{
"paper": {
"school": "Pei Hwa Presbyterian",
"year": 2023,
"level": "P4",
"label": "End of Year Exam",
"source_prefix": "Pei Hwa 2023 P4 End of Year Exam",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "73 thousands and 8 tens is the same as [?].",
"answer0": "738",
"answer1": "7380",
"answer2": "73 008",
"answer3": "73 080",
"correct_answer": 3,
"skill_id": 105,
"difficulty_id": 1,
"explanation": "73 thousands = 73 000 and 8 tens = 80. Total = 73 000 + 80 = 73 080.",
"hints": [
"1 thousand = 1000, 1 ten = 10.",
"Add 73 000 and 80."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (4) = 73 080."
},
{
"n": 2,
"type_id": 1,
"question": "13 845 rounded to the nearest hundred is [?].",
"answer0": "13 800",
"answer1": "13 850",
"answer2": "13 900",
"answer3": "14 000",
"correct_answer": 0,
"skill_id": 109,
"difficulty_id": 1,
"explanation": "The tens digit is 4, so round down. 13 845 to the nearest hundred is 13 800.",
"hints": [
"Look at the tens digit (4).",
"4 or less rounds down."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (1) = 13 800."
},
{
"n": 3,
"type_id": 1,
"question": "$$7\\frac{4}{5} = \\frac{[?]}{5}$$
What is the missing number in the box?",
"answer0": "28",
"answer1": "31",
"answer2": "35",
"answer3": "39",
"correct_answer": 3,
"skill_id": 119,
"difficulty_id": 1,
"explanation": "Convert the mixed number to an improper fraction: $$7\\frac{4}{5} = \\frac{7\\times5+4}{5} = \\frac{39}{5}$$. The missing number is 39.",
"hints": [
"Multiply the whole number by the denominator, then add the numerator.",
"7 × 5 + 4 = 39."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "The [?] in the stem is the box from the printed fraction. Key: option (4) = 39."
},
{
"n": 4,
"type_id": 1,
"question": "What fraction of the shapes are \\u25c6 ?",
"answer0": "$$\\frac{4}{6}$$",
"answer1": "$$\\frac{4}{10}$$",
"answer2": "$$\\frac{6}{10}$$",
"answer3": "$$\\frac{6}{4}$$",
"correct_answer": 2,
"skill_id": 120,
"difficulty_id": 1,
"explanation": "There are 10 shapes in total. 6 of them are diamonds. So the fraction of diamonds is $$\\frac{6}{10}$$.",
"hints": [
"Count all the shapes first.",
"Count only the diamonds, then write diamonds out of total."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q4",
"image_needed": true,
"image_options": false,
"image_file": "q4.png",
"image_page": 3,
"image_bbox": [
0.35,
0.14,
0.66,
0.27
],
"image_loc": "boxed grid of 10 shapes (diamonds and stars) below the question, top of page",
"notes": "Box shows 10 shapes: 6 diamonds, 4 stars. Key: option (3) = 6/10."
},
{
"n": 5,
"type_id": 1,
"question": "In the number 45.67, the digit [?] is in the tenths place.",
"answer0": "7",
"answer1": "6",
"answer2": "5",
"answer3": "4",
"correct_answer": 1,
"skill_id": 123,
"difficulty_id": 1,
"explanation": "The first digit after the decimal point is the tenths place. In 45.67 that digit is 6.",
"hints": [
"Tenths is the first place after the decimal point.",
"In 45.67, the digit right after the point is 6."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q5",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (2) = 6."
},
{
"n": 6,
"type_id": 1,
"question": "Write $$4\\frac{3}{20}$$ as a decimal.",
"answer0": "4.32",
"answer1": "4.3",
"answer2": "4.15",
"answer3": "4.015",
"correct_answer": 2,
"skill_id": 127,
"difficulty_id": 1,
"explanation": "$$\\frac{3}{20} = \\frac{15}{100} = 0.15$$. So $$4\\frac{3}{20} = 4.15$$.",
"hints": [
"Make the denominator 100: 3/20 = 15/100.",
"15/100 = 0.15."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (3) = 4.15."
},
{
"n": 7,
"type_id": 1,
"question": "Arrange these numbers from the smallest to the greatest.
5709, 5079, 5790",
"answer0": "5790 , 5709 , 5079",
"answer1": "5790 , 5079 , 5709",
"answer2": "5079 , 5709 , 5790",
"answer3": "5079 , 5790 , 5709",
"correct_answer": 2,
"skill_id": 107,
"difficulty_id": 1,
"explanation": "Compare digit by digit: 5079 < 5709 < 5790. Smallest to greatest is 5079, 5709, 5790.",
"hints": [
"Compare the hundreds digits first.",
"0 < 7 in the hundreds place, so 5079 is smallest."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (3) = 5079, 5709, 5790."
},
{
"n": 8,
"type_id": 1,
"question": "Which of the following is a multiple of both 3 and 4?",
"answer0": "7",
"answer1": "9",
"answer2": "16",
"answer3": "24",
"correct_answer": 3,
"skill_id": 115,
"difficulty_id": 1,
"explanation": "A multiple of both 3 and 4 is a multiple of 12. 24 = 12 × 2, which is divisible by both 3 and 4.",
"hints": [
"A common multiple of 3 and 4 is a multiple of 12.",
"Which option divides by both 3 and 4?"
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (4) = 24."
},
{
"n": 9,
"type_id": 1,
"question": "Beads are used to form a pattern as shown. How many beads will there be in Figure 6?",
"answer0": "15",
"answer1": "20",
"answer2": "21",
"answer3": "28",
"correct_answer": 2,
"skill_id": 108,
"difficulty_id": 2,
"explanation": "The pattern is triangular numbers: Figure 1=1, 2=3, 3=6, 4=10, 5=15, 6=21. Figure 6 has 21 beads.",
"hints": [
"Each figure adds one more row of beads than the last.",
"1, 3, 6, 10, 15, 21 — add 2, 3, 4, 5, 6."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q9",
"image_needed": true,
"image_options": false,
"image_file": "q9.png",
"image_page": 4,
"image_bbox": [
0.22,
0.62,
0.8,
0.76
],
"image_loc": "row of four triangular bead figures (Figure 1 to Figure 4) below the question",
"notes": "Triangular number pattern. Key: option (3) = 21."
},
{
"n": 10,
"type_id": 1,
"question": "Which of the numbers when rounded to the nearest tenth becomes 82.3?",
"answer0": "82.24",
"answer1": "82.34",
"answer2": "82.235",
"answer3": "82.354",
"correct_answer": 1,
"skill_id": 128,
"difficulty_id": 2,
"explanation": "Rounding to the nearest tenth: 82.34 has hundredths digit 4, so it rounds down to 82.3. (82.24 -> 82.2; 82.235 -> 82.2; 82.354 -> 82.4.)",
"hints": [
"Look at the hundredths digit to round to the nearest tenth.",
"82.34: hundredths is 4, so it stays 82.3."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q10",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (2) = 82.34."
},
{
"n": 11,
"type_id": 1,
"question": "Which of the following decimals is closest in value to 0.5?",
"answer0": "0.4",
"answer1": "0.6",
"answer2": "0.46",
"answer3": "0.56",
"correct_answer": 2,
"skill_id": 124,
"difficulty_id": 2,
"explanation": "Find the difference from 0.5: |0.4-0.5|=0.1, |0.6-0.5|=0.1, |0.46-0.5|=0.04, |0.56-0.5|=0.06. The smallest difference is 0.04, so 0.46 is closest.",
"hints": [
"Find how far each number is from 0.5.",
"0.46 differs by only 0.04."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q11",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (3) = 0.46."
},
{
"n": 12,
"type_id": 1,
"question": "Mrs Lee bought 9 similar packets of milk.
After she used 6 packets of milk to make some cakes, she had 3.42 $$l$$ of milk left.
How many litres of milk did she have at first?",
"answer0": "6.84 $$l$$",
"answer1": "10.26 $$l$$",
"answer2": "11.58 $$l$$",
"answer3": "13.68 $$l$$",
"correct_answer": 1,
"skill_id": 131,
"difficulty_id": 2,
"explanation": "9 - 6 = 3 packets left = 3.42 l, so 1 packet = 3.42 ÷ 3 = 1.14 l. At first she had 9 packets = 1.14 × 9 = 10.26 l.",
"hints": [
"The 3.42 l left is 3 packets (9 - 6).",
"Find 1 packet, then multiply by 9."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q12",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (2) = 10.26 l."
},
{
"n": 13,
"type_id": 1,
"question": "Similar balloons are tied on a pole and placed at an equal distance. Both ends of the pole are tied with balloons. The distance between two balloons is 1.65 m. What is the total distance between 8 balloons?",
"answer0": "9.9 m",
"answer1": "11.55 m",
"answer2": "13.2 m",
"answer3": "14.85 m",
"correct_answer": 1,
"skill_id": 131,
"difficulty_id": 2,
"explanation": "8 balloons make 8 - 1 = 7 gaps. Total distance = 7 × 1.65 = 11.55 m.",
"hints": [
"Count the gaps, not the balloons: 8 balloons give 7 gaps.",
"7 × 1.65 = 11.55."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q13",
"image_needed": true,
"image_options": false,
"image_file": "q13.png",
"image_page": 6,
"image_bbox": [
0.18,
0.27,
0.8,
0.38
],
"image_loc": "horizontal pole with balloons and a 1.65 m label, below the question text",
"notes": "Key: option (2) = 11.55 m. Gaps = balloons - 1."
},
{
"n": 14,
"type_id": 1,
"question": "ABCD is a rectangle. Find $$\\angle x$$.",
"answer0": "10\\u00b0",
"answer1": "30\\u00b0",
"answer2": "70\\u00b0",
"answer3": "80\\u00b0",
"correct_answer": 0,
"skill_id": 143,
"difficulty_id": 2,
"explanation": "Angle ADC of the rectangle is 90°. It is split into 20°, 60° and x. So x = 90° - 20° - 60° = 10°.",
"hints": [
"A corner of a rectangle is 90°.",
"90° - 20° - 60° = x."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q14",
"image_needed": true,
"image_options": false,
"image_file": "q14.png",
"image_page": 6,
"image_bbox": [
0.24,
0.58,
0.55,
0.74
],
"image_loc": "rectangle ABCD with lines from corner D marking angles 20°, 60° and x",
"notes": "Key: option (1) = 10°."
},
{
"n": 15,
"type_id": 1,
"question": "Study the piece of folded paper. Which symmetrical figure was cut out from it?",
"answer0": "Figure 1",
"answer1": "Figure 2",
"answer2": "Figure 3",
"answer3": "Figure 4",
"correct_answer": 0,
"skill_id": 144,
"difficulty_id": 2,
"explanation": "Unfolding a folded cut produces a figure symmetrical about the fold line. Only the figure in option (1) has line symmetry matching the folded shape.",
"hints": [
"Unfolding gives a figure with a line of symmetry.",
"Match the cut edges across the fold."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q15",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 7,
"image_bbox": [
0.34,
0.14,
0.46,
0.28
],
"image_loc": "folded-paper figure near top; four option figures (1)-(4) below it",
"notes": "Image-option MCQ. Stimulus = folded paper at top; the four answer shapes are the options -> crop q15_opt0..q15_opt3. Key: option (1)."
},
{
"n": 16,
"type_id": 1,
"question": "Jan has $$\\frac{3}{4}$$ m of cloth. She has $$\\frac{1}{2}$$ m more cloth than Helen. How much cloth do they have altogether?",
"answer0": "$$\\frac{1}{4}$$ m",
"answer1": "1 m",
"answer2": "$$1\\frac{1}{4}$$ m",
"answer3": "2 m",
"correct_answer": 1,
"skill_id": 122,
"difficulty_id": 2,
"explanation": "Helen has 3/4 - 1/2 = 1/4 m. Altogether: 3/4 + 1/4 = 1 m.",
"hints": [
"Find Helen's amount first: 3/4 - 1/2.",
"Add Jan's 3/4 m and Helen's 1/4 m."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q16",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (2) = 1 m."
},
{
"n": 17,
"type_id": 1,
"question": "How many minutes does it take for a minute hand of a clock to make $$1\\frac{1}{4}$$ turn round the clock?",
"answer0": "45 min",
"answer1": "60 min",
"answer2": "75 min",
"answer3": "115 min",
"correct_answer": 2,
"skill_id": 133,
"difficulty_id": 2,
"explanation": "One full turn of the minute hand = 60 min. 1 1/4 turns = 60 + (1/4 × 60) = 60 + 15 = 75 min.",
"hints": [
"One full turn of the minute hand takes 60 minutes.",
"Add a quarter turn = 15 minutes."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q17",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (3) = 75 min."
},
{
"n": 18,
"type_id": 1,
"question": "Jenny was working from 11 10 to 13 05. How much time did she take to complete her work?",
"answer0": "2 h 15 min",
"answer1": "2 h 05 min",
"answer2": "1 h 55 min",
"answer3": "1 h 15 min",
"correct_answer": 2,
"skill_id": 135,
"difficulty_id": 2,
"explanation": "From 11 10 to 13 10 is 2 h. But the end is 13 05, which is 5 min before 13 10. So duration = 2 h - 5 min = 1 h 55 min.",
"hints": [
"From 11 10 to 13 10 is exactly 2 hours.",
"13 05 is 5 minutes earlier than 13 10."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q18",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (3) = 1 h 55 min."
},
{
"n": 19,
"type_id": 1,
"question": "The area of a square is 36 cm\\u00b2. What is the perimeter of the square?",
"answer0": "6 cm",
"answer1": "24 cm",
"answer2": "36 cm",
"answer3": "72 cm",
"correct_answer": 1,
"skill_id": 137,
"difficulty_id": 2,
"explanation": "Side = √36 = 6 cm. Perimeter = 4 × 6 = 24 cm.",
"hints": [
"Area of a square = side × side, so side = √36.",
"Perimeter = 4 × side."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q19",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (2) = 24 cm."
},
{
"n": 20,
"type_id": 1,
"question": "The graph shows the hourly sales at a departmental store on Saturday. During which one-hour interval had the greatest decrease in sales?",
"answer0": "6 p.m. to 7 p.m.",
"answer1": "7 p.m. to 8 p.m.",
"answer2": "8 p.m. to 9 p.m.",
"answer3": "9 p.m. to 10 p.m.",
"correct_answer": 2,
"skill_id": 147,
"difficulty_id": 2,
"explanation": "Reading the graph: 7-8 p.m. drops 5000 to 4000 (1000); 8-9 p.m. drops 4000 to 1000 (3000); 9-10 p.m. drops 1000 to 0 (1000). The greatest decrease is 8 p.m. to 9 p.m.",
"hints": [
"A decrease is where the line goes down.",
"Find the steepest downward drop between two points."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q20",
"image_needed": true,
"image_options": false,
"image_file": "q20.png",
"image_page": 9,
"image_bbox": [
0.18,
0.16,
0.8,
0.38
],
"image_loc": "line graph of Sales ($) against Time (5 p.m. to 10 p.m.)",
"notes": "Key: option (3) = 8 p.m. to 9 p.m. (biggest drop 4000->1000)."
},
{
"n": 21,
"type_id": 2,
"question": "Write the missing number in the number pattern.
14 000, 13 400, 12 800, 12 200, [?], 11 000",
"answer0": "11 600",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 108,
"difficulty_id": 1,
"explanation": "Each term decreases by 600 (14 000 - 13 400 = 600). 12 200 - 600 = 11 600. Check: 11 600 - 600 = 11 000.",
"hints": [
"Find the difference between consecutive terms.",
"Subtract 600 from 12 200."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q21",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 11 600."
},
{
"n": 22,
"type_id": 2,
"question": "Two factors of 6 are 1 and 6. What are the other two factors of 6?
[?] and [?]",
"answer0": "2",
"answer1": "3",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 111,
"difficulty_id": 1,
"explanation": "The factors of 6 are 1, 2, 3 and 6. Besides 1 and 6, the other two factors are 2 and 3.",
"hints": [
"List all numbers that divide 6 exactly.",
"6 = 2 × 3."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q22",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 2 and 3."
},
{
"n": 23,
"type_id": 2,
"question": "What is the remainder when 1095 is divided by 9?
[?]",
"answer0": "6",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 117,
"difficulty_id": 1,
"explanation": "1095 ÷ 9 = 121 remainder 6 (since 9 × 121 = 1089 and 1095 - 1089 = 6).",
"hints": [
"9 × 121 = 1089.",
"1095 - 1089 = 6."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q23",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 6."
},
{
"n": 24,
"type_id": 2,
"question": "Find the value of $$1 - \\frac{1}{8} - \\frac{1}{4}$$. [?]",
"answer0": "5/8",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 121,
"difficulty_id": 2,
"explanation": "Use eighths: 1 = 8/8, 1/4 = 2/8. So 8/8 - 1/8 - 2/8 = 5/8.",
"hints": [
"Make all fractions into eighths.",
"8/8 - 1/8 - 2/8."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q24",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 5/8. FIB answer kept as plain a/b."
},
{
"n": 25,
"type_id": 2,
"question": "Write $$2\\frac{3}{7}$$ as an improper fraction. [?]",
"answer0": "17/7",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 119,
"difficulty_id": 1,
"explanation": "$$2\\frac{3}{7} = \\frac{2\\times7+3}{7} = \\frac{17}{7}$$.",
"hints": [
"Multiply the whole number by the denominator and add the numerator.",
"2 × 7 + 3 = 17."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q25",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 17/7. FIB answer kept as plain a/b."
},
{
"n": 26,
"type_id": 2,
"question": "Express 0.6 as a fraction. [?]",
"answer0": "3/5",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 126,
"difficulty_id": 1,
"explanation": "0.6 = 6/10 = 3/5 in simplest form.",
"hints": [
"0.6 = 6/10.",
"Simplify by dividing top and bottom by 2."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q26",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key shows 6/10 = 3/5; simplest form 3/5 used as FIB answer (plain a/b)."
},
{
"n": 27,
"type_id": 2,
"question": "Find the value of 4.73 \\u00d7 8. [?]",
"answer0": "37.84",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 130,
"difficulty_id": 1,
"explanation": "4.73 × 8 = 37.84.",
"hints": [
"Multiply 473 × 8 = 3784.",
"Place the decimal point two places from the right."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q27",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 37.84."
},
{
"n": 28,
"type_id": 2,
"question": "7.21 - 5.38 = [?].
Round your answer to the nearest 1 decimal place.",
"answer0": "1.8",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 132,
"difficulty_id": 2,
"explanation": "7.21 - 5.38 = 1.83. Rounded to 1 decimal place: 1.8.",
"hints": [
"Subtract: 7.21 - 5.38 = 1.83.",
"Look at the second decimal (3) to round to 1 dp."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q28",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 1.8."
},
{
"n": 29,
"type_id": 2,
"question": "In the figure, one of the angles is a right angle. Name the angle.
$$\\angle$$ [?]",
"answer0": "b",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 139,
"difficulty_id": 2,
"explanation": "By inspecting the figure, angle b is the right angle (90°).",
"hints": [
"A right angle looks like a square corner.",
"Compare each marked angle to a corner of a page."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q29",
"image_needed": true,
"image_options": false,
"image_file": "q29.png",
"image_page": 12,
"image_bbox": [
0.27,
0.33,
0.55,
0.52
],
"image_loc": "quadrilateral with angles a, b, c, d marked at its vertices",
"notes": "Key: Angle b. Answer is a letter -> entered as FIB after the printed angle symbol."
},
{
"n": 30,
"type_id": 2,
"question": "Measure and write down the size of $$\\angle x$$. [?]",
"answer0": "30",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 140,
"difficulty_id": 2,
"explanation": "Measuring the angle with a protractor gives 30°.",
"hints": [
"Place the protractor's centre on the vertex.",
"Read the scale where the other arm crosses."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q30",
"image_needed": true,
"image_options": false,
"image_file": "q30.png",
"image_page": 12,
"image_bbox": [
0.32,
0.59,
0.66,
0.74
],
"image_loc": "two lines meeting to form angle x near the top, opening downward-right",
"notes": "Key: 30 (degrees). FIB answer entered as 30 (the unit ° is on the printed answer line)."
},
{
"n": 31,
"type_id": 2,
"question": "David spent $$\\frac{1}{5}$$ of his money on a wallet and gave $90 to his mother. He had $104 left. How much money did he spend on the wallet?
$[?]",
"answer0": "48.50",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "The wallet was 1/5 of his money, so 4/5 remained after the wallet. That 4/5 = $90 + $104 = $194. So 1/5 = $194 ÷ 4 = $48.50 spent on the wallet.",
"hints": [
"After buying the wallet (1/5), 4/5 of his money is left.",
"4 units = $90 + $104 = $194, so 1 unit = $194 ÷ 4."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q31",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: $48.50 (4U -> $194, 1U -> $48.50). FIB answer entered after printed $ sign."
},
{
"n": 32,
"type_id": 2,
"question": "Doughnuts are sold in boxes of 6, 3 and 2. John bought exactly 119 doughnuts. What was the least number of boxes of each type of doughnuts John bought?
[?] box(es) of 6
[?] box(es) of 3
[?] box(es) of 2",
"answer0": "19",
"answer1": "1",
"answer2": "1",
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "To use the fewest boxes, use as many large (6) boxes as possible. 19 × 6 = 114, leaving 5. 5 = one box of 3 + one box of 2. So 19 boxes of 6, 1 box of 3, 1 box of 2.",
"hints": [
"Use as many boxes of 6 as you can first.",
"119 - 114 = 5, then split 5 into a 3 and a 2."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q32",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 19 boxes of 6, 1 box of 3, 1 box of 2. Doughnut box illustration is decorative only (not needed to solve)."
},
{
"n": 33,
"type_id": 0,
"question": "Complete the symmetric figure with line 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 given zig-zag line across the vertical line AB to produce a mirror image on the right side of the grid.",
"hints": [
"Each point's mirror image is the same distance on the other side of AB.",
"Reflect every line segment across AB."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q33",
"image_needed": true,
"image_options": false,
"image_file": "q33.png",
"image_page": 13,
"image_bbox": [
0.28,
0.5,
0.66,
0.8
],
"image_loc": "square grid with line AB vertical and a zig-zag line drawn on the left",
"notes": "Interactive draw-the-reflection task; no value answer -> type_id 0, skipped on insert. Answer is the reflected figure."
},
{
"n": 34,
"type_id": 2,
"question": "The table describes the properties of different figures W, X, Y and Z. Which figure is most likely to be a rectangle?
Figure [?]",
"answer0": "W",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 143,
"difficulty_id": 2,
"explanation": "A rectangle has four sides, at least one right angle, and exactly two pairs of parallel lines, but its sides are NOT all equal. Only Figure W has four sides, a right angle and two pairs of parallel lines while not having all sides equal.",
"hints": [
"A rectangle does not have all sides equal (that would be a square).",
"Find the figure with four sides, a right angle and two pairs of parallel lines but unequal sides."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q34",
"image_needed": true,
"image_options": false,
"image_file": "q34.png",
"image_page": 14,
"image_bbox": [
0.17,
0.2,
0.66,
0.32
],
"image_loc": "property table with columns Figure W, X, Y, Z and ticks for each property",
"notes": "Key: Figure W. Answer is a letter -> FIB after printed 'Figure'."
},
{
"n": 35,
"type_id": 2,
"question": "The figure is made up of a square ABEF and a rectangle BCDE. The area of the square is 16 cm\\u00b2. What is the area of the figure ACDF?
[?] cm\\u00b2",
"answer0": "68",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 2,
"explanation": "Square area 16 = 4 × 4, so each side is 4 cm; this is the height of the whole figure. Width of figure ACDF = AB + BC = 4 + 13 = 17 cm. Area = 17 × 4 = 68 cm².",
"hints": [
"Square area 16 cm² means each side is 4 cm.",
"Whole length = 4 + 13 = 17 cm; multiply by the height 4 cm."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q35",
"image_needed": true,
"image_options": false,
"image_file": "q35.png",
"image_page": 14,
"image_bbox": [
0.18,
0.44,
0.6,
0.56
],
"image_loc": "rectangle split into square ABEF and rectangle BCDE, with 13 cm marked across the top",
"notes": "Key: 68 cm² (square side 4, 13+4=17, 17×4=68)."
},
{
"n": 36,
"type_id": 2,
"question": "Find the perimeter of the figure.
[?] cm",
"answer0": "90",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "The L-shaped figure has total width 25 cm and total height 20 cm. By matching opposite sides, the horizontal sides total 25 + 25 and the vertical sides total 20 + 20. Perimeter = 25 + 20 + 25 + 20 = 90 cm.",
"hints": [
"Opposite horizontal sides of an L-shape add up to the full width.",
"Perimeter = 25 + 20 + 25 + 20."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q36",
"image_needed": true,
"image_options": false,
"image_file": "q36.png",
"image_page": 14,
"image_bbox": [
0.15,
0.62,
0.6,
0.8
],
"image_loc": "L-shaped (staircase) figure with sides 7 cm, 6 cm, 7 cm, 20 cm, 25 cm marked",
"notes": "Key: 90 cm."
},
{
"n": 37,
"type_id": 0,
"question": "The plan of the garden is shown in the square grid.
(a) In which direction is the pond from the tree?
(b) May stands at a location south-east of the statue and west of a bench. Cross out (x) in the square where May is standing.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 142,
"difficulty_id": 2,
"explanation": "(a) The pond is directly above the tree on the grid, so the pond is North of the tree. (b) South-east of the statue and west of the bench locates the single square the cross goes in (the cell one row below the bench's row and one column to the bench's left, per the key).",
"hints": [
"Use the N compass arrow: up is North.",
"Find a cell that is both south-east of the statue and directly west of the bench."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q37",
"image_needed": true,
"image_options": false,
"image_file": "q37.png",
"image_page": 15,
"image_bbox": [
0.18,
0.16,
0.62,
0.4
],
"image_loc": "5x5 square grid garden plan with Statue, Pond, Bench and Tree icons, plus a N compass",
"notes": "Part (a) is North (a value); part (b) is a cross-out on the grid (interactive). Combined two-part with an interactive component -> type_id 0, skipped on insert. Key: (a) North."
},
{
"n": 38,
"type_id": 2,
"question": "The line graph shows the amount of rainfall over 8 months. Which months had the same amount of rainfall?
[?]",
"answer0": "January, June and July",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 147,
"difficulty_id": 2,
"explanation": "Reading the graph, January, June and July all show 20 cm of rainfall.",
"hints": [
"Find the points at the same height on the graph.",
"Three months sit at the 20 cm line."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q38",
"image_needed": true,
"image_options": false,
"image_file": "q38.png",
"image_page": 16,
"image_bbox": [
0.18,
0.16,
0.74,
0.34
],
"image_loc": "line graph of Amount of rainfall (cm) against months Jan to Aug",
"notes": "Key: January, June and July (all 20 cm). Word answer -> single text FIB; exact-match grading may be fragile (note for QA)."
},
{
"n": 39,
"type_id": 2,
"question": "The table shows the number of marbles that 4 children have. Some numbers are missing. Sandy, Matt and Elena have the same total number of marbles. How many red marbles does Matt have?
[?]",
"answer0": "19",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 146,
"difficulty_id": 3,
"explanation": "Elena's total is 28. Sandy and Matt also total 28 each. Matt's blue = 9, so Matt's red = 28 - 9 = 19.",
"hints": [
"Elena's total is 28, so Matt's total is also 28.",
"Matt's red = total - blue = 28 - 9."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q39",
"image_needed": true,
"image_options": false,
"image_file": "q39.png",
"image_page": 16,
"image_bbox": [
0.2,
0.56,
0.78,
0.68
],
"image_loc": "table with rows Sandy, Russell, Elena, Matt and columns Blue, Red, Total",
"notes": "Key: 19 (28 - 9). Key working '28-9=19'."
},
{
"n": 40,
"type_id": 0,
"question": "The table shows the number of problem sums solved by each pupil in a group. Part of the table is covered by an ink blot. There were 35 pupils who solved 2 or more problem sums. For each statement, indicate True or False: (1) 7 pupils did not solve any problem sums. (2) The number of pupils who solved 3 problem sums is equal to the number of pupils who solved 4 problem sums. (3) There were 67 pupils in the group altogether.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 146,
"difficulty_id": 3,
"explanation": "(1) The '0 problem sums' column shows 7 pupils, so 7 solved none — True. (2) The number who solved 3 and the number who solved 4 are hidden by the ink blot, but they must total 35 - 20 = 15; there is no information that they are equal — False. (3) Total = 7 + 6 + 35 = 48, not 67 — False.",
"hints": [
"35 pupils solved 2 or more, and 20 solved exactly 2, so the 3- and 4-column hide 15 pupils between them.",
"Add the 0, 1 and (2-or-more) groups for the total."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q40",
"image_needed": true,
"image_options": false,
"image_file": "q40.png",
"image_page": 17,
"image_bbox": [
0.16,
0.2,
0.78,
0.28
],
"image_loc": "frequency table (problem sums 0-4 vs number of pupils) with an ink blot over the 3 and 4 columns",
"notes": "True/False tick-table (interactive) -> type_id 0, skipped on insert. Key answers: True, False, False."
},
{
"n": 41,
"type_id": 2,
"question": "At a concert, $$\\frac{3}{10}$$ of the audience are women and $$\\frac{1}{5}$$ of the audience are men. The rest of the audience are children.
(a) What fraction of the audience are children? [Leave your answer in the simplest form]
(b) There are 180 more children than women. How many women and men are there altogether?
(a) [?]
(b) [?]",
"answer0": "1/2",
"answer1": "450",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 122,
"difficulty_id": 3,
"explanation": "(a) Women + men = 3/10 + 1/5 = 3/10 + 2/10 = 5/10. Children = 1 - 5/10 = 5/10 = 1/2. (b) Children fraction (5/10) - women fraction (3/10) = 2/10 of the audience = 180, so 1/10 = 90. Women + men = 5/10 = 5 × 90 = 450.",
"hints": [
"Add the women and men fractions, then subtract from 1.",
"180 represents the 2/10 gap between children and women, so 1/10 = 90."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q41",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Two-part FIB. Key: (a) 1/2 [printed as 5/10 = 1/2], (b) 450 (women+men = 5U, 1U=90). answer0=1/2 plain a/b; answer1=450."
},
{
"n": 42,
"type_id": 2,
"question": "Andy, Ben and Cindy share $1900 altogether. Ben has $145 more than Cindy. Cindy has twice as much money as Andy.
(a) How much money does Andy have?
(b) Find the total amount of money Ben and Cindy have.
(a) $[?]
(b) $[?]",
"answer0": "351",
"answer1": "1549",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "Let Andy = 1 unit. Cindy = 2 units. Ben = 2 units + $145. Total = 1 + 2 + 2 = 5 units + $145 = $1900, so 5 units = $1900 - $145 = $1755, and 1 unit = $1755 ÷ 5 = $351 (Andy). (b) Ben + Cindy = $1900 - $351 = $1549.",
"hints": [
"Set Andy as 1 unit; Cindy is 2 units and Ben is 2 units + $145.",
"5 units + $145 = $1900."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q42",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Two-part FIB. Key: (a) $351, (b) $1549. NOTE: key prints '5U -> $1755, 1U -> $351' treating total as 5 units (Andy 1, Cindy 2, Ben 2) — consistent with answer. answer0=351; answer1=1549."
},
{
"n": 43,
"type_id": 2,
"question": "A bottle had some amount of milk at first. Peter drank $$\\frac{1}{4}$$ $$l$$ of milk in the morning and $$\\frac{1}{5}$$ $$l$$ of milk in the afternoon.
(a) How many litres of milk did Peter drink in total?
(b) Peter had $$\\frac{3}{5}$$ $$l$$ of milk at first. What was the amount of milk left in the bottle?
(a) [?]
(b) [?]",
"answer0": "9/20",
"answer1": "3/20",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 122,
"difficulty_id": 3,
"explanation": "(a) 1/4 + 1/5 = 5/20 + 4/20 = 9/20 l. (b) 3/5 = 12/20 l at first. Left = 12/20 - 9/20 = 3/20 l.",
"hints": [
"Use twentieths: 1/4 = 5/20, 1/5 = 4/20.",
"Convert 3/5 to 12/20, then subtract the amount drunk."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q43",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Two-part FIB. Key: (a) 9/20 l, (b) 3/20 l. answers kept as plain a/b. (Key labels these parts (c)/(d) but they map to this question's (a)/(b).)"
},
{
"n": 44,
"type_id": 2,
"question": "Mr Tan had an equal number of apples and oranges. After giving 48 apples and 36 oranges to Mr Lim, the oranges left was three times the number of apples left.
(a) How many apples did Mr Tan have at first?
(b) How many oranges were left?
(a) [?]
(b) [?]",
"answer0": "54",
"answer1": "18",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "Start equal; let apples left = 1 unit, oranges left = 3 units. Apples started = 1 unit + 48; oranges started = 3 units + 36. Equal start: 1 unit + 48 = 3 units + 36, so 2 units = 12 and 1 unit = 6. (a) Apples at first = 6 + 48 = 54. (b) Oranges left = 3 units = 3 × 6 = 18.",
"hints": [
"Apples left = 1 unit, oranges left = 3 units.",
"Apples started = oranges started: 1U + 48 = 3U + 36."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q44",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Two-part FIB. Key: (a) 54 apples, (b) 18 oranges. answer0=54; answer1=18."
},
{
"n": 45,
"type_id": 2,
"question": "Jean's Sunday schedule shows: 08 00 Wake up and wash up; 08 15 Breakfast; 08 50 Art and Craft; 10 50 Watch TV; ? Play computer games; 13 25 Lunch.
(a) Jean spent 90 minutes on computer games before having lunch. What time did she start playing? Express the time using the 12-hour clock.
(b) During the Art and Craft activity, Jean formed a figure by pasting 2 identical square papers over one another. Find the total area of the figure formed.
(a) [?]
(b) [?] cm\\u00b2",
"answer0": "11.55 a.m.",
"answer1": "175",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "(a) Lunch is at 13 25 = 1.25 p.m. Subtract 90 min: 1.25 p.m. - 90 min = 11.55 a.m. (b) Each square is 10 cm by 10 cm = 100 cm²; two squares = 200 cm². The overlap is a 5 cm by 5 cm square = 25 cm², counted once. Total area = 200 - 25 = 175 cm².",
"hints": [
"13 25 is 1.25 p.m.; go back 90 minutes (1 h 30 min).",
"Two 10×10 squares overlap in a 5×5 square; subtract the overlap once."
],
"source": "Pei Hwa 2023 P4 End of Year Exam Q45",
"image_needed": true,
"image_options": false,
"image_file": "q45.png",
"image_page": 22,
"image_bbox": [
0.2,
0.62,
0.78,
0.8
],
"image_loc": "'Figure formed' diagram of two overlapping squares with 5 cm and 10 cm labels (part b)",
"notes": "Two-part. Key: (a) 11.55 a.m., (b) 175 cm². Part (a) needs the schedule table (text-captured); part (b) needs the overlapping-squares figure (cropped). answer0='11.55 a.m.'; answer1=175."
}
]
}