{
"paper": {
"school": "Singapore Chinese Girls' School",
"year": 2024,
"level": "P4",
"label": "End-of-Year Exam",
"source_prefix": "SCGS 2024 P4 End-of-Year Exam",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "In which of the following does the digit 8 stand for 800?",
"answer0": "7 628",
"answer1": "7 682",
"answer2": "7 862",
"answer3": "8 762",
"correct_answer": 2,
"skill_id": 105,
"difficulty_id": 1,
"explanation": "The digit 8 stands for 800 when it is in the hundreds place. In 7 862, the 8 is in the hundreds position, so it stands for 800. Answer: 7 862.",
"hints": [
"Look at the place value of the digit 8 in each number.",
"800 means 8 is in the hundreds place."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key=option 3 (7 862), 0-based index 2."
},
{
"n": 2,
"type_id": 1,
"question": "10000 + 5000 + 600 + 4 = [?]",
"answer0": "15 640",
"answer1": "15 604",
"answer2": "15 064",
"answer3": "10 564",
"correct_answer": 1,
"skill_id": 105,
"difficulty_id": 1,
"explanation": "Add by place value: 10000 + 5000 + 600 + 4 = 15 604. Note there are no tens, so the tens digit is 0. Answer: 15 604.",
"hints": [
"Line up the place values: ten thousands, thousands, hundreds, tens, ones.",
"There is nothing in the tens place, so put 0 there."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key=option 2 (15 604), 0-based index 1. Stem shown verbatim with blank as [?]."
},
{
"n": 3,
"type_id": 1,
"question": "2 and 3 are factors of [?]",
"answer0": "10",
"answer1": "12",
"answer2": "21",
"answer3": "23",
"correct_answer": 1,
"skill_id": 111,
"difficulty_id": 1,
"explanation": "A number must be divisible by both 2 and 3. 12 = 2 x 6 and 12 = 3 x 4, so both 2 and 3 are factors of 12. Answer: 12.",
"hints": [
"The number must divide exactly by both 2 and 3.",
"A multiple of both 2 and 3 is a multiple of 6."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key=option 2 (12), 0-based index 1."
},
{
"n": 4,
"type_id": 1,
"question": "Which fraction is not in its simplest form?",
"answer0": "$$\\frac{3}{4}$$",
"answer1": "$$\\frac{4}{5}$$",
"answer2": "$$\\frac{6}{9}$$",
"answer3": "$$\\frac{9}{10}$$",
"correct_answer": 2,
"skill_id": 78,
"difficulty_id": 1,
"explanation": "A fraction is in simplest form when the numerator and denominator share no common factor other than 1. $$\\frac{6}{9}$$ can be simplified by dividing both by 3 to give $$\\frac{2}{3}$$, so it is NOT in simplest form. Answer: $$\\frac{6}{9}$$.",
"hints": [
"Check if the numerator and denominator have a common factor.",
"6 and 9 are both divisible by 3."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q4",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key=option 3 (6/9), 0-based index 2. Simplest-form skill mapped to P3 skill 78 (no dedicated P4 simplest-form skill)."
},
{
"n": 5,
"type_id": 1,
"question": "Write $$6\\frac{4}{25}$$ as a decimal.",
"answer0": "6.425",
"answer1": "6.4",
"answer2": "6.16",
"answer3": "6.016",
"correct_answer": 2,
"skill_id": 127,
"difficulty_id": 2,
"explanation": "Convert $$\\frac{4}{25}$$ to a decimal: $$\\frac{4}{25}=\\frac{16}{100}=0.16$$. So $$6\\frac{4}{25}=6.16$$. Answer: 6.16.",
"hints": [
"Make the denominator 100: multiply top and bottom of 4/25 by 4.",
"16/100 = 0.16."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q5",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key=option 3 (6.16), 0-based index 2."
},
{
"n": 6,
"type_id": 1,
"question": "Arrange these decimals from the smallest to the greatest.
7.3 , 0.73 , 7.03 , 0.75",
"answer0": "0.75 , 0.73 , 7.03 , 7.3",
"answer1": "0.73 , 0.75 , 7.03 , 7.3",
"answer2": "0.73 , 7.3 , 7.03 , 0.75",
"answer3": "0.75 , 0.73 , 7.3 , 7.03",
"correct_answer": 1,
"skill_id": 124,
"difficulty_id": 2,
"explanation": "Compare whole-number parts first: 0.73 and 0.75 are less than 1; 7.03 and 7.3 are over 7. Order the small pair: 0.73 < 0.75. Order the large pair: 7.03 < 7.3. So smallest to greatest: 0.73 , 0.75 , 7.03 , 7.3. Answer: option 2.",
"hints": [
"Compare the whole-number part first, then the tenths.",
"0.73 < 0.75 and 7.03 < 7.3."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key=option 2, 0-based index 1."
},
{
"n": 7,
"type_id": 1,
"question": "Which of the following object is not symmetrical?",
"answer0": "Object 1",
"answer1": "Object 2",
"answer2": "Object 3",
"answer3": "Object 4",
"correct_answer": 0,
"skill_id": 144,
"difficulty_id": 2,
"explanation": "A symmetrical figure can be folded so both halves match exactly. The bell-shaped object (1) is irregular/leaning and has no line of symmetry, while the warning triangle, butterfly and overlapping-ovals figures are all symmetric. Answer: Object 1.",
"hints": [
"A symmetric figure has matching halves on both sides of a fold line.",
"Look for the one shape whose two halves do not match."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q7",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 4,
"image_bbox": [
0.12,
0.58,
0.78,
0.92
],
"image_loc": "lower two-thirds of page: four labelled option pictures (1) bell, (2) warning triangle, (3) butterfly, (4) two overlapping ovals in a box",
"notes": "Image-option MCQ. Key=option 1 (the bell), 0-based index 0. Crop each option to q7_opt0..3.png downstream."
},
{
"n": 8,
"type_id": 1,
"question": "Which of the following angles in the figure is an obtuse angle?",
"answer0": "$$\\angle w$$",
"answer1": "$$\\angle x$$",
"answer2": "$$\\angle y$$",
"answer3": "$$\\angle z$$",
"correct_answer": 2,
"skill_id": 139,
"difficulty_id": 2,
"explanation": "An obtuse angle is between 90 degrees and 180 degrees. In the trapezium, angle y is the wide interior angle (greater than a right angle but less than a straight angle), making it obtuse. Answer: angle y.",
"hints": [
"An obtuse angle is larger than a right angle (90 degrees) but smaller than a straight angle (180 degrees).",
"Look for the widest-opening angle in the figure."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q8",
"image_needed": true,
"image_options": false,
"image_file": "q8.png",
"image_page": 5,
"image_bbox": [
0.2,
0.12,
0.52,
0.28
],
"image_loc": "top-left, an irregular four-sided figure (trapezium) with corners labelled w, x, y, z",
"notes": "Key=option 3 (angle y), 0-based index 2."
},
{
"n": 9,
"type_id": 1,
"question": "The mass of a pail of sand is 2.5 kg. It is 30.14 kg lighter than a pile of bricks. What is the mass of the bricks?",
"answer0": "27.64 kg",
"answer1": "29.89 kg",
"answer2": "30.39 kg",
"answer3": "32.64 kg",
"correct_answer": 3,
"skill_id": 129,
"difficulty_id": 2,
"explanation": "The sand is 30.14 kg lighter than the bricks, so the bricks are 30.14 kg heavier than the sand. Mass of bricks = 2.5 + 30.14 = 32.64 kg. Answer: 32.64 kg.",
"hints": [
"If the sand is lighter than the bricks, the bricks must be heavier.",
"Add: 2.5 + 30.14."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q9",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key=option 4 (32.64 kg), 0-based index 3."
},
{
"n": 10,
"type_id": 1,
"question": "Identify the net of the geometric figure.",
"answer0": "prism",
"answer1": "pyramid",
"answer2": "cube",
"answer3": "cuboid",
"correct_answer": 0,
"skill_id": 233,
"difficulty_id": 2,
"explanation": "The net is made of two triangular faces and three rectangular faces, which folds up into a triangular prism. Answer: prism.",
"hints": [
"Count the shapes in the net: how many triangles and how many rectangles?",
"Two triangles plus three rectangles form a triangular prism."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q10",
"image_needed": true,
"image_options": false,
"image_file": "q10.png",
"image_page": 6,
"image_bbox": [
0.24,
0.12,
0.52,
0.28
],
"image_loc": "top-centre, a net made of squares/rectangles and triangles (triangular prism net)",
"notes": "Key=option 1 (prism), 0-based index 0."
},
{
"n": 11,
"type_id": 1,
"question": "Round off 12.329 $$l$$ to the nearest tenth.",
"answer0": "12 $$l$$",
"answer1": "12.3 $$l$$",
"answer2": "12.4 $$l$$",
"answer3": "12.34 $$l$$",
"correct_answer": 1,
"skill_id": 128,
"difficulty_id": 2,
"explanation": "Rounding to the nearest tenth means keeping 1 decimal place. Look at the hundredths digit (2): since 2 is less than 5, round down. 12.329 rounds to 12.3 l. Answer: 12.3 l.",
"hints": [
"Nearest tenth = 1 decimal place.",
"Look at the second decimal digit (2) to decide rounding; 2 < 5 so round down."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q11",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key=option 2 (12.3 l), 0-based index 1."
},
{
"n": 12,
"type_id": 1,
"question": "The number of boys who liked [BLANK] pizza was twice the number of girls.",
"answer0": "Hawaiian",
"answer1": "Pepperoni",
"answer2": "Cheese",
"answer3": "BBQ Chicken",
"correct_answer": 2,
"skill_id": 104,
"difficulty_id": 2,
"explanation": "Read the bar graph and compare boys' and girls' bars for each pizza. For Cheese, the boys' bar is exactly twice the height of the girls' bar. Answer: Cheese.",
"hints": [
"Compare the height of the Boys bar to the Girls bar for each pizza.",
"Find the pizza where the boys' bar is double the girls' bar."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q12",
"image_needed": true,
"image_options": false,
"image_file": "q12.png",
"image_page": 7,
"image_bbox": [
0.13,
0.14,
0.85,
0.45
],
"image_loc": "upper half, bar graph titled 'My Favourite Pizza' with Girls/Boys bars for Hawaiian, Pepperoni, Cheese, BBQ Chicken",
"notes": "Shared bar graph for Q12 and Q13. Key=option 3 (Cheese), 0-based index 2. Stem blank rendered as [BLANK] word-option MCQ (options are pizza names)."
},
{
"n": 13,
"type_id": 1,
"question": "Which of the following sentences best describes the bar graph?",
"answer0": "The total number of girls was more than the total number of boys who chose their favourite pizzas.",
"answer1": "The number of girls who liked BBQ Chicken pizza was fewer than the number of girls who liked Hawaiian pizza.",
"answer2": "The number of boys who chose cheese pizza was the least among all the boys.",
"answer3": "Pepperoni was the most popular choice of the children.",
"correct_answer": 3,
"skill_id": 104,
"difficulty_id": 2,
"explanation": "Check each statement against the graph. Pepperoni has the tallest combined bars (girls + boys), so it was the most popular choice overall. Answer: option 4.",
"hints": [
"Add the girls and boys for each pizza to find the most popular overall.",
"Pepperoni has the highest total."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q13",
"image_needed": true,
"image_options": false,
"image_file": "q13.png",
"image_page": 7,
"image_bbox": [
0.13,
0.14,
0.85,
0.45
],
"image_loc": "upper half of page 7, the same 'My Favourite Pizza' bar graph",
"notes": "Shares the bar graph with Q12. Key=option 4, 0-based index 3."
},
{
"n": 14,
"type_id": 1,
"question": "The pie charts represent the number of fruits in a stall. Which of the following pie charts best represents the data in the table?
Apple: 12, Orange: 36, Pear: 30, Papaya: 22",
"answer0": "Pie chart 1",
"answer1": "Pie chart 2",
"answer2": "Pie chart 3",
"answer3": "Pie chart 4",
"correct_answer": 3,
"skill_id": 235,
"difficulty_id": 3,
"explanation": "Order the quantities: Orange (36) is largest, then Pear (30), then Papaya (22), then Apple (12, smallest). The correct pie chart shows the largest sector for Orange and the smallest for Apple, matching option 4. Answer: option 4.",
"hints": [
"Rank the fruits by quantity: Orange > Pear > Papaya > Apple.",
"The biggest sector must be Orange and the smallest must be Apple."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q14",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 8,
"image_bbox": [
0.13,
0.3,
0.88,
0.92
],
"image_loc": "lower two-thirds: four labelled pie charts (1)-(4) each with Apple/Orange/Pear/Papaya sectors; data table is at top",
"notes": "Image-option MCQ. Key=option 4, 0-based index 3. The data table is part of the stem (kept as text). Crop each pie chart to q14_opt0..3.png downstream."
},
{
"n": 15,
"type_id": 1,
"question": "How many more circles must be shaded such that $$\\frac{2}{3}$$ of the shapes are shaded?",
"answer0": "1",
"answer1": "2",
"answer2": "3",
"answer3": "4",
"correct_answer": 0,
"skill_id": 120,
"difficulty_id": 2,
"explanation": "There are 9 circles in total. $$\\frac{2}{3}$$ of 9 = 6 circles should be shaded. Currently 5 circles are shaded, so 6 - 5 = 1 more circle must be shaded. Answer: 1.",
"hints": [
"Count the total circles, then find 2/3 of that total.",
"Subtract the number already shaded from the target."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q15",
"image_needed": true,
"image_options": false,
"image_file": "q15.png",
"image_page": 9,
"image_bbox": [
0.15,
0.13,
0.6,
0.27
],
"image_loc": "top-left, a box of 9 circles (2 rows): 5 shaded grey and 4 unshaded",
"notes": "Count to verify: 9 circles total, 5 shaded. 2/3 of 9 = 6 needed, so 1 more. Key=option 1, 0-based index 0."
},
{
"n": 16,
"type_id": 2,
"question": "Round 8325 to the nearest ten. [?]",
"answer0": "8330",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 109,
"difficulty_id": 1,
"explanation": "To round to the nearest ten, look at the ones digit (5). Since 5 rounds up, the tens digit goes from 2 to 3. 8325 rounds to 8330. Answer: 8330.",
"hints": [
"Look at the ones digit to decide rounding.",
"5 or more rounds up."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q16",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key=8330."
},
{
"n": 17,
"type_id": 2,
"question": "How many one-elevenths are there in 1 whole? [?]",
"answer0": "11",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 119,
"difficulty_id": 1,
"explanation": "One whole = $$\\frac{11}{11}$$, which is eleven groups of $$\\frac{1}{11}$$. So there are 11 one-elevenths in 1 whole. Answer: 11.",
"hints": [
"1 whole = 11/11.",
"Count how many 1/11 pieces make 11/11."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q17",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key=11."
},
{
"n": 18,
"type_id": 2,
"question": "$$1 - \\frac{1}{8} - \\frac{1}{4}$$ = [?]",
"answer0": "5/8",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 121,
"difficulty_id": 2,
"explanation": "Use a common denominator of 8: $$1=\\frac{8}{8}$$, $$\\frac{1}{4}=\\frac{2}{8}$$. So $$\\frac{8}{8}-\\frac{1}{8}-\\frac{2}{8}=\\frac{5}{8}$$. Answer: $$\\frac{5}{8}$$.",
"hints": [
"Convert all to eighths: 1 = 8/8 and 1/4 = 2/8.",
"8/8 - 1/8 - 2/8 = 5/8."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q18",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key=5/8. FIB fraction answer kept plain a/b."
},
{
"n": 19,
"type_id": 2,
"question": "Write the decimal represented by A. [?]",
"answer0": "0.48",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 123,
"difficulty_id": 2,
"explanation": "The number line is divided into ten equal intervals between 0.4 and 0.5, so each small mark is 0.01. A is 8 marks after 0.4, giving 0.4 + 0.08 = 0.48. Answer: 0.48.",
"hints": [
"Each small division between 0.4 and 0.5 is 0.01.",
"Count the marks from 0.4 to the arrow A."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q19",
"image_needed": true,
"image_options": false,
"image_file": "q19.png",
"image_page": 11,
"image_bbox": [
0.2,
0.66,
0.85,
0.8
],
"image_loc": "middle of page, a number line marked 0.4 and 0.5 with an arrow labelled A pointing near 0.48",
"notes": "Key=0.48."
},
{
"n": 20,
"type_id": 2,
"question": "Find the value of 6.73 x 8. [?]",
"answer0": "53.84",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 130,
"difficulty_id": 2,
"explanation": "Multiply: 6.73 x 8 = 53.84. Answer: 53.84.",
"hints": [
"Multiply 673 x 8 = 5384, then place the decimal point (two decimal places).",
"6.73 x 8 = 53.84."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q20",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key=53.84."
},
{
"n": 21,
"type_id": 2,
"question": "4501 ÷ 7 = [?]",
"answer0": "643",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 117,
"difficulty_id": 2,
"explanation": "Divide: 4501 ÷ 7 = 643 exactly (7 x 643 = 4501). Answer: 643.",
"hints": [
"Use long division: 7 into 45, then 10, then 1.",
"Check: 643 x 7 = 4501."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q21",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key=643."
},
{
"n": 22,
"type_id": 2,
"question": "Write $$2\\frac{2}{3}$$ as an improper fraction. [?]",
"answer0": "8/3",
"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 x 3 + 2 = 8. Keep the denominator 3. So $$2\\frac{2}{3}=\\frac{8}{3}$$. Answer: $$\\frac{8}{3}$$.",
"hints": [
"Improper = (whole x denominator + numerator) over denominator.",
"2 x 3 + 2 = 8, over 3."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q22",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key=8/3. FIB fraction answer kept plain a/b."
},
{
"n": 23,
"type_id": 2,
"question": "Measure and write down the size of $$\\angle x$$. [?]",
"answer0": "160",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 140,
"difficulty_id": 2,
"explanation": "Using a protractor on the angle in the figure, the size of angle x measures 160 degrees. Answer: 160 degrees.",
"hints": [
"Place the protractor centre on the vertex and read off the scale.",
"The angle is reflex of a small turn; it measures 160 degrees."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q23",
"image_needed": true,
"image_options": false,
"image_file": "q23.png",
"image_page": 13,
"image_bbox": [
0.2,
0.13,
0.72,
0.27
],
"image_loc": "top, a bent line forming angle x to be measured (about 160 degrees), printed answer is in degrees",
"notes": "Key=160 (degrees). Answer unit is degrees; printed 'o' on page."
},
{
"n": 24,
"type_id": 2,
"question": "Name the two angles that are greater than 90°. [?] and [?]",
"answer0": "f",
"answer1": "d",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 194,
"difficulty_id": 2,
"explanation": "At the point where the lines cross, angles f and d are vertically opposite each other and both open wider than a right angle, so both are greater than 90 degrees. Answer: f and d.",
"hints": [
"Look for the two angles wider than a right angle.",
"Vertically opposite angles are equal; f and d are the obtuse pair."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q24",
"image_needed": true,
"image_options": false,
"image_file": "q24.png",
"image_page": 13,
"image_bbox": [
0.15,
0.42,
0.6,
0.62
],
"image_loc": "middle-left, several lines crossing at one point with angles labelled d, e, f, g, h around the intersection",
"notes": "Key='F and D' -> two-blank FIB, answers f and d (order interchangeable; key lists F and D)."
},
{
"n": 25,
"type_id": 2,
"question": "Find the sum of the first 2 common multiples of 4 and 6. [?]",
"answer0": "36",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 115,
"difficulty_id": 2,
"explanation": "Common multiples of 4 and 6 are multiples of 12. The first two are 12 and 24. Their sum is 12 + 24 = 36. Answer: 36.",
"hints": [
"The common multiples of 4 and 6 are multiples of 12.",
"First two: 12 and 24; add them."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q25",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key=36."
},
{
"n": 26,
"type_id": 2,
"question": "After spilling $$\\frac{2}{3}$$ $$l$$ of water, John has $$1\\frac{1}{2}$$ $$l$$ of water left. How much water does he have at first? Give your answer as a mixed number. [?]",
"answer0": "2 1/6",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 122,
"difficulty_id": 2,
"explanation": "At first = water left + water spilled = $$1\\frac{1}{2}+\\frac{2}{3}$$. Common denominator 6: $$1\\frac{3}{6}+\\frac{4}{6}=1\\frac{7}{6}=2\\frac{1}{6}$$. Answer: $$2\\frac{1}{6}$$ l.",
"hints": [
"Starting amount = amount left + amount spilled.",
"Add 1 1/2 and 2/3 using sixths: 1 3/6 + 4/6 = 1 7/6 = 2 1/6."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q26",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working shows 1 3/6 + 4/6 = 1 7/6 = 2 1/6. Answer as mixed number 2 1/6 (plain text for FIB)."
},
{
"n": 27,
"type_id": 2,
"question": "ABCD is a square. Find $$\\angle x$$. [?]",
"answer0": "50",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "Angle ADC of the square is 90 degrees. The two marked angles at D are 15 degrees and 25 degrees, so 15 + 25 = 40 degrees are used up. The remaining angle x = 90 - 40 = 50 degrees. Answer: 50 degrees.",
"hints": [
"A corner of a square is 90 degrees.",
"Subtract the two given angles (15 + 25 = 40) from 90."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q27",
"image_needed": true,
"image_options": false,
"image_file": "q27.png",
"image_page": 15,
"image_bbox": [
0.22,
0.13,
0.55,
0.32
],
"image_loc": "top-left, square ABCD with lines drawn from D; angles 15 degrees, x and 25 degrees marked at corner D",
"notes": "Key working: 15 + 25 = 40; 90 - 40 = 50. Answer 50 degrees."
},
{
"n": 28,
"type_id": 2,
"question": "The pie chart shows the number of cakes sold in a cafe. There were 120 cakes sold in a day. The same number of people bought cheese and lemon cakes. How many people bought cheesecake? [?]",
"answer0": "20",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 236,
"difficulty_id": 3,
"explanation": "Chocolate is $$\\frac{5}{12}$$ of 120 = 50. Strawberry is a right angle (quarter) = $$\\frac{1}{4}$$ of 120 = 30. Remaining for cheese + lemon = 120 - 50 - 30 = 40. Since cheese and lemon are equal, cheese = 40 ÷ 2 = 20. Answer: 20.",
"hints": [
"Chocolate = 5/12 of 120; the right-angle sector (Strawberry) = 1/4 of 120.",
"Subtract those from 120, then halve the remainder for cheese = lemon."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q28",
"image_needed": true,
"image_options": false,
"image_file": "q28.png",
"image_page": 15,
"image_bbox": [
0.28,
0.55,
0.68,
0.85
],
"image_loc": "lower-centre, pie chart 'Cakes sold in a cafe' with sectors Lemon, Strawberry, Cheese, Chocolate (Chocolate marked 5/12, right-angle mark at Strawberry)",
"notes": "Key=20."
},
{
"n": 29,
"type_id": 2,
"question": "The perimeter of a square is 48 cm. Find the area of the square. [?]",
"answer0": "144",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 137,
"difficulty_id": 2,
"explanation": "A square has 4 equal sides, so each side = 48 ÷ 4 = 12 cm. Area = side x side = 12 x 12 = 144 cm^2. Answer: 144 cm^2.",
"hints": [
"Side of a square = perimeter ÷ 4.",
"Area = side x side."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q29",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working 12 x 12 = 144. Answer unit cm^2."
},
{
"n": 30,
"type_id": 0,
"question": "Complete the following figure to make it symmetric.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 145,
"difficulty_id": 2,
"explanation": "Reflect the existing line drawing across the dashed line of symmetry to complete the symmetric figure.",
"hints": [
"Reflect each segment across the dashed line.",
"Each point's mirror image is the same distance on the other side."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q30",
"image_needed": true,
"image_options": false,
"image_file": "q30.png",
"image_page": 16,
"image_bbox": [
0.26,
0.42,
0.74,
0.74
],
"image_loc": "centre, square grid with a partial bold line drawing and a dashed diagonal line of symmetry",
"notes": "Interactive draw-to-complete task; no value answer. type_id 0 (skipped on insert). Answer key shows the completed reflected figure."
},
{
"n": 31,
"type_id": 0,
"question": "Each of the statements below is either true, false or not possible to tell based on the information given in the graph. For each statement, put a tick to indicate your answer.
(a) April is the wettest month.
(b) No two months has the same amount of rainfall.
(c) The greatest decrease in rainfall is from April to May.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 147,
"difficulty_id": 2,
"explanation": "From the rainfall line graph (Jan 200, Feb 150, Mar 250, Apr 400, May 200, June 300, July 150): (a) April at 400 is the highest = True. (b) Jan and May are both 200 (and Feb and July both 150), so this is False. (c) April to May drops 400 to 200 = 200, the largest single-month decrease = True. Answers: True, False, True.",
"hints": [
"Read each month's value off the line graph.",
"Check the highest value, look for repeated values, and compare month-to-month drops."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q31",
"image_needed": true,
"image_options": false,
"image_file": "q31.png",
"image_page": 17,
"image_bbox": [
0.13,
0.22,
0.85,
0.66
],
"image_loc": "centre of page 17, line graph 'Rainfall Chart' (Jan-July) used for Q31 and Q32",
"notes": "Tick-the-box True/False/Not-possible-to-tell table; no single value answer so type_id 0 (skipped on insert). Key=True, False, True. Graph is on page 17; this question is on page 18."
},
{
"n": 32,
"type_id": 2,
"question": "What was the difference between the highest and lowest amount of rainfall as shown on the graph? [?]",
"answer0": "250",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 147,
"difficulty_id": 2,
"explanation": "From the line graph the highest rainfall is 400 (April) and the lowest is 150 (Feb and July). Difference = 400 - 150 = 250 units. Answer: 250 units.",
"hints": [
"Find the highest point and the lowest point on the graph.",
"Subtract: 400 - 150."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q32",
"image_needed": true,
"image_options": false,
"image_file": "q32.png",
"image_page": 17,
"image_bbox": [
0.13,
0.22,
0.85,
0.66
],
"image_loc": "the 'Rainfall Chart' line graph on page 17 (shared with Q31)",
"notes": "Key working 400 - 150 = 250. Answer unit units. Graph on page 17; question on page 18."
},
{
"n": 33,
"type_id": 0,
"question": "The net of a cuboid has 2 missing faces. Shade 2 faces to complete the net of the cuboid.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 232,
"difficulty_id": 2,
"explanation": "A cuboid net needs 6 faces in 3 matching pairs. Shade the 2 faces (shown dashed) that complete the pairs so the net folds into a cuboid.",
"hints": [
"A cuboid has 3 pairs of equal opposite faces.",
"Shade the faces that complete the missing pairs."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q33",
"image_needed": true,
"image_options": false,
"image_file": "q33.png",
"image_page": 19,
"image_bbox": [
0.22,
0.14,
0.72,
0.42
],
"image_loc": "top-centre, partial cuboid net with some faces shaded grey and 2 dashed (missing) faces to be shaded",
"notes": "Interactive shade-the-faces task; no value answer so type_id 0 (skipped on insert). Key shows the 2 faces to shade."
},
{
"n": 34,
"type_id": 0,
"question": "Draw three more lines in the grid to complete a square.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 143,
"difficulty_id": 2,
"explanation": "One side of the tilted square is already drawn on the grid; draw the three remaining equal sides at right angles to complete the square (a diamond/tilted square).",
"hints": [
"A square has 4 equal sides and right-angle corners.",
"Use the grid to keep each new side the same length as the given one."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q34",
"image_needed": true,
"image_options": false,
"image_file": "q34.png",
"image_page": 19,
"image_bbox": [
0.17,
0.58,
0.7,
0.84
],
"image_loc": "lower-centre, rectangular grid with one or more lines of a tilted square already drawn",
"notes": "Interactive draw-to-complete task; no value answer so type_id 0 (skipped on insert)."
},
{
"n": 35,
"type_id": 2,
"question": "In a party, the children are told to get into groups to play a game. If they form groups of 5, there will be 2 children left without a group. If they form groups of 6, there will be 4 children left without a group. What is the least number of children at the party? [?]",
"answer0": "22",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 115,
"difficulty_id": 3,
"explanation": "The number leaves remainder 2 when divided by 5 (so ends in 2 or 7) and remainder 4 when divided by 6. Check numbers ending in 2 or 7: 22 ÷ 6 = 3 r 4 and 22 ÷ 5 = 4 r 2. So the least number is 22. Answer: 22.",
"hints": [
"List numbers that give remainder 2 when divided by 5: 7, 12, 17, 22, ...",
"Test which also gives remainder 4 when divided by 6."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q35",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key=22."
},
{
"n": 36,
"type_id": 2,
"question": "Mrs Tan had $188.70. She spent $39.90 on a blouse. She gave the rest of the money equally to her 3 children. How much did each child receive? [?]",
"answer0": "$49.60",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 131,
"difficulty_id": 2,
"explanation": "Money left after the blouse = 188.70 - 39.90 = 148.80. Shared among 3 children: 148.80 ÷ 3 = 49.60. Each child received $49.60. Answer: $49.60.",
"hints": [
"First subtract the blouse cost from the total.",
"Then divide the remainder by 3."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q36",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working: 188.70 - 39.90 = 148.8; 148.8 ÷ 3 = 49.60. Answer $49.60."
},
{
"n": 37,
"type_id": 2,
"question": "Katherine bought 10.25 $$l$$ of fruit juice. She fills them into 9 bottles. Each bottle is filled with 0.45 $$l$$ of fruit juice.
(a) How much fruit juice will be left?
(b) How much did Katherine pay for the fruit juice if it cost $4 per litre?",
"answer0": "6.2",
"answer1": "41",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 131,
"difficulty_id": 3,
"explanation": "(a) Juice used = 0.45 x 9 = 4.05 l. Left = 10.25 - 4.05 = 6.20 l. (b) Cost = 10.25 x $4 = $41. Answers: (a) 6.20 l, (b) $41.",
"hints": [
"(a) Multiply 0.45 by 9 for the juice used, then subtract from 10.25.",
"(b) Multiply the total litres (10.25) by $4."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q37",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Two-blank FIB (a then b). Key: a) 0.45 x 9 = 4.05; 10.25 - 4.05 = 6.20 l. b) 10.25 x 4 = $41. answer0=6.2 (litres), answer1=41 (dollars)."
},
{
"n": 38,
"type_id": 2,
"question": "The mass of a bag containing 9 packets of milk is 23.5 kg. After taking out 4 packets, the mass of the bag and remaining packets of milk is 19.36 kg. Find the mass of the bag. [?]",
"answer0": "14.185",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 131,
"difficulty_id": 3,
"explanation": "Mass of 4 packets = 23.5 - 19.36 = 4.14 kg. Mass of 1 packet = 4.14 ÷ 4 = 1.035 kg. Mass of 9 packets = 1.035 x 9 = 9.315 kg. Mass of bag = 23.5 - 9.315 = 14.185 kg. Answer: 14.185 kg.",
"hints": [
"4 packets weigh 23.5 - 19.36; find one packet, then 9 packets.",
"Bag = total mass - mass of 9 packets."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q38",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working has a typo (writes '1.035 x 9 = 9.315' then '23.5 - 9.15') but the correct final value is 23.5 - 9.315 = 14.185 kg, matching the key's stated answer 14.185. Answer unit kg."
},
{
"n": 39,
"type_id": 2,
"question": "Tom earned $5670 a month. He spent $$\\frac{2}{3}$$ of his salary on food and $$\\frac{1}{9}$$ of it on transport. He saved the rest. How much did he save in a month? [?]",
"answer0": "$1260",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 122,
"difficulty_id": 3,
"explanation": "Fraction spent = $$\\frac{2}{3}+\\frac{1}{9}=\\frac{6}{9}+\\frac{1}{9}=\\frac{7}{9}$$. Fraction saved = $$1-\\frac{7}{9}=\\frac{2}{9}$$. Saved = $$\\frac{2}{9}$$ of 5670. Since 5670 ÷ 9 = 630, saved = 630 x 2 = $1260. Answer: $1260.",
"hints": [
"Add the fractions spent (2/3 + 1/9) using ninths.",
"Saved fraction = 1 minus that; find 2/9 of $5670."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q39",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working: 5670 ÷ 9 = 630; 630 x 2 = 1260. Answer $1260."
},
{
"n": 40,
"type_id": 2,
"question": "The total area of the rectangle and square is 400 cm². The length of the square is 16 cm. The length of the square is twice the breadth of the rectangle. Find the length of the rectangle. [?]",
"answer0": "18",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Area of the square = 16 x 16 = 256 cm^2. Area of the rectangle = 400 - 256 = 144 cm^2. Breadth of rectangle = half the square's length = 16 ÷ 2 = 8 cm. Length of rectangle = area ÷ breadth = 144 ÷ 8 = 18 cm. Answer: 18 cm.",
"hints": [
"Find the square's area, then subtract from 400 for the rectangle's area.",
"The rectangle's breadth is half of 16; length = area ÷ breadth."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q40",
"image_needed": true,
"image_options": false,
"image_file": "q40.png",
"image_page": 25,
"image_bbox": [
0.24,
0.2,
0.62,
0.36
],
"image_loc": "upper-left, a rectangle joined to a square; rectangle length marked '?', square side marked 16cm",
"notes": "Key working: 16 x 16 = 256; 400 - 256 = 144; 144 ÷ 8 = 18. Answer 18 cm."
},
{
"n": 41,
"type_id": 2,
"question": "Aminah divided her garden into 4 equal plots, A, B, C and D. The area of her garden is 240 m². $$\\frac{1}{2}$$ of Plot A was planted with tulips and $$\\frac{1}{4}$$ of Plot B was planted with roses. What fraction of her garden did she plant with tulips and roses? [?]",
"answer0": "3/16",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 121,
"difficulty_id": 3,
"explanation": "Each plot is $$\\frac{1}{4}$$ of the garden. Tulips = $$\\frac{1}{2}\\times\\frac{1}{4}=\\frac{1}{8}$$ of the garden. Roses = $$\\frac{1}{4}\\times\\frac{1}{4}=\\frac{1}{16}$$ of the garden. Total = $$\\frac{1}{8}+\\frac{1}{16}=\\frac{2}{16}+\\frac{1}{16}=\\frac{3}{16}$$. Answer: $$\\frac{3}{16}$$.",
"hints": [
"Each plot is 1/4 of the whole garden.",
"Tulips = 1/2 of a plot = 1/8; roses = 1/4 of a plot = 1/16; add them."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q41",
"image_needed": true,
"image_options": false,
"image_file": "q41.png",
"image_page": 26,
"image_bbox": [
0.22,
0.2,
0.76,
0.36
],
"image_loc": "upper-centre, a long rectangle split into 4 equal plots labelled Plot A, Plot B, Plot C, Plot D",
"notes": "Key=3/16. The 240 m^2 figure is not needed for the fraction. FIB fraction answer kept plain 3/16."
},
{
"n": 42,
"type_id": 2,
"question": "Three squares are arranged side by side. Square B has an area of 100 cm². The length of Square C is half the length of Square B. The length of Square A is twice the length of Square B. Find the perimeter of the figure. [?]",
"answer0": "110",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Square B side = 10 cm (since 10 x 10 = 100). Square C side = 10 ÷ 2 = 5 cm. Square A side = 10 x 2 = 20 cm. Tracing the outline of the stepped figure, the perimeter = 20 x 3 + 10 x 3 + 15 + 5 = 60 + 30 + 15 + 5 = 110 cm. Answer: 110 cm.",
"hints": [
"Find each square's side: B = sqrt(100) = 10, C = 5, A = 20.",
"Add up all the outer edges of the combined figure."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q42",
"image_needed": true,
"image_options": false,
"image_file": "q42.png",
"image_page": 27,
"image_bbox": [
0.2,
0.22,
0.7,
0.42
],
"image_loc": "upper-centre, three squares A (large), B (100 cm^2), C (small) arranged side by side along a common baseline",
"notes": "Key working: 10 ÷ 2 = 5; 10 x 2 = 20; 20x3 + 10x3 + 15 + 5 = 110. Answer 110 cm."
},
{
"n": 43,
"type_id": 2,
"question": "Timmy had 4730 marbles and Ahmad had 1240 marbles at first. If Timmy gave some marbles to Ahmad, he would have twice as many marbles as Ahmad in the end. How many marbles did Timmy give Ahmad? [?]",
"answer0": "750",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "The total stays the same: 4730 + 1240 = 5970. In the end Timmy has twice Ahmad, so the total is 3 equal parts. Ahmad's final amount = 5970 ÷ 3 = 1990. Ahmad started with 1240, so he received 1990 - 1240 = 750 marbles. Answer: 750.",
"hints": [
"The total number of marbles never changes when one gives to the other.",
"In the end the ratio is 2:1, so divide the total into 3 parts; find Ahmad's gain."
],
"source": "SCGS 2024 P4 End-of-Year Exam Q43",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working: 4730 + 1240 = 5970; 5970 ÷ 3 = 1990; 1990 - 1240 = 750. Answer 750."
}
]
}