "image_loc": "centre, a semicircle with diameter labelled 14 cm", "notes": "Key: 77 cm²." }, { "n": 25, "type_id": 2, "question": "The shaded figure is formed using 3 different squares and a triangle. The perimeter of the triangle is 24 cm. What is the perimeter of the shaded figure?
Ans: [?] cm", "answer0": "72", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 223, "difficulty_id": 3, "explanation": "Each side of the triangle is also a side of one of the three squares. The outer perimeter of the figure equals 3 times the perimeter of the triangle: 24 x 3 = 72 cm.", "hints": ["Each square shares one side with the triangle.", "The exposed sides of the three squares total 3 x the triangle's perimeter."], "source": "Catholic High 2022 P6 Prelim Q25", "image_needed": true, "image_options": false, "image_file": "q25.png", "image_page": 16, "image_bbox": [0.30, 0.12, 0.66, 0.36], "image_loc": "upper centre, shaded figure of 3 squares around a central triangle", "notes": "Key: 24 x 3 = 72 cm." }, { "n": 26, "type_id": 2, "question": "9 pupils took turns to play 6 Rubik's cubes during a 30-min recess. At any one time, 6 pupils played the cubes while the other 3 waited. Each had the same amount of playing time. How many minutes did each pupil play on the Rubik's cube?
Ans: [?] min", "answer0": "20", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 205, "difficulty_id": 2, "explanation": "Total playing-slots = 6 cubes x 30 min = 180 cube-minutes. Shared equally among 9 pupils: 180 ÷ 9 = 20 min each.", "hints": ["6 cubes used for 30 min gives 180 cube-minutes of play.", "Divide equally among 9 pupils."], "source": "Catholic High 2022 P6 Prelim Q26", "image_needed": true, "image_options": false, "image_file": "q26.png", "image_page": 16, "image_bbox": [0.55, 0.52, 0.72, 0.66], "image_loc": "right of centre, a Rubik's cube", "notes": "Key: 6 x 30 = 180; 180 ÷ 9 = 20 min. Image is decorative; not essential to solve." }, { "n": 27, "type_id": 2, "question": "Lily bought some stickers based on the charges shown: First 10 stickers $7; Every additional sticker 50¢; Get 2 additional stickers free for every purchase of 30 stickers. She paid $17 for the stickers. How many stickers did she get in all?
Ans: [?]", "answer0": "32", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "First 10 stickers cost $7, leaving $17 - $7 = $10. Additional stickers at 50¢ each: $10 ÷ $0.50 = 20. Stickers paid for = 10 + 20 = 30. For 30 stickers she gets 2 free: 30 + 2 = 32 stickers in all.", "hints": ["Subtract the $7 for the first 10 stickers.", "Each extra sticker is 50¢; remember the 2 free for buying 30."], "source": "Catholic High 2022 P6 Prelim Q27", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 17 - 7 = 10; 10 ÷ 0.5 = 20; 20 + 10 + 2 = 32. Charges table transcribed into stem." }, { "n": 28, "type_id": 2, "question": "A cuboid was cut along the dotted line into two smaller cuboids. The shaded face is a square and the volume of cuboid S is 500 cm³ more than that of cuboid T. What is the height of cuboid T?
Ans: [?] cm", "answer0": "10", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 224, "difficulty_id": 3, "explanation": "Both cuboids share the same square cross-section (the shaded face). S has length 8 cm and T has length 3 cm, so S is 8 - 3 = 5 cm longer. That extra 5 cm of length accounts for the 500 cm³ difference: square-face area = 500 ÷ 5 = 100 cm². The square's side = \\(\\sqrt{100} = 10\\) cm, which is the height of cuboid T.", "hints": ["The 500 cm³ difference comes from the extra length (8 - 3 = 5 cm).", "Square-face area = 500 ÷ 5, then take the square root for the side."], "source": "Catholic High 2022 P6 Prelim Q28", "image_needed": true, "image_options": false, "image_file": "q28.png", "image_page": 17, "image_bbox": [0.18, 0.43, 0.82, 0.64], "image_loc": "centre, original 11 cm cuboid cut into cuboid S (8 cm) and cuboid T (3 cm) with height marked '?'", "notes": "Key: 8 - 3 = 5; 500 ÷ 5 = 100; √100 = 10 cm." }, { "n": 29, "type_id": 2, "question": "Mrs Lee wanted to buy 9 boxes of mooncakes but she was short of $28. She bought 7 boxes of mooncakes and had $22 left. How much money did she have at first?
Ans: $[?]", "answer0": "197", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "For 9 boxes she is short $28; for 7 boxes she has $22 left. The difference of 2 boxes = $28 + $22 = $50, so 1 box = $25. Money at first = 7 x $25 + $22 = $175 + $22 = $197.", "hints": ["The 2-box difference equals the $28 short plus the $22 left.", "Find the price of one box, then add up what she spent and had left."], "source": "Catholic High 2022 P6 Prelim Q29", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 22 + 28 = 50; 9 - 7 = 2; 2b = $50; 7b = 25 x 7 = 175; 175 + 22 = 197. ANS: $197." }, { "n": 30, "type_id": 0, "question": "A parallelogram ABCD is drawn on a square grid inside a box. By joining the dots on the grid with straight lines, (a) draw a triangle ACE such that AE is parallel to CB and it has the same area as triangle ABC. (b) draw a triangle BCF such that \\(\\angle CBF\\) is a right angle and BC = BF. Triangle BCF must not overlap with the parallelogram ABCD.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 201, "difficulty_id": 3, "explanation": "(a) Draw E so that AE is parallel to CB and AE = CB; triangle ACE then has the same base and height as triangle ABC. (b) Draw F so that BF is perpendicular to BC, BF = BC, and F lies outside the parallelogram. See the worked key diagram.", "hints": [], "source": "Catholic High 2022 P6 Prelim Q30", "image_needed": true, "image_options": false, "image_file": "q30.png", "image_page": 19, "image_bbox": [0.18, 0.12, 0.66, 0.42], "image_loc": "upper area, dotted square grid with parallelogram ABCD drawn", "notes": "Drawing/construction task — no app question type. type_id 0, skipped on insert." }, { "n": 101, "type_id": 2, "question": "Charlie needs 100 pieces of string, each of length 80 cm. The string is sold in rolls of 500 cm each. What is the least number of rolls of string that Charlie needs to buy?
Ans: [?]", "answer0": "17", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 2, "explanation": "Each 500 cm roll gives 500 ÷ 80 = 6 full pieces (with remainder). To get 100 pieces: 100 ÷ 6 = 16 remainder 4, so 17 rolls are needed.", "hints": ["Find how many 80 cm pieces come from one 500 cm roll (whole pieces only).", "Divide 100 by that number and round up."], "source": "Catholic High 2022 P6 Prelim Q31", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q1. Key: 500 ÷ 80 = 6 R20; 100 ÷ 6 = 16 R4 ≈ 17. ANS: 17. Numbered 101 to avoid clashing with Paper 1 Q1." }, { "n": 102, "type_id": 1, "question": "The table shows the number of sit-ups Ramesh did last week: Monday to Friday \\(3p\\) per day; Saturday 60; Sunday \\(4p - 8\\). What was the total number of sit-ups Ramesh did last week? Give your answer in terms of \\(p\\) in the simplest form.", "answer0": "\\(19p + 52\\)", "answer1": "\\(7p + 52\\)", "answer2": "\\(19p - 8\\)", "answer3": "\\(15p + 112\\)", "correct_answer": 0, "skill_id": 239, "difficulty_id": 2, "explanation": "Monday to Friday = 5 days x 3p = 15p. Total = 15p + 60 + (4p - 8) = 19p + 52.", "hints": ["Mon to Fri is 5 days, each 3p.", "Add 60 and (4p - 8), then collect like terms."], "source": "Catholic High 2022 P6 Prelim Q32", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q2. Key: 3p x 5 + 60 + 4p - 8 = 19p + 52. Answer is an algebraic expression — made MCQ since FIB cannot grade '19p + 52'. Distractors are common errors." }, { "n": 103, "type_id": 0, "question": "The nets drawn for the solids are incomplete and missing two faces. For each net, shade two faces so that the net can be folded to form the respective solids. (a) Cube. (b) Pyramid.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 232, "difficulty_id": 2, "explanation": "(a) Shade the two squares that complete the 6-face cube net. (b) Shade the two triangular faces that complete the pyramid net. See the worked key diagram.", "hints": [], "source": "Catholic High 2022 P6 Prelim Q33", "image_needed": true, "image_options": false, "image_file": "q33.png", "image_page": 22, "image_bbox": [0.18, 0.15, 0.78, 0.58], "image_loc": "two incomplete nets: a cube net (top) and a pyramid net (lower)", "notes": "Paper 2 Q3. Shading/construction task — no app question type. type_id 0, skipped on insert." }, { "n": 104, "type_id": 2, "question": "A roll of ribbon can be cut equally into 9 short ribbons or 5 long ribbons. A short ribbon is 24 cm shorter than a long ribbon. What is the length of a short ribbon?
Ans: [?] cm", "answer0": "30", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 241, "difficulty_id": 3, "explanation": "Let the roll length = L. Short = L/9, long = L/5. Long - short = 24: L/5 - L/9 = 4L/45 = 24, so L = 270 cm. Short ribbon = 270 ÷ 9 = 30 cm.", "hints": ["Express short and long ribbon lengths as fractions of the whole roll.", "Their difference is 24 cm; solve for the roll length."], "source": "Catholic High 2022 P6 Prelim Q34", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q4. Key working: 24 x 5 = 120, 9 - 5 = 4, 120 / 4 = 30. ANS: 30 cm." }, { "n": 105, "type_id": 0, "question": "Ben and Kai cycled in three races in a tournament. Their cycling times (min) were — Race 1: Ben 23, Kai 21; Race 2: Ben 22, Kai 29; Race 3: Ben 24, Kai 16. Both calculated their average cycling time for the three races. Who had a faster average cycling time? What was his average cycling time?", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 205, "difficulty_id": 2, "explanation": "Ben's average = (23 + 22 + 24) ÷ 3 = 69 ÷ 3 = 23 min. Kai's average = (21 + 29 + 16) ÷ 3 = 66 ÷ 3 = 22 min. Kai is faster (lower time) with an average of 22 min.", "hints": ["Average = total time ÷ 3 for each cyclist.", "Faster means the smaller average time."], "source": "Catholic High 2022 P6 Prelim Q35", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q5. Two-part answer (name + value) so cannot be a single FIB. Key: Name = Kai, Average = 22 min. type_id 0, skipped on insert." }, { "n": 106, "type_id": 0, "question": "A group of children was asked to choose one sandwich from Tuna, Sardine, Egg and Cheese. The pie chart represents the children's choices. The children's choices are also represented by a bar graph, but the number of children is not shown on the scale and the bar for Cheese is not drawn. (a) How many children chose Cheese? Draw the bar that represents the number of children who chose Cheese in the bar graph. (b) The number of children who chose Sardine was 56. How many children chose Egg?", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 236, "difficulty_id": 3, "explanation": "From the pie chart, Cheese is a quarter of the circle, so part (a) requires drawing the Cheese bar to match. (b) Sardine = 56 corresponds to the tallest bar; reading Egg's bar height relative to Sardine on the same scale gives the number who chose Egg.", "hints": [], "source": "Catholic High 2022 P6 Prelim Q36", "image_needed": true, "image_options": false, "image_file": "q36.png", "image_page": 24, "image_bbox": [0.22, 0.22, 0.72, 0.60], "image_loc": "pie chart (Tuna/Sardine/Egg/Cheese) above a bar graph with the Cheese bar missing", "notes": "Paper 2 Q6. Part (a) requires drawing a bar (construction) so cannot be a single FIB. type_id 0, skipped on insert. Image essential." }, { "n": 107, "type_id": 2, "question": "In the figure, ABCD is a rhombus and AEB is an equilateral triangle. FBD and EFC are straight lines. \\(\\angle BDA = 79^\\circ\\) and \\(\\angle FCB = 19^\\circ\\). Find \\(\\angle EFD\\).
Ans: [?]°", "answer0": "120", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "Consider triangle FBC where the angle at F (\\(\\angle BFC\\)) lies on the straight line EFC. The printed key gives \\(\\angle EFD = 180^\\circ - 60^\\circ = 120^\\circ\\) (using the equilateral triangle's 60° and angles on a straight line).", "hints": ["The equilateral triangle AEB contributes 60° angles.", "Use angles on the straight line EFC."], "source": "Catholic High 2022 P6 Prelim Q37", "image_needed": true, "image_options": false, "image_file": "q37.png", "image_page": 25, "image_bbox": [0.26, 0.16, 0.72, 0.36], "image_loc": "rhombus ABCD with equilateral triangle AEB, points E, F, angles 79° and 19° marked", "notes": "Paper 2 Q7. Key: ∠EFD = 180° - 60° = 120°. Answer is a whole number; FIB valid." }, { "n": 108, "type_id": 2, "question": "At a bread shop, a customer could buy one additional bun at half its usual price for every 3 buns bought. Petra paid $16.80 for 12 buns. What was the usual price of one bun?
Ans: $[?]", "answer0": "1.60", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 3, "explanation": "For every 3 buns at full price, 1 bun is half price, so a set = 4 buns costing 3 + 0.5 = 3.5 'usual prices' (units). 12 buns = 3 sets = 3 x 3.5u = 10.5u... using the key: 1 set = 4 buns, 12 ÷ 4 = 3 sets, 3 x 7u = 21u, $16.80 ÷ 21 = $0.80 (half a bun unit), so usual price = 0.80 x 2 = $1.60.", "hints": ["A 'set' is 3 full-price buns plus 1 half-price bun = 4 buns.", "12 buns = 3 sets; work out the cost per half-unit, then double."], "source": "Catholic High 2022 P6 Prelim Q38", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q8. Key: 1 set = 4 buns = 7u (half-units); 12/4 = 3 sets; 3 x 7u = 21u; 16.8/21 = 0.8; 0.8 x 2 = 1.6. ANS: $1.60." }, { "n": 109, "type_id": 2, "question": "A rectangular paper OPQS of area 432 cm² is folded along the dotted line OQ to form the figure OSRPQ of area 312 cm². RP = 16 cm. What is the length of PQ?
Ans: [?] cm", "answer0": "12", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "Half the rectangle (triangle OSQ) = 432 ÷ 2 = 216 cm². The overlapping triangle RPQ = 312 - 216 = 96 cm². Triangle RPQ has base RP = 16 cm: \\(\\dfrac{1}{2} \\times 16 \\times H = 96\\), so H = 12. Therefore PQ = 12 cm.", "hints": ["The folded area minus half the rectangle gives the overlap triangle's area.", "Use area = 1/2 x base x height with RP = 16 cm."], "source": "Catholic High 2022 P6 Prelim Q39", "image_needed": true, "image_options": false, "image_file": "q39.png", "image_page": 27, "image_bbox": [0.14, 0.14, 0.82, 0.30], "image_loc": "rectangle OPQS 'Before folding' and folded figure OSRPQ 'After folding' with RP = 16 cm", "notes": "Paper 2 Q9. Key: OSQ = 432/2 = 216; RPQ = 312 - 216 = 96; 1/2 x 16 x H = 96; H = 96 x 2 / 16 = 12. ANS: 12 cm." }, { "n": 110, "type_id": 2, "question": "In the figure, BEF is a triangle and BCDE is a trapezium. ABC is a straight line. \\(\\angle FAB = 41^\\circ\\), \\(\\angle ABE = 50^\\circ\\), \\(\\angle BCD = 21^\\circ\\) and \\(\\angle CDE = 118^\\circ\\). Find \\(\\angle BCE\\).
Ans: [?]°", "answer0": "41", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "Using the angles given, \\(\\angle BCE = 180^\\circ - 21^\\circ - 118^\\circ = 41^\\circ\\) (angle sum in the relevant triangle/straight-line work as in the key).", "hints": ["Use the angle sum of a triangle = 180°.", "Subtract the two known angles (21° and 118°)."], "source": "Catholic High 2022 P6 Prelim Q40", "image_needed": true, "image_options": false, "image_file": "q40.png", "image_page": 28, "image_bbox": [0.18, 0.12, 0.82, 0.30], "image_loc": "triangle BEF with trapezium BCDE; angles 41°, 50°, 21°, 118° marked", "notes": "Paper 2 Q10 part (a) only — part (b) is a true/false tick table (BCEF parallelogram = Not possible to tell; BE perpendicular to EC = False) which cannot be a single FIB; only the numeric part (a) is captured. Key: ∠BCE = 180° - 21° - 118° = 41°." }, { "n": 111, "type_id": 0, "question": "At first, a tank was filled with some water. Tap A was turned on for more water to flow into the tank. After 4 minutes, Tap B was turned on for water to flow out of the tank. Both taps were turned off at the same time when the tank was completely filled without overflowing. The graph shows the amount of water in the tank over the 18 minutes. (a) What fraction of the tank was filled with water at first before Tap A was turned on? Give your answer in the simplest form. (b) How many litres of water flowed into the tank per minute before Tap B was turned on? (c) From the 4th minute to the 14th minute, how much water flowed out of the tank?", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "(a) Tank full = 55 ℓ, water at start = 10 ℓ, fraction = 10/55 = 2/11. (b) From 0 to 4 min the volume rose from 10 ℓ to 25 ℓ: (25 - 10) ÷ 4 = 3.75 ℓ/min (15 ℓ over 4 min). (c) Tap A keeps adding 3.75 ℓ/min for 10 min (4th to 14th) = 37.5 ℓ in. The volume rose from 25 ℓ to 55 ℓ = 30 ℓ net. Water that flowed out = 37.5 - 30 = 7.5 ℓ.", "hints": [], "source": "Catholic High 2022 P6 Prelim Q41", "image_needed": true, "image_options": false, "image_file": "q41.png", "image_page": 29, "image_bbox": [0.22, 0.18, 0.74, 0.48], "image_loc": "line graph of volume of water (ℓ) versus time (min), 0 to 18 min", "notes": "Paper 2 Q11. Multi-part with a fraction answer (2/11) and a decimal/mixed answer; cannot be a single FIB. Key: a) 2/11, b) 3 3/4 ℓ/min, c) 7 1/2 ℓ. type_id 0 (multi-part)." }, { "n": 112, "type_id": 2, "question": "Bobby and Fanny started jogging from a park to their houses at the same time. A mall was exactly halfway between their houses. It was also 280 m away from the park. Bobby jogged at 120 m/min while Fanny jogged at 40 m/min faster than Bobby. Both did not change their speeds throughout and reached their houses at the same time. How far was Bobby's house from the park?
Ans: [?] m", "answer0": "1680", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 219, "difficulty_id": 3, "explanation": "Fanny's speed = 120 + 40 = 160 m/min. The mall is halfway between the houses and 280 m from the park, so the two houses are 2 x 280 = 560 m apart along the mall's measure... using the key: 280 x 2 = 560 m (Fanny's distance segment); time = 560 ÷ 160 = 14 min (both jog the same time). Bobby's distance = 120 x 14 = 1680 m.", "hints": ["Find Fanny's speed (40 m/min faster than Bobby).", "Both jog for the same time; use the mall's halfway position to get the time, then Bobby's distance = speed x time."], "source": "Catholic High 2022 P6 Prelim Q42", "image_needed": true, "image_options": false, "image_file": "q42.png", "image_page": 30, "image_bbox": [0.24, 0.16, 0.74, 0.28], "image_loc": "number-line diagram: Bobby's house, park, mall (280 m), Fanny's house", "notes": "Paper 2 Q12. Key: 280 x 2 = 560 (Fanny); 560 ÷ 40 = 14 min; 120 x 14 = 1680 m. ANS: 1680 m." }, { "n": 113, "type_id": 0, "question": "A fruit seller bought some plums. He threw away 152 plums that were damaged. After selling \\(\\dfrac{1}{5}\\) of the remaining plums, he was left with \\(\\dfrac{4}{7}\\) of the plums bought. He packed these into large boxes of 12 plums and small boxes of 8 plums. All the boxes were full and there was none left over. (a) How many plums were packed into boxes? (b) What was the least number of boxes used by the fruit seller?", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "(a) After throwing away 152, the remaining plums R have 4/5 left after selling 1/5, and 4/5 R = 4/7 of plums bought B, with R = B - 152. From the key: 152 / (2/4)... the key gives 152 / 2 x 4 = 304 plums packed. (b) Least boxes: use as many 12-plum boxes as possible: 304 = 12 x 25 + 4; adjust to fill with 8s: 24 large boxes (288) + 2 small boxes (16) = 304, total 24 + 2 = 26 boxes.", "hints": [], "source": "Catholic High 2022 P6 Prelim Q43", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q13. Multi-part. Key: a) 152 / 2 x 4 = 304; b) 304 / 12 = 25 R4, 24 large + 16 plums = 2 small, 24 + 2 = 26 boxes. type_id 0 (two answers)." }, { "n": 114, "type_id": 0, "question": "A funfair was decorated with red and white balloons. At first, there were 19 more white balloons than red balloons. 25% of the white balloons burst. More red balloons were added so that there were 26 more red balloons than white balloons. In the end, there was a total of 170 red and white balloons. (a) How many red balloons were there in the end? (b) What was the percentage increase in the number of red balloons? Round your answer to 1 decimal place.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 208, "difficulty_id": 3, "explanation": "(a) After 25% of white balloons burst, remaining white = 75%w. In the end red = white + 26 and red + white = 170, so 2(75%w) + 26 = 170, 150%w = 144, 75%w = 72, red = 72 + 26 = 98. (b) At first white = w and red = w - 19; 75%w = 72 so w = 96, original red = 96 - 19 = 77. Percentage increase in red = (98 - 77)/77 x 100% = 21/77 x 100% ≈ 27.3%.", "hints": [], "source": "Catholic High 2022 P6 Prelim Q44", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q14. Multi-part; part (b) answer 27.3% is a value but (a)=98 and (b)=27.3% together cannot be one FIB. Key: a) 98, b) 27.3%. type_id 0 (two answers)." }, { "n": 115, "type_id": 0, "question": "A metal box filled completely with 30 identical bolts weighs 1.18 kg. The same metal box when filled completely with 70 identical nuts weighs 1.54 kg. The ratio of the mass of a bolt to that of a nut is 5 : 3. (a) How many nuts have the same total mass of 3 bolts? (b) What is the mass of the metal box?", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 213, "difficulty_id": 3, "explanation": "(a) Bolt : nut = 5 : 3, so 3 bolts = 15 units = 5 nuts (each nut 3 units). (b) 30 bolts = 30 x 5 = 150 units; 70 nuts = 70 x 3 = 210 units. Difference in box-plus-contents mass: 1.54 - 1.18 = 0.36 kg for 210 - 150 = 60 units, so 1 unit = 0.006 kg. 30 bolts = 150 units = 0.9 kg, so box = 1.18 - 0.9 = 0.28 kg.", "hints": [], "source": "Catholic High 2022 P6 Prelim Q45", "image_needed": true, "image_options": false, "image_file": "q45.png", "image_page": 33, "image_bbox": [0.34, 0.16, 0.62, 0.30], "image_loc": "centre, picture of 'a bolt' and 'a nut'", "notes": "Paper 2 Q15. Multi-part. Key: a) 3 x 5 = 15, 15 / 3 = 5 nuts; b) 0.36 / (12 x 30) = 0.9, 1.18 - 0.9 = 0.28 kg. Image is decorative. type_id 0 (two answers)." }, { "n": 116, "type_id": 0, "question": "The figure is formed by 3 identical small quarter circles and 3 identical big quarter circles. The small quarter circle has radius 6 cm and the overall width is 57 cm. (a) Find the radius of the small circle. (b) Find the perimeter of the shaded figure. (Take \\(\\pi = 3.14\\))", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 222, "difficulty_id": 3, "explanation": "(a) Big quarter circle radius R: 6 + R + 6 + ... from the key, big radius = (57 - 12) ÷ 3 = 15 cm; the small circle radius is 6 cm (small quarter-circle radius). (b) Perimeter = (1/4 x 2π x 6) x 3 small arcs + (1/4 x 2π x 15) x 3 big arcs + straight edges: 1/4 x 3 x 3.14 x 30... key gives 1/4 x 3 x 3.14 x (small) + 1/4 x 3 x 3.14 x 42 = 169.56; plus 45 + 63 + 6 = 283.56 cm.", "hints": [], "source": "Catholic High 2022 P6 Prelim Q46", "image_needed": true, "image_options": false, "image_file": "q46.png", "image_page": 34, "image_bbox": [0.30, 0.12, 0.62, 0.30], "image_loc": "figure of 3 small and 3 big quarter circles; 6 cm and 57 cm marked", "notes": "Paper 2 Q16. Multi-part. Key: a) 57 - 12 = 45, 45 / 3 = 15 cm (the 'find the radius of the big circle' — paper hand-corrects 'diameter of small' to 'radius of big'); ANS 15 cm. b) 1/4 x 3 x 3.14 x 30 + 1/4 x 3 x 3.14 x 42 = 169.56; 169.56 + 45 + 63 + 6 = 283.56 cm. type_id 0 (two answers). Part (a) stem hand-edited in paper." }, { "n": 117, "type_id": 0, "question": "Raju used white and grey squares to form patterns (Figures 1 to 4). The table shows the number of white and grey squares in each figure — Figure 1: 0 white, 1 grey; Figure 2: 0 white, 4 grey; Figure 3: 2 white, 7 grey; Figure 4: 6 white, 10 grey. (a) Fill in the table for Figure 5. (b) What is the total number of squares in Figure 40? (c) How many more white squares than grey squares are used in Figure 40?", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 241, "difficulty_id": 3, "explanation": "(a) Figure 5: white = 12, grey = 13. (b) Total squares in Figure n = 40 x 40 = 1600 for Figure 40. (c) Grey in Figure n = (n - 1) x 3 + 1: Figure 40 grey = 39 x 3 + 1 = 118. White = 1600 - 118 = 1482. More white than grey = 1482 - 118 = 1364.", "hints": [], "source": "Catholic High 2022 P6 Prelim Q47", "image_needed": true, "image_options": false, "image_file": "q47.png", "image_page": 35, "image_bbox": [0.18, 0.12, 0.78, 0.24], "image_loc": "Figures 1 to 4 of white and grey square patterns (pyramids)", "notes": "Paper 2 Q17. Multi-part with a table fill-in. Key: a) white 12, grey 13; b) 40 x 40 = 1600; c) grey = 39 x 3 + 1 = 118, white = 1600 - 118 = 1482, 1482 - 118 = 1364. type_id 0 (multi-part)." } ] }