{
"paper": {
"school": "Nan Hua Primary School",
"year": 2024,
"level": "P4",
"label": "End-of-Year Exam",
"source_prefix": "Nan Hua 2024 P4 End-of-Year Exam",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "10 thousands and 7 tens is the same as [?].",
"answer0": "107",
"answer1": "1070",
"answer2": "10 007",
"answer3": "10 070",
"correct_answer": 3,
"skill_id": 105,
"difficulty_id": 1,
"explanation": "10 thousands = 10 000 and 7 tens = 70. 10 000 + 70 = 10 070.",
"hints": [
"1 thousand = 1000, so 10 thousands = 10 000.",
"7 tens = 70. Add them together."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (4) = 10 070."
},
{
"n": 2,
"type_id": 1,
"question": "Which of the following numbers when rounded to the nearest ten becomes 84 500?",
"answer0": "84 442",
"answer1": "84 498",
"answer2": "84 507",
"answer3": "84 553",
"correct_answer": 1,
"skill_id": 109,
"difficulty_id": 2,
"explanation": "Rounding to the nearest ten: 84 498 rounds up to 84 500. The others give 84 440, 84 510 and 84 550.",
"hints": [
"Look at the ones digit.",
"If the ones digit is 5 or more, round up."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (2) = 84 498."
},
{
"n": 3,
"type_id": 1,
"question": "Write $$5\\frac{7}{20}$$ as a decimal.",
"answer0": "5.72",
"answer1": "5.7",
"answer2": "5.35",
"answer3": "5.035",
"correct_answer": 2,
"skill_id": 127,
"difficulty_id": 2,
"explanation": "$$\\frac{7}{20}=\\frac{35}{100}=0.35$$, so $$5\\frac{7}{20}=5.35$$.",
"hints": [
"Make the denominator 100: $$\\frac{7}{20}=\\frac{35}{100}$$.",
"35 hundredths = 0.35, then add the whole number 5."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (3) = 5.35."
},
{
"n": 4,
"type_id": 1,
"question": "Which of the following is not an equivalent fraction of $$\\frac{1}{4}$$?",
"answer0": "$$\\frac{2}{8}$$",
"answer1": "$$\\frac{3}{12}$$",
"answer2": "$$\\frac{5}{16}$$",
"answer3": "$$\\frac{6}{24}$$",
"correct_answer": 2,
"skill_id": 77,
"difficulty_id": 2,
"explanation": "$$\\frac{2}{8}=\\frac{3}{12}=\\frac{6}{24}=\\frac{1}{4}$$, but $$\\frac{5}{16}$$ is not (4×5=20≠16).",
"hints": [
"An equivalent fraction of 1/4 has denominator = 4 × numerator.",
"Check: is the denominator 4 times the numerator?"
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q4",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (3) = 5/16."
},
{
"n": 5,
"type_id": 1,
"question": "How many one-quarters are there in 3 wholes?",
"answer0": "$$1\\frac{1}{3}$$",
"answer1": "$$\\frac{3}{4}$$",
"answer2": "12",
"answer3": "4",
"correct_answer": 2,
"skill_id": 119,
"difficulty_id": 1,
"explanation": "Each whole has 4 one-quarters. 3 wholes = 3 × 4 = 12 one-quarters.",
"hints": [
"1 whole = 4 quarters.",
"Multiply 3 by 4."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q5",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (3) = 12."
},
{
"n": 6,
"type_id": 1,
"question": "In the figure, which two lines are perpendicular?",
"answer0": "AB and BC",
"answer1": "AC and CD",
"answer2": "AE and CD",
"answer3": "AE and ED",
"correct_answer": 3,
"skill_id": 100,
"difficulty_id": 2,
"explanation": "AE and ED meet at a right angle at E, so they are perpendicular.",
"hints": [
"Perpendicular lines meet at a right angle (90°).",
"Look for the corner that forms a square right angle."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q6",
"image_needed": true,
"image_options": false,
"image_file": "q6.png",
"image_page": 4,
"image_bbox": [
0.4,
0.62,
0.72,
0.78
],
"image_loc": "right of the options, mid page: a 5-point figure with vertices A, B, C, D, E",
"notes": "Key: (4) = AE and ED."
},
{
"n": 7,
"type_id": 1,
"question": "Which of the following figures does not show AB as the line of symmetry?",
"answer0": "Figure 1",
"answer1": "Figure 2",
"answer2": "Figure 3",
"answer3": "Figure 4",
"correct_answer": 3,
"skill_id": 145,
"difficulty_id": 2,
"explanation": "The dashed line AB is a line of symmetry when the figure folds exactly onto itself along AB. The arrow figure (option 4) is not symmetric about AB.",
"hints": [
"A line of symmetry folds the figure into two matching halves.",
"Test each figure by folding along the dashed diagonal AB."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q7",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 5,
"image_bbox": [
0.1,
0.13,
0.92,
0.27
],
"image_loc": "row of 4 grid figures across the page top, each on a square grid with dashed diagonal AB",
"notes": "Image-option MCQ; crop each to q7_opt0.png..q7_opt3.png. Answer-key digit for Q7 partly obscured by watermark; per analysis the non-symmetric figure is option (4)."
},
{
"n": 8,
"type_id": 1,
"question": "The area of a rectangle is 72 cm$$^2$$. Given that the breadth is 4 cm, what is the length of the rectangle?",
"answer0": "64 cm",
"answer1": "32 cm",
"answer2": "18 cm",
"answer3": "14 cm",
"correct_answer": 2,
"skill_id": 136,
"difficulty_id": 2,
"explanation": "Length = Area ÷ breadth = 72 ÷ 4 = 18 cm.",
"hints": [
"Area = length × breadth.",
"So length = area ÷ breadth = 72 ÷ 4."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q8",
"image_needed": true,
"image_options": false,
"image_file": "q8.png",
"image_page": 5,
"image_bbox": [
0.36,
0.4,
0.55,
0.58
],
"image_loc": "centre of page: a vertical rectangle labelled 72 cm2 with breadth 4 cm and length marked ?",
"notes": "Key: (3) = 18 cm."
},
{
"n": 9,
"type_id": 1,
"question": "The square has the same area as the rectangle. Find the perimeter of the square.",
"answer0": "13 cm",
"answer1": "24 cm",
"answer2": "26 cm",
"answer3": "36 cm",
"correct_answer": 1,
"skill_id": 137,
"difficulty_id": 2,
"explanation": "Rectangle area = 9 × 4 = 36 cm². Square area = 36 cm², so side = 6 cm. Perimeter = 4 × 6 = 24 cm.",
"hints": [
"Find the rectangle's area first (9 × 4).",
"The square has the same area, so find the side then × 4 for perimeter."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q9",
"image_needed": true,
"image_options": false,
"image_file": "q9.png",
"image_page": 5,
"image_bbox": [
0.42,
0.66,
0.85,
0.8
],
"image_loc": "right of the options: a square next to a 9 cm by 4 cm rectangle",
"notes": "Key: (2) = 24 cm."
},
{
"n": 10,
"type_id": 1,
"question": "Which one-month period had the greatest difference in the number of visitors to Bird Paradise?",
"answer0": "January to February",
"answer1": "February to March",
"answer2": "March to April",
"answer3": "April to May",
"correct_answer": 2,
"skill_id": 147,
"difficulty_id": 2,
"explanation": "From the line graph: Jan→Feb ≈ 350, Feb→Mar ≈ 300, Mar→Apr ≈ 370, Apr→May ≈ 150. The greatest difference is March to April.",
"hints": [
"Read the visitor value at each month from the graph.",
"Find the size of the change for each one-month period."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q10",
"image_needed": true,
"image_options": false,
"image_file": "q10.png",
"image_page": 6,
"image_bbox": [
0.18,
0.13,
0.82,
0.4
],
"image_loc": "line graph near top of page: Number of Visitors vs months Jan-Jun (shared by Q10 and Q11)",
"notes": "Key: (3) = March to April. Graph shared with Q11."
},
{
"n": 11,
"type_id": 1,
"question": "250 more visitors visited Bird Paradise in July than in June. How many visitors were there in July?",
"answer0": "250",
"answer1": "275",
"answer2": "750",
"answer3": "775",
"correct_answer": 3,
"skill_id": 148,
"difficulty_id": 2,
"explanation": "From the graph, June ≈ 525. July = 525 + 250 ≈ 775.",
"hints": [
"Read June's value from the graph.",
"Add 250 to June's value."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q11",
"image_needed": true,
"image_options": false,
"image_file": "q11.png",
"image_page": 6,
"image_bbox": [
0.18,
0.13,
0.82,
0.4
],
"image_loc": "same line graph as Q10 near top of page",
"notes": "Key: (4) = 775. Uses the same Q10 graph."
},
{
"n": 12,
"type_id": 1,
"question": "Complete the number pattern.
7103 , 7753 , 7703 , 8353 , 8303 , 8953 , 8903 , [?]",
"answer0": "8253",
"answer1": "8853",
"answer2": "8953",
"answer3": "9553",
"correct_answer": 3,
"skill_id": 108,
"difficulty_id": 2,
"explanation": "The pattern alternates +650 then −50: 7103 (+650) 7753 (−50) 7703 (+650) 8353 (−50) 8303 (+650) 8953 (−50) 8903 (+650) 9553.",
"hints": [
"Look at the change between each pair of numbers.",
"It alternates: add 650, then subtract 50."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q12",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (4) = 9553. Stem shows the sequence as printed (correct_answer is the MCQ index)."
},
{
"n": 13,
"type_id": 1,
"question": "Which of the following is a multiple of 4 and 7?",
"answer0": "11",
"answer1": "35",
"answer2": "52",
"answer3": "84",
"correct_answer": 3,
"skill_id": 115,
"difficulty_id": 2,
"explanation": "A common multiple of 4 and 7 is a multiple of 28. 84 = 28 × 3, and 84 = 4 × 21 = 7 × 12.",
"hints": [
"The number must divide by both 4 and 7.",
"Common multiples of 4 and 7 are multiples of 28."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q13",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (4) = 84."
},
{
"n": 14,
"type_id": 1,
"question": "Alissa bought 5 m of ribbon to tie 4 similar presents. She used 0.87 m of the ribbon to tie each present. What was the length of the ribbon left?",
"answer0": "1.25 m",
"answer1": "1.52 m",
"answer2": "3.48 m",
"answer3": "4.13 m",
"correct_answer": 1,
"skill_id": 131,
"difficulty_id": 2,
"explanation": "Ribbon used = 4 × 0.87 = 3.48 m. Ribbon left = 5 − 3.48 = 1.52 m.",
"hints": [
"Find the total ribbon used: 4 × 0.87.",
"Subtract from 5 m."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q14",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (2) = 1.52 m."
},
{
"n": 15,
"type_id": 1,
"question": "A baker used $$\\frac{1}{5}$$ kg of sugar to make cookies and $$\\frac{1}{4}$$ kg of sugar to make brownies. After that, he had $$\\frac{1}{2}$$ kg of sugar left. How many kilograms of sugar did he have at first?",
"answer0": "$$\\frac{9}{20}$$ kg",
"answer1": "$$\\frac{7}{10}$$ kg",
"answer2": "$$\\frac{3}{4}$$ kg",
"answer3": "$$\\frac{19}{20}$$ kg",
"correct_answer": 3,
"skill_id": 122,
"difficulty_id": 2,
"explanation": "At first = $$\\frac{1}{5}+\\frac{1}{4}+\\frac{1}{2}=\\frac{4}{20}+\\frac{5}{20}+\\frac{10}{20}=\\frac{19}{20}$$ kg.",
"hints": [
"Add what he used and what was left.",
"Use a common denominator of 20."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q15",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (4) = 19/20 kg (1/5 + 1/4 + 1/2)."
},
{
"n": 16,
"type_id": 1,
"question": "The figure is made up of 2 squares, A and B. The area of Square A and Square B is 81 cm$$^2$$ and 36 cm$$^2$$ respectively. What is the perimeter of the figure?",
"answer0": "15 cm",
"answer1": "45 cm",
"answer2": "48 cm",
"answer3": "60 cm",
"correct_answer": 2,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Square A side = 9 cm (9×9=81); Square B side = 6 cm (6×6=36). Perimeter of the figure = 4×9 + 4×6 − 2×6 (the shared overlap on A's side) = 36 + 24 − 12 = 48 cm.",
"hints": [
"Find each square's side from its area.",
"Add the two perimeters, then subtract the overlapping edges where B touches A."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q16",
"image_needed": true,
"image_options": false,
"image_file": "q16.png",
"image_page": 8,
"image_bbox": [
0.5,
0.62,
0.78,
0.78
],
"image_loc": "right of the options: a large square A (81 cm2) with a smaller square B (36 cm2) attached to its right side",
"notes": "Key: (3) = 48 cm."
},
{
"n": 17,
"type_id": 1,
"question": "Find the area of the figure. All the lines meet at right angles.",
"answer0": "254 cm$$^2$$",
"answer1": "302 cm$$^2$$",
"answer2": "324 cm$$^2$$",
"answer3": "374 cm$$^2$$",
"correct_answer": 0,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Full outer rectangle = 22 × 17 = 374 cm². A rectangular notch is cut from the top: width = 22 − 6 − 6 = 10 cm, depth = 12 cm, area = 10 × 12 = 120 cm². Figure area = 374 − 120 = 254 cm².",
"hints": [
"Find the area of the whole outer rectangle (22 × 17).",
"Subtract the area of the rectangular notch cut out of it."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q17",
"image_needed": true,
"image_options": false,
"image_file": "q17.png",
"image_page": 9,
"image_bbox": [
0.45,
0.13,
0.9,
0.33
],
"image_loc": "right of the options: a rectilinear figure 22 cm wide, 17 cm tall, with a 6 cm-wide, 12 cm-deep notch at the top",
"notes": "Key: (1) = 254 cm2."
},
{
"n": 18,
"type_id": 1,
"question": "Name the two angles that are smaller than 90°.",
"answer0": "∠KLM and ∠JKL",
"answer1": "∠KLM and ∠MNJ",
"answer2": "∠JKL and ∠MNJ",
"answer3": "∠JKL and ∠NJK",
"correct_answer": 1,
"skill_id": 139,
"difficulty_id": 2,
"explanation": "In quadrilateral JKLM/N, the angles at L (∠KLM) and at N (∠MNJ) are acute (smaller than 90°).",
"hints": [
"An angle smaller than 90° is an acute angle (a sharp corner).",
"Compare each marked corner against a right angle."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q18",
"image_needed": true,
"image_options": false,
"image_file": "q18.png",
"image_page": 9,
"image_bbox": [
0.28,
0.45,
0.62,
0.66
],
"image_loc": "centre of page: a four-sided figure with vertices N, J, K, L (and M) and angle arcs marked at each vertex",
"notes": "Key: (2) = ∠KLM and ∠MNJ."
},
{
"n": 19,
"type_id": 1,
"question": "Which figure is a net of a pyramid?",
"answer0": "Figure 1",
"answer1": "Figure 2",
"answer2": "Figure 3",
"answer3": "Figure 4",
"correct_answer": 2,
"skill_id": 233,
"difficulty_id": 2,
"explanation": "A net of a (square-based) pyramid is one square base with a triangle on each of its four sides. Option 3 shows this arrangement.",
"hints": [
"A pyramid net has one base shape with triangular faces around it.",
"Count the triangles and check they all fold up to one apex."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q19",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 10,
"image_bbox": [
0.12,
0.12,
0.88,
0.28
],
"image_loc": "row of 4 candidate nets across the page top",
"notes": "Image-option MCQ; crop each to q19_opt0.png..q19_opt3.png. Key: (3)."
},
{
"n": 20,
"type_id": 1,
"question": "There were some country erasers in a box that were shared by some students. If each student took 2 erasers from the box, there would be 3 erasers left over. If each student took 3 erasers, there would be 1 eraser short. What is the total number of country erasers in the box?",
"answer0": "5",
"answer1": "6",
"answer2": "9",
"answer3": "11",
"correct_answer": 3,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "Let s = number of students. 2s + 3 = 3s − 1, so s = 4. Erasers = 2 × 4 + 3 = 11.",
"hints": [
"Write the total erasers two ways in terms of the number of students.",
"Set the two expressions equal: 2s + 3 = 3s − 1."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q20",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (4) = 11."
},
{
"n": 21,
"type_id": 2,
"question": "Write six thousand and thirteen in figures. [?]",
"answer0": "6013",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 106,
"difficulty_id": 1,
"explanation": "Six thousand = 6000, and thirteen = 13. 6000 + 13 = 6013.",
"hints": [
"Six thousand is 6000.",
"Add thirteen (13) to it."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q21",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 6013."
},
{
"n": 22,
"type_id": 2,
"question": "What is the remainder when 1013 is divided by 7? [?]",
"answer0": "5",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 117,
"difficulty_id": 2,
"explanation": "1013 ÷ 7 = 144 remainder 5 (144 × 7 = 1008, 1013 − 1008 = 5).",
"hints": [
"Find the largest multiple of 7 below 1013.",
"Subtract it from 1013 to get the remainder."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q22",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 1013 ÷ 7 = 144 R5. Remainder = 5."
},
{
"n": 23,
"type_id": 2,
"question": "Some factors of 32 are 1, 2, 4 and 32. What are the other two factors of 32? [?] , [?]",
"answer0": "8",
"answer1": "16",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 111,
"difficulty_id": 2,
"explanation": "The factors of 32 are 1, 2, 4, 8, 16, 32. The two missing factors are 8 and 16.",
"hints": [
"List all numbers that divide 32 exactly.",
"32 = 2 × 16 = 4 × 8."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q23",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 8 and 16."
},
{
"n": 24,
"type_id": 2,
"question": "Express $$\\frac{6}{18}$$ in its simplest form. [?]",
"answer0": "1/3",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 78,
"difficulty_id": 2,
"explanation": "Divide numerator and denominator by 6: $$\\frac{6}{18}=\\frac{1}{3}$$.",
"hints": [
"Find the largest number that divides both 6 and 18.",
"Divide top and bottom by 6."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q24",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 1/3. FIB fraction answer kept as plain 1/3."
},
{
"n": 25,
"type_id": 2,
"question": "Arrange the following fractions from the greatest to the smallest.
$$\\frac{1}{2}$$ , $$\\frac{5}{6}$$ , $$\\frac{7}{12}$$
[?] (greatest) , [?] , [?] (smallest)",
"answer0": "5/6",
"answer1": "7/12",
"answer2": "1/2",
"answer3": null,
"correct_answer": null,
"skill_id": 79,
"difficulty_id": 2,
"explanation": "Convert to twelfths: 1/2 = 6/12, 5/6 = 10/12, 7/12 = 7/12. Greatest to smallest: 10/12, 7/12, 6/12, i.e. 5/6, 7/12, 1/2.",
"hints": [
"Give all three fractions the common denominator 12.",
"Compare the numerators to order them."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q25",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 5/6, 7/12, 1/2 (greatest to smallest). Ordering FIB, one blank per position."
},
{
"n": 26,
"type_id": 2,
"question": "13.75 + 0.28 = [?]",
"answer0": "14.03",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 129,
"difficulty_id": 1,
"explanation": "13.75 + 0.28 = 14.03.",
"hints": [
"Line up the decimal points.",
"Add the hundredths, tenths, then whole numbers."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q26",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 14.03."
},
{
"n": 27,
"type_id": 2,
"question": "Round 13.56 to the nearest whole number. [?]",
"answer0": "14",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 128,
"difficulty_id": 1,
"explanation": "The tenths digit is 5, so round up: 13.56 rounds to 14.",
"hints": [
"Look at the digit after the decimal point (the tenths).",
"If it is 5 or more, round the whole number up."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q27",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 14."
},
{
"n": 28,
"type_id": 2,
"question": "Find the value of 6.94 × 6. [?]",
"answer0": "41.64",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 130,
"difficulty_id": 2,
"explanation": "6.94 × 6 = 41.64.",
"hints": [
"Multiply 694 × 6 = 4164.",
"Place the decimal point two places from the right: 41.64."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q28",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 41.64."
},
{
"n": 29,
"type_id": 2,
"question": "Measure and write down the size of ∠x. [?]",
"answer0": "130",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 140,
"difficulty_id": 2,
"explanation": "Measuring ∠x with a protractor gives 130° (the key accepts 129° to 131°).",
"hints": [
"Place the protractor's centre on the vertex of the angle.",
"Read off the scale where the arm crosses."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q29",
"image_needed": true,
"image_options": false,
"image_file": "q29.png",
"image_page": 13,
"image_bbox": [
0.12,
0.3,
0.55,
0.45
],
"image_loc": "below the question: an angle with vertex toward lower-left, one arm horizontal, labelled x",
"notes": "Key: 130° (accept 129°-131°). Answer is in degrees; stored as plain number 130."
},
{
"n": 30,
"type_id": 2,
"question": "10 030 children visited the zoo in June. 3109 more children than adults visited the zoo. How many people visited the zoo altogether in June? [?]",
"answer0": "16951",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 2,
"explanation": "Adults = 10 030 − 3109 = 6921. Total = 10 030 + 6921 = 16 951.",
"hints": [
"Find the number of adults: children − 3109.",
"Add children and adults together."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q30",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 16 951."
},
{
"n": 31,
"type_id": 2,
"question": "The height of a plant is 6.25 cm now. It grows 0.7 cm every day. What is the height of the plant after 4 days? [?]",
"answer0": "9.05",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 131,
"difficulty_id": 2,
"explanation": "Growth in 4 days = 0.7 × 4 = 2.8 cm. Height = 6.25 + 2.8 = 9.05 cm.",
"hints": [
"Find the total growth over 4 days: 0.7 × 4.",
"Add it to the starting height 6.25 cm."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q31",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 9.05 cm. Answer in cm."
},
{
"n": 32,
"type_id": 2,
"question": "Mr Chan planted 7 flagpoles around the border of a circular lake. The distance between each flagpole and the next was equal for all the flagpoles. The distance between the 1st flagpole and the 4th flagpole was 12.03 m. What was the distance of the border around the lake? [?]",
"answer0": "28.07",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 131,
"difficulty_id": 3,
"explanation": "From the 1st to the 4th flagpole there are 3 equal intervals: 1 interval = 12.03 ÷ 3 = 4.01 m. Around the circular border the 7 flagpoles form 7 intervals: 7 × 4.01 = 28.07 m.",
"hints": [
"Count the gaps between the 1st and 4th flagpole (that's 3 gaps).",
"Find one gap, then multiply by 7 gaps for the whole loop."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q32",
"image_needed": true,
"image_options": false,
"image_file": "q32.png",
"image_page": 14,
"image_bbox": [
0.13,
0.18,
0.42,
0.4
],
"image_loc": "left of the page: a circular lake labelled 'Lake' with 7 flagpoles around its border",
"notes": "Key: 28.07 m. Answer in m. 7 flagpoles around a closed loop = 7 intervals."
},
{
"n": 33,
"type_id": 2,
"question": "Cathy had $$\\frac{3}{4}$$ ℓ of milk. She drank $$\\frac{1}{4}$$ ℓ of the milk and spilled $$\\frac{1}{3}$$ ℓ of it. (a) How much milk did she drink and spill altogether? (b) How much milk did she have left? [?] , [?]",
"answer0": "7/12",
"answer1": "1/6",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 122,
"difficulty_id": 2,
"explanation": "(a) Drank + spilled = 1/4 + 1/3 = 3/12 + 4/12 = 7/12 ℓ. (b) Left = 3/4 − 7/12 = 9/12 − 7/12 = 2/12 = 1/6 ℓ.",
"hints": [
"(a) Add 1/4 and 1/3 using a common denominator of 12.",
"(b) Subtract the total used (7/12) from what she started with (3/4)."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q33",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (a) 7/12 ℓ, (b) 2/12 ℓ = 1/6 ℓ. Two-part FIB, answer0=(a), answer1=(b) in simplest form."
},
{
"n": 34,
"type_id": 0,
"question": "The figure shows 13 shaded squares. Shade 2 more squares to complete the symmetric pattern with AB as the line of symmetry.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 145,
"difficulty_id": 2,
"explanation": "Reflect the shaded squares across the diagonal AB; the 2 squares whose mirror images are currently unshaded must be shaded to make the pattern symmetric.",
"hints": [
"Each shaded square must have a matching shaded square on the other side of AB.",
"Find the shaded squares whose mirror image is still blank."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q34",
"image_needed": true,
"image_options": false,
"image_file": "q34.png",
"image_page": 15,
"image_bbox": [
0.25,
0.15,
0.55,
0.36
],
"image_loc": "a grid of squares with 13 shaded, dashed diagonal AB drawn from lower-left A to upper-right B",
"notes": "Interactive shading task — no value answer; type_id 0, will be skipped on insert. Answer: shade the 2 squares that mirror the existing shaded squares across AB."
},
{
"n": 35,
"type_id": 0,
"question": "Draw the following cuboid on the isometric grid.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 231,
"difficulty_id": 2,
"explanation": "Draw a 4 units × 2 units × 2 units cuboid on the isometric dot grid, matching the given solid.",
"hints": [
"Use the dots to keep edges parallel.",
"The cuboid is 4 units long, 2 units wide and 2 units tall."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q35",
"image_needed": true,
"image_options": false,
"image_file": "q35.png",
"image_page": 15,
"image_bbox": [
0.1,
0.42,
0.42,
0.62
],
"image_loc": "left of the page: a labelled cuboid 4 units × 2 units × 2 units to be copied onto the isometric grid",
"notes": "Interactive drawing task — no value answer; type_id 0, skipped on insert."
},
{
"n": 36,
"type_id": 2,
"question": "Andy and Ben had a total of $698. Andy and Carl had a total of $510. Ben had three times as much money as Carl. How much money did Andy have? [?]",
"answer0": "416",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "Ben − Carl = 698 − 510 = 188. Ben = 3 × Carl, so Ben − Carl = 2 units = 188, giving 1 unit (Carl) = 94. Andy = 510 − Carl = 510 − 94 = $416.",
"hints": [
"Subtract the two totals to compare Ben and Carl (698 − 510).",
"Ben = 3 × Carl, so the difference is 2 units; find Carl, then Andy = 510 − Carl."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q36",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working (p25): 698 − 510 = 188; 188 ÷ 2 = 94; 510 − 94 = 416. Answer = $416."
},
{
"n": 37,
"type_id": 2,
"question": "The table shows the types of CCA participated in by some Primary 4 students. What numbers do the letters A and B represent? A = [?] , B = [?]",
"answer0": "17",
"answer1": "15",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 146,
"difficulty_id": 2,
"explanation": "Dance column total = 24 = boys(7) + girls(A), so A = 24 − 7 = 17. Badminton column total = 32 = boys(B) + girls(17), so B = 32 − 17 = 15.",
"hints": [
"For each column, boys + girls = total.",
"A = Dance total − boys; B = Badminton total − girls."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q37",
"image_needed": true,
"image_options": false,
"image_file": "q37.png",
"image_page": 16,
"image_bbox": [
0.18,
0.12,
0.78,
0.22
],
"image_loc": "table near top of page: rows Number of boys / Number of girls / Total across columns Chess, Dance, Choir, Badminton",
"notes": "Key: A = 17, B = 15."
},
{
"n": 38,
"type_id": 2,
"question": "The table and the pie chart show the number of people in a cinema. Fill in the missing people and numbers in the pie chart. (a) [?] , (b) [?]",
"answer0": "Girls, 14",
"answer1": "Men, 30",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 235,
"difficulty_id": 2,
"explanation": "The pie chart already labels Boys (21) and Women (40). The remaining two sectors are (a) Girls = 14 and (b) Men = 30, read from the table.",
"hints": [
"Match the unlabelled sectors to the table values not yet shown.",
"Boys and Women are given; the missing groups are Men and Girls."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q38",
"image_needed": true,
"image_options": false,
"image_file": "q38.png",
"image_page": 16,
"image_bbox": [
0.13,
0.55,
0.45,
0.74
],
"image_loc": "lower-left: a pie chart with sectors Boys 21, Women 40 and two blank sectors (a) and (b)",
"notes": "Key: (a) Girls, Number 14; (b) Men, Number 30. answer0 = sector (a), answer1 = sector (b)."
},
{
"n": 39,
"type_id": 2,
"question": "The diagram shows the floor plan of a 9 m by 4 m rectangular room. In the room there is a rectangular desk and a square bookshelf. The shaded parts of the floor are not covered by furniture. Find the area of the floor that is not covered by furniture. [?]",
"answer0": "29",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Room area = 9 × 4 = 36 m². Desk = 3 × 1 = 3 m². Bookshelf (square) = 2 × 2 = 4 m². Uncovered area = 36 − 3 − 4 = 29 m².",
"hints": [
"Find the whole floor area (9 × 4).",
"Subtract the desk area and the bookshelf area."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q39",
"image_needed": true,
"image_options": false,
"image_file": "q39.png",
"image_page": 17,
"image_bbox": [
0.18,
0.2,
0.72,
0.42
],
"image_loc": "floor-plan diagram: 9 m by 4 m room with a Desk (3 m × 1 m) and a square Bookshelf (2 m), shaded uncovered floor (shared by Q39 and Q40)",
"notes": "Key: 29 m². Answer in m^2. Diagram shared with Q40."
},
{
"n": 40,
"type_id": 2,
"question": "Find the perimeter of the floor that is not covered by furniture. [?]",
"answer0": "32",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Tracing the boundary of the shaded (uncovered) region around the room and around the desk and bookshelf cut-outs gives a total perimeter of 32 m (e.g. (9+4)×2 + 3 + 3 = 26 + 6 = 32, or 9 + 2 + 2 + 2 + 7 + 4 + 3 + 3 = 32).",
"hints": [
"Trace the edge of the shaded floor, including the edges where the furniture meets it.",
"Add all the boundary lengths."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q40",
"image_needed": true,
"image_options": false,
"image_file": "q40.png",
"image_page": 17,
"image_bbox": [
0.18,
0.2,
0.72,
0.42
],
"image_loc": "same floor-plan diagram as Q39",
"notes": "Key: 32 m. Answer in m. Uses the same Q39 diagram."
},
{
"n": 41,
"type_id": 2,
"question": "A rope of length 6.3 m was cut into three pieces. The first piece was thrice as long as the second piece. The second piece was twice as long as the third piece. How long was the second piece? [?]",
"answer0": "1.4",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 131,
"difficulty_id": 3,
"explanation": "Let the third piece = 1 unit. Second = 2 units, first = 3 × 2 = 6 units. Total = 6 + 2 + 1 = 9 units = 6.3 m, so 1 unit = 0.7 m. Second piece = 2 × 0.7 = 1.4 m.",
"hints": [
"Let the third piece be 1 unit, then write the others in units.",
"Total units = 9; find 1 unit, then the second piece (2 units)."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q41",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: second piece = 1.4 m. Answer in m."
},
{
"n": 42,
"type_id": 2,
"question": "Cindy baked some muffins. $$\\frac{5}{12}$$ of the muffins are chocolate muffins and the rest are blueberry muffins. She baked 34 more blueberry muffins than chocolate muffins. How many muffins did she bake in all? [?]",
"answer0": "204",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 122,
"difficulty_id": 3,
"explanation": "Chocolate = 5/12, blueberry = 7/12. Difference = 7/12 − 5/12 = 2/12 of the total = 34 muffins. So 1/12 = 17, and total = 12 × 17 = 204.",
"hints": [
"Find the fraction that are blueberry (1 − 5/12).",
"The difference 7/12 − 5/12 equals 34; use it to find the total."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q42",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 204 muffins."
},
{
"n": 43,
"type_id": 2,
"question": "Peter bought 3 shirts and 2 bags for $289. Each bag cost $17 more than a shirt. How much did a bag cost? [?]",
"answer0": "68",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "Replace each bag with a shirt + $17: 3 shirts + 2 bags = 5 shirts + 2×$17 = 5 shirts + $34 = $289. So 5 shirts = $255, 1 shirt = $51. A bag = $51 + $17 = $68.",
"hints": [
"Each bag = a shirt + $17; rewrite everything in terms of shirts.",
"5 shirts + $34 = $289; find one shirt, then add $17 for a bag."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q43",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: a bag costs $68. Answer is a money value (68)."
},
{
"n": 44,
"type_id": 2,
"question": "Ken had 480 marbles. He had five times as many marbles as Jack. After Ken gave Jack some marbles, they each had the same number of marbles. How many marbles did Ken give to Jack? [?]",
"answer0": "192",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "Ken = 5 units = 480, so 1 unit = 96; Jack = 1 unit = 96. Total = 576, each ends with 288. Ken must give 480 − 288 = 192 marbles to Jack.",
"hints": [
"Find Jack's marbles (Ken ÷ 5).",
"They end up equal, so each has half the total; Ken gives away the difference."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q44",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: Ken gave Jack 192 marbles."
},
{
"n": 45,
"type_id": 2,
"question": "The table shows the favourite hobbies of some P4 students. (a) How many P4 students are there in total? (b) How many P4 students like swimming? (c) What fraction of the students like skipping? (d) Which is the least popular hobby among the P4 students? [?] , [?] , [?] , [?]",
"answer0": "120",
"answer1": "35",
"answer2": "1/5",
"answer3": "Drawing",
"correct_answer": null,
"skill_id": 120,
"difficulty_id": 3,
"explanation": "(a) Singing = 19 students = 19/120 of the total, so total = 120. (b) Swimming = 7/24 of 120 = 35. (c) Skipping = 24 students = 24/120 = 1/5. (d) Smallest number of students is Drawing (14), so Drawing is least popular.",
"hints": [
"(a) 19 students correspond to the fraction 19/120 — so the total is 120.",
"(b)–(c) use fraction × total or number ÷ total. (d) compare the counts."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q45",
"image_needed": true,
"image_options": false,
"image_file": "q45.png",
"image_page": 20,
"image_bbox": [
0.1,
0.12,
0.82,
0.25
],
"image_loc": "table near top: rows Number of students / Fraction of students across Singing, Drawing, Cycling, Swimming, Skipping",
"notes": "Key: (a) 120, (b) 35, (c) 1/5, (d) Drawing. Multi-part; answer0=(a) count, answer1=(b) count, answer2=(c) fraction (plain), answer3=(d) hobby word. Part (d) is a word answer embedded in this multi-part FIB; verify exact-match grading or treat (d) separately on insert."
},
{
"n": 46,
"type_id": 2,
"question": "Set Meal A costs $27 for 4 persons (8 nuggets, 4 pieces chicken, 4 drinks). Set Meal B costs $35 for 5 persons (10 nuggets, 5 pieces chicken, 5 drinks). Set Meal C costs $41 for 6 persons (12 nuggets, 6 pieces chicken, 6 drinks). (a) Mrs Chan wants to order food for 18 children at a party with no food wastage. Each child should get 2 pieces of nugget, 1 piece of chicken and 1 drink. What combination of set meals should Mrs Chan order if she wants to pay the least amount of money? Number of Set Meal A: [?] , B: [?] , C: [?] (b) How much money would Mrs Chan need to pay for the combination of set meals she has chosen? [?]",
"answer0": "3",
"answer1": "0",
"answer2": "1",
"answer3": "122",
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "For 18 children: nuggets needed = 18 × 2 = 36, chicken = 18, drinks = 18. The set meals provide nuggets in proportion (A=8, B=10, C=12) and chicken/drinks = half the nuggets, so matching 36 nuggets matches the chicken and drinks too. Cheapest combination giving 36 nuggets with no wastage is 3×A + 1×C (8×3 + 12 = 36). Cost (a) = 3A,0B,1C. (b) Cost = 3×$27 + $41 = $81 + $41 = $122.",
"hints": [
"Work out the total nuggets needed (18 × 2 = 36); chicken and drinks follow.",
"Find the cheapest mix of meals giving exactly 36 nuggets — compare $ per meal."
],
"source": "Nan Hua 2024 P4 End-of-Year Exam Q46",
"image_needed": true,
"image_options": false,
"image_file": "q46.png",
"image_page": 21,
"image_bbox": [
0.13,
0.13,
0.85,
0.24
],
"image_loc": "table near top: three set-meal columns A ($27), B ($35), C ($41) with their contents",
"notes": "Key: (a) 3 Set Meal A, 0 Set Meal B, 1 Set Meal C; (b) $122. answer0=A count, answer1=B count, answer2=C count, answer3=(b) total cost (122)."
}
]
}