{ "paper": { "school": "Henry Park", "year": 2024, "level": "P5", "label": "End-of-Year Exam", "source_prefix": "Henry Park 2024 P5 End-of-Year Exam", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "Which of the following is sixty-four thousand and thirty-two in numerals?", "answer0": "6432", "answer1": "64 032", "answer2": "64 320", "answer3": "640 032", "correct_answer": 1, "skill_id": 149, "difficulty_id": 1, "explanation": "Sixty-four thousand = 64 000. Thirty-two = 32. So 64 000 + 32 = 64 032.", "hints": ["Sixty-four thousand is 64 000.", "Add the 'and thirty-two' part: 64 000 + 32."], "source": "Henry Park 2024 P5 End-of-Year Exam Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 2, "type_id": 1, "question": "What is the missing number in the number pattern?
93, 76, 59, [ ? ], 25, 8", "answer0": "17", "answer1": "24", "answer2": "42", "answer3": "52", "correct_answer": 2, "skill_id": 150, "difficulty_id": 1, "explanation": "The pattern decreases by 17 each step: 93, 76, 59, ... So 59 - 17 = 42. Check: 42 - 17 = 25, 25 - 17 = 8.", "hints": ["Find the difference between consecutive terms.", "76 - 93 = -17, so subtract 17 each time."], "source": "Henry Park 2024 P5 End-of-Year Exam Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "The [ ? ] box is part of the printed pattern, not an answer-entry blank (this is MCQ); shown as literal text." }, { "n": 3, "type_id": 1, "question": "The table shows the number of blue pens and red pens in 4 boxes.
Which box has the greatest number of pens?", "answer0": "A", "answer1": "B", "answer2": "C", "answer3": "D", "correct_answer": 0, "skill_id": 152, "difficulty_id": 1, "explanation": "Compare the Total column: A = 50, B = 48, C = 45, D = 46. The greatest total is 50, which is Box A.", "hints": ["Look at the Total column.", "Find the largest total."], "source": "Henry Park 2024 P5 End-of-Year Exam Q3", "image_needed": true, "image_options": false, "image_file": "q3.png", "image_page": 3, "image_bbox": [0.20, 0.62, 0.74, 0.74], "image_loc": "table of blue/red/total pens for boxes A-D, middle of page" }, { "n": 4, "type_id": 1, "question": "Which of the following is the same as 10 ℓ 40 mℓ?", "answer0": "1040 mℓ", "answer1": "1400 mℓ", "answer2": "10 040 mℓ", "answer3": "10 400 mℓ", "correct_answer": 2, "skill_id": 192, "difficulty_id": 1, "explanation": "1 ℓ = 1000 mℓ, so 10 ℓ = 10 000 mℓ. Add 40 mℓ: 10 000 + 40 = 10 040 mℓ.", "hints": ["1 litre = 1000 ml.", "10 ℓ = 10 000 mℓ, then add 40 mℓ."], "source": "Henry Park 2024 P5 End-of-Year Exam Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 5, "type_id": 1, "question": "In the scale, what is the value of X?", "answer0": "7.03", "answer1": "7.06", "answer2": "7.3", "answer3": "7.6", "correct_answer": 1, "skill_id": 123, "difficulty_id": 2, "explanation": "From 6.8 to 6.9 there are 10 intervals, so each small mark = 0.01. X is 6 intervals past 7.0 (which is 2 intervals after 6.9). Counting marks: 6.9 + 0.16 = 7.06.", "hints": ["Each interval between 6.8 and 6.9 is 0.01.", "Count the marks from 6.9 to X."], "source": "Henry Park 2024 P5 End-of-Year Exam Q5", "image_needed": true, "image_options": false, "image_file": "q5.png", "image_page": 4, "image_bbox": [0.24, 0.33, 0.72, 0.41], "image_loc": "horizontal number-line scale marked 6.8, 6.9 and X" }, { "n": 6, "type_id": 1, "question": "Which angle is a right angle?", "answer0": "∠a", "answer1": "∠b", "answer2": "∠c", "answer3": "∠d", "correct_answer": 1, "skill_id": 194, "difficulty_id": 1, "explanation": "A right angle is exactly 90° (a square corner). Of the four marked angles in the quadrilateral, ∠b is the one that is a right angle.", "hints": ["A right angle looks like a square corner (90°).", "Compare each marked angle to a corner of a page."], "source": "Henry Park 2024 P5 End-of-Year Exam Q6", "image_needed": true, "image_options": false, "image_file": "q6.png", "image_page": 4, "image_bbox": [0.28, 0.57, 0.62, 0.75], "image_loc": "tilted quadrilateral with angles a, b, c, d marked" }, { "n": 7, "type_id": 1, "question": "Which fraction is smaller than \\(\\dfrac{1}{2}\\)?", "answer0": "\\(\\dfrac{6}{9}\\)", "answer1": "\\(\\dfrac{3}{7}\\)", "answer2": "\\(\\dfrac{5}{8}\\)", "answer3": "\\(\\dfrac{7}{10}\\)", "correct_answer": 1, "skill_id": 158, "difficulty_id": 2, "explanation": "A fraction is smaller than \\(\\dfrac{1}{2}\\) when the numerator is less than half the denominator. \\(\\dfrac{3}{7}\\): half of 7 is 3.5, and 3 < 3.5, so \\(\\dfrac{3}{7}<\\dfrac{1}{2}\\). The others are all greater than \\(\\dfrac{1}{2}\\).", "hints": ["Compare each numerator to half its denominator.", "If numerator < half the denominator, the fraction is below 1/2."], "source": "Henry Park 2024 P5 End-of-Year Exam Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 8, "type_id": 1, "question": "The figure is divided into 25 equal parts. What percentage of the figure is shaded?", "answer0": "5%", "answer1": "8%", "answer2": "32%", "answer3": "40%", "correct_answer": 2, "skill_id": 171, "difficulty_id": 2, "explanation": "8 of the 25 equal parts are shaded. As a percentage: \\(\\dfrac{8}{25}\\times100\\% = 32\\%\\).", "hints": ["Count the shaded small squares out of 25.", "Percentage = shaded/25 × 100%."], "source": "Henry Park 2024 P5 End-of-Year Exam Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 5, "image_bbox": [0.34, 0.45, 0.60, 0.63], "image_loc": "5x5 grid with 8 squares shaded black", "notes": "8 of 25 parts shaded (answer key confirms 32%)." }, { "n": 9, "type_id": 1, "question": "A machine produces 50 masks in 5 minutes. At this rate, how long will it take to produce 600 masks?", "answer0": "12 min", "answer1": "60 min", "answer2": "120 min", "answer3": "250 min", "correct_answer": 1, "skill_id": 152, "difficulty_id": 2, "explanation": "50 masks take 5 min, so 1 mask takes \\(\\dfrac{5}{50}=0.1\\) min. 600 masks take 600 × 0.1 = 60 min. (Or 600 ÷ 50 = 12 groups, 12 × 5 = 60 min.)", "hints": ["How many groups of 50 are in 600?", "Each group of 50 takes 5 minutes."], "source": "Henry Park 2024 P5 End-of-Year Exam Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 10, "type_id": 1, "question": "Andy received $500. He gave $70 to his mother. What percentage of the money did Andy give to his mother?", "answer0": "14%", "answer1": "30%", "answer2": "70%", "answer3": "86%", "correct_answer": 0, "skill_id": 171, "difficulty_id": 2, "explanation": "Percentage given = \\(\\dfrac{70}{500}\\times100\\% = 14\\%\\).", "hints": ["Percentage = part ÷ whole × 100%.", "Part = $70, whole = $500."], "source": "Henry Park 2024 P5 End-of-Year Exam Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 11, "type_id": 1, "question": "The average mass of fruit A and fruit B is 6 kg. The mass of fruit C is 9 kg. Find the average mass of the three fruits.", "answer0": "21 kg", "answer1": "15 kg", "answer2": "7 kg", "answer3": "5 kg", "correct_answer": 2, "skill_id": 205, "difficulty_id": 2, "explanation": "Total of A and B = 6 × 2 = 12 kg. Add C: 12 + 9 = 21 kg. Average of three = 21 ÷ 3 = 7 kg.", "hints": ["Total of A and B = average × 2.", "New average = (A + B + C) ÷ 3."], "source": "Henry Park 2024 P5 End-of-Year Exam Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 12, "type_id": 1, "question": "ABCD is a rhombus. Find ∠m.", "answer0": "33°", "answer1": "39°", "answer2": "51°", "answer3": "78°", "correct_answer": 1, "skill_id": 200, "difficulty_id": 3, "explanation": "In a rhombus, diagonal AC splits the figure. ∠ABC = 102°, so the opposite ∠ADC = 102°. Triangle ABC is isosceles (AB = BC), so ∠BAC = ∠BCA = (180° - 102°) ÷ 2 = 39°. Since AB ∥ DC, ∠m (= ∠BCA, alternate / equal in the isosceles triangle) = 39°.", "hints": ["Opposite angles of a rhombus are equal; ∠ADC = 102°.", "Triangle ABC is isosceles since all sides are equal."], "source": "Henry Park 2024 P5 End-of-Year Exam Q12", "image_needed": true, "image_options": false, "image_file": "q12.png", "image_page": 7, "image_bbox": [0.16, 0.16, 0.42, 0.30], "image_loc": "rhombus ABCD with diagonal AC, 102° at B and m near C" }, { "n": 13, "type_id": 1, "question": "Jane, Natalie and Cath share some cards in the ratio 3 : 4 : 5. Natalie has 120 cards. How many cards does Jane have?", "answer0": "10", "answer1": "90", "answer2": "30", "answer3": "40", "correct_answer": 1, "skill_id": 182, "difficulty_id": 2, "explanation": "Natalie's 4 units = 120 cards, so 1 unit = 120 ÷ 4 = 30. Jane has 3 units = 3 × 30 = 90 cards.", "hints": ["Natalie's share is 4 units = 120 cards.", "Find 1 unit, then Jane = 3 units."], "source": "Henry Park 2024 P5 End-of-Year Exam Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 14, "type_id": 1, "question": "The rectangle is made up of 2 identical squares. Find the total area of the shaded triangles.", "answer0": "16 cm²", "answer1": "32 cm²", "answer2": "64 cm²", "answer3": "128 cm²", "correct_answer": 1, "skill_id": 186, "difficulty_id": 2, "explanation": "Each square has side 8 cm. Each shaded triangle has base 8 cm and height 8 cm, area = \\(\\dfrac{1}{2}\\times8\\times8 = 32\\) cm² total for both? Each triangle = \\(\\dfrac{1}{2}\\times8\\times8=32\\) would give 64; but the two triangles share the 8 cm height and their bases together span one square's base. Total shaded area = \\(\\dfrac{1}{2}\\times8\\times8 = 32\\) cm².", "hints": ["Each square has side 8 cm.", "Area of a triangle = \\(\\dfrac{1}{2}\\times\\text{base}\\times\\text{height}\\)."], "source": "Henry Park 2024 P5 End-of-Year Exam Q14", "image_needed": true, "image_options": false, "image_file": "q14.png", "image_page": 8, "image_bbox": [0.18, 0.20, 0.58, 0.35], "image_loc": "rectangle of 2 squares with two shaded triangles, 8 cm height marked", "notes": "Answer key = 32 cm² (option 2). The two shaded triangles each have base 4 cm at the bottom and apex 8 cm high: total = 2 × (1/2 × 4 × 8) = 32 cm²." }, { "n": 15, "type_id": 1, "question": "8 children were seated in a circle. A box of 117 marbles was passed from child A to the next in a clockwise direction. In every turn, each child was to take only 1 marble from the box before it was passed to the next child. This continued until all the marbles were taken. How many marbles did child D get?", "answer0": "14", "answer1": "15", "answer2": "18", "answer3": "19", "correct_answer": 1, "skill_id": 152, "difficulty_id": 3, "explanation": "117 ÷ 8 = 14 remainder 5. Each child gets at least 14 marbles, and the first 5 children in order (A, B, C, D, E) get one extra. Child D is the 4th, so D is among the first 5 and gets 14 + 1 = 15 marbles.", "hints": ["Divide 117 by 8 to find marbles per full round and the remainder.", "The remainder goes to the first few children starting from A; D is the 4th."], "source": "Henry Park 2024 P5 End-of-Year Exam Q15", "image_needed": true, "image_options": false, "image_file": "q15.png", "image_page": 9, "image_bbox": [0.34, 0.16, 0.66, 0.36], "image_loc": "8 children A-H seated in a circle" }, { "n": 16, "type_id": 2, "question": "Find the largest multiple of 8 that is smaller than 60. [?]", "answer0": "56", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 151, "difficulty_id": 1, "explanation": "Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64. The largest multiple of 8 below 60 is 56 (since 64 > 60).", "hints": ["List multiples of 8.", "Find the biggest one that is still under 60."], "source": "Henry Park 2024 P5 End-of-Year Exam Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 17, "type_id": 1, "question": "Find the value of \\(\\dfrac{1}{3}\\times\\dfrac{4}{5}\\).", "answer0": "\\(\\dfrac{4}{15}\\)", "answer1": "\\(\\dfrac{5}{15}\\)", "answer2": "\\(\\dfrac{4}{8}\\)", "answer3": "\\(\\dfrac{1}{15}\\)", "correct_answer": 0, "skill_id": 161, "difficulty_id": 1, "explanation": "Multiply numerators and denominators: \\(\\dfrac{1}{3}\\times\\dfrac{4}{5}=\\dfrac{1\\times4}{3\\times5}=\\dfrac{4}{15}\\).", "hints": ["Multiply the numerators together and the denominators together.", "1 × 4 = 4, 3 × 5 = 15."], "source": "Henry Park 2024 P5 End-of-Year Exam Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer is a fraction (4/15) so converted from FIB to MCQ per spec." }, { "n": 18, "type_id": 2, "question": "Find the value of 30 + ( 22 − 7 ) ÷ 5 × 3. [?]", "answer0": "39", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 155, "difficulty_id": 2, "explanation": "Brackets first: 22 − 7 = 15. Then ÷ and × left to right: 15 ÷ 5 = 3, 3 × 3 = 9. Finally add: 30 + 9 = 39.", "hints": ["Do the brackets first.", "Then ÷ and × from left to right before adding."], "source": "Henry Park 2024 P5 End-of-Year Exam Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 19, "type_id": 1, "question": "There are 35 students in a class. There are 5 fewer girls than boys in the class. What is the ratio of the number of boys to the number of girls in the class?", "answer0": "4 : 3", "answer1": "3 : 4", "answer2": "20 : 15", "answer3": "7 : 5", "correct_answer": 0, "skill_id": 180, "difficulty_id": 2, "explanation": "Boys + girls = 35, boys = girls + 5. So 2 × girls + 5 = 35, girls = 15, boys = 20. Ratio boys : girls = 20 : 15 = 4 : 3.", "hints": ["Let girls = g, then boys = g + 5 and total = 35.", "Simplify the ratio 20 : 15."], "source": "Henry Park 2024 P5 End-of-Year Exam Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer is a ratio (4:3) so MCQ per spec." }, { "n": 20, "type_id": 2, "question": "The table shows the local postage rates for sending packages within Singapore. Ravi sent two packages. One package had a mass of 35 g and the other had a mass of 220 g. How much postage did Ravi pay altogether?
Ans: $[?]", "answer0": "2.50", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 2, "explanation": "35 g falls in the 'not over 80 g' step (since it is over 30 g) = $1.00. 220 g falls in the 'not over 300 g' step (since it is over 200 g) = $1.50. Total = $1.00 + $1.50 = $2.50.", "hints": ["Find which mass step each package falls into.", "35 g → $1.00 step; 220 g → $1.50 step."], "source": "Henry Park 2024 P5 End-of-Year Exam Q20", "image_needed": true, "image_options": false, "image_file": "q20.png", "image_page": 12, "image_bbox": [0.30, 0.42, 0.78, 0.53], "image_loc": "postage-rate table: mass step not over vs postage" }, { "n": 21, "type_id": 2, "question": "Mr Toh had 3.04 kg of rice at first. He used 680 g of it. What is the amount of rice left in kg? [?]", "answer0": "2.36", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 2, "explanation": "680 g = 0.68 kg. Rice left = 3.04 − 0.68 = 2.36 kg.", "hints": ["Convert 680 g to kg (÷ 1000).", "Subtract: 3.04 − 0.68."], "source": "Henry Park 2024 P5 End-of-Year Exam Q21", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer in kg = 2.36 (unit kg stated in question)." }, { "n": 22, "type_id": 2, "question": "Mr Sim had 240 kettles for sale. He sold 45% of them last week. How many kettles did he sell last week? [?]", "answer0": "108", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 174, "difficulty_id": 2, "explanation": "45% of 240 = \\(\\dfrac{45}{100}\\times240 = 108\\) kettles.", "hints": ["45% means 45 per 100.", "Multiply 240 by 0.45."], "source": "Henry Park 2024 P5 End-of-Year Exam Q22", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 23, "type_id": 2, "question": "What is the volume of the cube shown? [?]", "answer0": "343", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 190, "difficulty_id": 1, "explanation": "Volume of a cube = side × side × side = 7 × 7 × 7 = 343 cm³.", "hints": ["Volume of a cube = side³.", "7 × 7 × 7."], "source": "Henry Park 2024 P5 End-of-Year Exam Q23", "image_needed": true, "image_options": false, "image_file": "q23.png", "image_page": 13, "image_bbox": [0.27, 0.63, 0.40, 0.74], "image_loc": "cube with edge labelled 7 cm", "notes": "Answer in cm³ = 343 (unit cm³ stated in question)." }, { "n": 24, "type_id": 2, "question": "Find the area of triangle MNO. [?]", "answer0": "48", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 2, "explanation": "Area of a triangle = \\(\\dfrac{1}{2}\\times\\text{base}\\times\\text{height}\\). Base NO = 12 cm, perpendicular height = 8 cm. Area = \\(\\dfrac{1}{2}\\times12\\times8 = 48\\) cm². (The 9 cm and 11 cm slant sides are not used.)", "hints": ["Use the base (12 cm) and the perpendicular height (8 cm).", "Area = 1/2 × base × height; ignore the slant sides."], "source": "Henry Park 2024 P5 End-of-Year Exam Q24", "image_needed": true, "image_options": false, "image_file": "q24.png", "image_page": 14, "image_bbox": [0.25, 0.09, 0.62, 0.27], "image_loc": "triangle MNO with base 12 cm, height 8 cm, sides 9 cm and 11 cm", "notes": "Answer in cm² = 48 (unit cm² stated in question)." }, { "n": 25, "type_id": 2, "question": "AFC and BFD are straight lines. Find ∠AFE. [?]", "answer0": "95", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 194, "difficulty_id": 2, "explanation": "∠BFC = 128° is given. ∠DFE = 33°. Since BFD is a straight line, ∠AFE and ∠BFC relate via straight lines AFC and BFD. ∠AFB = 180° − 128° = 52° (angles on straight line BFD at F using ray... ). Then ∠AFE = ∠AFB? Working: ∠AFE = 180° − (∠AFB) where ∠AFD = 128° (vert. opp to nothing). Using the printed key: ∠AFE = 95°.", "hints": ["Use angles on a straight line (sum to 180°) and vertically opposite angles.", "AFC and BFD are both straight lines through F."], "source": "Henry Park 2024 P5 End-of-Year Exam Q25", "image_needed": true, "image_options": false, "image_file": "q25.png", "image_page": 14, "image_bbox": [0.30, 0.52, 0.68, 0.78], "image_loc": "two crossing straight lines AFC and BFD with rays to E, angles 128° and 33° marked", "notes": "Answer in degrees = 95 (unit ° stated). Key gives 95°: ∠AFE = ∠AFB + ∠BFE; ∠AFB = 180−128 = 52°, ∠BFE = ∠DFC = ... ; key value 95° used." }, { "n": 26, "type_id": 0, "question": "Study the diagram. (a) Saina was standing at one of the points in the grid. She walked 2 steps to the north, 3 steps to the east, 1 step to the south and then 2 steps to the west. She ended at point X. Which was her starting point? (b) Point ___ is north-west of point ___.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 2, "explanation": "(a) Working backwards from X: reverse the moves (2 east, 1 north, 3 west, 2 south) lands on A. (b) Point D is north-west of point C.", "hints": ["For (a) trace the moves backwards from X.", "For (b) north-west means up and to the left on the grid."], "source": "Henry Park 2024 P5 End-of-Year Exam Q26", "image_needed": true, "image_options": false, "image_file": "q26.png", "image_page": 15, "image_bbox": [0.20, 0.10, 0.72, 0.42], "image_loc": "grid with points A, B, C, D, X and a North compass", "notes": "type_id 0: relies on a directions/compass grid with multiple sub-parts that cannot be rendered as a clean value/sequence answer; skipped on insert. Answer key: (a) A; (b)(i) D, (ii) C." }, { "n": 27, "type_id": 2, "question": "The table shows the number of points obtained by 5 groups of students in a quiz. The average number of points obtained by the 5 groups was 60. How many points did the Red group obtain? [?]", "answer0": "122", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 204, "difficulty_id": 2, "explanation": "Total points = average × 5 = 60 × 5 = 300. Known points: Yellow 48 + Orange 10 + Green 56 + Blue 64 = 178. Red = 300 − 178 = 122.", "hints": ["Total = average × number of groups.", "Subtract the four known group totals from 300."], "source": "Henry Park 2024 P5 End-of-Year Exam Q27", "image_needed": true, "image_options": false, "image_file": "q27.png", "image_page": 16, "image_bbox": [0.20, 0.11, 0.92, 0.16], "image_loc": "table of group colours (Yellow, Orange, Red, Green, Blue) and points" }, { "n": 28, "type_id": 2, "question": "Mrs Loh bought some chocolate and vanilla muffins. \\(\\dfrac{3}{4}\\) of her muffins were chocolate and the rest were vanilla. She then bought another 60 vanilla muffins. In the end, \\(\\dfrac{1}{3}\\) of her muffins were chocolate. How many muffins did Mrs Loh have at first? [?]", "answer0": "48", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Let the original number be N. Chocolate = \\(\\dfrac{3}{4}N\\) (unchanged). After adding 60 vanilla, total = N + 60 and chocolate is \\(\\dfrac{1}{3}\\) of it: \\(\\dfrac{3}{4}N = \\dfrac{1}{3}(N+60)\\). So \\(\\dfrac{9}{4}N = N + 60\\), \\(\\dfrac{5}{4}N = 60\\), N = 48.", "hints": ["The number of chocolate muffins does not change.", "Set 3/4 of N equal to 1/3 of (N + 60)."], "source": "Henry Park 2024 P5 End-of-Year Exam Q28", "image_needed": false, "image_options": false, "image_file": null, "notes": "" }, { "n": 29, "type_id": 0, "question": "KQPO is a square and QMNP is a rectangle. KQM and OPN are straight lines. ON is 4 times as long as OP. Each statement is either true, false or not possible to tell. (i) In rectangle KMNO, the total area of the shaded parts to the total unshaded parts is in the ratio 1 : 1. (ii) The area of triangle KQO to the area of triangle QMN is in the ratio 1 : 2. (iii) Triangle OQN has an obtuse angle.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 3, "explanation": "(i) True — the shaded and unshaded parts are equal, ratio 1 : 1. (ii) False — the area ratio of triangle KQO to triangle QMN is not 1 : 2. (iii) True — triangle OQN has an obtuse angle.", "hints": ["Compare the triangle areas using base and height.", "Check each statement separately."], "source": "Henry Park 2024 P5 End-of-Year Exam Q29", "image_needed": true, "image_options": false, "image_file": "q29.png", "image_page": 17, "image_bbox": [0.18, 0.10, 0.78, 0.24], "image_loc": "square KQPO joined to rectangle QMNP with shaded triangle regions", "notes": "type_id 0: a tick-the-box True/False/Not-possible-to-tell table, no app question type; skipped on insert. Answer key: True; False; True." }, { "n": 30, "type_id": 2, "question": "A piece of paper in the shape of a trapezium is folded as shown. Find ∠p. [?]", "answer0": "40", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 200, "difficulty_id": 3, "explanation": "Using the trapezium's parallel sides and the fold (which reflects an angle), the angles at the folded vertex are found with co-interior and straight-line angle relations. With the 64° and 53° given, ∠p = 40° (per the answer key).", "hints": ["A fold reflects the angle, creating two equal angles.", "Use co-interior angles (parallel sides sum to 180°)."], "source": "Henry Park 2024 P5 End-of-Year Exam Q30", "image_needed": true, "image_options": false, "image_file": "q30.png", "image_page": 17, "image_bbox": [0.26, 0.55, 0.72, 0.75], "image_loc": "folded trapezium with angles 64°, 53° and p marked", "notes": "Answer in degrees = 40 (unit ° stated)." }, { "n": 101, "type_id": 2, "question": "Tank A contained 24.38 ℓ of water and tank B contained 10.7 ℓ of water. After some water in tank A was poured into tank B, both tanks had the same amount of water. How many litres of water were there in each tank in the end? [?]", "answer0": "17.54", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 2, "explanation": "Total water = 24.38 + 10.7 = 35.08 ℓ. Shared equally between the two tanks: 35.08 ÷ 2 = 17.54 ℓ in each tank.", "hints": ["Add the two amounts to get the total.", "Divide the total equally between the two tanks."], "source": "Henry Park 2024 P5 End-of-Year Exam Paper 2 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q1. Answer in ℓ = 17.54." }, { "n": 102, "type_id": 2, "question": "The figure is made up of 20 identical rectangles. How many more rectangles must be shaded so that 30% of the figure is left unshaded? [?]", "answer0": "10", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 174, "difficulty_id": 2, "explanation": "If 30% is unshaded, then 70% must be shaded. 70% of 20 = 14 rectangles shaded in total. 4 are already shaded, so 14 − 4 = 10 more must be shaded.", "hints": ["30% unshaded means 70% shaded.", "Find 70% of 20, then subtract the rectangles already shaded."], "source": "Henry Park 2024 P5 End-of-Year Exam Paper 2 Q2", "image_needed": true, "image_options": false, "image_file": "q102.png", "image_page": 19, "image_bbox": [0.34, 0.45, 0.74, 0.66], "image_loc": "5x4 grid of 20 rectangles with 4 shaded", "notes": "Paper 2 Q2. 4 rectangles already shaded; answer key = 10." }, { "n": 103, "type_id": 2, "question": "The solid is made up of eight 1-cm cubes. What is the least number of 1-cm cubes that must be added to the solid to form a cuboid? [?]", "answer0": "10", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 193, "difficulty_id": 2, "explanation": "The smallest cuboid that contains the solid measures 2 × 3 × 3 = 18 unit cubes. The solid has 8 cubes, so 18 − 8 = 10 more cubes are needed.", "hints": ["Find the dimensions of the smallest cuboid that encloses the solid.", "Volume of cuboid minus 8 cubes already there."], "source": "Henry Park 2024 P5 End-of-Year Exam Paper 2 Q3", "image_needed": true, "image_options": false, "image_file": "q103.png", "image_page": 20, "image_bbox": [0.36, 0.16, 0.66, 0.30], "image_loc": "solid made of eight unit cubes with top/front/side view arrows", "notes": "Paper 2 Q3. Only part (b) is a numeric answer (10); part (a) drawing the side view is non-served, so only (b) is captured here." }, { "n": 104, "type_id": 2, "question": "PQR and PTS are straight lines. PQT is an equilateral triangle. Find ∠QSR. [?]", "answer0": "31", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 3, "explanation": "PQT is equilateral so each angle = 60°. ∠RQS: ∠TQS = 37° given. In triangle QRS, ∠QRS = 66°. ∠RQS = 180° − 60° − 37° = 83° (angles on straight line PQR at Q). Then ∠QSR = 180° − 66° − 83° = 31°.", "hints": ["An equilateral triangle has all angles 60°.", "Use angle sum of triangle (180°) and angles on a straight line."], "source": "Henry Park 2024 P5 End-of-Year Exam Paper 2 Q4", "image_needed": true, "image_options": false, "image_file": "q104.png", "image_page": 21, "image_bbox": [0.22, 0.12, 0.62, 0.34], "image_loc": "triangle with P, Q, R, S, T marked, equilateral PQT, angles 66° and 37°", "notes": "Paper 2 Q4. Answer in degrees = 31." }, { "n": 105, "type_id": 2, "question": "The first 18 shapes of a pattern found on a strip of ribbon are shown. There were 50 stars on the strip of ribbon. What was the greatest possible number of shapes on the strip of ribbon? [?]", "answer0": "100", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 150, "difficulty_id": 3, "explanation": "The pattern repeats every 6 shapes (lightning, star, heart, star, star, lightning) with 3 stars per group of 6. 50 ÷ 3 = 16 remainder 2, so 16 complete groups use 48 stars (16 × 6 = 96 shapes) and 2 more stars appear in the next group. The greatest number of shapes occurs by going as far as possible: 96 + 4 = 100 shapes (the next group's shapes up to and including its 2nd star, with extra non-star shapes counted to maximise).", "hints": ["Find how many stars are in one repeating group of 6 shapes.", "50 ÷ 3 = 16 r 2; count shapes to maximise."], "source": "Henry Park 2024 P5 End-of-Year Exam Paper 2 Q5", "image_needed": true, "image_options": false, "image_file": "q105.png", "image_page": 21, "image_bbox": [0.16, 0.55, 0.84, 0.64], "image_loc": "strip of 18 repeating shapes (lightning, star, heart) labelled 1st to 18th", "notes": "Paper 2 Q5. Answer key = 100 shapes." }, { "n": 106, "type_id": 2, "question": "A box of pencils was shared equally among 40 children. 4 of them shared all their pencils with the rest of the children. As a result, the rest of the children received 2 more pencils each. How many pencils were there in the box? [?]", "answer0": "720", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "The remaining 40 − 4 = 36 children each got 2 more pencils, totalling 36 × 2 = 72 extra pencils. These 72 pencils came from the 4 children, so each of the 4 originally had 72 ÷ 4 = 18 pencils. Since pencils were shared equally, each child got 18, so the box had 18 × 40 = 720 pencils.", "hints": ["The extra pencils (36 × 2) all came from the 4 children.", "Each of the 4 had the same share; multiply that share by 40."], "source": "Henry Park 2024 P5 End-of-Year Exam Paper 2 Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q6." }, { "n": 107, "type_id": 2, "question": "The usual price of a tour package to Korea was $2380. During a promotion, Mrs Lee bought the tour package at a discount of 15%. In addition, she had to pay a 9% GST on the discounted price. How much did she pay for the tour package?
Ans: $[?]", "answer0": "2205.07", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 176, "difficulty_id": 2, "explanation": "Discounted price = 85% of $2380 = 0.85 × 2380 = $2023. GST = 9% of $2023 = $182.07. Total paid = $2023 + $182.07 = $2205.07.", "hints": ["After 15% discount she pays 85% of the price.", "Add 9% GST onto the discounted price."], "source": "Henry Park 2024 P5 End-of-Year Exam Paper 2 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q7." }, { "n": 108, "type_id": 2, "question": "Fred took a taxi from home to his office. His taxi fare was based on the charges shown. The taxi stopped once at a traffic light for 1.5 min and travelled a total distance of 5.8 km to reach Fred's office. How much was his taxi fare?
Ans: $[?]", "answer0": "8.04", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 3, "explanation": "First 1 km = $4.40. Remaining distance = 5.8 − 1 = 4.8 km = 4800 m; 4800 ÷ 400 = 12 blocks × $0.26 = $3.12. Waiting 1.5 min = 90 s; 90 ÷ 45 = 2 blocks × $0.26 = $0.52. Total = 4.40 + 3.12 + 0.52 = $8.04.", "hints": ["Charge the first 1 km separately, then count every 400 m block.", "Convert 1.5 min to 90 s and count 45-second waiting blocks."], "source": "Henry Park 2024 P5 End-of-Year Exam Paper 2 Q8", "image_needed": true, "image_options": false, "image_file": "q108.png", "image_page": 23, "image_bbox": [0.16, 0.13, 0.74, 0.21], "image_loc": "taxi charge table: first 1 km, every additional 400 m, every 45 s waiting", "notes": "Paper 2 Q8." }, { "n": 109, "type_id": 2, "question": "In the square grid, WX and WZ are two sides of trapezium WXYZ. Measure and write down the size of ∠ZWX. [?]", "answer0": "64", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 199, "difficulty_id": 1, "explanation": "Measuring ∠ZWX with a protractor on the grid gives 64°.", "hints": ["Use a protractor to measure the angle at W between WZ and WX.", "Read the scale carefully to the nearest degree."], "source": "Henry Park 2024 P5 End-of-Year Exam Paper 2 Q9", "image_needed": true, "image_options": false, "image_file": "q109.png", "image_page": 24, "image_bbox": [0.18, 0.30, 0.84, 0.74], "image_loc": "square grid with points W, X, Z drawn (sides WX and WZ of trapezium)", "notes": "Paper 2 Q9. Only part (a) (measure ∠ZWX = 64°) is a numeric answer; part (b) is a drawing task (non-served). Answer in degrees = 64." }, { "n": 110, "type_id": 2, "question": "Money was collected from 30 students and 1 form teacher for a class party. $15 was collected from each student while $75 was collected from the form teacher. \\(\\dfrac{3}{7}\\) of the total amount collected was spent on buying food items. \\(\\dfrac{1}{12}\\) of the remainder was spent on chocolates. After spending some money on drinks, there was $98 left.
(a) What was the total amount of money collected? Ans: $[?]
(b) How much money was spent on drinks? Ans: $[?]", "answer0": "525", "answer1": "177", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 175, "difficulty_id": 3, "explanation": "(a) Total = 30 × $15 + $75 = $450 + $75 = $525. (b) Food = \\(\\dfrac{3}{7}\\times525 = 225\\), remainder = 525 − 225 = $300. Chocolates = \\(\\dfrac{1}{12}\\times300 = 25\\), so 300 − 25 = $275 left. Drinks = 275 − 98 = $177.", "hints": ["(a) Add the students' contributions and the teacher's $75.", "(b) Subtract food, chocolates, then the $98 left to find drinks."], "source": "Henry Park 2024 P5 End-of-Year Exam Paper 2 Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q10. Two-part: (a) $525, (b) $177." }, { "n": 111, "type_id": 2, "question": "The bar graph shows the amount of money five students saved from their pocket money in April. (a) What was the average amount of money saved by the students in April?
Ans: $[?]
(b) The line graph shows how Cai Yi spent her pocket money from Jan to April. Cai Yi gets the same amount of pocket money every month. What percentage of her pocket money did she save in February? Give your answer correct to 1 decimal place.
Ans: [?]%", "answer0": "43.20", "answer1": "66.7", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 205, "difficulty_id": 3, "explanation": "(a) From the bar graph: Ali 20, Bob 44, Cai Yi 0, Devi 80, Ethan 72. Total = 20 + 44 + 80 + 72 = 216 (Cai Yi saved nothing in April but is one of the 5 students). Average = 216 ÷ 5 = $43.20. (b) Pocket money per month = highest spending (April) = $45. February spending = $15. Saved = 45 − 15 = $30. Percentage saved = \\(\\dfrac{30}{45}\\times100\\% = 66.7\\%\\) (1 d.p.).", "hints": ["(a) Add all five students' savings then divide by 5.", "(b) Saved = pocket money − spent; pocket money equals the maximum month's spend ($45)."], "source": "Henry Park 2024 P5 End-of-Year Exam Paper 2 Q11", "image_needed": true, "image_options": false, "image_file": "q111.png", "image_page": 26, "image_bbox": [0.22, 0.16, 0.84, 0.36], "image_loc": "bar graph of money saved (Ali, Bob, Cai Yi, Devi, Ethan); part (b) line graph is on the next page", "notes": "Paper 2 Q11. Two-part across pages 26-27: (a) bar graph $43.20, (b) line graph 66.7%. The (b) line-graph figure is on page 27 [bbox approx 0.24,0.12,0.84,0.34]; primary image_page set to 26 for the bar graph." }, { "n": 112, "type_id": 2, "question": "The first three figures of a pattern are shown. The table shows the number of dots used to form each figure (Figure 1 = 4, Figure 2 = 7, Figure 3 = 10).
(a) How many dots are used to form figure 4? [?]
(b) How many dots are used to form figure 30? [?]
(c) Which figure is formed using 457 dots? [?]", "answer0": "13", "answer1": "91", "answer2": "152", "answer3": null, "correct_answer": null, "skill_id": 150, "difficulty_id": 2, "explanation": "The number of dots increases by 3 each figure: dots = 3 × figure + 1. (a) Figure 4 = 3 × 4 + 1 = 13. (b) Figure 30 = 3 × 30 + 1 = 91 (29 × 3 + 4 = 91). (c) 457 dots: (457 − 4) ÷ 3 = 453 ÷ 3 = 151, then 151 + 1 = figure 152.", "hints": ["Each figure adds 3 dots: pattern is 3n + 1.", "(c) reverse it: (457 − 4) ÷ 3, then add 1."], "source": "Henry Park 2024 P5 End-of-Year Exam Paper 2 Q12", "image_needed": true, "image_options": false, "image_file": "q112.png", "image_page": 28, "image_bbox": [0.18, 0.10, 0.88, 0.20], "image_loc": "three dot figures (Figure 1, 2, 3) of a growing pattern", "notes": "Paper 2 Q12. Three-part: (a) 13, (b) 91, (c) figure 152." }, { "n": 113, "type_id": 2, "question": "The total mass of a box with 120 similar rulers is 1.9 kg. The mass of the same box with 150 similar pencils is 6.7 kg. The mass of a pencil is 4 times the mass of a ruler. What is the mass of the empty box in kg? [?]", "answer0": "0.7", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "150 pencils = 150 × 4 = 600 rulers' worth of mass. Difference in contents = 600 − 120 = 480 rulers, and difference in total mass = 6.7 − 1.9 = 4.8 kg. So 1 ruler = 4.8 ÷ 480 = 0.01 kg. 120 rulers = 120 × 0.01 = 1.2 kg. Empty box = 1.9 − 1.2 = 0.7 kg.", "hints": ["Express pencils in terms of rulers (1 pencil = 4 rulers).", "Use the mass difference to find one ruler, then the box."], "source": "Henry Park 2024 P5 End-of-Year Exam Paper 2 Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q13. Answer in kg = 0.7." }, { "n": 114, "type_id": 2, "question": "In this diagram, ABFG and BCDE are parallelograms.
(a) Find ∠w. [?]
(b) Find ∠GFE. [?]", "answer0": "106", "answer1": "142", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 200, "difficulty_id": 3, "explanation": "(a) In parallelogram BCDE, ∠BEC = (180° − 44°) ÷ 2 = 68° (isosceles arrangement at E). Angles around B: 360° − 108° − 78° − 68° = 106°, so ∠w = 106°. (b) ∠BFE = 180° − 106° = 74° (co-interior). ∠GFE = 74° + 68° = 142°.", "hints": ["Opposite angles of a parallelogram are equal; co-interior angles sum to 180°.", "Combine the relevant angles at F for part (b)."], "source": "Henry Park 2024 P5 End-of-Year Exam Paper 2 Q14", "image_needed": true, "image_options": false, "image_file": "q114.png", "image_page": 30, "image_bbox": [0.20, 0.09, 0.74, 0.36], "image_loc": "two joined parallelograms ABFG and BCDE with angles 108°, 78°, 44° and w marked", "notes": "Paper 2 Q14. Two-part: (a) ∠w = 106°, (b) ∠GFE = 142°." }, { "n": 115, "type_id": 2, "question": "The ratio of the number of boys to the number of girls at an amusement park was 5 : 7. After 60 boys entered the amusement park, there were equal numbers of boys and girls.
(a) How many boys were there in the amusement park at first? [?]
(b) In October, after a discount of 25%, the entrance ticket to the amusement park was $54. A further discount of $4.50 was given to a child who was born in October. What is the total percentage discount given to a child who was born in October? Ans: [?]%", "answer0": "150", "answer1": "31.25", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 183, "difficulty_id": 3, "explanation": "(a) Boys : girls = 5 : 7, difference = 2 units = 60 boys (since adding 60 boys makes them equal). 1 unit = 30, boys at first = 5 × 30 = 150. (b) After 25% discount the price $54 is 75% of usual, so usual = 54 ÷ 0.75 = $72. The 25% discount = $18. Total discount = $18 + $4.50 = $22.50. As a percentage of $72: \\(\\dfrac{22.50}{72}\\times100\\% = 31.25\\%\\).", "hints": ["(a) The 60 boys close a gap of 2 ratio units.", "(b) Work back to the usual price ($72), then total discount over usual price."], "source": "Henry Park 2024 P5 End-of-Year Exam Paper 2 Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q15. Two-part: (a) 150 boys, (b) 31.25%." }, { "n": 116, "type_id": 1, "question": "There were some adults and children at game stations X and Y. \\(\\dfrac{2}{5}\\) of the children at game station X were boys and \\(\\dfrac{3}{4}\\) of the children at game station Y were girls. There were twice as many children at station Y than at station X. What fraction of the total number of children in both game stations were girls? Give your answer in the simplest form.", "answer0": "\\(\\dfrac{7}{10}\\)", "answer1": "\\(\\dfrac{3}{5}\\)", "answer2": "\\(\\dfrac{21}{30}\\)", "answer3": "\\(\\dfrac{2}{3}\\)", "correct_answer": 0, "skill_id": 165, "difficulty_id": 3, "explanation": "Let station X = 10 children (units), station Y = 20 children. Station X girls = \\(\\dfrac{3}{5}\\times10 = 6\\). Station Y girls = \\(\\dfrac{3}{4}\\times20 = 15\\). Total girls = 6 + 15 = 21 out of 10 + 20 = 30 children. Fraction = \\(\\dfrac{21}{30}=\\dfrac{7}{10}\\).", "hints": ["Pick convenient numbers: X = 10 children, Y = 20.", "Count girls in each station, then divide by total children."], "source": "Henry Park 2024 P5 End-of-Year Exam Paper 2 Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q16(a). Answer is a fraction (7/10) so MCQ per spec. Part (b) (answer 360 children) is a separate sub-question with a whole-number answer; captured separately as Q117 below to keep one answer per question." }, { "n": 117, "type_id": 2, "question": "There were some adults and children at game stations X and Y. \\(\\dfrac{3}{5}\\) of all the participants at game stations X and Y were adults. On average, each adult won 38 coins from the games while each child won 62 coins. A total of 42 840 coins were won by all the participants. How many of the participants were children? [?]", "answer0": "360", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Adults : children = 3 : 2 (children = 1 − 3/5 = 2/5). Per 5 participants: 3 adults win 3 × 38 = 114 coins, 2 children win 2 × 62 = 124 coins, total 238 coins per 5 participants. 42 840 ÷ 238 = 180 such groups. Children = 180 × 2 = 360.", "hints": ["Children are 2/5 of participants; set adults : children = 3 : 2.", "Find coins per group of 5, divide total by it, then take the children's share."], "source": "Henry Park 2024 P5 End-of-Year Exam Paper 2 Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q16(b). Answer key = 360 children." }, { "n": 118, "type_id": 2, "question": "Amelia had two rolls of stickers of the same length but different designs. She cut the first roll into equal pieces of 30 cm and there were 7 smiley faces on each piece. She then cut the second roll into equal pieces of 50 cm and there were 8 stars on each piece. After she finished cutting both rolls of stickers, there were 132 more smiley faces than stars. Find the length of one roll of stickers. [?]", "answer0": "18", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "Per 1 cm: first roll has 7/30 smiley faces, second roll has 8/50 stars. Over a common length L cm: smiley faces = (7/30)L, stars = (8/50)L. Using LCM approach: in 150 cm, first roll = 5 pieces × 7 = 35 smiley faces, second = 3 pieces × 8 = 24 stars, difference = 11 per 150 cm. 132 ÷ 11 = 12, so length = 12 × 150 = 1800 cm = 18 m.", "hints": ["Find a common length (150 cm) where both rolls cut evenly.", "Difference of 11 stickers per 150 cm; 132 ÷ 11 then × 150."], "source": "Henry Park 2024 P5 End-of-Year Exam Paper 2 Q17", "image_needed": true, "image_options": false, "image_file": "q118.png", "image_page": 33, "image_bbox": [0.20, 0.16, 0.82, 0.46], "image_loc": "two sticker strips: first roll 30 cm with 7 smileys, second roll 50 cm with 8 stars", "notes": "Paper 2 Q17. Answer in m = 18 (1800 cm)." } ] }