{
"paper": {
"school": "Tao Nan",
"year": 2023,
"level": "P4",
"label": "End of Year Exam",
"source_prefix": "Tao Nan 2023 P4 End of Year Exam",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "30 000 + 4000 + 200 + 8 = [?]",
"answer0": "34 280",
"answer1": "34 208",
"answer2": "34 028",
"answer3": "30 428",
"correct_answer": 1,
"skill_id": 105,
"difficulty_id": 1,
"explanation": "Add the place values: 30 000 + 4000 + 200 + 8 = 34 208.",
"hints": [
"Line up the place values: ten thousands, thousands, hundreds, tens, ones.",
"30 000 + 4000 + 200 + 8 = 34 208."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (2) = 34 208."
},
{
"n": 2,
"type_id": 1,
"question": "Which of the following is a multiple of 6?",
"answer0": "30",
"answer1": "2",
"answer2": "28",
"answer3": "16",
"correct_answer": 0,
"skill_id": 114,
"difficulty_id": 1,
"explanation": "A multiple of 6 can be divided exactly by 6. 30 = 6 x 5, so 30 is a multiple of 6.",
"hints": [
"Check which number is in the 6 times table.",
"6 x 5 = 30."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (1) = 30."
},
{
"n": 3,
"type_id": 1,
"question": "$$\\frac{1}{3}$$ + $$\\frac{1}{9}$$ = [?]",
"answer0": "$$\\frac{1}{27}$$",
"answer1": "$$\\frac{2}{3}$$",
"answer2": "$$\\frac{2}{12}$$",
"answer3": "$$\\frac{4}{9}$$",
"correct_answer": 3,
"skill_id": 121,
"difficulty_id": 2,
"explanation": "Make the denominators the same: $$\\frac{1}{3}$$ = $$\\frac{3}{9}$$. Then $$\\frac{3}{9}$$ + $$\\frac{1}{9}$$ = $$\\frac{4}{9}$$.",
"hints": [
"Convert $$\\frac{1}{3}$$ to ninths.",
"$$\\frac{3}{9}$$ + $$\\frac{1}{9}$$ = $$\\frac{4}{9}$$."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (4) = 4/9."
},
{
"n": 4,
"type_id": 1,
"question": "The digit 8 in 9.283 stands for 8 [?].",
"answer0": "ones",
"answer1": "tens",
"answer2": "tenths",
"answer3": "hundredths",
"correct_answer": 3,
"skill_id": 123,
"difficulty_id": 1,
"explanation": "In 9.283, the digit 8 is the second place after the decimal point, so it stands for 8 hundredths.",
"hints": [
"First decimal place is tenths, second is hundredths.",
"8 is in the hundredths place."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q4",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (4) = hundredths."
},
{
"n": 5,
"type_id": 1,
"question": "Which of the following decimals is the smallest?",
"answer0": "3.07",
"answer1": "3.15",
"answer2": "3.038",
"answer3": "3.304",
"correct_answer": 2,
"skill_id": 124,
"difficulty_id": 2,
"explanation": "Compare place values. 3.038 has only 3 hundredths (0.038), while 3.07 = 0.070, 3.15, 3.304 are larger. So 3.038 is the smallest.",
"hints": [
"Compare the tenths first, then the hundredths.",
"3.038 has the smallest tenths/hundredths value."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q5",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (3) = 3.038."
},
{
"n": 6,
"type_id": 1,
"question": "In the figure, which angle is greater than a right angle?",
"answer0": "$$\\angle$$a",
"answer1": "$$\\angle$$b",
"answer2": "$$\\angle$$c",
"answer3": "$$\\angle$$d",
"correct_answer": 2,
"skill_id": 99,
"difficulty_id": 2,
"explanation": "An angle greater than a right angle is more than 90 degrees (obtuse). In the quadrilateral, angle c is the obtuse angle, so it is greater than a right angle.",
"hints": [
"A right angle is 90 degrees; look for the angle that opens wider than a corner of a square.",
"Angle c is obtuse."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q6",
"image_needed": true,
"image_options": false,
"image_file": "q6.png",
"image_page": 4,
"image_bbox": [
0.26,
0.46,
0.82,
0.66
],
"image_loc": "middle of page, quadrilateral with angles a, b, c, d marked",
"notes": "Key: option (3) = angle c."
},
{
"n": 7,
"type_id": 1,
"question": "Laura clocked 6804 steps on Friday. She clocked 2 times as many steps on Saturday as on Friday. How many steps did she clock on both days?",
"answer0": "6806",
"answer1": "10 206",
"answer2": "13 608",
"answer3": "20 412",
"correct_answer": 3,
"skill_id": 118,
"difficulty_id": 2,
"explanation": "Saturday = 2 x 6804 = 13 608. Both days = 6804 + 13 608 = 20 412.",
"hints": [
"Find Saturday's steps first: 2 x 6804.",
"Add Friday and Saturday: 6804 + 13 608 = 20 412."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (4) = 20 412. Step-counter wristband image is decorative (just shows 6804), not required to solve."
},
{
"n": 8,
"type_id": 1,
"question": "Square S and rectangle R have the same perimeter. Find the length of each side of square S.",
"answer0": "6 cm",
"answer1": "12 cm",
"answer2": "24 cm",
"answer3": "48 cm",
"correct_answer": 1,
"skill_id": 137,
"difficulty_id": 2,
"explanation": "Perimeter of rectangle R = 2 x (19 + 5) = 48 cm. Square S has the same perimeter, so each side = 48 div 4 = 12 cm.",
"hints": [
"Find the perimeter of rectangle R = 2 x (length + breadth).",
"Divide the perimeter by 4 to get one side of the square."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q8",
"image_needed": true,
"image_options": false,
"image_file": "q8.png",
"image_page": 5,
"image_bbox": [
0.27,
0.34,
0.83,
0.48
],
"image_loc": "middle of page, square S beside rectangle R labelled 19 cm by 5 cm",
"notes": "Key: option (2) = 12 cm."
},
{
"n": 9,
"type_id": 1,
"question": "The total mass of a papaya and a durian is 8.2 kg. The total mass of the papaya and a watermelon is 11.4 kg. The watermelon weighs 3 times as heavy as the papaya. What is the mass of the durian?",
"answer0": "2.85 kg",
"answer1": "4.4 kg",
"answer2": "5.35 kg",
"answer3": "6.6 kg",
"correct_answer": 2,
"skill_id": 131,
"difficulty_id": 3,
"explanation": "Papaya + watermelon = 11.4 kg and watermelon = 3 x papaya, so 4 units of papaya = 11.4 kg, papaya = 2.85 kg. Durian = 8.2 - 2.85 = 5.35 kg.",
"hints": [
"Papaya + 3 x papaya = 4 units = 11.4 kg, so find the papaya mass.",
"Durian = 8.2 - papaya."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q9",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (3) = 5.35 kg."
},
{
"n": 10,
"type_id": 1,
"question": "At an animal shelter, there were dogs, cats and rabbits. $$\\frac{1}{3}$$ of the animals were dogs. There were 38 more cats than dogs. The remaining 56 animals were rabbits. How many animals were there altogether?",
"answer0": "282",
"answer1": "206",
"answer2": "141",
"answer3": "130",
"correct_answer": 0,
"skill_id": 122,
"difficulty_id": 3,
"explanation": "Dogs = $$\\frac{1}{3}$$ of total, so cats + rabbits = $$\\frac{2}{3}$$ of total. Cats = dogs + 38 = $$\\frac{1}{3}$$total + 38. Then $$\\frac{1}{3}$$total + 38 + 56 = $$\\frac{2}{3}$$total, so $$\\frac{1}{3}$$total = 94 and total = 282.",
"hints": [
"Let the total be 3 units; dogs = 1 unit, so cats + rabbits = 2 units.",
"Cats = 1 unit + 38, rabbits = 56, so 1 unit = 94, total = 282."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q10",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (1) = 282."
},
{
"n": 11,
"type_id": 2,
"question": "Round 2818 to the nearest ten. [?]",
"answer0": "2820",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 109,
"difficulty_id": 1,
"explanation": "The ones digit is 8, which is 5 or more, so round up the tens: 2818 rounds to 2820.",
"hints": [
"Look at the ones digit to decide rounding.",
"8 rounds up, giving 2820."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q11",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 2820."
},
{
"n": 12,
"type_id": 2,
"question": "Write the missing number in the number pattern below.
17 000 , 16 100 , 15 200 , 14 300 , [?] , 12 500",
"answer0": "13 400",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 108,
"difficulty_id": 2,
"explanation": "Each term decreases by 900. 14 300 - 900 = 13 400 (and 13 400 - 900 = 12 500, which checks).",
"hints": [
"Find the difference between consecutive numbers.",
"Subtract 900 from 14 300."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q12",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 13 400."
},
{
"n": 13,
"type_id": 2,
"question": "Find the value of 1 - $$\\frac{1}{4}$$ - $$\\frac{1}{8}$$. [?]",
"answer0": "5/8",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 121,
"difficulty_id": 2,
"explanation": "Write everything in eighths: 1 = $$\\frac{8}{8}$$, $$\\frac{1}{4}$$ = $$\\frac{2}{8}$$. Then $$\\frac{8}{8}$$ - $$\\frac{2}{8}$$ - $$\\frac{1}{8}$$ = $$\\frac{5}{8}$$.",
"hints": [
"Make all denominators 8.",
"8/8 - 2/8 - 1/8 = 5/8."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q13",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 5/8."
},
{
"n": 14,
"type_id": 2,
"question": "21.96 + 0.18 = [?]",
"answer0": "22.14",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 129,
"difficulty_id": 1,
"explanation": "Line up the decimal points: 21.96 + 0.18 = 22.14.",
"hints": [
"Align the decimal points before adding.",
"21.96 + 0.18 = 22.14."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q14",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key prints 22.4 but this is a typo; 21.96 + 0.18 = 22.14. Answer corrected to 22.14."
},
{
"n": 15,
"type_id": 2,
"question": "Find the value of 8.27 x 9. [?]",
"answer0": "74.43",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 130,
"difficulty_id": 2,
"explanation": "8.27 x 9 = 74.43.",
"hints": [
"Multiply 827 x 9 then place the decimal point (2 d.p.).",
"827 x 9 = 7443, so 8.27 x 9 = 74.43."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q15",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 74.43."
},
{
"n": 16,
"type_id": 2,
"question": "In the figure, ABCD is a rectangle. Find the value of $$\\angle$$y. [?]",
"answer0": "65",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 197,
"difficulty_id": 2,
"explanation": "Angle A of the rectangle is a right angle (90 degrees). The 25 degree angle is part of angle A, so y = 90 - 25 = 65 degrees.",
"hints": [
"Angle DAB of a rectangle is 90 degrees.",
"y = 90 - 25 = 65 degrees."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q16",
"image_needed": true,
"image_options": false,
"image_file": "q16.png",
"image_page": 8,
"image_bbox": [
0.28,
0.55,
0.72,
0.74
],
"image_loc": "middle of page, rectangle ABCD with a diagonal line from A, marking 25 degrees at top and y below it",
"notes": "Key: 90 - 25 = 65 degrees. Answer unit is degrees."
},
{
"n": 17,
"type_id": 2,
"question": "Write $$\\frac{29}{4}$$ as a mixed number. [?]",
"answer0": "7 1/4",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 119,
"difficulty_id": 2,
"explanation": "29 div 4 = 7 remainder 1, so $$\\frac{29}{4}$$ = $$7\\frac{1}{4}$$.",
"hints": [
"Divide 29 by 4 to find the whole number and remainder.",
"29 = 4 x 7 + 1, so it is 7 and 1/4."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q17",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 7 1/4. FIB answer kept plain as '7 1/4'."
},
{
"n": 18,
"type_id": 2,
"question": "Arrange the following fractions from the smallest to the greatest.
$$\\frac{7}{11}$$ , $$\\frac{1}{2}$$ , $$\\frac{10}{11}$$
[?] (smallest) , [?] , [?] (greatest)",
"answer0": "1/2",
"answer1": "7/11",
"answer2": "10/11",
"answer3": null,
"correct_answer": null,
"skill_id": 79,
"difficulty_id": 2,
"explanation": "$$\\frac{1}{2}$$ = $$\\frac{5.5}{11}$$, so $$\\frac{1}{2}$$ is less than $$\\frac{7}{11}$$. $$\\frac{10}{11}$$ is the largest. Order: $$\\frac{1}{2}$$, $$\\frac{7}{11}$$, $$\\frac{10}{11}$$.",
"hints": [
"Compare 1/2 with 7/11 by thinking of 1/2 as 5.5/11.",
"Then order from smallest to greatest."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q18",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 1/2 , 7/11 , 10/11."
},
{
"n": 19,
"type_id": 2,
"question": "Write the decimal represented by A. [?]",
"answer0": "0.37",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 123,
"difficulty_id": 2,
"explanation": "Between 0.3 and 0.4 the number line is divided into 10 equal parts (each 0.01). A is at the 7th mark after 0.3, so A = 0.37.",
"hints": [
"Each small interval between 0.3 and 0.4 is 0.01.",
"Count the marks: A is 7 marks past 0.3, so 0.37."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q19",
"image_needed": true,
"image_options": false,
"image_file": "q19.png",
"image_page": 9,
"image_bbox": [
0.22,
0.62,
0.62,
0.75
],
"image_loc": "middle of page, number line marked 0.3 and 0.4 with arrow A pointing up between them",
"notes": "Key: 0.37."
},
{
"n": 20,
"type_id": 2,
"question": "What is the area of the figure? [?] $$cm^2$$",
"answer0": "600",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 2,
"explanation": "Split into rectangles. Left part: 12 x (10+10) = 240. Middle bottom part: 12 x 10 = 120. Right part: 12 x 20 = 240. Total = 240 + 120 + 240 = 600 cm squared.",
"hints": [
"Divide the U-shaped figure into rectangles.",
"Add the areas: 240 + 120 + 240 = 600."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q20",
"image_needed": true,
"image_options": false,
"image_file": "q20.png",
"image_page": 10,
"image_bbox": [
0.2,
0.14,
0.72,
0.36
],
"image_loc": "upper portion of page, U-shaped composite figure with dimensions 12 cm widths, 10 cm and 10 cm heights, 12 cm notch",
"notes": "Key: 600 cm squared. Answer unit cm squared."
},
{
"n": 21,
"type_id": 2,
"question": "The figure is made up of square A and 2 identical rectangles, X and Y. The area of the square is 49 $$cm^2$$. Find the perimeter of the figure. [?] $$cm$$",
"answer0": "50",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 137,
"difficulty_id": 3,
"explanation": "Square A has area 49, so its side = 7 cm. Square A plus rectangle X span 11 cm, so X width = 11 - 7 = 4 cm; X height = 7 cm. Rectangle Y is identical to X (4 cm by 7 cm) placed lower. Tracing the outline: 11 + 3 + 7 + 4 + 7 + 11 + 7 = 50 cm.",
"hints": [
"Side of square A = square root of 49 = 7 cm.",
"Width of each rectangle = 11 - 7 = 4 cm; add up all outer edges."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q21",
"image_needed": true,
"image_options": false,
"image_file": "q21.png",
"image_page": 11,
"image_bbox": [
0.2,
0.18,
0.74,
0.36
],
"image_loc": "upper-middle of page, square A with rectangles X and Y; top edge labelled 11 cm",
"notes": "Key: perimeter = 50 cm. Answer unit cm."
},
{
"n": 22,
"type_id": 2,
"question": "Find the sum of all the common factors of 30 and 54. [?]",
"answer0": "6",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 113,
"difficulty_id": 2,
"explanation": "Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30. Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54. Common factors: 1, 2, 3, 6. Sum = 1 + 2 + 3 + 6 = 12.",
"hints": [
"List the factors of each number and find the ones they share.",
"Common factors are 1, 2, 3, 6; add them."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q22",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key lists common factors as 1, 2, 3 (omits 6) so the printed working is incomplete; 6 IS a common factor (30=6x5, 54=6x9). Correct sum = 1+2+3+6 = 12. Answer corrected to 12."
},
{
"n": 23,
"type_id": 2,
"question": "Mr Tan used 21 $$l$$ 75 $$ml$$ of petrol in the first week. He used 3 $$l$$ 25 $$ml$$ more petrol in the second week. He used the same amount of petrol in the second and third week. How much petrol did he use in the 3 weeks? Express your answer in litres and millilitres. [?]",
"answer0": "69 l 275 ml",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 86,
"difficulty_id": 3,
"explanation": "Second week = 21 l 75 ml + 3 l 25 ml = 24 l 100 ml. Third week = 24 l 100 ml. Total = 21 l 75 ml + 24 l 100 ml + 24 l 100 ml = 69 l 275 ml.",
"hints": [
"Find the second week amount first, then the third week equals it.",
"Add all three weeks, carrying ml into litres if needed."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q23",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 69 l 275 ml. Answer field labelled ml in paper but question asks for litres and millilitres."
},
{
"n": 24,
"type_id": 1,
"question": "After making a $$\\frac{1}{4}$$ turn in an anti-clockwise direction, Sarah makes a 270 degree clockwise turn and is now facing north. Which direction was she facing at first?",
"answer0": "North",
"answer1": "South",
"answer2": "East",
"answer3": "West",
"correct_answer": 1,
"skill_id": 142,
"difficulty_id": 3,
"explanation": "Work backwards from facing north. Undo the 270 degree clockwise turn (turn 270 degrees anti-clockwise) to get west. Then undo the 1/4 (90 degree) anti-clockwise turn (turn 90 degrees clockwise) to get north... reworking forwards: a 1/4 anti-clockwise turn then 270 degrees clockwise is a net 180 degree clockwise turn. To end facing north, she must have started facing south.",
"hints": [
"A 1/4 anti-clockwise turn is 90 degrees; combine it with the 270 degree clockwise turn.",
"Net effect is a half turn, so the start direction is opposite to north."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q24",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: South. Open-ended direction question converted to MCQ (4 compass options) since FIB word answers are fragile; correct option is South (index 1)."
},
{
"n": 25,
"type_id": 0,
"question": "Study the figures. In each box, put a tick if the figure is symmetric and a cross (X) if it is not symmetric.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 144,
"difficulty_id": 2,
"explanation": "(i) four circles in a 2x2 arrangement is symmetric (tick). (ii) heart with letter C inside is not symmetric because the C breaks symmetry (cross). (iii) ribbon/banner with a > arrow is not symmetric (cross). (iv) rectangle with arch and crescent C is not symmetric (cross).",
"hints": [
"A figure is symmetric if one half is a mirror image of the other.",
"Letters/shapes added inside can break the symmetry."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q25",
"image_needed": true,
"image_options": false,
"image_file": "q25.png",
"image_page": 13,
"image_bbox": [
0.31,
0.21,
0.7,
0.82
],
"image_loc": "tall boxed panel, four sub-figures (i) four circles (ii) heart with C (iii) banner with arrow (iv) rectangle with arch and crescent",
"notes": "Interactive tick/cross task, no app type. Key answers: (i) tick (symmetric), (ii) cross, (iii) cross, (iv) cross. type_id 0 - skipped on insert."
},
{
"n": 26,
"type_id": 2,
"question": "Complete the table to show the information in the line graph.
Temperature (degrees C) at 9 a.m. is [?], at 11 a.m. is [?], at 1 p.m. is [?], at 5 p.m. is [?].",
"answer0": "25",
"answer1": "28",
"answer2": "29",
"answer3": "30",
"correct_answer": null,
"skill_id": 147,
"difficulty_id": 2,
"explanation": "Read the line graph at each time. 9 a.m. = 25, 11 a.m. = 28, 1 p.m. = 29, 5 p.m. = 30 (given values: 7 a.m. = 23, 3 p.m. = 33, 7 p.m. = 29).",
"hints": [
"Read the height of the line at each time on the graph.",
"Match each reading to the temperature axis."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q26",
"image_needed": true,
"image_options": false,
"image_file": "q26.png",
"image_page": 14,
"image_bbox": [
0.2,
0.16,
0.82,
0.42
],
"image_loc": "upper portion of page, line graph titled 'Temperature on a Sunday', time on x-axis 7 a.m. to 7 p.m.",
"notes": "Key: 9a.m.=25, 11a.m.=28, 1p.m.=29, 5p.m.=30 (handwritten on key). The four blanks fill the missing table cells in order."
},
{
"n": 27,
"type_id": 2,
"question": "What was the difference in temperature between the lowest and highest temperature on that day? [?] $$\\degree C$$",
"answer0": "10",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 148,
"difficulty_id": 1,
"explanation": "Highest temperature = 33 degrees C (at 3 p.m.), lowest = 23 degrees C (at 7 a.m.). Difference = 33 - 23 = 10 degrees C.",
"hints": [
"Find the highest and lowest values on the graph.",
"Subtract: 33 - 23 = 10."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q27",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 33 - 23 = 10 degrees C. Uses the line graph from Q26. Answer unit degrees C."
},
{
"n": 28,
"type_id": 2,
"question": "Harry planted 10 seedlings in a row. The seedlings were planted at the same distance apart. The distance between the second and the fifth seedling was 125.4 m. What was the distance between the first and the tenth seedling? [?] $$m$$",
"answer0": "376.2",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 131,
"difficulty_id": 3,
"explanation": "From the 2nd to the 5th seedling there are 3 gaps = 125.4 m, so 1 gap = 125.4 div 3 = 41.8 m. From the 1st to the 10th seedling there are 9 gaps = 41.8 x 9 = 376.2 m.",
"hints": [
"Count the gaps between the 2nd and 5th seedlings (3 gaps).",
"1 gap = 41.8 m; the 1st to 10th has 9 gaps."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q28",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 1 gap = 41.8, 9 gaps = 376.2 m. Answer unit m."
},
{
"n": 29,
"type_id": 2,
"question": "3 files and 3 pens cost $32.10. I paid $40 for 4 such files and 3 such pens. Find the cost of 3 pens. [?]",
"answer0": "$8.40",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 131,
"difficulty_id": 3,
"explanation": "4 files + 3 pens = $40 and 3 files + 3 pens = $32.10. The difference is 1 file = $40 - $32.10 = $7.90. So 3 files = $23.70. 3 pens = $32.10 - $23.70 = $8.40.",
"hints": [
"Compare the two purchases to find the cost of 1 file.",
"Subtract the cost of 3 files from $32.10 to get 3 pens."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q29",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 1 file = $7.90, 3 pens = $8.40. Answer field labelled $."
},
{
"n": 30,
"type_id": 2,
"question": "I am a 4-digit even number. The sum of the digits is 14. I am 2250 when rounded to the nearest 10. What number am I? [?]",
"answer0": "2246",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 109,
"difficulty_id": 3,
"explanation": "Rounding to 2250 to the nearest 10 means the number is 2245 to 2254. It must be even, so it ends in 6 (2246), 8 (2248), 0/2/4 (2250, 2252, 2254). Digit sum 14: 2+2+4+6 = 14. So the number is 2246.",
"hints": [
"Numbers rounding to 2250 to the nearest 10 are 2245 to 2254.",
"Pick the even one whose digits add to 14: 2246."
],
"source": "Tao Nan 2023 P4 End of Year Exam P1 Q30",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 2246."
},
{
"n": 31,
"type_id": 2,
"question": "A tailor had 500 buttons. He sewed 7 buttons on each shirt and had 248 buttons left.
(a) How many buttons did he use? [?]
(b) How many shirts did he sew the buttons on? [?]",
"answer0": "252",
"answer1": "36",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 2,
"explanation": "(a) Buttons used = 500 - 248 = 252. (b) Shirts = 252 div 7 = 36.",
"hints": [
"Subtract the leftover buttons from the total to get the buttons used.",
"Divide the buttons used by 7 to get the number of shirts."
],
"source": "Tao Nan 2023 P4 End of Year Exam P2 Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (a) 252, (b) 36. Two-part question with two blanks."
},
{
"n": 32,
"type_id": 2,
"question": "Tom had 4730 marbles and Muthu had 1240 marbles at first. Tom gave some marbles to Muthu so that Muthu would have twice as many marbles as Tom in the end. How many marbles did Tom give Muthu? [?]",
"answer0": "2740",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "Total marbles stay 4730 + 1240 = 5970. In the end Muthu has twice Tom, so 3 units = 5970, 1 unit (Tom) = 1990, Muthu = 3980. Tom gave = 3980 - 1240 = 2740 marbles.",
"hints": [
"The total number of marbles does not change.",
"Split the total into 3 equal parts; Muthu ends with 2 parts."
],
"source": "Tao Nan 2023 P4 End of Year Exam P2 Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 5970, Tom end 1990, Muthu end 3980, gave 2740."
},
{
"n": 33,
"type_id": 0,
"question": "The bar graph shows the amount of rainfall recorded at the end of each month from September 2022 to February 2023. Each of the statements is either true, false or not possible to tell based on the information given in the graph.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 104,
"difficulty_id": 2,
"explanation": "(a) December was the wettest: False (November 50 cm is highest). (b) September and January rainfall the same: True (both 20 cm). (c) Difference smallest between November and December: False (November 50, December 40, difference 10; other adjacent pairs are smaller). (d) March 2023 rainfall higher than February 2023: Not possible to tell (no March data).",
"hints": [
"Read each bar's height from the graph.",
"If the graph has no data for a month, the answer is 'not possible to tell'."
],
"source": "Tao Nan 2023 P4 End of Year Exam P2 Q3",
"image_needed": true,
"image_options": false,
"image_file": "q33.png",
"image_page": 20,
"image_bbox": [
0.18,
0.15,
0.82,
0.4
],
"image_loc": "upper portion of page, bar graph titled 'Rainfall recorded from September 2022 to February 2023'",
"notes": "Interactive true/false/not-possible tick table, no app type. Key: (a) False, (b) True, (c) False, (d) Not possible to tell. type_id 0 - skipped on insert."
},
{
"n": 34,
"type_id": 2,
"question": "The mass of a wooden vase is 3.3 kg. The mass of a glass vase is 4.05 kg. What is the total mass of 3 identical wooden vases and 3 identical glass vases? Give your answer to the nearest kilogram. [?] $$kg$$",
"answer0": "22",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 131,
"difficulty_id": 2,
"explanation": "3 wooden vases = 3.3 x 3 = 9.9 kg. 3 glass vases = 4.05 x 3 = 12.15 kg. Total = 9.9 + 12.15 = 22.05 kg, which rounds to 22 kg.",
"hints": [
"Find the mass of 3 of each type, then add.",
"Round 22.05 kg to the nearest kilogram."
],
"source": "Tao Nan 2023 P4 End of Year Exam P2 Q4",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 22.05 kg, rounds to 22 kg. Answer unit kg (nearest kilogram)."
},
{
"n": 35,
"type_id": 2,
"question": "The table shows the departure times from Singapore to Penang and Kuala Lumpur as well as their arrival times. SP 100 to Penang departs 10.40 p.m. and arrives 12.05 a.m. SP 246 to Kuala Lumpur departs 8.15 p.m. and arrives 9.20 p.m.
(a) How long is the flight from Singapore to Penang? Give your answer in h and min. [?]
(b) Mr Bala took SP 246 to Kuala Lumpur. His flight was delayed for 45 minutes. At what time did Mr Bala finally arrive in Kuala Lumpur? Leave your answer in 24-hour clock. [?]",
"answer0": "1 h 25 min",
"answer1": "2205",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 135,
"difficulty_id": 3,
"explanation": "(a) From 10.40 p.m. to 12.05 a.m.: 10.40 p.m. to 11.00 p.m. is 20 min, 11.00 p.m. to 12.05 a.m. is 1 h 5 min, total 1 h 25 min. (b) Scheduled arrival 9.20 p.m. + 45 min delay = 10.05 p.m. = 2205 in 24-hour clock.",
"hints": [
"For (a), count the minutes to the next hour, then add the rest.",
"For (b), add 45 min to 9.20 p.m. and convert to 24-hour time."
],
"source": "Tao Nan 2023 P4 End of Year Exam P2 Q5",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (a) 1 h 25 min, (b) 2205. Table data is reproduced in the stem (short, no figure crop needed)."
},
{
"n": 36,
"type_id": 2,
"question": "A newly opened chicken stall had a promotion. For every chicken bought, the second chicken was sold at half price. Each chicken is $4.70. Mrs Dee bought 4 chickens.
(a) How much did she pay? [?]
(b) At the end of the day, the stall collected $440. There were two $100 notes, three $50 notes and some $10 notes. How many $10 notes were there? [?]",
"answer0": "$14.10",
"answer1": "9",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 131,
"difficulty_id": 3,
"explanation": "(a) Half price = $4.70 div 2 = $2.35. For 4 chickens, 2 are full price and 2 are half price: 2 x $4.70 + 2 x $2.35 = $9.40 + $4.70 = $14.10. (b) Two $100 notes + three $50 notes = $200 + $150 = $350. Remaining = $440 - $350 = $90. Number of $10 notes = $90 div $10 = 9.",
"hints": [
"For (a), every second chicken is half of $4.70.",
"For (b), subtract the value of the $100 and $50 notes from $440."
],
"source": "Tao Nan 2023 P4 End of Year Exam P2 Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (a) $14.10, (b) 9. Chicken sprite + price tag '$4.70 each, Buy a second chicken at HALF price' are decorative; price stated in stem, no crop needed."
},
{
"n": 37,
"type_id": 2,
"question": "The figure is made up of square X and 2 rectangles, Y and Z. Find the area of Z. The figure is 16 cm wide, X has area 36 $$cm^2$$ and Y has area 40 $$cm^2$$. [?] $$cm^2$$",
"answer0": "20",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Square X has area 36, so its side = 6 cm (height of X = 6 cm). The whole figure is 16 cm wide, so Y and Z have width 16 - 6 = 10 cm. Rectangle Y area = 40, width 10, so Y height = 40 div 10 = 4 cm. Z height = 6 - 4 = 2 cm. Area of Z = 10 x 2 = 20 cm squared.",
"hints": [
"Side of square X = square root of 36 = 6 cm; the width of Y and Z = 16 - 6.",
"Find Y's height from its area, then Z's height = X's side minus Y's height."
],
"source": "Tao Nan 2023 P4 End of Year Exam P2 Q7",
"image_needed": true,
"image_options": false,
"image_file": "q37.png",
"image_page": 24,
"image_bbox": [
0.16,
0.18,
0.7,
0.36
],
"image_loc": "upper portion of page, square X (36 cm squared) beside stacked rectangles Y (40 cm squared) and Z; total width 16 cm",
"notes": "Key: X side 6, Y height 4, Z = 10 x 2 = 20 cm squared. Answer unit cm squared."
},
{
"n": 38,
"type_id": 2,
"question": "There are some people attending a carnival. $$\\frac{3}{5}$$ of them are children, $$\\frac{1}{6}$$ of them are men and the rest are women. There are 42 more women than men at the carnival. How many people are at the carnival? [?]",
"answer0": "630",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 122,
"difficulty_id": 3,
"explanation": "Children + men = $$\\frac{3}{5}$$ + $$\\frac{1}{6}$$ = $$\\frac{18}{30}$$ + $$\\frac{5}{30}$$ = $$\\frac{23}{30}$$. Women = 1 - $$\\frac{23}{30}$$ = $$\\frac{7}{30}$$. Difference women - men = $$\\frac{7}{30}$$ - $$\\frac{5}{30}$$ = $$\\frac{2}{30}$$ = $$\\frac{1}{15}$$ of total = 42. So total = 42 x 15 = 630.",
"hints": [
"Find the fraction that are women: 1 minus (children + men).",
"The difference between the women and men fractions equals 42 people."
],
"source": "Tao Nan 2023 P4 End of Year Exam P2 Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: women 7/30, men 5/30, difference 2/30 = 1/15 = 42, total 15 x 42 = 630."
},
{
"n": 39,
"type_id": 2,
"question": "A group of 3 adults and 5 children bought tickets to watch a concert. Each adult ticket cost $7 more than each child ticket. The group paid a total of $125. What was the cost of each adult ticket? [?]",
"answer0": "$20",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "Replace the 3 adult tickets with child-ticket value: 3 adults cost 3 x $7 = $21 more than 3 children. So 8 child tickets cost $125 - $21 = $104. 1 child ticket = $104 div 8 = $13. 1 adult ticket = $13 + $7 = $20.",
"hints": [
"Each adult is $7 more than a child; remove the extra to make all 8 like child tickets.",
"Find the child ticket price first, then add $7."
],
"source": "Tao Nan 2023 P4 End of Year Exam P2 Q9",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 8 children = $104, 1 child = $13, 1 adult = $20."
},
{
"n": 40,
"type_id": 2,
"question": "A curry puff cost $3 and a hotdog cost $4. Miss Gaya spent a total of $238 on 70 curry puffs and hotdogs. How many hotdogs did she buy? [?]",
"answer0": "28",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "Assume all 70 are curry puffs: 70 x $3 = $210. Extra spent = $238 - $210 = $28. Each hotdog costs $4 - $3 = $1 more, so number of hotdogs = $28 div $1 = 28.",
"hints": [
"Assume everything is the cheaper item first, then find the extra cost.",
"Each hotdog adds $1 over a curry puff; divide the extra by $1."
],
"source": "Tao Nan 2023 P4 End of Year Exam P2 Q10",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: assume all curry puffs $210, extra $28, hotdogs = 28. Curry puff/hotdog sprites with $3/$4 price tags are decorative; prices in stem, no crop needed."
}
]
}