{ "paper": { "school": "Ai Tong School", "year": 2023, "level": "P5", "label": "End-of-Year Exam", "source_prefix": "Ai Tong 2023 P5 End-of-Year Exam", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "There were 312 089 visitors to a tourist attraction last year. Express this number to the nearest thousand.", "answer0": "300 000", "answer1": "310 000", "answer2": "312 000", "answer3": "313 000", "correct_answer": 2, "skill_id": 150, "difficulty_id": 1, "explanation": "Round 312 089 to the nearest thousand. The hundreds digit is 0, which is less than 5, so round down. 312 089 ≈ 312 000.", "hints": ["Look at the hundreds digit to decide whether to round up or down.", "Hundreds digit is 0, so round down to 312 000."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q1 = option (3) = 312 000" }, { "n": 2, "type_id": 1, "question": "What is the value of $30 - (6 + 12) \\div 3 \\times 2$?", "answer0": "8", "answer1": "2", "answer2": "18", "answer3": "27", "correct_answer": 2, "skill_id": 155, "difficulty_id": 2, "explanation": "Brackets first: 6 + 12 = 18. Then division and multiplication left to right: 18 ÷ 3 = 6, 6 × 2 = 12. Finally 30 - 12 = 18.", "hints": ["Work out the brackets first.", "Do ÷ and × from left to right before the subtraction."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q2 = option (3) = 18" }, { "n": 3, "type_id": 1, "question": "Which fraction is greater than \\(\\dfrac{1}{2}\\)?", "answer0": "\\(\\dfrac{4}{7}\\)", "answer1": "\\(\\dfrac{3}{8}\\)", "answer2": "\\(\\dfrac{4}{9}\\)", "answer3": "\\(\\dfrac{5}{10}\\)", "correct_answer": 0, "skill_id": 158, "difficulty_id": 1, "explanation": "Compare each to \\(\\dfrac{1}{2}\\). \\(\\dfrac{4}{7}\\approx0.57>0.5\\); \\(\\dfrac{3}{8}=0.375\\); \\(\\dfrac{4}{9}\\approx0.44\\); \\(\\dfrac{5}{10}=0.5\\). Only \\(\\dfrac{4}{7}\\) is greater than \\(\\dfrac{1}{2}\\).", "hints": ["Half of the denominator gives the numerator equal to 1/2.", "A fraction is more than 1/2 when its numerator is more than half its denominator."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Fraction options → MCQ. Key Q3 = option (1) = 4/7" }, { "n": 4, "type_id": 1, "question": "Which of the following is equal to \\(3\\dfrac{5}{6}\\)?", "answer0": "\\(\\dfrac{15}{6}\\)", "answer1": "\\(\\dfrac{21}{6}\\)", "answer2": "\\(\\dfrac{23}{6}\\)", "answer3": "\\(\\dfrac{35}{6}\\)", "correct_answer": 2, "skill_id": 119, "difficulty_id": 1, "explanation": "Convert the mixed number: \\(3\\dfrac{5}{6} = \\dfrac{3\\times6+5}{6} = \\dfrac{23}{6}\\).", "hints": ["Multiply the whole number by the denominator, then add the numerator.", "3 × 6 + 5 = 23, so the answer is 23/6."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Fraction options → MCQ. Key Q4 = option (3) = 23/6" }, { "n": 5, "type_id": 1, "question": "What does the digit 9 in 7.698 stand for?", "answer0": "9 ones", "answer1": "9 tenths", "answer2": "9 hundredths", "answer3": "9 thousandths", "correct_answer": 2, "skill_id": 123, "difficulty_id": 1, "explanation": "In 7.698, the digits after the point are tenths (6), hundredths (9) and thousandths (8). So the 9 stands for 9 hundredths.", "hints": ["The first place after the decimal point is tenths.", "The second place after the point is hundredths."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q5 = option (3) = 9 hundredths" }, { "n": 6, "type_id": 1, "question": "Which of the following is likely to be the total mass of 6 one-dollar coins?", "answer0": "4000 g", "answer1": "400 g", "answer2": "40 g", "answer3": "4 g", "correct_answer": 2, "skill_id": 184, "difficulty_id": 2, "explanation": "A one-dollar coin has a mass of about 7 g, so 6 coins are roughly 40 g. The other amounts are far too heavy or too light.", "hints": ["Estimate the mass of a single coin.", "A coin is a few grams, so 6 coins are around 40 g, not 400 g or 4 g."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Estimation/reasonableness of measurement. Key Q6 = option (3) = 40 g" }, { "n": 7, "type_id": 1, "question": "What is the missing number in the box?
$\\boxed{\\phantom{0}} : 49 = 30 : 42$", "answer0": "19", "answer1": "23", "answer2": "35", "answer3": "37", "correct_answer": 2, "skill_id": 181, "difficulty_id": 2, "explanation": "Simplify 30 : 42 by dividing by 6 to get 5 : 7. Since the second term is 49 = 7 × 7, the first term is 5 × 7 = 35.", "hints": ["Simplify 30 : 42 first.", "30 : 42 = 5 : 7, and 49 = 7 × 7, so the missing term is 5 × 7."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Equivalent ratios. Key Q7 = option (3) = 35" }, { "n": 8, "type_id": 1, "question": "In the figure, which two lines are parallel to each other?", "answer0": "DA and CB", "answer1": "DA and DC", "answer2": "AB and CB", "answer3": "AB and DC", "correct_answer": 3, "skill_id": 199, "difficulty_id": 2, "explanation": "ABCD is a rhombus-shaped quadrilateral. Opposite sides are parallel, so AB is parallel to DC (and AD parallel to BC). Among the options, AB and DC are parallel.", "hints": ["In a parallelogram/rhombus, opposite sides are parallel.", "AB and DC are opposite sides."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 5, "image_bbox": [0.35, 0.13, 0.62, 0.32], "image_loc": "diamond/rhombus ABCD figure near top of page, below the question", "notes": "Key Q8 = option (4) = AB and DC" }, { "n": 9, "type_id": 1, "question": "In the figure, EF and GH are straight lines. Which one of the following is true?", "answer0": "$\\angle a + \\angle c = 180^\\circ$", "answer1": "$\\angle b + \\angle c = 180^\\circ$", "answer2": "$\\angle a = \\angle c$", "answer3": "$\\angle b = \\angle d$", "correct_answer": 2, "skill_id": 194, "difficulty_id": 2, "explanation": "Where two straight lines cross, vertically opposite angles are equal. \\(\\angle a\\) and \\(\\angle c\\) are vertically opposite, so \\(\\angle a = \\angle c\\).", "hints": ["Two crossing straight lines make pairs of vertically opposite angles.", "Vertically opposite angles are equal."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q9", "image_needed": true, "image_options": false, "image_file": "q9.png", "image_page": 5, "image_bbox": [0.22, 0.55, 0.78, 0.82], "image_loc": "intersecting lines E-F and G-H-K with angles a,b,c,d in middle of page", "notes": "Key Q9 = option (3) = ∠a = ∠c" }, { "n": 10, "type_id": 1, "question": "What is the area of triangle ABC?", "answer0": "22 cm²", "answer1": "26 cm²", "answer2": "44 cm²", "answer3": "52 cm²", "correct_answer": 0, "skill_id": 186, "difficulty_id": 2, "explanation": "Base CB = 8 + 3 = 11 cm and the perpendicular height is 4 cm. Area \\(= \\dfrac{1}{2} \\times 11 \\times 4 = 22\\) cm².", "hints": ["The base is the whole bottom side, 8 + 3 = 11 cm.", "Area of a triangle = ½ × base × height = ½ × 11 × 4."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q10", "image_needed": true, "image_options": false, "image_file": "q10.png", "image_page": 6, "image_bbox": [0.22, 0.10, 0.78, 0.30], "image_loc": "triangle ABC with height 4 cm, side 5 cm, base segments 8 cm and 3 cm", "notes": "Base = 8+3 = 11 cm. Key Q10 = option (1) = 22 cm²" }, { "n": 11, "type_id": 1, "question": "There are apples, oranges and pears in a basket. The ratio of the number of apples to the number of oranges is 5 : 2. The ratio of the number of oranges to the number of pears is 1 : 4. What is the ratio of the number of apples to the total number of fruits in the basket?", "answer0": "5 : 11", "answer1": "5 : 12", "answer2": "1 : 2", "answer3": "1 : 3", "correct_answer": 3, "skill_id": 183, "difficulty_id": 3, "explanation": "A : O = 5 : 2 and O : P = 1 : 4 = 2 : 8, so A : O : P = 5 : 2 : 8. Total = 5 + 2 + 8 = 15 units. Apples : total = 5 : 15 = 1 : 3.", "hints": ["Make the oranges term the same in both ratios.", "A : O : P = 5 : 2 : 8, total = 15, so 5 : 15 = 1 : 3."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q11 = option (4) = 1 : 3" }, { "n": 12, "type_id": 1, "question": "The average mass of Ali, Boon and Chai is 48 kg. Ali is 7 kg heavier than Boon. Ali is also 5 kg heavier than Chai. What is the mass of Ali?", "answer0": "52 kg", "answer1": "50 kg", "answer2": "47 kg", "answer3": "45 kg", "correct_answer": 0, "skill_id": 205, "difficulty_id": 3, "explanation": "Total mass = 48 × 3 = 144 kg. Let Ali = A. Boon = A - 7, Chai = A - 5. So A + (A-7) + (A-5) = 144, 3A - 12 = 144, 3A = 156, A = 52 kg.", "hints": ["Total of the three = average × 3 = 144 kg.", "Express Boon and Chai in terms of Ali, then solve 3A - 12 = 144."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q12 = option (1) = 52 kg" }, { "n": 13, "type_id": 1, "question": "AOB is a straight line, $\\angle AOD = 100^\\circ$ and $\\angle COB = 123^\\circ$. Find $\\angle COD$.", "answer0": "23°", "answer1": "43°", "answer2": "57°", "answer3": "80°", "correct_answer": 1, "skill_id": 194, "difficulty_id": 2, "explanation": "Angles on a straight line add to 180°. \\(\\angle AOD + \\angle COB\\) overlap in \\(\\angle COD\\): \\(\\angle COD = \\angle AOD + \\angle COB - 180^\\circ = 100^\\circ + 123^\\circ - 180^\\circ = 43^\\circ\\).", "hints": ["The two given angles overlap over ∠COD.", "∠COD = 100° + 123° - 180°."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q13", "image_needed": true, "image_options": false, "image_file": "q13.png", "image_page": 7, "image_bbox": [0.20, 0.40, 0.62, 0.58], "image_loc": "rays OC and OD above straight line AOB, angles 100° and 123° marked, ? for COD", "notes": "Key Q13 = option (2) = 43°" }, { "n": 14, "type_id": 1, "question": "Ethan received $200 as a prize. He gave $70 to his mother. What percentage of the prize money did Ethan give to his mother?", "answer0": "30%", "answer1": "35%", "answer2": "65%", "answer3": "70%", "correct_answer": 1, "skill_id": 171, "difficulty_id": 2, "explanation": "Fraction given = \\(\\dfrac{70}{200}\\). As a percentage: \\(\\dfrac{70}{200} \\times 100\\% = 35\\%\\).", "hints": ["Write the amount given over the total as a fraction.", "70/200 × 100% = 35%."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q14 = option (2) = 35%" }, { "n": 15, "type_id": 1, "question": "A rectangular glass box is filled with some 1-cm cubes. How many more 1-cm cubes are needed to fill up the rectangular glass box completely?", "answer0": "13", "answer1": "32", "answer2": "36", "answer3": "45", "correct_answer": 1, "skill_id": 190, "difficulty_id": 3, "explanation": "The full box holds 5 × 3 × 3 = 45 cubes. There are 13 cubes already inside, so cubes needed = 45 - 13 = 32.", "hints": ["Work out how many cubes the full box can hold from its length, width and height.", "Subtract the number of cubes already placed."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q15", "image_needed": true, "image_options": false, "image_file": "q15.png", "image_page": 8, "image_bbox": [0.30, 0.43, 0.70, 0.58], "image_loc": "rectangular glass box partly filled with 1-cm cubes", "notes": "Key Q15 = option (2) = 32 (full box 45 cubes, 13 already in)" }, { "n": 16, "type_id": 2, "question": "What is 6% of 3100? [?]", "answer0": "186", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 174, "difficulty_id": 1, "explanation": "6% of 3100 = \\(\\dfrac{6}{100} \\times 3100 = 186\\).", "hints": ["6% means 6 out of every 100.", "6/100 × 3100 = 186."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q16 = 186" }, { "n": 17, "type_id": 2, "question": "Find the value of $10.5 - 0.99$. [?]", "answer0": "9.51", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 129, "difficulty_id": 1, "explanation": "10.5 - 0.99 = 9.51.", "hints": ["Line up the decimal points; 10.50 - 0.99.", "10.50 - 0.99 = 9.51."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q17 = 9.51" }, { "n": 18, "type_id": 1, "question": "Arrange these fractions from the smallest to the largest.
\\(\\dfrac{7}{6}\\), \\(1\\dfrac{1}{3}\\), \\(\\dfrac{4}{5}\\)", "answer0": "\\(\\dfrac{4}{5}\\), \\(\\dfrac{7}{6}\\), \\(1\\dfrac{1}{3}\\)", "answer1": "\\(\\dfrac{7}{6}\\), \\(\\dfrac{4}{5}\\), \\(1\\dfrac{1}{3}\\)", "answer2": "\\(1\\dfrac{1}{3}\\), \\(\\dfrac{7}{6}\\), \\(\\dfrac{4}{5}\\)", "answer3": "\\(\\dfrac{4}{5}\\), \\(1\\dfrac{1}{3}\\), \\(\\dfrac{7}{6}\\)", "correct_answer": 0, "skill_id": 158, "difficulty_id": 2, "explanation": "As decimals: \\(\\dfrac{4}{5}=0.8\\), \\(\\dfrac{7}{6}\\approx1.17\\), \\(1\\dfrac{1}{3}\\approx1.33\\). Smallest to largest: \\(\\dfrac{4}{5}\\), \\(\\dfrac{7}{6}\\), \\(1\\dfrac{1}{3}\\).", "hints": ["Convert each fraction to a decimal to compare.", "0.8 < 1.17 < 1.33."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Ordering of fractions/mixed number → MCQ (answers are fractions). Key Q18 = 4/5, 7/6, 1 1/3" }, { "n": 19, "type_id": 2, "question": "The original price of a tablet was $550. During a sale, Melvin was given a 30% discount for the tablet. How much did he pay for the tablet?
$[?]", "answer0": "385", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 176, "difficulty_id": 2, "explanation": "A 30% discount means he paid 70% of $550. 70% of 550 = \\(\\dfrac{70}{100} \\times 550 = \\$385\\).", "hints": ["After a 30% discount, the price paid is 100% - 30% = 70%.", "70% of $550 = $385."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q19 = $385. Answer stored as 385 (dollar sign in stem)." }, { "n": 20, "type_id": 2, "question": "Find the value of $0.27 \\times 80$. [?]", "answer0": "21.6", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 1, "explanation": "0.27 × 80 = 0.27 × 8 × 10 = 2.16 × 10 = 21.6.", "hints": ["0.27 × 8 = 2.16.", "Then multiply by 10 to get 21.6."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q20", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q20 = 21.6" }, { "n": 21, "type_id": 2, "question": "The figure is made up of four identical squares. The area of each square is 36 cm². What is the perimeter of the figure?
[?] cm", "answer0": "60", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "Each square has area 36 cm², so its side = 6 cm (since 6 × 6 = 36). Tracing the boundary of the four-square figure gives a perimeter of 10 side-lengths = 10 × 6 = 60 cm.", "hints": ["Find the side of one square from its area: side = √36 = 6 cm.", "Count the outer edges of the figure (10 sides), then × 6 cm."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q21", "image_needed": true, "image_options": false, "image_file": "q21.png", "image_page": 11, "image_bbox": [0.18, 0.18, 0.62, 0.40], "image_loc": "figure made of four overlapping/staggered identical squares", "notes": "Side = 6 cm. Key Q21 = 60 cm" }, { "n": 22, "type_id": 2, "question": "Three friends shared the cost of 60 mangoes in the ratio $1 : 2 : 2$. There is a special offer of $10 for one box of 15 mangoes. What was the cost of the smallest share?
$[?]", "answer0": "8", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 183, "difficulty_id": 2, "explanation": "60 mangoes = 60 ÷ 15 = 4 boxes, costing 4 × $10 = $40. The ratio 1 : 2 : 2 has 5 units in total, so 1 unit (smallest share) = $40 ÷ 5 = $8.", "hints": ["Find the total cost: 60 ÷ 15 = 4 boxes at $10 each.", "Total = $40 over 5 units, so the smallest (1 unit) = $8."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q22", "image_needed": true, "image_options": false, "image_file": "q22.png", "image_page": 11, "image_bbox": [0.10, 0.58, 0.40, 0.72], "image_loc": "tray of mangoes drawing (left of the Special Offer box)", "notes": "Special Offer text ($10 for one box of 15 mangoes) included in stem. Key Q22 = $8. Image is decorative." }, { "n": 23, "type_id": 0, "question": "Joash stacked 14 unit cubes to form the solid. Draw the front view and the top view of the solid on the grids.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 188, "difficulty_id": 2, "explanation": "Draw the front view and top view of the given solid on the dot grids. See the answer key diagram for the correct shaded grids (front view: an L-shaped/stepped outline; top view: the base footprint of the solid).", "hints": ["Look along the front-view arrow and shade the squares you see.", "For the top view, look straight down and shade the base footprint."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q23", "image_needed": true, "image_options": false, "image_file": "q23.png", "image_page": 12, "image_bbox": [0.30, 0.10, 0.72, 0.36], "image_loc": "isometric drawing of 14-unit-cube solid with Top/Side/Front view arrows", "notes": "Interactive draw-on-grid task → type_id 0 (skipped on insert). Key Q23 shows the front-view and top-view grids." }, { "n": 24, "type_id": 1, "question": "Ming drew three circles to form a figure. The areas of the circles were in the ratio $1 : 4 : 16$. She then shaded some parts of the figure. Find the ratio of the total area of the shaded parts to the area of the unshaded parts.", "answer0": "13 : 3", "answer1": "3 : 13", "answer2": "12 : 4", "answer3": "4 : 12", "correct_answer": 0, "skill_id": 183, "difficulty_id": 3, "explanation": "Let the areas be 1, 4 and 16 units. The smallest circle (1) is shaded; the ring between the middle and small circle (4 - 1 = 3) is unshaded; the ring between the largest and middle circle (16 - 4 = 12) is shaded. Shaded = 1 + 12 = 13; unshaded = 3. Ratio shaded : unshaded = 13 : 3.", "hints": ["Use the area units 1, 4 and 16 for the three circles.", "Work out each ring (4-1 and 16-4), then add up the shaded parts: 1 + 12 = 13 vs 3."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q24", "image_needed": true, "image_options": false, "image_file": "q24.png", "image_page": 13, "image_bbox": [0.55, 0.10, 0.82, 0.28], "image_loc": "three nested/overlapping circles with shaded and unshaded regions, top-right of page", "notes": "Ratio answers → MCQ. Key Q24 = 13 : 3. Distractors added." }, { "n": 25, "type_id": 2, "question": "ABCD is a parallelogram. $\\angle ADE = 32^\\circ$, $\\angle DCE = 46^\\circ$ and $\\angle BCE = 54^\\circ$. Find $\\angle z$.
[?]°", "answer0": "274", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 200, "difficulty_id": 3, "explanation": "In parallelogram ABCD, \\(\\angle ADC = \\angle ADE + \\angle EDC\\). \\(\\angle BCD = \\angle DCE + \\angle BCE = 46^\\circ + 54^\\circ = 100^\\circ\\). Co-interior angles: \\(\\angle ADC = 180^\\circ - 100^\\circ = 80^\\circ\\), so \\(\\angle EDC = 80^\\circ - 32^\\circ = 48^\\circ\\). In triangle DEC, \\(\\angle DEC = 180^\\circ - 48^\\circ - 46^\\circ = 86^\\circ\\). \\(z\\) is the reflex/exterior angle at E: \\(z = 360^\\circ - 86^\\circ = 274^\\circ\\).", "hints": ["Find ∠BCD = 46° + 54°, then use co-interior angles to get ∠ADC.", "Find ∠DEC in triangle DEC, then z = 360° - ∠DEC = 274°."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q25", "image_needed": true, "image_options": false, "image_file": "q25.png", "image_page": 13, "image_bbox": [0.16, 0.46, 0.62, 0.72], "image_loc": "parallelogram ABCD with point E inside, angles 32°, 46°, 54° and z marked", "notes": "Answer is whole number degrees → FIB. Key Q25 = 274°" }, { "n": 26, "type_id": 2, "question": "Priya spent \\(\\dfrac{5}{9}\\) of her money on some pens and \\(\\dfrac{1}{4}\\) of the remainder on 3 notebooks. A notebook cost 4 times as much as a pen. How many pens did she buy?
[?]", "answer0": "60", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Let her money be 36 units. Pens: \\(\\dfrac{5}{9} \\times 36 = 20\\) units. Remainder = 16 units; notebooks: \\(\\dfrac{1}{4} \\times 16 = 4\\) units for 3 notebooks, so 1 notebook = \\(\\dfrac{4}{3}\\) units. A pen costs \\(\\dfrac{1}{4}\\) of a notebook = \\(\\dfrac{1}{3}\\) unit. Number of pens = 20 ÷ \\(\\dfrac{1}{3}\\) = 60.", "hints": ["Choose a money total that splits nicely (e.g. 36 units).", "Money on pens ÷ cost of one pen = number of pens; a pen costs 1/4 of a notebook."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q26", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q26 = 60" }, { "n": 27, "type_id": 2, "question": "The table shows the rate of charges for each overdue book borrowed from a library.
OVERDUE CHARGES
For the first 7 days: 20¢ per day
After 7 days: 50¢ per day
Peter borrowed a book from the library. The book was overdue when he returned it. He paid a total of $3.90 for the overdue book. How many days was it overdue?
[?] days", "answer0": "12", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "First 7 days cost 7 × 20¢ = 140¢ = $1.40. Remaining charge = $3.90 - $1.40 = $2.50 = 250¢ at 50¢/day = 5 extra days. Total overdue = 7 + 5 = 12 days.", "hints": ["Work out the cost for the first 7 days at 20¢/day.", "Divide the leftover amount by 50¢ to find the extra days, then add 7."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q27", "image_needed": false, "image_options": false, "image_file": null, "notes": "Charges table transcribed into stem. Key Q27 = 12 days" }, { "n": 28, "type_id": 2, "question": "Dexter has $27 more than Asher. After Asher gave $6 to Dexter, Dexter had 4 times as much money as Asher. What was the amount of money Asher had in the end?
$[?]", "answer0": "13", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "After Asher gives $6, Dexter has $27 + $6 + $6 = $39 more than Asher's new amount (the gap widens by $12 from the original $27). With Dexter = 4 units and Asher = 1 unit, the difference is 3 units = $39, so 1 unit = $13. Asher had $13 in the end.", "hints": ["Giving $6 makes the difference grow by $12 to $39.", "Difference 3 units = $39, so Asher (1 unit) = $13."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q28", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q28 = $13 (Asher's amount in the end)" }, { "n": 29, "type_id": 2, "question": "ACD and BCE are straight lines. $\\angle ABE = 55^\\circ$, $\\angle DEB = 114^\\circ$ and $\\angle DAB = 90^\\circ$. Find $\\angle ADE$.
[?]°", "answer0": "31", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 3, "explanation": "In triangle ABC, \\(\\angle ACB = 180^\\circ - 90^\\circ - 55^\\circ = 35^\\circ\\). \\(\\angle DCE\\) is vertically opposite \\(\\angle ACB\\), so \\(\\angle DCE = 35^\\circ\\). In triangle CDE, \\(\\angle ADE = 180^\\circ - 114^\\circ - 35^\\circ = 31^\\circ\\).", "hints": ["Find ∠ACB in triangle ABC, then use vertically opposite angles for ∠DCE.", "In triangle CDE, ∠ADE = 180° - 114° - 35°."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q29", "image_needed": true, "image_options": false, "image_file": "q29.png", "image_page": 15, "image_bbox": [0.18, 0.34, 0.72, 0.56], "image_loc": "two triangles sharing crossing straight lines ACD and BCE; angles 55°, 114° and right angle marked", "notes": "Answer whole-number degrees → FIB. Key Q29 = 31°" }, { "n": 30, "type_id": 0, "question": "Triangle ABC is drawn by joining the dots on the square grid. (a) Draw Triangle ACD with the same area as Triangle ABC. Triangle ACD does not overlap with Triangle ABC. (b) Draw a square with thrice the area of Triangle ABC.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 3, "explanation": "Triangle ABC has base AC and a height, giving an area of 6 square units. (a) Draw triangle ACD on the same base AC but on the opposite side with the same height, so it has the same area and does not overlap. (b) Triangle ABC = 6 square units, so a square of thrice that area = 18 square units (which is not a perfect-square side on the grid; the key draws an 18-square-unit square, e.g. a tilted square).", "hints": ["Same base, same height gives the same area; flip the triangle to the other side.", "Thrice 6 = 18 square units for the square."], "source": "Ai Tong 2023 P5 End-of-Year Exam Q30", "image_needed": true, "image_options": false, "image_file": "q30.png", "image_page": 16, "image_bbox": [0.14, 0.10, 0.78, 0.30], "image_loc": "square dot grid with Triangle ABC drawn (A bottom-left, B top, C right)", "notes": "Interactive draw-on-grid task → type_id 0 (skipped on insert). Key Q30a/Q30b show the drawn triangle and square." }, { "n": 31, "type_id": 2, "question": "Cathleen has 1.2 m of ribbon at first. She used 45 cm of it. What is the length of the ribbon left?
[?] m", "answer0": "0.75", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 184, "difficulty_id": 2, "explanation": "Convert 45 cm to metres: 45 cm = 0.45 m. Ribbon left = 1.2 m - 0.45 m = 0.75 m.", "hints": ["Change 45 cm to metres (45 cm = 0.45 m).", "1.2 - 0.45 = 0.75 m."], "source": "Ai Tong 2023 P5 End-of-Year Exam Paper 2 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q1. Key = 0.75 m" }, { "n": 32, "type_id": 2, "question": "The figure is made up of 3 identical squares. What percentage of the figure is shaded?
[?]%", "answer0": "25", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 171, "difficulty_id": 3, "explanation": "The shaded triangle covers half of one square, i.e. \\(\\dfrac{1}{2}\\) of 1 out of 3 squares. As a fraction of the whole figure: \\(\\dfrac{1/2}{3} = \\dfrac{1}{6}\\)... using the key's working, shaded = \\(\\dfrac{1.5}{12}\\) of the equal small parts = \\(\\dfrac{3}{12} \\times 100\\% = 25\\%\\).", "hints": ["Divide the figure into equal small parts to compare the shaded part.", "Shaded = 3/12 = 25% (per the answer key)."], "source": "Ai Tong 2023 P5 End-of-Year Exam Paper 2 Q2", "image_needed": true, "image_options": false, "image_file": "q32.png", "image_page": 19, "image_bbox": [0.18, 0.45, 0.42, 0.72], "image_loc": "L-shaped figure of 3 identical squares with a shaded triangle in the top-left square", "notes": "Paper 2 Q2. Key working: 3/12 × 100% = 25%." }, { "n": 33, "type_id": 2, "question": "A machine takes 2 min to print 3 posters. At this rate, how many posters will it print in 2 hours?
[?]", "answer0": "180", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 2, "explanation": "2 hours = 120 min. Number of 2-min intervals = 120 ÷ 2 = 60. Posters = 60 × 3 = 180.", "hints": ["Change 2 hours into minutes (120 min).", "120 ÷ 2 = 60 sets of 3 posters, so 60 × 3 = 180."], "source": "Ai Tong 2023 P5 End-of-Year Exam Paper 2 Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q3. Key = 180" }, { "n": 34, "type_id": 2, "question": "7 chocolate bars weigh 384.51 g each. How much do they weigh altogether? Round the answer to the nearest kilogram.
[?] kg", "answer0": "3", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 168, "difficulty_id": 2, "explanation": "Total = 384.51 × 7 = 2691.57 g ≈ 3000 g = 3 kg (to the nearest kilogram).", "hints": ["Multiply 384.51 by 7 to get the total in grams.", "2691.57 g rounds to 3000 g = 3 kg."], "source": "Ai Tong 2023 P5 End-of-Year Exam Paper 2 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q4. Key = 3 kg" }, { "n": 35, "type_id": 2, "question": "A bag containing 12 oranges weighs 980 g. The mass of the empty bag is 20 g. What is the average mass of 1 orange?
[?] g", "answer0": "80", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 205, "difficulty_id": 2, "explanation": "Mass of oranges = 980 g - 20 g = 960 g. Average mass of 1 orange = 960 ÷ 12 = 80 g.", "hints": ["Subtract the empty-bag mass first.", "960 g ÷ 12 oranges = 80 g."], "source": "Ai Tong 2023 P5 End-of-Year Exam Paper 2 Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q5. Key = 80 g" }, { "n": 36, "type_id": 2, "question": "ABCD is a parallelogram. $\\angle ABD = 29^\\circ$, $\\angle ADB = 38^\\circ$ and $\\angle BCE = 66^\\circ$.
(a) Find $\\angle BCD$. [?]°
(b) ABED is a [?] a trapezium and AB is [?] parallel to DE.", "answer0": "113", "answer1": "is not", "answer2": "is not", "answer3": null, "correct_answer": null, "skill_id": 200, "difficulty_id": 3, "explanation": "(a) In a parallelogram, \\(\\angle BCD = \\angle BAD\\). In triangle ABD, \\(\\angle BAD = 180^\\circ - 29^\\circ - 38^\\circ = 113^\\circ\\), so \\(\\angle BCD = 113^\\circ\\). (b) ABED is NOT a trapezium and AB is NOT parallel to DE.", "hints": ["(a) Opposite angles of a parallelogram are equal; find ∠BAD in triangle ABD.", "(b) Check whether AB and DE can be parallel — they are not."], "source": "Ai Tong 2023 P5 End-of-Year Exam Paper 2 Q6", "image_needed": true, "image_options": false, "image_file": "q36.png", "image_page": 21, "image_bbox": [0.20, 0.14, 0.72, 0.34], "image_loc": "parallelogram ABCD extended to E with angles 29°, 38°, 66° marked", "notes": "Paper 2 Q6. Combined (a)+(b). Key Q6a = 113°; Q6b = is not, is not. Part (b) is a circle-the-word task rendered as fill-in choices." }, { "n": 37, "type_id": 2, "question": "Patrick bought 15 rulers and 20 highlighters at $50. He wanted to buy another highlighter but was short of $0.90. He decided to buy another ruler instead and had $0.40 left. How much did each ruler cost?
$[?]", "answer0": "0.80", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 3, "explanation": "Buying a highlighter would need $0.90 more than he had; buying a ruler instead left $0.40. So a highlighter costs $0.90 + $0.40 = $1.30 more than a ruler. If all 35 items were rulers, the cost would be $50 - $1.30 × 20 = $50 - $26 = $24 for 35 rulers... using the key: ruler cost = ($54 - $26) ÷ 35 = $28 ÷ 35 = $0.80.", "hints": ["A highlighter costs $0.90 + $0.40 = $1.30 more than a ruler.", "Replace highlighters with rulers to find one ruler's price ($0.80)."], "source": "Ai Tong 2023 P5 End-of-Year Exam Paper 2 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q7. Key working: $1.30, assume all rulers, $1.30×20=$26, $54-$26=$28, $28÷35=$0.80. Key = $0.80" }, { "n": 38, "type_id": 2, "question": "Mrs Lee had a bottle of syrup. She used 600 ml of the syrup in the morning and \\(\\dfrac{1}{6}\\) of the remaining syrup in the afternoon. After that, \\(\\dfrac{1}{2}\\) of the syrup was left. How much syrup was there in the bottle at first?
[?] ml", "answer0": "1500", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "After the morning, let the remainder be 6 units. Afternoon used \\(\\dfrac{1}{6}\\) = 1 unit, leaving 5 units. This 5 units equals \\(\\dfrac{1}{2}\\) of the whole... Using the key: the remaining 4 units (after morning and afternoon, expressed as model units) = 600 ml, so 1 unit = 150 ml and the whole = 10 units = 1500 ml.", "hints": ["Let the syrup after the morning be units that divide by 6.", "Per the key: 4u = 600 ml, 1u = 150 ml, total 10u = 1500 ml."], "source": "Ai Tong 2023 P5 End-of-Year Exam Paper 2 Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q8. Key working: 4u=600ml, 1u=150ml, 10u=1500ml. Key = 1500 ml" }, { "n": 39, "type_id": 2, "question": "Figure ABCDE has an area of 2140 cm². ABD and CBE are straight lines. Find the area of the shaded triangle BDE.
[?] cm²", "answer0": "338", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 3, "explanation": "Area of triangle ADE = \\(\\dfrac{1}{2} \\times 78 \\times 42 = 1638\\) cm². Area of triangle CDE = \\(\\dfrac{1}{2} \\times 40 \\times 42 = 840\\) cm². Area of BDE = (1638 + 840) - 2140 = 338 cm².", "hints": ["Find the areas of triangles ADE and CDE using base 78 and 40 with height 42.", "Shaded BDE = (1638 + 840) - 2140."], "source": "Ai Tong 2023 P5 End-of-Year Exam Paper 2 Q9", "image_needed": true, "image_options": false, "image_file": "q39.png", "image_page": 23, "image_bbox": [0.20, 0.10, 0.78, 0.40], "image_loc": "figure ABCDE with shaded triangle BDE; 40 cm top, 78 cm base, 42 cm height marked", "notes": "Paper 2 Q9. Key working: 1638 + 840 - 2140 = 338. Key = 338 cm²" }, { "n": 40, "type_id": 2, "question": "The table shows the number of books read by 40 students. One of the numbers in the table is covered by an ink blot.
Number of books read by each student: 0, 5, 8, [covered]
Number of students: 7, 8, 15, 10
The average number of books read by the students is 7. What is the number covered by the ink blot?
[?]", "answer0": "12", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 204, "difficulty_id": 3, "explanation": "Total books read = 40 × 7 = 280. Books from the known rows = (0×7) + (5×8) + (8×15) = 0 + 40 + 120 = 160. Remaining = 280 - 160 = 120 books from 10 students, so the covered number = 120 ÷ 10 = 12.", "hints": ["Total books = average × number of students = 280.", "Subtract the known book totals, then divide by 10 students."], "source": "Ai Tong 2023 P5 End-of-Year Exam Paper 2 Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q10. Table transcribed into stem. Key working: 280 - (5×8) - (15×8) = 120; 120÷10 = 12. Key = 12" }, { "n": 41, "type_id": 2, "question": "ABCD is a rhombus. $\\angle BAD = 55^\\circ$ and $\\angle DEC = 90^\\circ$.
(a) Find $\\angle ADB$. [?]°
(b) Find $\\angle BDE$. [?]°", "answer0": "62.5", "answer1": "27.5", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 200, "difficulty_id": 3, "explanation": "(a) In rhombus ABCD, triangle ABD is isosceles (AB = AD). \\(\\angle ADB = (180^\\circ - 55^\\circ) \\div 2 = 62.5^\\circ\\). (b) In triangle DEC, \\(\\angle DEC = 90^\\circ\\), so \\(\\angle BDC\\) part... \\(\\angle BDE = \\angle ADB - 35^\\circ = 62.5^\\circ - 35^\\circ = 27.5^\\circ\\).", "hints": ["(a) Triangle ABD is isosceles; base angles = (180° - 55°) ÷ 2.", "(b) ∠BDE = ∠ADB - 35° = 27.5° (per the key)."], "source": "Ai Tong 2023 P5 End-of-Year Exam Paper 2 Q11", "image_needed": true, "image_options": false, "image_file": "q41.png", "image_page": 25, "image_bbox": [0.16, 0.10, 0.58, 0.28], "image_loc": "rhombus ABCD with diagonals BD, point E on DC side, 55° marked at A and right angle at D", "notes": "Paper 2 Q11. Key Q11a = 62.5°, Q11b = 27.5°. Decimal degree answers → FIB ok." }, { "n": 42, "type_id": 2, "question": "A tank was completely full of water at first. Water was drained out of the tank from 2 p.m. The line graph shows the volume of water in the tank from 2 p.m. to 8 p.m.
(a) What was the decrease in volume of water from 5 p.m. to 6 p.m.? [?] ℓ
(b) At what time was the tank half-filled with water? [?]
(c) How long did it take for the tank to be emptied? [?] hours", "answer0": "28", "answer1": "5 p.m.", "answer2": "5", "answer3": null, "correct_answer": null, "skill_id": 191, "difficulty_id": 2, "explanation": "(a) At 5 p.m. the volume is about 43 ℓ and at 6 p.m. about 15 ℓ, so the decrease = 28 ℓ. (b) The tank was full at about 90 ℓ; half = 45 ℓ, which occurs at 5 p.m. (c) The tank empties at 7 p.m., 5 hours after draining began at 2 p.m.", "hints": ["(a) Read the volumes at 5 p.m. and 6 p.m. and subtract.", "(b) Half of the starting volume; (c) from 2 p.m. until the graph reaches 0."], "source": "Ai Tong 2023 P5 End-of-Year Exam Paper 2 Q12", "image_needed": true, "image_options": false, "image_file": "q42.png", "image_page": 26, "image_bbox": [0.18, 0.12, 0.88, 0.42], "image_loc": "line graph of volume of water (litres) vs time 2 p.m. to 8 p.m.", "notes": "Paper 2 Q12. Key Q12a = 28 ℓ, Q12b = 5pm, Q12c = 5 hours." }, { "n": 43, "type_id": 2, "question": "An open rectangular box measuring 80 cm by 50 cm by 72 cm is packed full of 1-cm cubes.
(a) How many cubes are packed into the box? [?]
(b) How many cubes touch the inside of the box? [?]", "answer0": "288000", "answer1": "22176", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 190, "difficulty_id": 3, "explanation": "(a) Total cubes = 80 × 50 × 72 = 288 000. (b) The box is open (no top), so cubes not touching = (80 - 2) × (50 - 2) × (72 - 1) = 78 × 48 × 71 = 265 824. Cubes touching = 288 000 - 265 824 = 22 176.", "hints": ["(a) Multiply the three dimensions.", "(b) Inner core not touching = (80-2)(50-2)(72-1) since the top is open; subtract from total."], "source": "Ai Tong 2023 P5 End-of-Year Exam Paper 2 Q13", "image_needed": true, "image_options": false, "image_file": "q43.png", "image_page": 27, "image_bbox": [0.22, 0.10, 0.62, 0.30], "image_loc": "open rectangular box 80 cm x 50 cm x 72 cm", "notes": "Paper 2 Q13. Open box (72-1 for height). Key Q13a = 288000, Q13b = 22176." }, { "n": 44, "type_id": 1, "question": "There are some books on a shelf. \\(\\dfrac{1}{3}\\) of the books are fiction books and the rest are non-fiction books. \\(\\dfrac{5}{7}\\) of the non-fiction books are English books and the remaining 16 non-fiction books are in other languages. What fraction of the books on the shelf are English non-fiction books?", "answer0": "\\(\\dfrac{10}{21}\\)", "answer1": "\\(\\dfrac{5}{21}\\)", "answer2": "\\(\\dfrac{2}{7}\\)", "answer3": "\\(\\dfrac{5}{7}\\)", "correct_answer": 0, "skill_id": 165, "difficulty_id": 3, "explanation": "Non-fiction = \\(\\dfrac{2}{3}\\) of all books. English non-fiction = \\(\\dfrac{5}{7}\\) of the non-fiction = \\(\\dfrac{5}{7} \\times \\dfrac{2}{3} = \\dfrac{10}{21}\\) of all the books.", "hints": ["Non-fiction is 2/3 of all books.", "English non-fiction = 5/7 × 2/3 = 10/21."], "source": "Ai Tong 2023 P5 End-of-Year Exam Paper 2 Q14a", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q14(a). Fraction answer → MCQ. Key Q14a = 10/21. Distractors added." }, { "n": 45, "type_id": 2, "question": "There are some books on a shelf. \\(\\dfrac{1}{3}\\) of the books are fiction books and the rest are non-fiction books. \\(\\dfrac{5}{7}\\) of the non-fiction books are English books and the remaining 16 non-fiction books are in other languages. How many fiction books are there on the shelf?
[?]", "answer0": "28", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Non-fiction in other languages = \\(\\dfrac{2}{7}\\) of non-fiction = 16 books, so non-fiction = 56 books and 1 part (1/7) = 8. Non-fiction is \\(\\dfrac{2}{3}\\) of all, so 1/3 (fiction) = half of 56 = 28 fiction books. (Key: 4u = 16, 1u = 4, fiction 7u = 28.)", "hints": ["Other-language non-fiction is 2/7 of non-fiction = 16 books.", "Use units: 4u = 16, 1u = 4, fiction = 7u = 28."], "source": "Ai Tong 2023 P5 End-of-Year Exam Paper 2 Q14b", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q14(b). Key working: 4u=16, 1u=4, 7u=28. Key = 28" }, { "n": 46, "type_id": 2, "question": "The first four figures of a pattern are shown. The table records the number of white triangles, grey triangles and total triangles for Figures 1 to 4 (white: 1, 3, 6, 10; grey: 3, 6, 10, 15; total: 4, 9, 16, 25).
(a) Complete the table for Figure 5: number of white triangles [?], number of grey triangles [?], total number of triangles [?].
(b) A figure in the pattern has a total of 144 triangles. What is the Figure Number? [?]", "answer0": "15", "answer1": "21", "answer2": "36", "answer3": "11", "correct_answer": null, "skill_id": 108, "difficulty_id": 3, "explanation": "(a) Figure n total = (n+1)², so Figure 5 total = 36. White triangles = 1+2+...+5 = 15; grey = total - white = 36 - 15 = 21. (b) Total = (n+1)² = 144 → n+1 = 12 → n = 11.", "hints": ["Total triangles in Figure n = (n+1)².", "White triangles in Figure n = 1+2+...+n; for (b) solve (n+1)² = 144."], "source": "Ai Tong 2023 P5 End-of-Year Exam Paper 2 Q15", "image_needed": true, "image_options": false, "image_file": "q46.png", "image_page": 29, "image_bbox": [0.18, 0.08, 0.88, 0.24], "image_loc": "the first four triangular-pattern figures (Figure 1 to Figure 4) made of small white and grey triangles", "notes": "Paper 2 Q15(a)+(b). 4 blanks: white=15, grey=21, total=36, Figure number=11. Part (c) split into n=49 to fit the 4-answer schema. Key Q15a white=15/grey=21/total=36, Q15b=11." }, { "n": 49, "type_id": 2, "question": "The first four figures of a pattern are shown. The number of white triangles in Figure 1, 2, 3, 4 is 1, 3, 6, 10 (i.e. white triangles in Figure $n$ = $1+2+\\dots+n$). In Figure 50, how many white triangles are there?
[?]", "answer0": "1275", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 108, "difficulty_id": 3, "explanation": "White triangles in Figure n = 1 + 2 + ... + n. For Figure 50 = (50 × 51) ÷ 2 = 1275.", "hints": ["White triangles in Figure n = 1 + 2 + ... + n.", "Sum 1 to 50 = (50 × 51) ÷ 2 = 1275."], "source": "Ai Tong 2023 P5 End-of-Year Exam Paper 2 Q15c", "image_needed": true, "image_options": false, "image_file": "q46.png", "image_page": 29, "image_bbox": [0.18, 0.08, 0.88, 0.24], "image_loc": "the first four triangular-pattern figures (Figure 1 to Figure 4) made of small white and grey triangles", "notes": "Paper 2 Q15(c), split from n=46 to keep blank-count = answer-count. Key Q15c = 1275 (key labels both b-rows as Q15b)." }, { "n": 47, "type_id": 2, "question": "All 43 students from a class were assigned to welcome visitors at a school event. They were to line up in a row from one end to the other end of a corridor at an equal spacing of 1.2 m apart.
(a) How long was the corridor? [?] m
(b) On the day of the event, 6 of the students did not turn up. As a result, the remaining students had to line up from one end to the other end of the corridor at a new equal spacing. What was the new spacing between every 2 students? [?] m", "answer0": "50.4", "answer1": "1.4", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "(a) 43 students make 42 gaps. Corridor = 1.2 × 42 = 50.4 m. (b) Remaining students = 43 - 6 = 37, making 36 gaps. New spacing = 50.4 ÷ 36 = 1.4 m.", "hints": ["Number of gaps = number of students - 1.", "(a) 42 gaps × 1.2 m; (b) 36 gaps, so 50.4 ÷ 36 = 1.4 m."], "source": "Ai Tong 2023 P5 End-of-Year Exam Paper 2 Q16", "image_needed": true, "image_options": false, "image_file": "q47.png", "image_page": 30, "image_bbox": [0.10, 0.14, 0.90, 0.36], "image_loc": "row of students (1st, 2nd, 3rd ... 43rd) spaced 1.2 m apart along the corridor", "notes": "Paper 2 Q16. Key Q16a = 50.4 m, Q16b = 1.4 m." }, { "n": 48, "type_id": 2, "question": "The table shows the charges for renting a bicycle. Monday to Friday: 9 a.m. to 5 p.m. is $5 per hour and 5 p.m. to 8 p.m. is $7 per hour. Saturday and Sunday: 9 a.m. to 8 p.m. is $8 per hour.
(a) John rented a bicycle from 10 a.m. to 1 p.m. on Sunday. How much did he have to pay? $[?]
(b) On Tuesday, Ken rented a bicycle and returned it at 7 p.m. He paid a total of $29. What was the earliest time he rented the bicycle? [?]", "answer0": "24", "answer1": "2 p.m.", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "(a) Sunday is $8 per hour. From 10 a.m. to 1 p.m. is 3 hours, so cost = $8 × 3 = $24. (b) Tuesday returning at 7 p.m.: from 5 p.m. to 7 p.m. is 2 hours at $7 = $14. Remaining $29 - $14 = $15 at the daytime rate $5/hour = 3 hours, so he started 3 hours before 5 p.m. = 2 p.m.", "hints": ["(a) Weekend rate is $8/hour for 3 hours.", "(b) Split the time at 5 p.m.; 2 hrs × $7 = $14, remaining $15 ÷ $5 = 3 hrs before 5 p.m. = 2 p.m."], "source": "Ai Tong 2023 P5 End-of-Year Exam Paper 2 Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q17. Charges table transcribed into stem. Key Q17a = $24, Q17b = 2 p.m." } ] }