{
"paper": {
"school": "St Joseph's Institution Junior",
"year": 2024,
"level": "P4",
"label": "End-of-Year Exam",
"source_prefix": "St Joseph 2024 P4 End-of-Year Exam",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "The value of the digit 6 in 48 630 is [?].",
"answer0": "60",
"answer1": "600",
"answer2": "6000",
"answer3": "60 000",
"correct_answer": 1,
"skill_id": 105,
"difficulty_id": 1,
"explanation": "In 48 630, the digit 6 is in the hundreds place. So its value is 6 × 100 = 600.",
"hints": [
"Identify which place the digit 6 sits in.",
"Hundreds place value = digit × 100."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Stem rewritten with [?] replacing the printed answer blank; this remains an MCQ. Key = option 2 (600)."
},
{
"n": 2,
"type_id": 1,
"question": "Which of the following are common factors of 9 and 18?",
"answer0": "1 and 18",
"answer1": "2 and 3",
"answer2": "3 and 6",
"answer3": "3 and 9",
"correct_answer": 3,
"skill_id": 113,
"difficulty_id": 2,
"explanation": "Factors of 9: 1, 3, 9. Factors of 18: 1, 2, 3, 6, 9, 18. Common factors are 1, 3, 9. Of the options, only 3 and 9 are both common factors.",
"hints": [
"List the factors of each number.",
"A common factor must divide BOTH numbers exactly."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key = option 4 (3 and 9)."
},
{
"n": 3,
"type_id": 1,
"question": "Find the product of 1485 and 3.",
"answer0": "495",
"answer1": "1488",
"answer2": "3245",
"answer3": "4455",
"correct_answer": 3,
"skill_id": 116,
"difficulty_id": 1,
"explanation": "Product means multiply: 1485 × 3 = 4455.",
"hints": [
"\"Product\" means multiply the two numbers.",
"1485 × 3."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key = option 4 (4455)."
},
{
"n": 4,
"type_id": 1,
"question": "There are 40 students in each class. The table shows the number of students who do not wear spectacles in each class.
Which class has twice as many students as class 4D who wear spectacles?",
"answer0": "4A",
"answer1": "4B",
"answer2": "4C",
"answer3": "4D",
"correct_answer": 1,
"skill_id": 147,
"difficulty_id": 2,
"explanation": "Students who WEAR spectacles = 40 − (do not wear). 4A: 40−30=10, 4B: 40−31=9, 4C: 40−26=14, 4D: 40−35=5. Twice 4D's wearers = 2×5 = 10, which matches 4A.",
"hints": [
"Wearers = 40 − number who do not wear.",
"Find 4D's wearers, double it, then match a class."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q4",
"image_needed": true,
"image_options": false,
"image_file": "q4.png",
"image_page": 4,
"image_bbox": [
0.22,
0.18,
0.8,
0.3
],
"image_loc": "table 'Number of students who do not wear spectacles' near top of page, below the question text",
"notes": "DATA TABLE figure needed (4A=30,4B=31,4C=26,4D=35). KEY MISMATCH: printed key says option 2 (4B), but mathematically the answer is 4A (10 wearers = twice 4D's 5). Recorded correct_answer=1 (4A) as the verified solution; key appears erroneous."
},
{
"n": 5,
"type_id": 1,
"question": "What fraction of the shapes are ♡ ?",
"answer0": "$$\\frac{8}{12}$$",
"answer1": "$$\\frac{4}{8}$$",
"answer2": "$$\\frac{4}{12}$$",
"answer3": "$$\\frac{1}{2}$$",
"correct_answer": 0,
"skill_id": 120,
"difficulty_id": 1,
"explanation": "There are 12 shapes in total. Counting the hearts gives 8 hearts. So the fraction that are hearts is $$\\frac{8}{12}$$.",
"hints": [
"Count the total number of shapes.",
"Count only the hearts, then write hearts over total."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q5",
"image_needed": true,
"image_options": false,
"image_file": "q5.png",
"image_page": 4,
"image_bbox": [
0.3,
0.55,
0.64,
0.67
],
"image_loc": "boxed row of 12 shapes (hearts and diamonds) in the middle of the page",
"notes": "8 hearts out of 12 shapes. Key = option 1 (8/12)."
},
{
"n": 6,
"type_id": 1,
"question": "Which angle is smaller than a right angle?",
"answer0": "∠p",
"answer1": "∠q",
"answer2": "∠r",
"answer3": "∠s",
"correct_answer": 3,
"skill_id": 140,
"difficulty_id": 2,
"explanation": "An angle smaller than a right angle (less than 90°) is an acute angle. In the figure, ∠s is the acute angle (the sharp corner), so ∠s is smaller than a right angle.",
"hints": [
"A right angle is 90°; smaller means an acute angle.",
"Look for the sharpest (narrowest) corner in the figure."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q6",
"image_needed": true,
"image_options": false,
"image_file": "q6.png",
"image_page": 5,
"image_bbox": [
0.33,
0.13,
0.62,
0.3
],
"image_loc": "tilted quadrilateral with angles p, q, r, s labelled, near top of page",
"notes": "Key = option 4 (∠s)."
},
{
"n": 7,
"type_id": 1,
"question": "The figure is made up of a square A of side 3 cm and a rectangle B with breadth 4 cm. What is the length of the rectangle?",
"answer0": "7 cm",
"answer1": "8 cm",
"answer2": "11 cm",
"answer3": "12 cm",
"correct_answer": 2,
"skill_id": 143,
"difficulty_id": 2,
"explanation": "The total height on the left is 8 cm (rectangle B). The square A has side 3 cm at the bottom right. The length of rectangle B = 8 + 3 = 11 cm.",
"hints": [
"The rectangle's length runs the full height of the figure.",
"Add the marked 8 cm portion to the square's 3 cm side."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q7",
"image_needed": true,
"image_options": false,
"image_file": "q7.png",
"image_page": 5,
"image_bbox": [
0.47,
0.43,
0.66,
0.65
],
"image_loc": "L-shaped figure (rectangle B over square A) on the right, with 8 cm, 4 cm and 3 cm marked",
"notes": "Key = option 3 (11 cm)."
},
{
"n": 8,
"type_id": 1,
"question": "Which decimal is represented by Y in the number line?",
"answer0": "3.013",
"answer1": "3.018",
"answer2": "3.058",
"answer3": "3.08",
"correct_answer": 1,
"skill_id": 123,
"difficulty_id": 2,
"explanation": "The number line runs from 3.01 to 3.02, divided into 10 equal parts, so each small mark is 0.001. Y is at the 8th mark from 3.01, giving 3.01 + 0.008 = 3.018.",
"hints": [
"Find the value of one small interval between 3.01 and 3.02.",
"Count the marks from 3.01 to Y."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q8",
"image_needed": true,
"image_options": false,
"image_file": "q8.png",
"image_page": 5,
"image_bbox": [
0.24,
0.72,
0.62,
0.84
],
"image_loc": "horizontal number line from 3.01 to 3.02 with arrow Y near lower middle of page",
"notes": "Key = option 2 (3.018)."
},
{
"n": 9,
"type_id": 1,
"question": "The area of the rectangle UVWX is 48 cm$$^2$$. The length of UV is 8 cm. Find the length of VW.",
"answer0": "56 cm",
"answer1": "40 cm",
"answer2": "16 cm",
"answer3": "6 cm",
"correct_answer": 3,
"skill_id": 136,
"difficulty_id": 2,
"explanation": "Area = length × breadth. VW = area ÷ UV = 48 ÷ 8 = 6 cm.",
"hints": [
"Area of a rectangle = length × breadth.",
"Divide the area by the known side."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q9",
"image_needed": true,
"image_options": false,
"image_file": "q9.png",
"image_page": 6,
"image_bbox": [
0.45,
0.16,
0.74,
0.31
],
"image_loc": "rectangle UVWX labelled, '8 cm' across top, 'Area = 48 cm2' inside, '?' on right side",
"notes": "Key = option 4 (6 cm)."
},
{
"n": 10,
"type_id": 1,
"question": "Which of these dotted lines is a line of symmetry of the number 8?",
"answer0": "AB",
"answer1": "CD",
"answer2": "EF",
"answer3": "GH",
"correct_answer": 0,
"skill_id": 145,
"difficulty_id": 2,
"explanation": "The number 8 has a vertical line of symmetry. In the figure, line AB is the vertical dotted line, so AB is the line of symmetry.",
"hints": [
"Folding along a line of symmetry makes both halves match exactly.",
"The number 8 is symmetric about a vertical line."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q10",
"image_needed": true,
"image_options": false,
"image_file": "q10.png",
"image_page": 6,
"image_bbox": [
0.4,
0.37,
0.8,
0.62
],
"image_loc": "figure-8 shape with dotted lines AB (vertical), CD (horizontal), EF and GH (diagonal) through centre, middle of page",
"notes": "Key = option 1 (AB)."
},
{
"n": 11,
"type_id": 1,
"question": "In which of the following are the numbers arranged from the smallest to the greatest?",
"answer0": "17 420 , 17 204 , 17 024",
"answer1": "17 024 , 17 420 , 17 204",
"answer2": "17 204 , 17 024 , 17 420",
"answer3": "17 024 , 17 204 , 17 420",
"correct_answer": 3,
"skill_id": 107,
"difficulty_id": 2,
"explanation": "Compare the numbers: 17 024 < 17 204 < 17 420. Only option 4 lists them smallest to greatest.",
"hints": [
"Compare digit by digit from the left.",
"Smallest first, greatest last."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q11",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key = option 4 (17 024, 17 204, 17 420)."
},
{
"n": 12,
"type_id": 1,
"question": "Complete the number pattern.
50 970 , 50 973 , 50 976 , [?] , [?] , 50 985",
"answer0": "50 977 , 50 978",
"answer1": "50 977 , 50 984",
"answer2": "50 979 , 50 980",
"answer3": "50 979 , 50 982",
"correct_answer": 3,
"skill_id": 108,
"difficulty_id": 2,
"explanation": "The pattern increases by 3 each time: 50 970, 50 973, 50 976, 50 979, 50 982, 50 985. So the two missing numbers are 50 979 and 50 982.",
"hints": [
"Find the difference between consecutive given terms.",
"Add 3 each time to fill the blanks."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q12",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "MCQ with two missing terms shown as [?] in the stem; options give both blanks. Key = option 4 (50 979, 50 982)."
},
{
"n": 13,
"type_id": 1,
"question": "What is $$\\frac{3}{4}$$ of 24?",
"answer0": "30",
"answer1": "18",
"answer2": "8",
"answer3": "6",
"correct_answer": 1,
"skill_id": 120,
"difficulty_id": 1,
"explanation": "$$\\frac{3}{4}$$ of 24 = 24 ÷ 4 × 3 = 6 × 3 = 18.",
"hints": [
"Find $$\\frac{1}{4}$$ of 24 first.",
"Then multiply that by 3."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q13",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key = option 2 (18)."
},
{
"n": 14,
"type_id": 1,
"question": "Find the value of $$\\frac{6}{8}-\\frac{1}{2}$$ .",
"answer0": "$$\\frac{5}{6}$$",
"answer1": "$$\\frac{7}{10}$$",
"answer2": "$$\\frac{5}{8}$$",
"answer3": "$$\\frac{1}{4}$$",
"correct_answer": 3,
"skill_id": 121,
"difficulty_id": 2,
"explanation": "Make denominators the same: $$\\frac{1}{2}=\\frac{4}{8}$$. Then $$\\frac{6}{8}-\\frac{4}{8}=\\frac{2}{8}=\\frac{1}{4}$$.",
"hints": [
"Convert $$\\frac{1}{2}$$ to eighths.",
"Subtract, then simplify."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q14",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key = option 4 (1/4)."
},
{
"n": 15,
"type_id": 1,
"question": "Which of the following nets cannot be folded to form a cube?",
"answer0": "Net 1",
"answer1": "Net 2",
"answer2": "Net 3",
"answer3": "Net 4",
"correct_answer": 0,
"skill_id": 232,
"difficulty_id": 3,
"image_options": true,
"image_needed": true,
"image_file": null,
"image_page": 8,
"image_bbox": [
0.18,
0.12,
0.45,
0.55
],
"image_loc": "four square-grid nets labelled (1)-(4) stacked down the upper-left of the page",
"explanation": "A valid cube net has 6 squares arranged so no two faces overlap when folded. Net 1 (a row of 5 squares with one extra on top) has 6 squares but the arrangement folds with overlapping faces, so it cannot form a cube. Nets 2, 3 and 4 fold correctly.",
"hints": [
"A cube net must have exactly 6 squares.",
"Mentally fold each net and check whether any faces overlap or are missing."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q15",
"notes": "Image-option MCQ: the four options are net pictures. Crop each net to q15_opt0..3.png. Key = option 1 (Net 1)."
},
{
"n": 16,
"type_id": 2,
"question": "Write twenty thousand, four hundred and eleven in numerals.",
"answer0": "20411",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 106,
"difficulty_id": 1,
"explanation": "Twenty thousand = 20 000, four hundred = 400, eleven = 11. Adding: 20 000 + 400 + 11 = 20 411.",
"hints": [
"Break the words into thousands, hundreds, and ones.",
"Add the parts together."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q16",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key = 20411."
},
{
"n": 17,
"type_id": 2,
"question": "Round 72 650 to the nearest hundred.",
"answer0": "72700",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 109,
"difficulty_id": 2,
"explanation": "The tens digit of 72 650 is 5, so we round up. 72 650 rounded to the nearest hundred is 72 700.",
"hints": [
"Look at the tens digit to decide rounding.",
"5 or more rounds the hundreds up."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q17",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key = 72700."
},
{
"n": 18,
"type_id": 2,
"question": "What is the remainder when 2046 is divided by 9?",
"answer0": "3",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 117,
"difficulty_id": 2,
"explanation": "2046 ÷ 9 = 227 remainder 3 (since 227 × 9 = 2043, and 2046 − 2043 = 3).",
"hints": [
"Divide 2046 by 9 using long division.",
"The leftover after the largest whole multiple is the remainder."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q18",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key = 3."
},
{
"n": 19,
"type_id": 2,
"question": "Write $$2\\frac{5}{7}$$ as an improper fraction.",
"answer0": "19/7",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 119,
"difficulty_id": 1,
"explanation": "Multiply the whole number by the denominator and add the numerator: 2 × 7 + 5 = 19. Keep the denominator: $$\\frac{19}{7}$$.",
"hints": [
"Whole number × denominator + numerator gives the new numerator.",
"The denominator stays the same."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q19",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "FIB fraction answer kept as plain 19/7. Key = 19/7."
},
{
"n": 20,
"type_id": 2,
"question": "Measure ∠ABC.",
"answer0": "45",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 140,
"difficulty_id": 2,
"explanation": "Reading the protractor where ray BA crosses the scale (measuring from BC at 0°), ∠ABC = 45°.",
"hints": [
"Line up the protractor base line with one arm of the angle.",
"Read the scale that starts at 0° on that arm."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q20",
"image_needed": true,
"image_options": false,
"image_file": "q20.png",
"image_page": 10,
"image_bbox": [
0.22,
0.13,
0.78,
0.35
],
"image_loc": "protractor with rays from B to A and C drawn, upper part of page",
"notes": "Answer in degrees. Key = 45 (degrees)."
},
{
"n": 21,
"type_id": 2,
"question": "Round 56.75 to 1 decimal place.",
"answer0": "56.8",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 128,
"difficulty_id": 2,
"explanation": "The second decimal digit is 5, so round the first decimal place up: 56.75 → 56.8.",
"hints": [
"Look at the digit in the hundredths place.",
"5 or more rounds the tenths digit up."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q21",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key = 56.8."
},
{
"n": 22,
"type_id": 2,
"question": "23 − 1.85 = [?]",
"answer0": "21.15",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 129,
"difficulty_id": 2,
"explanation": "Align decimal points: 23.00 − 1.85 = 21.15.",
"hints": [
"Write 23 as 23.00 to line up decimals.",
"Subtract carefully."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q22",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key = 21.15."
},
{
"n": 23,
"type_id": 1,
"question": "Name the geometric figure of the object.",
"answer0": "Cylinder",
"answer1": "Cone",
"answer2": "Cuboid",
"answer3": "Prism",
"correct_answer": 0,
"skill_id": 231,
"difficulty_id": 1,
"explanation": "The object shown is a round solid with two flat circular ends and a curved surface — this is a cylinder.",
"hints": [
"Look at the flat ends: are they circles or polygons?",
"A solid with two circular ends and a curved side is a cylinder."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q23",
"image_needed": true,
"image_options": false,
"image_file": "q23.png",
"image_page": 11,
"image_bbox": [
0.19,
0.13,
0.36,
0.27
],
"image_loc": "shaded 3-D cylindrical object near top-left of page",
"notes": "Originally an open FIB (name the solid). Converted to MCQ with 4 solid-name options since word answers must be MCQ. Key = cylinder = option 1."
},
{
"n": 24,
"type_id": 2,
"question": "Write the missing number in the number pattern.
14 060 , 14 010 , 13 910 , 13 860 , [?] , 13 710 , 13 610",
"answer0": "13760",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 108,
"difficulty_id": 2,
"explanation": "Looking at the differences, the pattern decreases by 50 each step (14 060 → 14 010 = −50; 13 910 → 13 860 = −50). So after 13 860 comes 13 860 − 100 ... the consistent pattern gives 13 760 (13 860 − 100). 13 760 → 13 710 → 13 610. Missing number is 13 760.",
"hints": [
"Find the difference between terms you are given.",
"Apply the same step to find the missing term."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q24",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key = 13760."
},
{
"n": 25,
"type_id": 2,
"question": "Some factors of 24 are 1, 3, 4, 6, 8 and 24. What are the other two factors of 24?",
"answer0": "2",
"answer1": "12",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 111,
"difficulty_id": 2,
"explanation": "All factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The ones not listed are 2 and 12.",
"hints": [
"List every number that divides 24 exactly.",
"Compare with the given list to find what's missing."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q25",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Two-blank FIB (answer0=2, answer1=12). Key = 2 and 12."
},
{
"n": 26,
"type_id": 2,
"question": "The line graph shows the number of apples sold at a fruit stall from August to December. The number of apples sold was recorded at the end of every month.
a) During which 1-month period was the increase in the number of apples sold the greatest? [?]
b) What is the difference between the number of apples sold in August and December? [?]",
"answer0": "September to October",
"answer1": "40",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 147,
"difficulty_id": 2,
"explanation": "a) Reading the graph: Aug=130, Sep=90, Oct=160, Nov=130, Dec=170. Increases: Sep→Oct = +70 (largest), Nov→Dec = +40. Greatest increase is September to October. b) August=130, December=170. Difference = 170 − 130 = 40.",
"hints": [
"For (a), find the steepest upward segment of the line.",
"For (b), subtract the August value from the December value."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q26",
"image_needed": true,
"image_options": false,
"image_file": "q26.png",
"image_page": 12,
"image_bbox": [
0.18,
0.18,
0.8,
0.48
],
"image_loc": "line graph 'Number of Apples Sold' vs Month (Aug-Dec), upper half of page",
"notes": "Two-part FIB: answer0 = 'September to October' (the period), answer1 = 40. Key: a) September to October, b) 170−130=40."
},
{
"n": 27,
"type_id": 2,
"question": "$$5\\frac{1}{2}=\\frac{[?]}{10}$$
What is the missing number in the box?",
"answer0": "55",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 119,
"difficulty_id": 2,
"explanation": "Convert $$5\\frac{1}{2}$$ to tenths: $$5\\frac{1}{2}=\\frac{11}{2}=\\frac{11\\times5}{2\\times5}=\\frac{55}{10}$$. The missing number is 55.",
"hints": [
"First write the mixed number as an improper fraction.",
"Make the denominator 10 by multiplying top and bottom by the same number."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q27",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Single missing numerator. Key = 55."
},
{
"n": 28,
"type_id": 2,
"question": "What is the sum of $$\\frac{1}{3}$$ and $$\\frac{3}{4}$$ ? Give your answer as a mixed number in its simplest form.",
"answer0": "1 1/12",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 121,
"difficulty_id": 2,
"explanation": "Common denominator 12: $$\\frac{1}{3}=\\frac{4}{12}$$, $$\\frac{3}{4}=\\frac{9}{12}$$. Sum = $$\\frac{13}{12}=1\\frac{1}{12}$$.",
"hints": [
"Use a common denominator of 12.",
"Add, then convert the improper fraction to a mixed number."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q28",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "FIB mixed-number answer kept plain as '1 1/12'. Key working: 9/12 + 4/12 = 13/12 = 1 1/12."
},
{
"n": 29,
"type_id": 2,
"question": "Measure and write down the size of ∠x.",
"answer0": "120",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 140,
"difficulty_id": 2,
"explanation": "Measuring the angle x with a protractor gives 120°.",
"hints": [
"Place the protractor centre at the vertex of x.",
"Read the scale starting from one arm at 0°."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q29",
"image_needed": true,
"image_options": false,
"image_file": "q29.png",
"image_page": 13,
"image_bbox": [
0.18,
0.66,
0.72,
0.9
],
"image_loc": "obtuse angle marked x near the bottom of the page",
"notes": "Answer in degrees. Key = 120 (degrees)."
},
{
"n": 30,
"type_id": 2,
"question": "EFGH is a rectangle. Find ∠z.",
"answer0": "66",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 143,
"difficulty_id": 2,
"explanation": "Each corner of a rectangle is 90°. At corner E, the diagonal makes a 24° angle with the top side, so ∠z = 90° − 24° = 66°.",
"hints": [
"The angle at a rectangle's corner is 90°.",
"Subtract the marked 24° from 90°."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q30",
"image_needed": true,
"image_options": false,
"image_file": "q30.png",
"image_page": 14,
"image_bbox": [
0.18,
0.12,
0.52,
0.27
],
"image_loc": "rectangle EFGH with diagonal EG, 24° and z marked at corner E, top-left of page",
"notes": "Answer in degrees. Key = 90−24 = 66 (degrees)."
},
{
"n": 31,
"type_id": 2,
"question": "Arrange the following from the smallest to greatest.
0.804 , 0.084 , $$\\frac{4}{5}$$",
"answer0": "0.084",
"answer1": "4/5",
"answer2": "0.804",
"answer3": null,
"correct_answer": null,
"skill_id": 124,
"difficulty_id": 3,
"explanation": "Convert $$\\frac{4}{5}=0.8$$. Comparing: 0.084 < 0.8 < 0.804. So smallest to greatest: 0.084, $$\\frac{4}{5}$$, 0.804.",
"hints": [
"Change the fraction to a decimal first ($$\\frac{4}{5}=0.8$$).",
"Then compare all three decimals."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q31",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Ordering FIB, one [?] per position: answer0=0.084 (smallest), answer1=4/5, answer2=0.804 (greatest). FIB fraction kept plain 4/5. Key = 0.084, 4/5, 0.804."
},
{
"n": 32,
"type_id": 2,
"question": "Express 0.43 as a fraction.",
"answer0": "43/100",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 126,
"difficulty_id": 1,
"explanation": "0.43 has 2 decimal places (hundredths), so 0.43 = $$\\frac{43}{100}$$. 43 and 100 share no common factor, so it is already in simplest form.",
"hints": [
"Two decimal places means hundredths.",
"Write the digits over 100."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q32",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "FIB fraction answer kept plain as 43/100. Key = 43/100."
},
{
"n": 33,
"type_id": 2,
"question": "The figure is made up of 2 identical rectangles. What is the perimeter of the figure?",
"answer0": "40",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Each rectangle is 8 cm by 4 cm. The two identical rectangles form an L-shape. Perimeter: longer side 8+4=12 across the top, and the marked working gives 8+4=12, 8×2=16, 12×2=24, then 24+16=40 cm.",
"hints": [
"Each rectangle measures 8 cm by 4 cm.",
"Add up all the outer sides of the L-shape."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q33",
"image_needed": true,
"image_options": false,
"image_file": "q33.png",
"image_page": 15,
"image_bbox": [
0.18,
0.13,
0.55,
0.27
],
"image_loc": "L-shaped figure of two rectangles, '8 cm' on left, '4 cm' on right, top of page",
"notes": "Answer in cm. Key working: 8+4=12, 8x2=16, 12x2=24, 24+16=40. Answer = 40 cm."
},
{
"n": 34,
"type_id": 2,
"question": "The figure is made up of a rectangle, ABCD and a square, CDEF. Find the area of the figure.",
"answer0": "73",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Rectangle ABCD: 8 cm × 3 cm = 24 cm² (top strip; AB = 7+1 = 8, height 3). Square CDEF has side 7 cm, area 7 × 7 = 49 cm². Total area = 49 + 24 = 73 cm².",
"hints": [
"Find the area of the rectangle and the square separately.",
"Add the two areas together."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q34",
"image_needed": true,
"image_options": false,
"image_file": "q34.png",
"image_page": 15,
"image_bbox": [
0.22,
0.5,
0.56,
0.78
],
"image_loc": "composite figure of rectangle ABCD on top and square below, with 3 cm, 1 cm, 7 cm marked, middle-lower of page",
"notes": "Answer in cm^2. Key working: 8x3=24, 7x7=49, 49+24=73. Answer = 73 cm^2."
},
{
"n": 35,
"type_id": 0,
"question": "The figure is made up of identical squares. Shade two more squares to form a symmetric figure with the dotted line as the line of symmetry.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 145,
"difficulty_id": 3,
"explanation": "Reflect the existing shaded squares across the dotted diagonal line of symmetry; the two squares needed to complete the mirror image are the answer (shading task).",
"hints": [
"Each shaded square must have a mirror partner across the dotted line.",
"Find which reflections are still empty and shade them."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q35",
"image_needed": true,
"image_options": false,
"image_file": "q35.png",
"image_page": 16,
"image_bbox": [
0.28,
0.14,
0.72,
0.46
],
"image_loc": "7x7 grid of squares with several shaded and a diagonal dotted line of symmetry, upper part of page",
"notes": "type_id 0 (interactive shading task — no value/sequence answer). Skipped on insert. Key shows the completed shaded grid (two more squares shaded to mirror the figure across the diagonal)."
},
{
"n": 36,
"type_id": 2,
"question": "Every month, Xavier gives $650 to his father. He gives thrice the amount to his mother. How much money does he give to his parents per month?",
"answer0": "$2600",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 2,
"explanation": "Father gets $650. Mother gets thrice that: 3 × $650 = $1950. Total to parents = $650 + $1950 = $2600.",
"hints": [
"Find the amount given to the mother (thrice the father's).",
"Add the father's and mother's amounts."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q36",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Money word problem. Key working: 650x4 = 2600 (650 + 3x650). Answer = $2600."
},
{
"n": 37,
"type_id": 2,
"question": "A bookshop owner has 3095 pens. He wanted to pack all the pens into bags. A bag can pack at most 6 pens. What was the least number of bags he needed?",
"answer0": "516",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 2,
"explanation": "3095 ÷ 6 = 515 remainder 5. The leftover 5 pens still need 1 more bag. So least number of bags = 515 + 1 = 516.",
"hints": [
"Divide the total pens by the bag capacity.",
"The leftover pens still need one extra bag — round up."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q37",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working: 3095 ÷ 6 = 515 R5, 515+1 = 516. Answer = 516 bags."
},
{
"n": 38,
"type_id": 2,
"question": "The graph shows the number of people in a shopping mall on one of the evenings.
(a) At what time was the number of people three times the number of people at 4 p.m.? [?]
(b) How many more people were there at 7 p.m. than at 5 p.m.? [?]",
"answer0": "8 p.m.",
"answer1": "200",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 148,
"difficulty_id": 2,
"explanation": "From the bar graph: 4 p.m.=200, 5 p.m.=650, 6 p.m.=700, 7 p.m.=850, 8 p.m.=600, 9 p.m.=450. (a) Three times 4 p.m. = 3×200 = 600, which is at 8 p.m. (b) 850 − 650 = 200.",
"hints": [
"For (a), compute 3 × the 4 p.m. value, then find the matching bar.",
"For (b), subtract the 5 p.m. bar from the 7 p.m. bar."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q38",
"image_needed": true,
"image_options": false,
"image_file": "q38.png",
"image_page": 18,
"image_bbox": [
0.14,
0.16,
0.74,
0.45
],
"image_loc": "bar graph 'Number of people' vs Time (4 p.m.-9 p.m.), upper-left of page",
"notes": "Two-part FIB: answer0 = '8 p.m.', answer1 = 200. Key: a) 200x3=600 -> 8pm, b) 850-650=200."
},
{
"n": 39,
"type_id": 2,
"question": "There are 112 children at an indoor playground. $$\\frac{3}{8}$$ of them are girls and the rest are boys.
a) How many boys are there? [?]
b) How many fewer girls than boys are there? [?]",
"answer0": "70",
"answer1": "28",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 122,
"difficulty_id": 2,
"explanation": "a) Girls = $$\\frac{3}{8}$$ of 112 = 42, so boys = $$\\frac{5}{8}$$ of 112 = 5 × 14 = 70. b) Boys − girls = 70 − 42 = 28 fewer girls.",
"hints": [
"Find one eighth of 112 first (112 ÷ 8).",
"Boys are the remaining 5/8; the difference is boys − girls."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q39",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Two-part FIB: answer0=70, answer1=28. Key: a) 112÷8=14, 14x5=70; b) 14x3=42, 70-42=28."
},
{
"n": 40,
"type_id": 2,
"question": "Mrs Gopal bought $$\\frac{9}{10}$$ kg of flour. She bought $$\\frac{3}{5}$$ kg less of sugar than flour.
(a) What was the mass of sugar Mrs Gopal bought? [?]
(b) How much flour and sugar did Mrs Gopal buy? Give your answer in the simplest form. [?]",
"answer0": "3/10",
"answer1": "1 1/5",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 122,
"difficulty_id": 3,
"explanation": "a) Sugar = flour − $$\\frac{3}{5}$$ = $$\\frac{9}{10}-\\frac{6}{10}=\\frac{3}{10}$$ kg. b) Flour + sugar = $$\\frac{9}{10}+\\frac{3}{10}=\\frac{12}{10}=1\\frac{2}{10}=1\\frac{1}{5}$$ kg.",
"hints": [
"Convert $$\\frac{3}{5}$$ to tenths to subtract from $$\\frac{9}{10}$$.",
"For (b), add flour and sugar, then simplify."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q40",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Two-part FIB, fractions kept plain: answer0=3/10 (kg), answer1=1 1/5 (kg). Key: a) 9/10-6/10=3/10; b) 9/10+3/10=1 1/5."
},
{
"n": 41,
"type_id": 2,
"question": "The cost of 3 identical ties and 2 identical belts cost $168.50. Each belt cost $21.50 more than a tie. How much did each belt cost?",
"answer0": "$46.60",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 131,
"difficulty_id": 3,
"explanation": "Replace each belt with (tie + $21.50). Then 3 ties + 2 belts = 5 ties + 2×$21.50 = 5 ties + $43 = $168.50, so 5 ties = $125.50 and 1 tie = $25.10. Belt = $25.10 + $21.50 = $46.60. (Matches key working: 21.50×3=64.50, 168.50+64.50=233, 233÷5=46.60.)",
"hints": [
"Express belts in terms of ties using the $21.50 difference.",
"Find the cost of one tie first, then add the difference for a belt."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q41",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Money word problem. Key working: 21.5x3=64.5, 168.5+64.5=233, 233÷5=46.60. Answer = $46.60 per belt."
},
{
"n": 42,
"type_id": 2,
"question": "Some lampposts were placed along a stretch of road at equal distances apart, starting from the beginning of the road. The distance between the third and eighth lamppost was 45 m.
a) What was the distance between the first and fourth lamppost? [?]
b) The stretch of road was 8136 m long. How many lampposts were placed from the beginning to the end of that stretch of road? [?]",
"answer0": "27 m",
"answer1": "905",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "From the 3rd to the 8th lamppost there are 5 gaps = 45 m, so each gap = 45 ÷ 5 = 9 m. a) From 1st to 4th lamppost there are 3 gaps = 3 × 9 = 27 m. b) Number of gaps in 8136 m = 8136 ÷ 9 = 904 gaps, so number of lampposts = 904 + 1 = 905.",
"hints": [
"Count GAPS, not posts: between the 3rd and 8th post are 5 gaps.",
"Number of posts = number of gaps + 1."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q42",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Two-part FIB: answer0=27 (m), answer1=905. Key: a) 45÷5=9, (4-1)=3, 9x3=27; b) 8136÷9=904, 904+1=905."
},
{
"n": 43,
"type_id": 2,
"question": "A gardener wanted to surround his garden with a rectangular fence. The area of the garden is 64 m$$^2$$. How much did the gardener pay if 1-metre of fence cost $8?",
"answer0": "$512",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 137,
"difficulty_id": 3,
"explanation": "The garden is a square of area 64 m², so its side = √64 = 8 m. The dashed rectangular fence sits 2 m beyond the garden on each side, giving fence dimensions (6+6) by ... ; using the key working: each side of fence = 8+2+... Perimeter from working: 6+6+8=20 and 2+2+8=12, so perimeter = 20×2 + 12×2 = ... = 64 m. Cost = 64 × $8 = $512.",
"hints": [
"Find the garden's side length from its area (√64).",
"Work out the fence's perimeter, then multiply by $8 per metre."
],
"source": "St Joseph 2024 P4 End-of-Year Exam Q43",
"image_needed": true,
"image_options": false,
"image_file": "q43.png",
"image_page": 23,
"image_bbox": [
0.22,
0.21,
0.66,
0.38
],
"image_loc": "shaded square garden inside a dashed rectangular fence, 2 m and 6 m gaps marked, upper-middle of page",
"notes": "Key working: √64=8, 6+6+8=20, 2+2+8=12, 20+12x2=64 (fence perimeter 64 m), 64x8=512. Answer = $512."
}
]
}