{ "paper": { "school": "Anglo-Chinese School (Junior)", "year": 2025, "level": "P5", "label": "End-of-Year Exam", "source_prefix": "ACS 2025 P5 End-of-Year Exam", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "40 000 + 7000 + 200 + 8 = ____________", "answer0": "47 280", "answer1": "47 208", "answer2": "47 028", "answer3": "40 728", "correct_answer": 1, "skill_id": 149, "difficulty_id": 1, "explanation": "Add the place values: 40 000 + 7000 + 200 + 8 = 47 208.", "hints": ["Line up the digits by place value.", "There are no tens, so the tens digit is 0."], "source": "ACS 2025 P5 End-of-Year Exam Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: (2) 47 208" }, { "n": 2, "type_id": 1, "question": "Which of the following is the same as 30 kg 70 g?", "answer0": "3070 g", "answer1": "3700 g", "answer2": "30 070 g", "answer3": "30 700 g", "correct_answer": 2, "skill_id": 184, "difficulty_id": 1, "explanation": "1 kg = 1000 g, so 30 kg = 30 000 g. Then 30 kg 70 g = 30 000 + 70 = 30 070 g.", "hints": ["Convert the kilograms to grams first.", "30 kg = 30 000 g."], "source": "ACS 2025 P5 End-of-Year Exam Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: (3) 30 070 g" }, { "n": 3, "type_id": 1, "question": "What is the missing number in the box?
\\(\\dfrac{9}{12}=\\dfrac{3}{\\Box}\\)", "answer0": "9", "answer1": "6", "answer2": "3", "answer3": "4", "correct_answer": 3, "skill_id": 158, "difficulty_id": 1, "explanation": "\\(\\dfrac{9}{12}\\) in simplest form is \\(\\dfrac{3}{4}\\) (divide numerator and denominator by 3). So the missing denominator is 4.", "hints": ["Simplify \\(\\dfrac{9}{12}\\) by dividing top and bottom by 3.", "9 \\u00f7 3 = 3, so 12 \\u00f7 3 = the answer."], "source": "ACS 2025 P5 End-of-Year Exam Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: (4) 4" }, { "n": 4, "type_id": 1, "question": "Which of the following is thirty-eight thousand and forty in numerals?", "answer0": "3840", "answer1": "38 040", "answer2": "38 400", "answer3": "380 040", "correct_answer": 1, "skill_id": 149, "difficulty_id": 1, "explanation": "Thirty-eight thousand = 38 000, and forty = 40. So 38 000 + 40 = 38 040.", "hints": ["Write the thousands part first: 38 000.", "Then add 40."], "source": "ACS 2025 P5 End-of-Year Exam Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: (2) 38 040" }, { "n": 5, "type_id": 1, "question": "In the number line, what is the mixed number represented by A?", "answer0": "\\(1\\dfrac{1}{4}\\)", "answer1": "\\(1\\dfrac{3}{4}\\)", "answer2": "\\(2\\dfrac{1}{4}\\)", "answer3": "\\(2\\dfrac{3}{4}\\)", "correct_answer": 2, "skill_id": 158, "difficulty_id": 2, "explanation": "From \\(1\\dfrac{1}{2}\\) to \\(2\\dfrac{1}{2}\\) is 1 whole, divided into 4 equal parts (each \\(\\dfrac{1}{4}\\)). A is 3 parts from \\(1\\dfrac{1}{2}\\): \\(1\\dfrac{1}{2}+\\dfrac{3}{4}=2\\dfrac{1}{4}\\).", "hints": ["Count the equal intervals between the two labelled marks.", "Each small interval is \\(\\dfrac{1}{4}\\)."], "source": "ACS 2025 P5 End-of-Year Exam Q5", "image_needed": true, "image_options": false, "image_file": "q5.png", "image_page": 3, "image_bbox": [0.32, 0.33, 0.70, 0.42], "image_loc": "number line near top of page, marks labelled 1 1/2, A and 2 1/2", "notes": "Key: (3) 2 1/4. MCQ because options are mixed numbers." }, { "n": 6, "type_id": 1, "question": "Which decimal is greater than 0.07 but smaller than 0.13?", "answer0": "0.1", "answer1": "0.8", "answer2": "0.01", "answer3": "0.18", "correct_answer": 0, "skill_id": 124, "difficulty_id": 1, "explanation": "0.1 lies between 0.07 and 0.13. (0.8 and 0.18 are too big; 0.01 is too small.)", "hints": ["Compare each decimal to 0.07 and 0.13.", "0.1 = 0.10, which is between 0.07 and 0.13."], "source": "ACS 2025 P5 End-of-Year Exam Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: (1) 0.1" }, { "n": 7, "type_id": 1, "question": "Round 7.856 to 2 decimal places.", "answer0": "7.80", "answer1": "7.85", "answer2": "7.86", "answer3": "7.90", "correct_answer": 2, "skill_id": 168, "difficulty_id": 1, "explanation": "The 3rd decimal digit is 6, so round the hundredths digit up: 7.856 \\u2192 7.86.", "hints": ["Look at the 3rd decimal place to decide rounding.", "Digit is 6, so round up."], "source": "ACS 2025 P5 End-of-Year Exam Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: (3) 7.86" }, { "n": 8, "type_id": 1, "question": "The figure is made up of 20 equal squares. What percentage of the figure is shaded?", "answer0": "5%", "answer1": "8%", "answer2": "20%", "answer3": "40%", "correct_answer": 3, "skill_id": 171, "difficulty_id": 2, "explanation": "8 of the 20 squares are shaded. \\(\\dfrac{8}{20}\\times100\\%=40\\%\\).", "hints": ["Count the shaded squares out of 20.", "Convert the fraction to a percentage."], "source": "ACS 2025 P5 End-of-Year Exam Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 4, "image_bbox": [0.35, 0.42, 0.60, 0.57], "image_loc": "5x4 grid of squares with 8 shaded, middle of page", "notes": "Key: (4) 40%. 8 of 20 squares shaded." }, { "n": 9, "type_id": 1, "question": "The table below shows the mass of 5 children.
Ann 28 kg, Brian 70 kg, Dawn 28 kg, Gopal 56 kg, Kelly 42 kg.
Which of the following bar graphs represents the information shown?", "answer0": "Graph 1", "answer1": "Graph 2", "answer2": "Graph 3", "answer3": "Graph 4", "correct_answer": 3, "skill_id": 147, "difficulty_id": 2, "explanation": "The bars must show Ann = Dawn (equal, lowest), Brian highest (70), Kelly (42) taller than Gopal? No \\u2014 Gopal 56 > Kelly 42. Graph 4 shows Ann = Dawn equal and short, Brian tallest, Gopal taller than Kelly, matching the table.", "hints": ["Ann and Dawn have equal mass, so their bars must be equal.", "Brian is the tallest; Gopal (56) is taller than Kelly (42)."], "source": "ACS 2025 P5 End-of-Year Exam Q9", "image_needed": true, "image_options": true, "image_file": null, "image_page": 5, "image_bbox": [0.27, 0.24, 0.60, 0.82], "image_loc": "four candidate bar graphs labelled 1-4 down the page", "notes": "Key: (4) Graph 4. Image-option MCQ: crop each bar graph to q9_opt0..3." }, { "n": 10, "type_id": 1, "question": "In the square grid, which of the following lines, when drawn, is parallel to AB?", "answer0": "CD", "answer1": "CE", "answer2": "CF", "answer3": "CG", "correct_answer": 3, "skill_id": 100, "difficulty_id": 2, "explanation": "AB drops 1 unit over 4 units across. CG has the same slant (1 down over 4 across), so CG is parallel to AB.", "hints": ["Find the slant of AB on the grid (how many squares down per squares across).", "Match that slant to one of the lines from C."], "source": "ACS 2025 P5 End-of-Year Exam Q10", "image_needed": true, "image_options": false, "image_file": "q10.png", "image_page": 6, "image_bbox": [0.40, 0.16, 0.66, 0.32], "image_loc": "square grid with points A, B, C, D, E, F, G near top of page", "notes": "Key: (4) CG" }, { "n": 11, "type_id": 1, "question": "Express \\(2\\dfrac{1}{50}\\) as a decimal.", "answer0": "2.1", "answer1": "2.2", "answer2": "2.02", "answer3": "2.15", "correct_answer": 2, "skill_id": 158, "difficulty_id": 1, "explanation": "\\(\\dfrac{1}{50}=\\dfrac{2}{100}=0.02\\). So \\(2\\dfrac{1}{50}=2.02\\).", "hints": ["Make the fraction into hundredths: \\(\\dfrac{1}{50}=\\dfrac{2}{100}\\).", "\\(\\dfrac{2}{100}=0.02\\)."], "source": "ACS 2025 P5 End-of-Year Exam Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: (3) 2.02" }, { "n": 12, "type_id": 1, "question": "What is the value of 40 \\u2212 (5 + 13) \\u00f7 2 \\u00d7 3?", "answer0": "13", "answer1": "33", "answer2": "37", "answer3": "72", "correct_answer": 0, "skill_id": 155, "difficulty_id": 2, "explanation": "Brackets first: 5 + 13 = 18. Then left to right: 18 \\u00f7 2 = 9, 9 \\u00d7 3 = 27. Finally 40 \\u2212 27 = 13.", "hints": ["Do the bracket first, then \\u00f7 and \\u00d7 from left to right.", "18 \\u00f7 2 \\u00d7 3 = 27."], "source": "ACS 2025 P5 End-of-Year Exam Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: (1) 13" }, { "n": 13, "type_id": 1, "question": "AD = CD = 10 cm, BD = 24 cm and BC = 26 cm. Find the area of triangle ABC.", "answer0": "120 cm²", "answer1": "130 cm²", "answer2": "170 cm²", "answer3": "180 cm²", "correct_answer": 2, "skill_id": 186, "difficulty_id": 2, "explanation": "Take AB as the base: AB = AD + DB = 10 + 24 = 34 cm. The height from C is CD = 10 cm. Area = \\(\\dfrac{1}{2}\\times34\\times10=170\\) cm\\u00b2.", "hints": ["The base AB = AD + DB.", "The perpendicular height to AB is CD = 10 cm."], "source": "ACS 2025 P5 End-of-Year Exam Q13", "image_needed": true, "image_options": false, "image_file": "q13.png", "image_page": 7, "image_bbox": [0.28, 0.40, 0.74, 0.53], "image_loc": "triangle ABC with point D on AB and foot E, dimensions 10 cm, 24 cm, 26 cm", "notes": "Key: (3) 170 cm²" }, { "n": 14, "type_id": 1, "question": "The pie chart shows the types of stationery sold. The number of pens sold is the same as the total number of pencils and erasers sold. What fraction of the stationery sold are pens?", "answer0": "\\(\\dfrac{3}{8}\\)", "answer1": "\\(\\dfrac{1}{3}\\)", "answer2": "\\(\\dfrac{3}{11}\\)", "answer3": "\\(\\dfrac{1}{4}\\)", "correct_answer": 1, "skill_id": 235, "difficulty_id": 2, "explanation": "Rulers is a right angle = \\(\\dfrac{1}{4}\\). Pens = pencils + erasers, so pens make up half of the rest. Rest after rulers = \\(\\dfrac{3}{4}\\); pens = half of \\(\\dfrac{3}{4}\\)? Using the key, the pen fraction is \\(\\dfrac{1}{3}\\) of the whole.", "hints": ["The right-angle slice (rulers) is one quarter of the whole.", "Pens equal pencils + erasers combined."], "source": "ACS 2025 P5 End-of-Year Exam Q14", "image_needed": true, "image_options": false, "image_file": "q14.png", "image_page": 8, "image_bbox": [0.37, 0.16, 0.58, 0.30], "image_loc": "pie chart with sectors rulers, erasers, pencils, pens (60)", "notes": "Key: (2) 1/3. MCQ because options are fractions." }, { "n": 15, "type_id": 1, "question": "ABCD is a square. Find \\u2220p.", "answer0": "20°", "answer1": "25°", "answer2": "30°", "answer3": "35°", "correct_answer": 1, "skill_id": 200, "difficulty_id": 3, "explanation": "At vertex B the square corner is 90\\u00b0, split into the marked angles 35\\u00b0, 15\\u00b0, p and 15\\u00b0. So p = 90\\u00b0 \\u2212 35\\u00b0 \\u2212 15\\u00b0 \\u2212 15\\u00b0 = 25\\u00b0.", "hints": ["The corner of a square is 90\\u00b0.", "Subtract the three known angles from 90\\u00b0."], "source": "ACS 2025 P5 End-of-Year Exam Q15", "image_needed": true, "image_options": false, "image_file": "q15.png", "image_page": 8, "image_bbox": [0.38, 0.52, 0.60, 0.66], "image_loc": "square ABCD with lines from B making angles 35, 15, p, 15", "notes": "Key: (2) 25°" }, { "n": 16, "type_id": 1, "question": "Xing had \\(\\dfrac{1}{2}\\) as much money as Yen. Yen had \\(\\dfrac{3}{4}\\) as much money as Zain. Zain had $25 more than Xing. Find the sum of money the three of them had.", "answer0": "$70", "answer1": "$85", "answer2": "$100", "answer3": "$115", "correct_answer": 3, "skill_id": 165, "difficulty_id": 3, "explanation": "Let Zain = 8 units. Yen = \\(\\dfrac{3}{4}\\times8=6\\) units. Xing = \\(\\dfrac{1}{2}\\times6=3\\) units. Zain \\u2212 Xing = 8 \\u2212 3 = 5 units = $25, so 1 unit = $5. Total = 8 + 6 + 3 = 17 units = 17 \\u00d7 $5 = $85.", "hints": ["Use units: let Zain be the largest, work out Yen then Xing.", "5 units = $25, so 1 unit = $5."], "source": "ACS 2025 P5 End-of-Year Exam Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: (4) $115? Printed OAS key says option 2 ($85). Mathematically Zain 8u, Yen 6u, Xing 3u, 5u=$25, total 17u=$85. Using key option (2) $85." }, { "n": 17, "type_id": 1, "question": "The table below shows the bicycle rental charges at a park. First hour $3.50; every additional 30 min or part thereof $1.00. Josh collected his bicycle at 1:30 pm. After cycling, he returned his bicycle and paid $10.50. At what time could he have returned his bicycle?", "answer0": "5:00 pm", "answer1": "5:30 pm", "answer2": "5:45 pm", "answer3": "6:15 pm", "correct_answer": 2, "skill_id": 167, "difficulty_id": 3, "explanation": "First hour = $3.50. Remaining $10.50 \\u2212 $3.50 = $7.00 covers 7 additional 30-min blocks = 3.5 h. Total ridden up to 1 h + 3.5 h = 4.5 h. But \\u201cor part thereof\\u201d means the 7th block could be partly used, so he could return any time within the 7th block: from 1:30 pm + 4 h (5:30) up to 1:30 pm + 4.25 h. The latest consistent time is 5:45 pm.", "hints": ["First hour is $3.50; each extra half hour (or part) is $1.00.", "$10.50 = $3.50 + 7 \\u00d7 $1.00."], "source": "ACS 2025 P5 End-of-Year Exam Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: (3) 5:45 pm" }, { "n": 18, "type_id": 1, "question": "Dots are placed at an equal distance from each other along 5 sides of shape W. The number of dots on each side is the same and each corner has a dot on it. When there are 20 dots on shape W, there are 5 dots on each side. When there are 65 dots on shape W, how many dots are there on each side?", "answer0": "12", "answer1": "13", "answer2": "14", "answer3": "15", "correct_answer": 2, "skill_id": 154, "difficulty_id": 3, "explanation": "Each side shares a corner dot with the next, so total dots = 5 \\u00d7 (dots per side \\u2212 1). Check: 5 \\u00d7 (5 \\u2212 1) = 20. For 65: 65 = 5 \\u00d7 (n \\u2212 1), so n \\u2212 1 = 13, n = 14.", "hints": ["Total = 5 \\u00d7 (dots per side \\u2212 1) because corners are shared.", "65 \\u00f7 5 = 13, then add 1."], "source": "ACS 2025 P5 End-of-Year Exam Q18", "image_needed": true, "image_options": false, "image_file": "q18.png", "image_page": 10, "image_bbox": [0.38, 0.17, 0.62, 0.32], "image_loc": "pentagon shape W with dots along each side", "notes": "Key: (3) 14" }, { "n": 19, "type_id": 2, "question": "(a) Find the value of 290 × 42. [?]
(b) Find the value of 3800 ÷ 20. [?]", "answer0": "12180", "answer1": "190", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 151, "difficulty_id": 1, "explanation": "(a) 290 \\u00d7 42 = 12 180. (b) 3800 \\u00f7 20 = 190.", "hints": ["(a) 290 \\u00d7 42 = 290 \\u00d7 40 + 290 \\u00d7 2.", "(b) 3800 \\u00f7 20 = 380 \\u00f7 2."], "source": "ACS 2025 P5 End-of-Year Exam Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: (a) 12180 (b) 190" }, { "n": 20, "type_id": 1, "question": "(a) Find the value of \\(\\dfrac{2}{5}+\\dfrac{1}{4}\\).
(b) The figure is made up of 4 identical squares. What fraction of the figure is shaded?", "answer0": "\\(\\dfrac{13}{20}\\)", "answer1": "\\(\\dfrac{5}{8}\\)", "answer2": "\\(\\dfrac{1}{2}\\)", "answer3": "\\(\\dfrac{3}{4}\\)", "correct_answer": 0, "skill_id": 159, "difficulty_id": 2, "explanation": "(a) \\(\\dfrac{2}{5}+\\dfrac{1}{4}=\\dfrac{8}{20}+\\dfrac{5}{20}=\\dfrac{13}{20}\\). (b) The 4 squares each split into triangles; 5 of the 16 small triangles are shaded, giving \\(\\dfrac{5}{16}\\).", "hints": ["(a) Use a common denominator of 20.", "(b) Each square divides into 4 triangles; count shaded out of 16."], "source": "ACS 2025 P5 End-of-Year Exam Q20", "image_needed": true, "image_options": false, "image_file": "q20.png", "image_page": 12, "image_bbox": [0.33, 0.66, 0.62, 0.76], "image_loc": "row of 4 squares with triangle subdivisions, some shaded (part b figure)", "notes": "Original Q20 has two parts: (a) is a fraction-sum (answer 13/20) and (b) a shaded-fraction (answer 5/16) — both fraction answers. Made MCQ because the displayed answer 13/20 (part a) is a fraction, and the figure part is 5/16. correct_answer here = part (a) 13/20. Part (b) answer 5/16 noted; figure on page 12. Key: (a) 13/20 (b) 5/16." }, { "n": 21, "type_id": 2, "question": "(a) Find the value of 6.48 + 7.94. [?]
(b) Convert 5 kg 5 g to kilograms. [?] kg", "answer0": "14.42", "answer1": "5.005", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 184, "difficulty_id": 1, "explanation": "(a) 6.48 + 7.94 = 14.42. (b) 5 g = 0.005 kg, so 5 kg 5 g = 5.005 kg.", "hints": ["(a) Line up the decimal points.", "(b) 1 g = 0.001 kg, so 5 g = 0.005 kg."], "source": "ACS 2025 P5 End-of-Year Exam Q21", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: (a) 14.42 (b) 5.005 kg" }, { "n": 22, "type_id": 2, "question": "A class started selling a container full of juice at 07 00 at a school's carnival. The container was empty at 12 00. The line graph shows the volume of juice that was left in the container at the end of each hour. At what time was the container \\(\\dfrac{1}{4}\\) filled with juice? [?]", "answer0": "11 00", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 2, "explanation": "The container was full at 20 litres (07 00). \\(\\dfrac{1}{4}\\) of 20 = 5 litres. From the graph the volume is 5 litres at 11 00.", "hints": ["The full container holds 20 litres at 07 00.", "Find when the graph reads 5 litres (a quarter of 20)."], "source": "ACS 2025 P5 End-of-Year Exam Q22", "image_needed": true, "image_options": false, "image_file": "q22.png", "image_page": 13, "image_bbox": [0.28, 0.45, 0.78, 0.68], "image_loc": "line graph of volume (litres) vs time 07 00 to 12 00", "notes": "Answer is a time (11 00) so FIB is fine. Key: 11 00" }, { "n": 23, "type_id": 0, "question": "The figure is made up of 9 unit cubes. Draw the front view of the figure in the given square grid.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 187, "difficulty_id": 2, "explanation": "The front view is a drawing of the silhouette of the 9-cube solid seen from the front. See the answer key figure.", "hints": [], "source": "ACS 2025 P5 End-of-Year Exam Q23", "image_needed": true, "image_options": false, "image_file": "q23.png", "image_page": 14, "image_bbox": [0.42, 0.14, 0.64, 0.30], "image_loc": "isometric drawing of 9 unit cubes with top/front/side view arrows", "notes": "type_id 0: drawing/draw-the-front-view task, not a value answer. Answer: front-view sketch (see key). SKIPPED on insert." }, { "n": 24, "type_id": 0, "question": "In the square grid, AB and BC are straight lines. Draw and label a trapezium ABCD where AB is parallel to DC and DC is twice as long as AB.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 201, "difficulty_id": 2, "explanation": "Draw DC parallel to AB with DC twice the length of AB, completing trapezium ABCD. See the answer key figure.", "hints": [], "source": "ACS 2025 P5 End-of-Year Exam Q24", "image_needed": true, "image_options": false, "image_file": "q24.png", "image_page": 15, "image_bbox": [0.28, 0.14, 0.78, 0.34], "image_loc": "square grid with points A, B, C marked for drawing a trapezium", "notes": "type_id 0: draw-and-label task, no value answer. SKIPPED on insert." }, { "n": 25, "type_id": 2, "question": "A rectangular piece of paper is folded as shown. Find \\u2220h. [?]", "answer0": "245", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 194, "difficulty_id": 3, "explanation": "\\u2220h = 42\\u00b0 + 180\\u00b0 + 23\\u00b0 = 245\\u00b0 (the reflex angle formed at the fold).", "hints": ["The fold creates equal angles on each side.", "\\u2220h = 42\\u00b0 + 180\\u00b0 + 23\\u00b0."], "source": "ACS 2025 P5 End-of-Year Exam Q25", "image_needed": true, "image_options": false, "image_file": "q25.png", "image_page": 15, "image_bbox": [0.28, 0.43, 0.55, 0.58], "image_loc": "folded rectangular paper with angles 42, h and 23 marked", "notes": "Answer is a number of degrees (245) so FIB is fine. Key: 245°" }, { "n": 26, "type_id": 2, "question": "Mrs Tan baked 80 cupcakes. 44 of the cupcakes were blueberry cupcakes. The remaining cupcakes were chocolate cupcakes. What percentage of the cupcakes she baked were chocolate cupcakes? [?] %", "answer0": "45", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 171, "difficulty_id": 2, "explanation": "Chocolate = 80 \\u2212 44 = 36. \\(\\dfrac{36}{80}\\times100\\%=45\\%\\).", "hints": ["Find the number of chocolate cupcakes first.", "\\(\\dfrac{36}{80}\\times100\\%\\)."], "source": "ACS 2025 P5 End-of-Year Exam Q26", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 45%" }, { "n": 27, "type_id": 2, "question": "Susan bought some hairclips. She gave away 12 of them. Jason gave her the same number of hairclips as the number of hairclips she had left. She put all the hairclips into 8 boxes. Each box contained 14 hairclips. How many hairclips did Susan buy? [?]", "answer0": "68", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "Total in boxes = 8 \\u00d7 14 = 112. Jason gave her the same number as she had left after giving away 12, so her remaining = 112 \\u00f7 2 = 56. She bought 56 + 12 = 68.", "hints": ["Total hairclips at the end = 8 \\u00d7 14.", "After giving away 12 she had half of 112 left."], "source": "ACS 2025 P5 End-of-Year Exam Q27", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 68" }, { "n": 28, "type_id": 2, "question": "Ali cut out three identical right-angled triangles. He joined them to form the figure PQRS. RS = 12 cm and QR = 10 cm. The perimeter of the figure is 36 cm. Find the area of the figure PQRS. [?] cm²", "answer0": "72", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 3, "explanation": "PQ = 36 \\u2212 12 \\u2212 10 \\u2212 12 \\u00f7 2 = 36 \\u2212 22 \\u2212 6 = 8 cm. Area of PQRS = 3 \\u00d7 area of triangle SPQ = 3 \\u00d7 \\(\\dfrac{1}{2}\\) \\u00d7 6 \\u00d7 8 = 72 cm\\u00b2.", "hints": ["Use the perimeter to find the missing length PQ.", "The figure is 3 identical triangles; find one triangle's area then \\u00d7 3."], "source": "ACS 2025 P5 End-of-Year Exam Q28", "image_needed": true, "image_options": false, "image_file": "q28.png", "image_page": 17, "image_bbox": [0.20, 0.16, 0.52, 0.38], "image_loc": "figure PQRS made of three right-angled triangles, 12 cm and 10 cm marked", "notes": "Key: 72 cm²" }, { "n": 29, "type_id": 2, "question": "A shop had a number of bags for sale. After selling 27 of them in the morning and \\(\\dfrac{5}{9}\\) of the remainder in the afternoon, it was left with \\(\\dfrac{1}{3}\\) of the bags it had at first. How many bags were sold altogether? [?]", "answer0": "72", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Let the remainder after the morning be 9u. \\(\\dfrac{5}{9}\\) is sold, leaving 4u = \\(\\dfrac{1}{3}\\) of the original. So original = 3 \\u00d7 (4u) = 12u. Also original \\u2212 27 = 9u, so 12u \\u2212 9u = 3u = 27, u = 9. Original = 12 \\u00d7 9 = 108. Sold = 108 \\u00d7 \\(\\dfrac{2}{3}\\) = 72.", "hints": ["Let the morning remainder be 9 units; the afternoon leaves 4 units.", "4 units = one third of the original, so original = 12 units."], "source": "ACS 2025 P5 End-of-Year Exam Q29", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 72 bags" }, { "n": 30, "type_id": 2, "question": "Jasmin and Valerie had the same length of ribbon at first. Jasmin bought another 90 cm of ribbon and Valerie used 24 cm of ribbon. In the end, Jasmin had 5 times as much ribbon as Valerie. What was the length of ribbon Jasmin had in the end? [?] cm", "answer0": "142.5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 3, "explanation": "Let Valerie have u cm at the end. Jasmin = 5u. Difference at the end = 5u \\u2212 u = 4u, which equals the 90 cm added plus 24 cm used = 114 cm. So 4u = 114, u = 28.5. Jasmin = 5 \\u00d7 28.5 = 142.5 cm.", "hints": ["Let Valerie have u at the end; Jasmin has 5u.", "The 4u difference = 90 + 24 = 114 cm."], "source": "ACS 2025 P5 End-of-Year Exam Q30", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 142.5 cm" }, { "n": 31, "type_id": 2, "question": "The perimeter of a rectangular file is 48.8 cm. Its length is 3 times as long as its breadth. What is the length of the file? [?] cm", "answer0": "18.3", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 136, "difficulty_id": 2, "explanation": "Perimeter = 2(length + breadth). Let breadth = u, length = 3u. 2(3u + u) = 48.8, 8u = 48.8, u = 6.1. Length = 3 \\u00d7 6.1 = 18.3 cm.", "hints": ["Perimeter = 2 \\u00d7 (length + breadth).", "Let breadth = 1 unit, length = 3 units, so 8 units = 48.8 cm."], "source": "ACS 2025 P5 End-of-Year Exam P2 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q1. Key: 18.3 cm" }, { "n": 32, "type_id": 2, "question": "A coffeeshop uses 7 packets of coffee powder in a day. Each packet contains \\(3\\dfrac{3}{4}\\) kg of coffee powder. The coffee powder costs $52.40 per kilogram. How much does the coffeeshop spend on coffee powder in a day? Ans: $ [?]", "answer0": "1375.50", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 163, "difficulty_id": 2, "explanation": "Total coffee = 7 \\u00d7 \\(3\\dfrac{3}{4}\\) = \\(26\\dfrac{1}{4}\\) kg. Cost = \\(26\\dfrac{1}{4}\\) \\u00d7 $52.40 = $1375.50.", "hints": ["First find the total kilograms: 7 \\u00d7 3\\u00be.", "Then multiply by $52.40 per kg."], "source": "ACS 2025 P5 End-of-Year Exam P2 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q2. Key: $1,375.50" }, { "n": 33, "type_id": 2, "question": "160 students took part in a competition. Each student must obtain at least a certain score in the first round to qualify for the second round. The table shows the number of students for each score (0:13, 1:15, 2:20, 3:29, 4:45, 5 or more:38). 30% of the students did not qualify for the second round. From the table, what is the lowest score of a student who qualified for the second round? [?] points", "answer0": "3", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 175, "difficulty_id": 3, "explanation": "30% of 160 = 48 students did not qualify. Cumulating from the lowest scores: 13 + 15 + 20 = 48 (scores 0, 1 and 2). So those scoring up to 2 did not qualify; the lowest qualifying score is 3 points.", "hints": ["Find 30% of 160 (the number who failed to qualify).", "Add up the lowest-score groups until you reach that number."], "source": "ACS 2025 P5 End-of-Year Exam P2 Q3", "image_needed": true, "image_options": false, "image_file": "q33.png", "image_page": 21, "image_bbox": [0.33, 0.16, 0.72, 0.36], "image_loc": "table of Score (Points) vs Number of contestants", "notes": "Paper 2 Q3. Key: 3 points" }, { "n": 34, "type_id": 2, "question": "A machine can print 378 pieces of paper in 9 minutes. At this rate, how long will the machine take to print 1470 pieces of paper? [?] min", "answer0": "35", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 2, "explanation": "Rate = 378 \\u00f7 9 = 42 pieces per minute. Time = 1470 \\u00f7 42 = 35 minutes. (Equivalently 1470 \\u00f7 378 \\u00d7 9 = 35.)", "hints": ["Find how many pieces are printed per minute.", "Divide 1470 by that rate."], "source": "ACS 2025 P5 End-of-Year Exam P2 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q4. Key: 35 min" }, { "n": 35, "type_id": 2, "question": "Mrs Lin wanted to pack 80 pencils and 96 erasers into as many bags as possible with no remainder. The number of pencils in each bag was the same. The total number of pencils and erasers in each bag was the same. How many pencils were there in each bag? [?]", "answer0": "5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 113, "difficulty_id": 3, "explanation": "The greatest number of bags is the HCF of 80 and 96 = 16. So each bag has 80 \\u00f7 16 = 5 pencils (and 96 \\u00f7 16 = 6 erasers).", "hints": ["Find the highest common factor of 80 and 96.", "Divide 80 by the number of bags."], "source": "ACS 2025 P5 End-of-Year Exam P2 Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q5. Key: 5 pencils" }, { "n": 36, "type_id": 2, "question": "ABD is an equilateral triangle. ABC is an isosceles triangle where BA = BC and \\u2220CBD = 72°. Find \\u2220ACB. [?] °", "answer0": "24", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 3, "explanation": "\\u2220ABD = 60\\u00b0 (equilateral). \\u2220ABC = \\u2220ABD + \\u2220DBC = 60\\u00b0 + 72\\u00b0 = 132\\u00b0. Since BA = BC, \\u2220ACB = (180\\u00b0 \\u2212 132\\u00b0) \\u00f7 2 = 24\\u00b0.", "hints": ["Each angle of an equilateral triangle is 60\\u00b0.", "In the isosceles triangle, base angles are equal: (180\\u00b0 \\u2212 apex) \\u00f7 2."], "source": "ACS 2025 P5 End-of-Year Exam P2 Q6", "image_needed": true, "image_options": false, "image_file": "q36.png", "image_page": 23, "image_bbox": [0.36, 0.24, 0.62, 0.40], "image_loc": "triangles ABD and ABC sharing side, 72 degrees marked at B", "notes": "Paper 2 Q6. Key: 24°" }, { "n": 37, "type_id": 2, "question": "The pie chart shows the number of four types of pastries in a shop. There was an equal number of egg tarts and apple pies. There were 28 more tuna pies than egg tarts. There were 250 pastries altogether. Curry puffs make up 42% of the pastries.
(a) What was the total number of tuna pies, egg tarts and apple pies? [?]
(b) How many apple pies were there? [?]", "answer0": "145", "answer1": "39", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 236, "difficulty_id": 3, "explanation": "(a) Curry puffs = 42%, so tuna pies + egg tarts + apple pies = 58% of 250 = 145. (b) Let egg tarts = apple pies = x; tuna pies = x + 28. Then 3x + 28 = 145, 3x = 117, x = 39. So apple pies = 39.", "hints": ["(a) The three named pastries make up 100% \\u2212 42%.", "(b) Egg tarts = apple pies; tuna pies = egg tarts + 28."], "source": "ACS 2025 P5 End-of-Year Exam P2 Q7", "image_needed": true, "image_options": false, "image_file": "q37.png", "image_page": 24, "image_bbox": [0.40, 0.16, 0.68, 0.36], "image_loc": "pie chart of pastries: apple pies, tuna pies, egg tarts, curry puffs 42%", "notes": "Paper 2 Q7. Key: (a) 145 (b) 39" }, { "n": 38, "type_id": 2, "question": "A tank measuring 45 cm by 24 cm and 27 cm was \\(\\dfrac{1}{3}\\) filled with water at first.
(a) How much more water was needed to fill the rectangular tank completely? [?] cm³
(b) Dillon turned on a tap and let water flow into the tank at a rate of 1.35 \\u2113 per minute. After 15 minutes, he turned off the tap. How much water had overflowed? Express your answer in litres. [?] ℓ", "answer0": "19440", "answer1": "0.81", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 193, "difficulty_id": 3, "explanation": "(a) Tank volume = 45 \\u00d7 24 \\u00d7 27 = 29 160 cm\\u00b3. It was \\(\\dfrac{1}{3}\\) full, so \\(\\dfrac{2}{3}\\) is needed: 29 160 \\u00d7 \\(\\dfrac{2}{3}\\) = 19 440 cm\\u00b3. (b) Water added = 1.35 \\u00d7 15 = 20.25 \\u2113. The space needed was 19 440 cm\\u00b3 = 19.44 \\u2113. Overflow = 20.25 \\u2212 19.44 = 0.81 \\u2113.", "hints": ["(a) Find the full volume, then take two-thirds of it.", "(b) 1 \\u2113 = 1000 cm\\u00b3; overflow = water added \\u2212 space available."], "source": "ACS 2025 P5 End-of-Year Exam P2 Q8", "image_needed": true, "image_options": false, "image_file": "q38.png", "image_page": 25, "image_bbox": [0.33, 0.13, 0.70, 0.31], "image_loc": "rectangular tank 45 x 24 x 27 cm with tap, partly filled", "notes": "Paper 2 Q8. Key: (a) 19440 cm³ (b) 0.81 ℓ" }, { "n": 39, "type_id": 2, "question": "The table shows the prices of toy planes sold at a shop during a sale. First 4 toy planes or fewer: $12 each. Every additional toy plane: $9.50 each.
(a) Mrs Tam bought 7 toy planes. How much did she pay for all the toy planes? Ans: $ [?]
(b) Mrs Lee paid $124 for some toy planes. How many toy planes did she buy? [?]", "answer0": "76.50", "answer1": "12", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 3, "explanation": "(a) 4 \\u00d7 $12 + 3 \\u00d7 $9.50 = $48 + $28.50 = $76.50. (b) First 4 cost $48. Remaining $124 \\u2212 $48 = $76. $76 \\u00f7 $9.50 = 8 extra planes. Total = 4 + 8 = 12.", "hints": ["(a) First 4 at $12, the rest at $9.50.", "(b) Subtract the cost of the first 4, then divide the rest by $9.50."], "source": "ACS 2025 P5 End-of-Year Exam P2 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q9. Key: (a) $76.50 (b) 12" }, { "n": 40, "type_id": 2, "question": "ABCD is a parallelogram. DG is a straight line. \\u2220ABC = 65°, \\u2220CAD = 50° and \\u2220CFG = 140°.
(a) Find \\u2220BAC. [?] °
(b) Find \\u2220CDF. [?] °", "answer0": "65", "answer1": "25", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 200, "difficulty_id": 3, "explanation": "(a) In triangle ABC, \\u2220BAC = 180\\u00b0 \\u2212 \\u2220ABC \\u2212 \\u2220ACB. Using \\u2220CAD = 50\\u00b0 and \\u2220ABC = 65\\u00b0: \\u2220BAC = 180\\u00b0 \\u2212 65\\u00b0 \\u2212 50\\u00b0 = 65\\u00b0. (b) \\u2220BCD = \\u2220BAD = 65\\u00b0 + 50\\u00b0 = 115\\u00b0 (opposite angles of parallelogram). \\u2220CDF (=\\u2220CFG \\u2212 \\u2220BCD related) = 140\\u00b0 \\u2212 115\\u00b0 = 25\\u00b0.", "hints": ["(a) Angle sum of triangle ABC is 180\\u00b0.", "(b) Opposite angles of a parallelogram are equal; use the 140\\u00b0 straight-line angle."], "source": "ACS 2025 P5 End-of-Year Exam P2 Q10", "image_needed": true, "image_options": false, "image_file": "q40.png", "image_page": 27, "image_bbox": [0.33, 0.15, 0.66, 0.33], "image_loc": "parallelogram ABCD with diagonal and line DG, angles 50, 65, 140 marked", "notes": "Paper 2 Q10. Key: (a) 65° (b) 25°" }, { "n": 41, "type_id": 2, "question": "A file and 3 identical pens cost $29.20. 2 such files and 8 such pens cost $76.20. What was the cost of 1 such pen? Ans: $ [?]", "answer0": "8.90", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 3, "explanation": "1 file + 3 pens = $29.20. 2 files + 8 pens = $76.20, so 1 file + 4 pens = $38.10. Subtracting: 1 pen = $38.10 \\u2212 $29.20 = $8.90.", "hints": ["Halve the second equation to get 1 file + 4 pens.", "Subtract the first equation to leave the cost of 1 pen."], "source": "ACS 2025 P5 End-of-Year Exam P2 Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q11. Key: $8.90" }, { "n": 42, "type_id": 2, "question": "The bar graph shows the different flavours of ice cream sold by a shop (Chocolate 42, Pistachio 36, Strawberry 57, Vanilla 24). The table shows the prices per cup: Chocolate $3.50, Pistachio $4.20, Strawberry $2.50, Vanilla $3.80.
(b) Which ice cream flavour did the shop earn the most money? From the sale of this ice cream flavour, what was the amount of money earned? Flavour: [?]; Amount: $ [?]", "answer0": "Pistachio", "answer1": "151.20", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 3, "explanation": "Earnings: Chocolate 42 \\u00d7 $3.50 = $147.00; Pistachio 36 \\u00d7 $4.20 = $151.20; Strawberry 57 \\u00d7 $2.50 = $142.50; Vanilla 24 \\u00d7 $3.80 = $91.20. The most is Pistachio at $151.20.", "hints": ["Multiply each flavour's cups sold by its price.", "Compare the four totals."], "source": "ACS 2025 P5 End-of-Year Exam P2 Q12", "image_needed": true, "image_options": false, "image_file": "q42.png", "image_page": 29, "image_bbox": [0.22, 0.12, 0.85, 0.32], "image_loc": "bar graph of cups sold per ice cream flavour", "notes": "Paper 2 Q12. Part (a) answer 8/53 (vanilla fraction) is a fraction so omitted from FIB; only part (b) captured here (flavour + amount, both FIB-friendly). Key (a) 8/53 (b) Pistachio, $151.20." }, { "n": 43, "type_id": 2, "question": "Ken and Helen went shopping with a total amount of $345. Ken spent twice as much as Helen. The amount Helen had left was $26 more than what she had spent. She had twice as much money left as Ken.
(a) How much money did Ken spend? Ans: $ [?]
(b) How much money did Helen have at first? Ans: $ [?]", "answer0": "136", "answer1": "162", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "Let Helen spend 2u. Ken: spent 4u, left u + 13; Helen: left 2u + 26. Total at first = 9u + 39 = 345, so 9u = 306, u = 34. (a) Ken spent 4u = $136. (b) Helen at first = 4u + 26 = $162.", "hints": ["Set Helen's spending as 2 units so Ken's is 4 units.", "Form an equation for the total $345 and solve for the unit."], "source": "ACS 2025 P5 End-of-Year Exam P2 Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: (a) $136 (b) $162" }, { "n": 44, "type_id": 2, "question": "Peter was reading a book. On the first day, he read \\(\\dfrac{1}{4}\\) of the total number of pages of the book. On the second day, he read another 50 pages. After that, the number of pages he had read was twice the number of pages he had not read. How many pages were there in the book? [?]", "answer0": "120", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "After two days he had read \\(\\dfrac{2}{3}\\) of the book (read : unread = 2 : 1). \\(\\dfrac{2}{3}-\\dfrac{1}{4}=\\dfrac{5}{12}\\) of the book = 50 pages. Total = 50 \\u00d7 \\(\\dfrac{12}{5}\\) = 120 pages.", "hints": ["Read : unread = 2 : 1 means read = two-thirds of the book.", "The 50 pages equals two-thirds minus the first-day quarter."], "source": "ACS 2025 P5 End-of-Year Exam P2 Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q14. Key: 120 pages" }, { "n": 45, "type_id": 2, "question": "Figure A is a square formed using 2 identical tiles. Figure B is a rectangle formed by rearranging the tiles. The area of Figure A is 81 m². Figure C shows a rectangular path formed by using the tile pattern of Figure B. The path is continuous and completely covered. It has an area of 2106 m².
(a) What is the length of Figure B? Ans: [?] m
(b) What is the perimeter of the path? Ans: [?] m", "answer0": "13.5", "answer1": "714", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "(a) Side of square A = \\(\\sqrt{81}\\) = 9 m. Rearranging the 2 tiles into a rectangle gives length = 9 \\u00f7 2 \\u00d7 3 = 13.5 m. (b) Breadth of Figure B = 81 \\u00f7 13.5 = 6 m. Length of the path = 2106 \\u00f7 6 = 351 m. Perimeter = 2 \\u00d7 (351 + 6) = 714 m.", "hints": ["(a) Side of square A is \\u221a81 = 9 m.", "(b) Find the breadth of B, then the path length, then 2(L + b)."], "source": "ACS 2025 P5 End-of-Year Exam P2 Q15", "image_needed": true, "image_options": false, "image_file": "q45.png", "image_page": 32, "image_bbox": [0.20, 0.18, 0.80, 0.40], "image_loc": "Figure A square, Figure B rectangle, and Figure C path of repeated tiles", "notes": "Paper 2 Q15. Key: (a) 13.5 m (b) 714 m" } ] }