{ "paper": { "school": "Tao Nan", "year": 2023, "level": "P3", "label": "End of Year Exam", "source_prefix": "Tao Nan 2023 P3 End of Year Exam", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "What is the smallest 4-digit even number that can be formed with the digits 7, 3, 6 and 2 ?", "answer0": "2367", "answer1": "2376", "answer2": "2673", "answer3": "2736", "correct_answer": 1, "skill_id": 66, "difficulty_id": 2, "explanation": "An even number ends in an even digit. To be smallest, put smallest digits first: 2, 3, then last digit must be even. Remaining digits 7 and 6; smallest hundreds is 3, so 23_6 -> 2376 (ends in even 6).", "hints": ["Smallest number puts smallest digits in the highest place values.", "Even numbers end in 0, 2, 4, 6 or 8 — the last digit must be even."], "source": "Tao Nan 2023 P3 End of Year Exam Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key = option (2) = 2376." }, { "n": 2, "type_id": 1, "question": "How many right angles are there in the figure ?", "answer0": "10", "answer1": "8", "answer2": "6", "answer3": "4", "correct_answer": 1, "skill_id": 99, "difficulty_id": 2, "explanation": "Rectangle ABCD has 4 corner right angles. The horizontal mid-line meeting the two vertical sides adds 4 more right angles. Total = 8.", "hints": ["Count the right angles at the four corners of the rectangle first.", "Where the horizontal line meets each vertical side it forms more right angles."], "source": "Tao Nan 2023 P3 End of Year Exam Q2", "image_needed": true, "image_page": 3, "image_loc": "below the question, rectangle ABCD with diagonals and a horizontal mid-line", "image_options": false, "image_file": "q2.png", "notes": "Key = option (2) = 8." }, { "n": 3, "type_id": 1, "question": "Which of the following fractions is smaller than 1/2 ?", "answer0": "2/3", "answer1": "3/7", "answer2": "3/5", "answer3": "2/4", "correct_answer": 1, "skill_id": 79, "difficulty_id": 2, "explanation": "Compare each to 1/2. 2/3>1/2, 3/7<1/2 (since 3.5/7=1/2), 3/5>1/2, 2/4=1/2. Only 3/7 is smaller than 1/2.", "hints": ["A fraction equals 1/2 when the numerator is half the denominator.", "3/7: half of 7 is 3.5, so 3/7 is less than 1/2."], "source": "Tao Nan 2023 P3 End of Year Exam Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key = option (2) = 3/7." }, { "n": 4, "type_id": 1, "question": "Betty has a roll of ribbon which is 5 m long. She uses 1 m 25 cm to wrap a gift box and 85 cm to make a ribbon bow. What is the length of ribbon left ?", "answer0": "415 cm", "answer1": "375 cm", "answer2": "290 cm", "answer3": "210 cm", "correct_answer": 2, "skill_id": 87, "difficulty_id": 2, "explanation": "5 m = 500 cm. Used = 125 cm + 85 cm = 210 cm. Left = 500 - 210 = 290 cm.", "hints": ["Convert everything to centimetres: 5 m = 500 cm, 1 m 25 cm = 125 cm.", "Add the two amounts used, then subtract from 500 cm."], "source": "Tao Nan 2023 P3 End of Year Exam Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key = option (3) = 290 cm." }, { "n": 5, "type_id": 1, "question": "The figure is made up of a square and a rectangle. The total area is 67 cm². What is the area of the rectangle ?", "answer0": "49 cm²", "answer1": "39 cm²", "answer2": "18 cm²", "answer3": "14 cm²", "correct_answer": 2, "skill_id": 97, "difficulty_id": 2, "explanation": "The square has side 7 cm, so its area = 7 x 7 = 49 cm². Rectangle area = total - square = 67 - 49 = 18 cm².", "hints": ["The square's side is 7 cm — find its area first.", "Subtract the square's area from the total area of 67 cm²."], "source": "Tao Nan 2023 P3 End of Year Exam Q5", "image_needed": true, "image_page": 4, "image_loc": "below the question, an L-shape made of a 7 cm square joined to a smaller rectangle on the lower right", "image_options": false, "image_file": "q5.png", "notes": "Key = option (3) = 18 cm². Square side labelled 7 cm." }, { "n": 6, "type_id": 1, "question": "What is the shortest route to the shopping centre from Susan's house ?", "answer0": "1 km 375 m", "answer1": "1 km 480 m", "answer2": "2 km 225 m", "answer3": "2 km 325 m", "correct_answer": 2, "skill_id": 87, "difficulty_id": 3, "explanation": "Routes: via Library = 1 km 480 m + 845 m = 2 km 325 m. Via playground = 850 m + 1 km 375 m = 2 km 225 m. The shortest is via the playground = 2 km 225 m.", "hints": ["There are two paths to the shopping centre — add up the distances on each.", "Compare the two totals and pick the smaller one."], "source": "Tao Nan 2023 P3 End of Year Exam Q6", "image_needed": true, "image_page": 5, "image_loc": "below the question, a route map: Susan's house, Library, playground, Shopping centre with distances 1 km 480 m, 845 m, 850 m, 1 km 375 m", "image_options": false, "image_file": "q6.png", "notes": "Key = option (3) = 2 km 225 m (via playground)." }, { "n": 7, "type_id": 1, "question": "Which figures have the same perimeter ?", "answer0": "A and C", "answer1": "B and C", "answer2": "B and D", "answer3": "C and D", "correct_answer": 0, "skill_id": 96, "difficulty_id": 3, "explanation": "Count grid-edge perimeters of the four shapes drawn on the 1 cm grid; figures A and C have equal perimeters.", "hints": ["Each grid square is 1 cm by 1 cm — count the unit edges around each figure.", "Two L-shaped or stepped figures can share the same perimeter even if their areas differ."], "source": "Tao Nan 2023 P3 End of Year Exam Q7", "image_needed": true, "image_page": 5, "image_loc": "below the question, a 1 cm square grid containing four shaded figures labelled A, B (top) and C, D (bottom)", "image_options": false, "image_file": "q7.png", "notes": "Key = option (1) = A and C. Figures drawn on a 1 cm grid — crop must show full grid and all four shapes." }, { "n": 8, "type_id": 1, "question": "Which of the following shows 1/3 of the figure shaded ?", "answer0": "Figure 1", "answer1": "Figure 2", "answer2": "Figure 3", "answer3": "Figure 4", "correct_answer": 3, "skill_id": 42, "difficulty_id": 2, "explanation": "Each figure is split into equal parts; 1/3 means one third of the parts are shaded. Figure 4 has exactly one third of its cells shaded.", "hints": ["Count the total equal parts and the shaded parts in each figure.", "1/3 shaded means shaded parts are one out of every three."], "source": "Tao Nan 2023 P3 End of Year Exam Q8", "image_needed": true, "image_page": 6, "image_loc": "the four option figures (1)-(4) down the left of the page, each a grid with some cells shaded", "image_options": true, "image_file": null, "notes": "Key = option (4). image_options true: crop each option grid to q8_opt0.png .. q8_opt3.png." }, { "n": 9, "type_id": 0, "question": "Draw a line parallel to RS, passing through T.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 100, "difficulty_id": 2, "explanation": "Through point T draw a straight line that never meets RS — i.e. keeps the same slant/distance as RS everywhere.", "hints": [], "source": "Tao Nan 2023 P3 End of Year Exam Q9", "image_needed": true, "image_page": 7, "image_loc": "below the question, line segment RS slanting down to the right; point T below the segment", "image_options": false, "image_file": "q9.png", "notes": "Interactive draw-a-line task — no value answer. type_id 0 (skipped on insert). Answer: a line through T parallel to RS." }, { "n": 10, "type_id": 2, "question": "Study the diagram. What is the mass of each block of X? [?]", "answer0": "400", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 87, "difficulty_id": 3, "explanation": "Left scale (2 X + 1 Y + 1 X = 3 X + 1 Y... reading) and right scale (1 X + 1 Y) let you find X. Left reads about 1.6 kg for 3X+Y, right reads 2 kg... using the difference, each X = 400 g.", "hints": ["Read both scale dials in kilograms, then convert to grams.", "The two pans differ by the extra blocks of X — use the difference in mass."], "source": "Tao Nan 2023 P3 End of Year Exam Q10", "image_needed": true, "image_page": 7, "image_loc": "below 'Study the diagram', two kg dial scales: left pan with blocks X,X,Y plus one X on top; right pan with blocks X,Y", "image_options": false, "image_file": "q10.png", "notes": "Key = 400 g. Answer unit is g (printed beside the box). FIB numeric blank = 400." }, { "n": 11, "type_id": 2, "question": "Arrange the fractions, from the smallest to the biggest fraction. 3/6 1/3 4/9 [?] , [?] , [?]", "answer0": "1/3", "answer1": "4/9", "answer2": "3/6", "answer3": null, "correct_answer": null, "skill_id": 79, "difficulty_id": 2, "explanation": "Convert to a common comparison: 1/3 = 0.333, 4/9 = 0.444, 3/6 = 0.5. Smallest to biggest: 1/3, 4/9, 3/6.", "hints": ["Find the value of each fraction as a decimal or over a common denominator.", "3/6 simplifies to 1/2 = 0.5, the biggest here."], "source": "Tao Nan 2023 P3 End of Year Exam Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Ordering task -> FIB, one blank per position. Key order: 1/3, 4/9, 3/6 (smallest first)." }, { "n": 12, "type_id": 2, "question": "Some sticks are placed, at an equal distance from each other, in a straight line. The distance between the 1st and the 4th stick is 24 cm. The distance between the 1st and the last stick is 56 cm. How many sticks are there altogether ? [?]", "answer0": "8", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 76, "difficulty_id": 3, "explanation": "From 1st to 4th stick there are 3 gaps = 24 cm, so each gap = 8 cm. From 1st to last = 56 cm = 56 / 8 = 7 gaps, so number of sticks = 7 + 1 = 8.", "hints": ["From the 1st to the 4th stick there are 3 equal gaps, not 4.", "Find one gap, then the number of gaps from 1st to last; sticks = gaps + 1."], "source": "Tao Nan 2023 P3 End of Year Exam Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key = 8. Working: 24/3 = 8 cm per gap; 56/8 = 7 gaps -> 7+1 = 8 sticks." }, { "n": 13, "type_id": 1, "question": "Miss Foo paid $12 for a highlighter, a stapler and a file. The file cost $5.30. The stapler cost more than the highlighter. The total cost of the highlighter and the stapler was less than the cost of the file.", "answer0": "True", "answer1": "False", "answer2": "Not possible to tell", "answer3": "Cannot be calculated", "correct_answer": 1, "skill_id": 83, "difficulty_id": 3, "explanation": "Highlighter + stapler = $12 - $5.30 = $6.70, which is more than the file's $5.30. So the statement that their total was less than the file is False.", "hints": ["Find the combined cost of the highlighter and stapler: $12 - $5.30.", "Compare that combined cost with the file's $5.30."], "source": "Tao Nan 2023 P3 End of Year Exam Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Original is a True/False/Not-possible tick table with statements a) and b). Statement a) modelled here as MCQ; key a) = False. (Statement b) 'The stapler cost more than the file' key = Not possible to tell.)" }, { "n": 14, "type_id": 2, "question": "The bar graph shows the CCAs that a class of 40 students had chosen. Each student signed up for one CCA only. Some students were absent and did not choose their CCA. How many students were absent ? [?]", "answer0": "3", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 104, "difficulty_id": 2, "explanation": "Add all bars: Arts 4+7=11, Sports 9+3=12, Club 3+11=14. Total who chose = 11+12+14 = 37. Absent = 40 - 37 = 3.", "hints": ["Add the boys and girls bars for every CCA to get the total who chose.", "Subtract that total from the whole class of 40."], "source": "Tao Nan 2023 P3 End of Year Exam Q14", "image_needed": true, "image_page": 9, "image_loc": "below the question, a double bar graph 'Students' CCA Choices' (Arts, Sports, Club) with Boys (dotted) and Girls (hatched) keys", "image_options": false, "image_file": "q14.png", "notes": "Key = 3. Bar values: Arts 4/7, Sports 9/3, Club 3/11." }, { "n": 15, "type_id": 2, "question": "The diagram shows 1/4 of the bar shaded. What fraction of the bar must be further shaded, so that 5/8 of the bar is shaded altogether ? Express the answer in its simplest form. [?]", "answer0": "3/8", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 81, "difficulty_id": 2, "explanation": "5/8 - 1/4 = 5/8 - 2/8 = 3/8. So 3/8 more of the bar must be shaded.", "hints": ["Write 1/4 with denominator 8: 1/4 = 2/8.", "Subtract 2/8 from 5/8."], "source": "Tao Nan 2023 P3 End of Year Exam Q15", "image_needed": true, "image_page": 10, "image_loc": "below 'Express the answer in its simplest form', a bar divided into 4 equal cells with the first cell shaded", "image_options": false, "image_file": "q15.png", "notes": "Key = 3/8. Bar diagram shows 1/4 shaded." }, { "n": 16, "type_id": 1, "question": "The four cylinders contain some water. Clare wants to pour all the water from her cylinder into one of the cylinders (A, B, or C). Which cylinder will hold all her water ?", "answer0": "Cylinder A", "answer1": "Cylinder B", "answer2": "Cylinder C", "answer3": "Clare's cylinder", "correct_answer": 1, "skill_id": 87, "difficulty_id": 3, "explanation": "Clare's water is about 80 ml. The cylinder must have enough empty space above its current water plus its capacity. Cylinder B (marked to 200, water at ~120) has the most spare capacity, so B can hold all her water.", "hints": ["Read how much water Clare has, then how much empty space is left in A, B and C.", "Choose the cylinder whose remaining space can fit all of Clare's water."], "source": "Tao Nan 2023 P3 End of Year Exam Q16", "image_needed": true, "image_page": 10, "image_loc": "below the question, four measuring cylinders: Clare's cylinder, then A, B, C with scale markings and shaded water levels", "image_options": false, "image_file": "q16.png", "notes": "Key = B. Single text answer 'B' on key; modelled as MCQ choosing cylinder B." }, { "n": 17, "type_id": 2, "question": "Alvin has 5070 LEGO bricks. He has 1094 more bricks than Farhan. a) How many bricks does Farhan have ? b) How many bricks do the two boys have altogether ? [?] , [?]", "answer0": "3976", "answer1": "9046", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 71, "difficulty_id": 2, "explanation": "a) Farhan = 5070 - 1094 = 3976 bricks. b) Altogether = 5070 + 3976 = 9046 bricks.", "hints": ["'1094 more than Farhan' means subtract 1094 from Alvin's bricks to get Farhan's.", "Add Alvin's and Farhan's amounts for the total."], "source": "Tao Nan 2023 P3 End of Year Exam Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two-part question -> 2 blanks. a) Key = 3976. b) Key sheet computes 5070 + 3976 = 9040, but 5070 + 3976 = 9046; key has an arithmetic slip. Correct total = 9046." }, { "n": 18, "type_id": 2, "question": "The Chin family attended a birthday dinner that ended at 19 20, according to the clock in the dining room. However, the clock was 10 minutes slower. The dinner lasted 1 h 30 min. What was the actual time the dinner started ? [?]", "answer0": "1800", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 93, "difficulty_id": 3, "explanation": "Dining-room clock showed 19 20 at the end; it was 10 min slow, so actual end time = 19 30. The dinner lasted 1 h 30 min, so actual start = 19 30 - 1 h 30 min = 18 00.", "hints": ["The clock is 10 minutes slow, so add 10 minutes to its time to get the actual time.", "Then subtract the 1 h 30 min duration from the actual end time."], "source": "Tao Nan 2023 P3 End of Year Exam Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key sheet writes 1815, but that ignores the 10-min slow clock. Actual end = 19 30; start = 19 30 - 1 h 30 = 18 00. Key appears to be wrong; correct answer 1800 (18 00). Flagged for human review." }, { "n": 19, "type_id": 2, "question": "Uncle Daniel bought an apple pie and cut it into 12 pieces. He gave 1/4 of the pie to his niece and 4 pieces to his neighbour. What fraction of the pie was left ? Express your answer in its simplest form. [?]", "answer0": "5/12", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 81, "difficulty_id": 2, "explanation": "1/4 of 12 = 3 pieces to niece; 4 pieces to neighbour; given away = 7 pieces. Left = 12 - 7 = 5 pieces = 5/12 (already simplest).", "hints": ["1/4 of the 12 pieces is how many pieces?", "Add the pieces given away, then write what is left over 12."], "source": "Tao Nan 2023 P3 End of Year Exam Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key = 5/12." }, { "n": 20, "type_id": 2, "question": "Annie made 3 times as many clay stars as Eileen. Linda made 75 fewer clay stars than Annie. The three girls made a total of 919 clay stars. How many clay stars did Eileen make ? [?]", "answer0": "142", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 76, "difficulty_id": 3, "explanation": "Let Eileen = 1 unit, Annie = 3 units, Linda = 3 units - 75. Total = 1u + 3u + 3u - 75 = 7u - 75 = 919, so 7u = 994, u = 142. Eileen made 142.", "hints": ["Let Eileen = 1 unit; write Annie and Linda in units too.", "Add the 75 back to the total, then divide by the number of units (7)."], "source": "Tao Nan 2023 P3 End of Year Exam Q20", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key = 142. (Key sheet 919+75=994, 994/7=142.)" }, { "n": 21, "type_id": 0, "question": "Jimmy is making a shape pattern: triangle, circle, inverted-triangle, square, repeating. a) Draw the 12th shape. b) Given that the pattern continues, draw the 58th shape.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 69, "difficulty_id": 2, "explanation": "The cycle of 4 is triangle, circle, inverted-triangle, square. a) 12 / 4 = 3 r 0, so the 12th shape is the 4th in the cycle = square. b) 58 / 4 = 14 r 2, so the 58th shape is the 2nd in the cycle = circle.", "hints": [], "source": "Tao Nan 2023 P3 End of Year Exam Q21", "image_needed": true, "image_page": 14, "image_loc": "below the question stem, the repeating shape sequence: triangle, circle, inverted triangle, square, ... starting at '1st'", "image_options": false, "image_file": "q21.png", "notes": "Draw-the-shape task -> type_id 0 (skipped on insert). a) 12th = square (12/4 r0). b) 58th = circle (58/4 = 14 r2 -> 2nd shape). Key sheet notes b) 58/4=14r2 -> '2 steps' (circle)." }, { "n": 22, "type_id": 2, "question": "2 badminton rackets and 1 basketball cost $102.50. 1 badminton racket and 2 basketballs cost $107.50. What is the total cost of 1 badminton racket and 1 basketball ? [?]", "answer0": "70", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 83, "difficulty_id": 3, "explanation": "Adding both: 3 rackets + 3 basketballs = $102.50 + $107.50 = $210. So 3 x (1 racket + 1 basketball) = $210, giving 1 racket + 1 basketball = $210 / 3 = $70.", "hints": ["Add the two equations together — you get 3 rackets and 3 basketballs.", "Divide that total by 3 to get one racket plus one basketball."], "source": "Tao Nan 2023 P3 End of Year Exam Q22", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key = $70. Answer is a money value 70 (dollars)." }, { "n": 23, "type_id": 2, "question": "The incomplete graph shows the number of stickers collected by three friends, Derek, Indra and Aileen. After Indra gave some stickers to Aileen, the three children had an equal number of stickers each. How many stickers did Aileen have at first ? [?]", "answer0": "20", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 104, "difficulty_id": 3, "explanation": "Derek = 50, Indra = 80. Total stickers stay the same; Derek does not change, so each child ends with 50. Indra gives 80 - 50 = 30 to Aileen, so Aileen ends with 50 and had 50 - 30 = 20 at first.", "hints": ["Derek's stickers don't change, so the final equal amount must equal Derek's 50.", "Indra gives away (80 - 50) stickers — Aileen received that many, so subtract to find her start."], "source": "Tao Nan 2023 P3 End of Year Exam Q23", "image_needed": true, "image_page": 16, "image_loc": "below the question, bar graph 'Stickers Collection' with Derek (50) and Indra (80) bars; Aileen's bar incomplete (dashed)", "image_options": false, "image_file": "q23.png", "notes": "Key = 20. Graph reads Derek 50, Indra 80, Aileen unknown." }, { "n": 24, "type_id": 2, "question": "Samy arranged three pieces of tiles. All the tiles were of the same size. What was the area of each tile ? [?]", "answer0": "162", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 97, "difficulty_id": 3, "explanation": "The whole arrangement is 27 cm by 18 cm, area = 27 x 18 = 486 cm². It is made of 3 equal tiles, so each tile = 486 / 3 = 162 cm².", "hints": ["Find the area of the whole rectangle first: 27 cm x 18 cm.", "Three equal tiles make up that area — divide by 3."], "source": "Tao Nan 2023 P3 End of Year Exam Q24", "image_needed": true, "image_page": 17, "image_loc": "below the question, a 27 cm by 18 cm rectangle divided into three equal tiles (one tall tile on the left, two stacked on the right)", "image_options": false, "image_file": "q24.png", "notes": "Key = 162 cm². Answer is a number with unit cm²; blank = 162. Whole figure 27 cm x 18 cm = 486; /3 = 162." } ] }