{
"paper": {
"school": "Paya Lebar Methodist Girls' School (Primary)",
"year": 2023,
"level": "P4",
"label": "End of Year Exam",
"source_prefix": "PLMGS 2023 P4 End of Year Exam",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "Which of the following is a factor of both 18 and 27?",
"answer0": "27",
"answer1": "18",
"answer2": "9",
"answer3": "6",
"correct_answer": 2,
"skill_id": 113,
"difficulty_id": 1,
"explanation": "Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 27: 1, 3, 9, 27. The common factors are 1, 3 and 9. Among the options, only 9 is a factor of both. Answer: 9.",
"hints": [
"List the factors of each number separately.",
"Find the number that appears in both lists."
],
"source": "PLMGS 2023 P4 End of Year Exam Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": ""
},
{
"n": 2,
"type_id": 1,
"question": "Which of the following numbers when rounded to the nearest ten becomes 72 500?",
"answer0": "72 443",
"answer1": "72 495",
"answer2": "72 539",
"answer3": "72 554",
"correct_answer": 1,
"skill_id": 109,
"difficulty_id": 2,
"explanation": "Rounding to the nearest ten gives 72 500 for numbers from 72 495 to 72 504. 72 443 rounds to 72 440; 72 495 rounds to 72 500; 72 539 rounds to 72 540; 72 554 rounds to 72 550. Answer: 72 495.",
"hints": [
"Look at the ones digit to decide whether to round up or down.",
"The result must be 72 500, so the number must be from 72 495 to 72 504."
],
"source": "PLMGS 2023 P4 End of Year Exam Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": ""
},
{
"n": 3,
"type_id": 1,
"question": "What fraction of the shapes in the box are circles?",
"answer0": "$$\\frac{4}{10}$$",
"answer1": "$$\\frac{4}{6}$$",
"answer2": "$$\\frac{6}{4}$$",
"answer3": "$$\\frac{6}{10}$$",
"correct_answer": 3,
"skill_id": 120,
"difficulty_id": 1,
"explanation": "There are 10 shapes in total: 4 triangles and 6 circles. The fraction that are circles is $$\\frac{6}{10}$$. Answer: $$\\frac{6}{10}$$.",
"hints": [
"Count the total number of shapes in the box.",
"Count how many of them are circles, then write circles over total."
],
"source": "PLMGS 2023 P4 End of Year Exam Q3",
"image_needed": true,
"image_options": false,
"image_file": "q3.png",
"image_page": 3,
"image_bbox": [
0.33,
0.5,
0.66,
0.66
],
"image_loc": "boxed row of triangles and circles, centre of page below the question",
"notes": "Box contains 4 triangles and 6 circles (10 shapes total)."
},
{
"n": 4,
"type_id": 1,
"question": "$$6\\frac{4}{7}=\\frac{[?]}{7}$$
What is the missing number in the box?",
"answer0": "24",
"answer1": "38",
"answer2": "42",
"answer3": "46",
"correct_answer": 3,
"skill_id": 119,
"difficulty_id": 1,
"explanation": "Convert the mixed number to an improper fraction: $$6\\frac{4}{7}=\\frac{6\\times7+4}{7}=\\frac{42+4}{7}=\\frac{46}{7}$$. The missing number is 46.",
"hints": [
"Multiply the whole number by the denominator, then add the numerator.",
"6 × 7 + 4 gives the new numerator."
],
"source": "PLMGS 2023 P4 End of Year Exam Q4",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Stem shows the equation as an image of a mixed number equal to a fraction with a missing numerator; transcribed in LaTeX."
},
{
"n": 5,
"type_id": 1,
"question": "Which of the following decimals is represented by letter A in the number line?",
"answer0": "3.012",
"answer1": "3.017",
"answer2": "3.023",
"answer3": "3.027",
"correct_answer": 1,
"skill_id": 123,
"difficulty_id": 2,
"explanation": "The number line is divided into ten equal intervals between 3.01 and 3.02, so each small mark is 0.001. Letter A is at the 7th mark after 3.01, giving 3.01 + 0.007 = 3.017. Answer: 3.017.",
"hints": [
"Find what one small interval on the number line is worth.",
"Count the marks from 3.01 to A."
],
"source": "PLMGS 2023 P4 End of Year Exam Q5",
"image_needed": true,
"image_options": false,
"image_file": "q5.png",
"image_page": 4,
"image_bbox": [
0.18,
0.4,
0.82,
0.52
],
"image_loc": "number line with arrow marked A between 3.01 and 3.02, below the question",
"notes": "A sits at the 7th of ten 0.001 intervals after 3.01."
},
{
"n": 6,
"type_id": 1,
"question": "Express 0.05 as a fraction in its simplest form.",
"answer0": "$$\\frac{1}{20}$$",
"answer1": "$$\\frac{1}{2}$$",
"answer2": "$$\\frac{1}{10}$$",
"answer3": "$$\\frac{1}{5}$$",
"correct_answer": 0,
"skill_id": 126,
"difficulty_id": 1,
"explanation": "0.05 = $$\\frac{5}{100}$$. Dividing numerator and denominator by 5 gives $$\\frac{1}{20}$$. Answer: $$\\frac{1}{20}$$.",
"hints": [
"Write 0.05 as a fraction over 100.",
"Simplify by dividing top and bottom by their common factor."
],
"source": "PLMGS 2023 P4 End of Year Exam Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": ""
},
{
"n": 7,
"type_id": 1,
"question": "In the figure shown, ABCD is a rectangle. Find $$\\angle x$$.",
"answer0": "43°",
"answer1": "47°",
"answer2": "64°",
"answer3": "69°",
"correct_answer": 1,
"skill_id": 143,
"difficulty_id": 2,
"explanation": "Angle ADC of the rectangle is 90°. The three angles at D add up to 90°: 26° + x + 21° = 90°, so x = 90° − 26° − 21° = 43°. Answer: 43°.",
"hints": [
"Each corner angle of a rectangle is 90°.",
"The 26°, x and 21° angles together make up the 90° corner at D."
],
"source": "PLMGS 2023 P4 End of Year Exam Q7",
"image_needed": true,
"image_options": false,
"image_file": "q7.png",
"image_page": 5,
"image_bbox": [
0.3,
0.14,
0.62,
0.3
],
"image_loc": "rectangle ABCD with angles 26° and 21° and x marked at corner D, below the question",
"notes": "Key gives option 1 = 43°. (26 + x + 21 = 90 -> x = 43.)"
},
{
"n": 8,
"type_id": 1,
"question": "The table shows the prices of tickets to a theme park.
Adult: $15
Child: $9
Mrs Tan wants to buy tickets for two adults and three children. How much does she have to pay in total?",
"answer0": "$24",
"answer1": "$30",
"answer2": "$57",
"answer3": "$63",
"correct_answer": 2,
"skill_id": 118,
"difficulty_id": 1,
"explanation": "Two adults cost 2 × $15 = $30. Three children cost 3 × $9 = $27. Total = $30 + $27 = $57. Answer: $57.",
"hints": [
"Find the cost of the adult tickets and the child tickets separately.",
"Add the two amounts together."
],
"source": "PLMGS 2023 P4 End of Year Exam Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Ticket prices given in the table are transcribed into the stem."
},
{
"n": 9,
"type_id": 1,
"question": "The table shows 4 different types of CCA that 225 children participated in. Each child participated only in one CCA.
Rope Skipping: ?
Gymnastics: 73
International Dance: 50
Girls' Brigade: 64
How many children participated in Rope Skipping?",
"answer0": "38",
"answer1": "40",
"answer2": "162",
"answer3": "187",
"correct_answer": 0,
"skill_id": 118,
"difficulty_id": 1,
"explanation": "Add the three known groups: 73 + 50 + 64 = 187. Subtract from the total: 225 − 187 = 38. Answer: 38.",
"hints": [
"Add up the children in the three known CCAs.",
"Subtract that total from 225."
],
"source": "PLMGS 2023 P4 End of Year Exam Q9",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Table data transcribed into the stem."
},
{
"n": 10,
"type_id": 1,
"question": "Which of the following fractions has the value closest to 1?",
"answer0": "$$\\frac{2}{3}$$",
"answer1": "$$\\frac{3}{4}$$",
"answer2": "$$\\frac{5}{6}$$",
"answer3": "$$\\frac{7}{8}$$",
"correct_answer": 3,
"skill_id": 121,
"difficulty_id": 2,
"explanation": "The difference from 1 is: $$1-\\frac{2}{3}=\\frac{1}{3}$$; $$1-\\frac{3}{4}=\\frac{1}{4}$$; $$1-\\frac{5}{6}=\\frac{1}{6}$$; $$1-\\frac{7}{8}=\\frac{1}{8}$$. The smallest gap is $$\\frac{1}{8}$$, so $$\\frac{7}{8}$$ is closest to 1. Answer: $$\\frac{7}{8}$$.",
"hints": [
"Work out how far each fraction is from 1.",
"The fraction with the smallest gap is the closest."
],
"source": "PLMGS 2023 P4 End of Year Exam Q10",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": ""
},
{
"n": 11,
"type_id": 1,
"question": "Jamie bought 8 boxes of biscuits. Each box of biscuits cost $1.20. She gave the cashier $50. How much change did Jamie receive?",
"answer0": "$9.20",
"answer1": "$9.60",
"answer2": "$40.40",
"answer3": "$41.60",
"correct_answer": 2,
"skill_id": 131,
"difficulty_id": 1,
"explanation": "Cost of biscuits = 8 × $1.20 = $9.60. Change = $50 − $9.60 = $40.40. Answer: $40.40.",
"hints": [
"First find the total cost of the 8 boxes.",
"Subtract the total cost from $50."
],
"source": "PLMGS 2023 P4 End of Year Exam Q11",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": ""
},
{
"n": 12,
"type_id": 1,
"question": "Both the square and rectangle have the same area. Find the perimeter of the rectangle given that its breadth is 4 cm.",
"answer0": "16 cm",
"answer1": "20 cm",
"answer2": "40 cm",
"answer3": "64 cm",
"correct_answer": 2,
"skill_id": 136,
"difficulty_id": 2,
"explanation": "Area of the square = 8 cm × 8 cm = 64 cm². The rectangle has the same area, so its length = 64 ÷ 4 = 16 cm. Perimeter of the rectangle = 2 × (16 + 4) = 2 × 20 = 40 cm. Answer: 40 cm.",
"hints": [
"Find the area of the square first (side × side).",
"Use that area to find the rectangle's length, then add up all four sides."
],
"source": "PLMGS 2023 P4 End of Year Exam Q12",
"image_needed": true,
"image_options": false,
"image_file": "q12.png",
"image_page": 7,
"image_bbox": [
0.22,
0.2,
0.78,
0.34
],
"image_loc": "an 8 cm square beside a rectangle of breadth 4 cm, below the question",
"notes": "Square side 8 cm; rectangle breadth 4 cm. Area 64, length 16, perimeter 40 cm."
},
{
"n": 13,
"type_id": 1,
"question": "Harun and Ming Hui started reading their storybooks at 9.45 a.m. Harun took 1 h 20 min to finish reading his storybook. He took 25 min longer than Ming Hui. At what time did Ming Hui finish reading his storybook?",
"answer0": "10.20 a.m.",
"answer1": "10.40 a.m.",
"answer2": "11.05 a.m.",
"answer3": "11.30 a.m.",
"correct_answer": 1,
"skill_id": 93,
"difficulty_id": 2,
"explanation": "Ming Hui took 25 min less than Harun: 1 h 20 min − 25 min = 55 min. Starting at 9.45 a.m. and adding 55 min gives 10.40 a.m. Answer: 10.40 a.m.",
"hints": [
"Find how long Ming Hui took (25 min less than Harun).",
"Add that duration to the 9.45 a.m. start time."
],
"source": "PLMGS 2023 P4 End of Year Exam Q13",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Time word problem; P4 24-hour-clock skills don't fit, mapped to nearest time skill 93."
},
{
"n": 14,
"type_id": 1,
"question": "The graph shows the Math test results of 100 students.
How many students scored below 70 marks?",
"answer0": "10",
"answer1": "15",
"answer2": "25",
"answer3": "45",
"correct_answer": 2,
"skill_id": 148,
"difficulty_id": 2,
"explanation": "Below 70 marks covers the bars '50 to 69' and '0 to 49'. From the bar graph, 50 to 69 has 10 students and 0 to 49 has 15 students. Total = 10 + 15 = 25. Answer: 25.",
"hints": [
"'Below 70' means the bars for 50 to 69 and 0 to 49.",
"Read the height of each of those two bars and add them."
],
"source": "PLMGS 2023 P4 End of Year Exam Q14",
"image_needed": true,
"image_options": false,
"image_file": "q14.png",
"image_page": 8,
"image_bbox": [
0.18,
0.16,
0.8,
0.42
],
"image_loc": "bar graph 'Math Test Results' near top of page",
"notes": "Bars: 50-69 = 10, 0-49 = 15; sum below 70 = 25."
},
{
"n": 15,
"type_id": 1,
"question": "How many letters in the word ANGEL have a line of symmetry?",
"answer0": "5",
"answer1": "2",
"answer2": "3",
"answer3": "4",
"correct_answer": 1,
"skill_id": 144,
"difficulty_id": 2,
"explanation": "Checking each letter: A has a vertical line of symmetry; N has none; G has none; E has a horizontal line of symmetry; L has none. So 2 letters (A and E) have a line of symmetry. Answer: 2.",
"hints": [
"Test each letter for a line that folds it onto itself.",
"A and E are symmetrical; N, G and L are not."
],
"source": "PLMGS 2023 P4 End of Year Exam Q15",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Letters shown as a grid image of the word ANGEL; transcribed as plain word. Symmetrical letters: A, E (2)."
},
{
"n": 16,
"type_id": 1,
"question": "Olivia used sticks to make triangles and squares. She used 6 sticks for each triangle and 8 sticks for each square. Olivia made the same number of triangles and squares. She used 14 more sticks to make the squares than the triangles. How many triangles did she make?",
"answer0": "7",
"answer1": "8",
"answer2": "3",
"answer3": "4",
"correct_answer": 0,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "Each square uses 8 − 6 = 2 more sticks than each triangle. The total extra is 14 sticks, so the number of squares (and triangles) = 14 ÷ 2 = 7. Olivia made 7 triangles. Answer: 7.",
"hints": [
"Find how many more sticks one square uses than one triangle.",
"Divide the total extra sticks (14) by that difference."
],
"source": "PLMGS 2023 P4 End of Year Exam Q16",
"image_needed": true,
"image_options": false,
"image_file": "q16.png",
"image_page": 9,
"image_bbox": [
0.24,
0.16,
0.62,
0.26
],
"image_loc": "a triangle made of sticks beside a square made of sticks, below the first line",
"notes": "Figure is illustrative (one triangle, one square). 14 / (8-6) = 7 triangles."
},
{
"n": 17,
"type_id": 2,
"question": "Write thirteen thousand and twenty-six in figures.
[?]",
"answer0": "13026",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 106,
"difficulty_id": 1,
"explanation": "Thirteen thousand = 13 000 and twenty-six = 26. Together: 13 000 + 26 = 13 026. Answer: 13 026.",
"hints": [
"Write the thousands part first.",
"Then add the tens and ones."
],
"source": "PLMGS 2023 P4 End of Year Exam Q17",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 13026."
},
{
"n": 18,
"type_id": 2,
"question": "Write the missing number in the number pattern below.
14 100, 13 200, 12 300, 11 400, [?], 9600",
"answer0": "10500",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 108,
"difficulty_id": 1,
"explanation": "The numbers decrease by 900 each time (14 100 − 900 = 13 200, and so on). After 11 400, the next term is 11 400 − 900 = 10 500. Check: 10 500 − 900 = 9 600. Answer: 10 500.",
"hints": [
"Find the difference between consecutive numbers.",
"Subtract that difference from 11 400."
],
"source": "PLMGS 2023 P4 End of Year Exam Q18",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 10500 (pattern decreases by 900)."
},
{
"n": 19,
"type_id": 2,
"question": "What is the remainder when 1536 is divided by 7?
[?]",
"answer0": "3",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 117,
"difficulty_id": 2,
"explanation": "1536 ÷ 7 = 219 remainder 3, because 7 × 219 = 1533 and 1536 − 1533 = 3. The remainder is 3.",
"hints": [
"Find the largest multiple of 7 that is not greater than 1536.",
"Subtract that multiple from 1536 to get the remainder."
],
"source": "PLMGS 2023 P4 End of Year Exam Q19",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 3."
},
{
"n": 20,
"type_id": 2,
"question": "Which two of the fractions below are equivalent to $$\\frac{6}{8}$$?
$$\\frac{12}{16}$$, $$\\frac{5}{7}$$, $$\\frac{4}{5}$$, $$\\frac{3}{4}$$
[?] and [?]",
"answer0": "12/16",
"answer1": "3/4",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 77,
"difficulty_id": 2,
"explanation": "$$\\frac{6}{8}$$ simplifies to $$\\frac{3}{4}$$. $$\\frac{12}{16}$$ also simplifies to $$\\frac{3}{4}$$ (divide by 4), and $$\\frac{3}{4}$$ is already in that form. So the two equivalent fractions are $$\\frac{12}{16}$$ and $$\\frac{3}{4}$$.",
"hints": [
"Simplify 6/8 to its lowest terms.",
"Simplify each option and compare."
],
"source": "PLMGS 2023 P4 End of Year Exam Q20",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 12/16 and 3/4. Two-blank FIB; either order accepted. Option fractions listed in stem in LaTeX; answers kept plain a/b for grading."
},
{
"n": 21,
"type_id": 2,
"question": "What is the value of $$\\frac{5}{6}+\\frac{2}{3}$$? Express your answer as a mixed number.
[?]",
"answer0": "1 1/2",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 121,
"difficulty_id": 2,
"explanation": "Make the denominators the same: $$\\frac{2}{3}=\\frac{4}{6}$$. Then $$\\frac{5}{6}+\\frac{4}{6}=\\frac{9}{6}=\\frac{3}{2}=1\\frac{1}{2}$$. Answer: $$1\\frac{1}{2}$$.",
"hints": [
"Change 2/3 to sixths so both fractions have the same denominator.",
"Add, then convert the improper fraction to a mixed number."
],
"source": "PLMGS 2023 P4 End of Year Exam Q21",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 1 1/2. FIB answer kept plain as a typed mixed number."
},
{
"n": 22,
"type_id": 2,
"question": "Write 5 thousandths as a decimal.
[?]",
"answer0": "0.005",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 123,
"difficulty_id": 1,
"explanation": "5 thousandths means 5 in the thousandths place (the third decimal place): 0.005. Answer: 0.005.",
"hints": [
"Thousandths is the third place after the decimal point.",
"Place the 5 in that position with zeros before it."
],
"source": "PLMGS 2023 P4 End of Year Exam Q22",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 0.005."
},
{
"n": 23,
"type_id": 2,
"question": "Round 23.51 to the nearest whole number.
[?]",
"answer0": "24",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 128,
"difficulty_id": 1,
"explanation": "The first decimal digit is 5, so round up: 23.51 rounds to 24. Answer: 24.",
"hints": [
"Look at the digit just after the decimal point.",
"If it is 5 or more, round the whole number up."
],
"source": "PLMGS 2023 P4 End of Year Exam Q23",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 24."
},
{
"n": 24,
"type_id": 2,
"question": "Name the two angles in the figure that are smaller than 90°.
[?] and [?]",
"answer0": "w",
"answer1": "z",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 99,
"difficulty_id": 2,
"explanation": "Comparing each marked angle with a right angle, angles w and z are acute (smaller than 90°) while v, x and y are not. The two angles smaller than 90° are w and z.",
"hints": [
"An angle smaller than 90° is an acute angle (looks 'sharper' than a square corner).",
"Compare each marked angle with a right-angle corner."
],
"source": "PLMGS 2023 P4 End of Year Exam Q24",
"image_needed": true,
"image_options": false,
"image_file": "q24.png",
"image_page": 13,
"image_bbox": [
0.3,
0.13,
0.62,
0.32
],
"image_loc": "irregular pentagon with angles v, w, x, y, z marked, below the question",
"notes": "Key: W and Z. Letter answers needed (geometry naming); kept as FIB exact-match since answers are single fixed letters."
},
{
"n": 25,
"type_id": 1,
"question": "Suhana is facing the Police Station after making a $$\\frac{3}{4}$$ anti-clockwise turn. Where was she facing at first?",
"answer0": "Stadium",
"answer1": "Food Centre",
"answer2": "Community Club",
"answer3": "Car Park",
"correct_answer": 0,
"skill_id": 141,
"difficulty_id": 3,
"explanation": "A $$\\frac{3}{4}$$ anti-clockwise turn is the same as a $$\\frac{1}{4}$$ clockwise turn. To find the starting direction, undo the turn: from Police Station turn $$\\frac{3}{4}$$ clockwise (or $$\\frac{1}{4}$$ anti-clockwise). This lands on the Stadium. Answer: Stadium.",
"hints": [
"A 3/4 anti-clockwise turn ends at Police Station; work backwards to the start.",
"Undoing it is a 3/4 clockwise (or 1/4 anti-clockwise) turn from Police Station."
],
"source": "PLMGS 2023 P4 End of Year Exam Q25",
"image_needed": true,
"image_options": false,
"image_file": "q25.png",
"image_page": 13,
"image_bbox": [
0.15,
0.52,
0.8,
0.78
],
"image_loc": "8-direction compass diagram of places around 'Suhana', lower half of page",
"notes": "Key: Stadium. Converted to MCQ from the eight labelled directions on the diagram; the four options include the correct answer (Stadium)."
},
{
"n": 26,
"type_id": 2,
"question": "In the figure, one of the lines is parallel to BE. Which line is parallel to BE?
[?]",
"answer0": "FA",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 100,
"difficulty_id": 2,
"explanation": "Comparing the lines in the figure, line FA runs in the same direction as BE and never meets it, so FA is parallel to BE. Answer: FA.",
"hints": [
"Parallel lines point in the same direction and never cross.",
"Check which of the drawn lines runs the same way as BE."
],
"source": "PLMGS 2023 P4 End of Year Exam Q26",
"image_needed": true,
"image_options": false,
"image_file": "q26.png",
"image_page": 14,
"image_bbox": [
0.28,
0.14,
0.66,
0.3
],
"image_loc": "figure with points A, B, C, D, E, F and line BE, below the question",
"notes": "Key: FA. Letter-pair answer; kept as FIB exact-match (single fixed label)."
},
{
"n": 27,
"type_id": 2,
"question": "The line graph shows the number of cupcakes sold in a shop over a period of 6 days. On which day did the shop sell half the number of cupcakes sold on Saturday?
[?]",
"answer0": "Friday",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 147,
"difficulty_id": 2,
"explanation": "On Saturday the shop sold 450 cupcakes. Half of 450 is 225. The day with 225 cupcakes on the graph is Friday. Answer: Friday.",
"hints": [
"Read off the number of cupcakes sold on Saturday.",
"Find the day whose value is half of that."
],
"source": "PLMGS 2023 P4 End of Year Exam Q27",
"image_needed": true,
"image_options": false,
"image_file": "q27.png",
"image_page": 14,
"image_bbox": [
0.15,
0.46,
0.8,
0.72
],
"image_loc": "line graph 'Number of Cupcakes Sold' over Mon-Sat, lower half of page",
"notes": "Key: Friday. Saturday = 450, half = 225 = Friday. Day-name answer kept as FIB exact-match (single fixed word)."
},
{
"n": 28,
"type_id": 2,
"question": "At a funfair, $$\\frac{5}{12}$$ of the people were children, $$\\frac{1}{3}$$ of the people were men and the rest were women. What fraction of the people were women? Express your answer as a fraction in its simplest form.
[?]",
"answer0": "1/4",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 122,
"difficulty_id": 2,
"explanation": "Children and men together: $$\\frac{5}{12}+\\frac{1}{3}=\\frac{5}{12}+\\frac{4}{12}=\\frac{9}{12}$$. Women = $$1-\\frac{9}{12}=\\frac{3}{12}=\\frac{1}{4}$$. Answer: $$\\frac{1}{4}$$.",
"hints": [
"Add the children's and men's fractions (use a common denominator of 12).",
"Subtract that total from 1 and simplify."
],
"source": "PLMGS 2023 P4 End of Year Exam Q28",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working: 1 - 5/12 - 4/12 = 3/12 = 1/4. FIB answer kept plain a/b."
},
{
"n": 29,
"type_id": 2,
"question": "Express 3 ÷ 7 as a decimal. Round your answer to the nearest hundredth.
[?]",
"answer0": "0.43",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 125,
"difficulty_id": 2,
"explanation": "3 ÷ 7 = 0.4285... The thousandths digit is 8, so round the hundredths up: 0.43. Answer: 0.43.",
"hints": [
"Divide 3 by 7 to at least three decimal places.",
"Look at the third decimal digit to round to the nearest hundredth."
],
"source": "PLMGS 2023 P4 End of Year Exam Q29",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 0.43."
},
{
"n": 30,
"type_id": 1,
"question": "Eliza is standing at Point F and facing south. She makes a 135° clockwise turn. Which point (A, B, C or D) would she be facing?",
"answer0": "A",
"answer1": "B",
"answer2": "C",
"answer3": "D",
"correct_answer": 0,
"skill_id": 141,
"difficulty_id": 3,
"explanation": "Facing south and turning 135° clockwise points Eliza towards the north-west region of the grid. From point F that direction leads to point A. Answer: A.",
"hints": [
"A 135° clockwise turn is one and a half right angles past the starting direction.",
"Find which labelled point lies in that direction from F."
],
"source": "PLMGS 2023 P4 End of Year Exam Q30",
"image_needed": true,
"image_options": false,
"image_file": "q30.png",
"image_page": 16,
"image_bbox": [
0.28,
0.18,
0.74,
0.42
],
"image_loc": "square grid with points A, B, C, D and F marked, plus a North arrow, below the question",
"notes": "Key: A. Original is a short-answer 'which point'; rendered as MCQ over the four labelled points A-D."
},
{
"n": 31,
"type_id": 0,
"question": "One side of Square ABCD is drawn in the square grid. Draw three straight lines to complete the square and label the missing points.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 143,
"difficulty_id": 2,
"explanation": "Side AB is drawn diagonally across the grid. To complete square ABCD, draw three more sides equal in length and at right angles, labelling the new corners C and D so that ABCD forms a square.",
"hints": [
"All four sides of a square are equal and meet at right angles.",
"Use the grid to step off equal lengths from each end of AB."
],
"source": "PLMGS 2023 P4 End of Year Exam Q31",
"image_needed": true,
"image_options": false,
"image_file": "q31.png",
"image_page": 16,
"image_bbox": [
0.28,
0.58,
0.66,
0.86
],
"image_loc": "square grid with side AB drawn, lower half of page",
"notes": "Drawing/construction task (draw three lines to complete the square) — interactive, no app question type, set type_id 0. SKIPPED on insert."
},
{
"n": 32,
"type_id": 2,
"question": "In the figure, ACDF is a square. ABEF and BCDE are rectangles. AF is 12 cm and BC is 3 cm. Find the area of rectangle ABEF.
Ans: [?] $$cm^2$$",
"answer0": "108",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 2,
"explanation": "ACDF is a square with side AF = 12 cm, so AC = 12 cm. AB = AC − BC = 12 − 3 = 9 cm. Rectangle ABEF has length AF = 12 cm and breadth AB = 9 cm, so its area = 12 × 9 = 108 cm². Answer: 108 cm².",
"hints": [
"The square has all sides 12 cm, so AC = 12 cm.",
"Subtract BC from AC to get AB, then multiply by 12."
],
"source": "PLMGS 2023 P4 End of Year Exam Q32",
"image_needed": true,
"image_options": false,
"image_file": "q32.png",
"image_page": 17,
"image_bbox": [
0.3,
0.16,
0.62,
0.34
],
"image_loc": "square ACDF split into rectangles ABEF and BCDE, 12 cm and 3 cm labelled, below the question",
"notes": "Key: 12 x 9 = 108 cm2. Answer unit cm2 stated separately; blank holds the number only."
},
{
"n": 33,
"type_id": 2,
"question": "A train took 2 h 25 min to travel from Station A to Station B. It arrived at Station B at 23 45. What time did the train leave Station A? Express your answer using the 24-hour clock.
[?]",
"answer0": "2120",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 135,
"difficulty_id": 2,
"explanation": "Subtract the travel time from the arrival time: 23 45 − 2 h 25 min. 23 45 − 2 h = 21 45; 21 45 − 25 min = 21 20. The train left at 21 20. Answer: 21 20.",
"hints": [
"Work backwards from the arrival time of 23 45.",
"Subtract the hours first, then the minutes."
],
"source": "PLMGS 2023 P4 End of Year Exam Q33",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 21 20 (written as 2120 in 24-hour clock)."
},
{
"n": 34,
"type_id": 2,
"question": "The table shows the number of stickers collected by each pupil in a group. Part of the table is covered by an ink blot. There were 87 pupils who collected at least 70 stickers.
Number of stickers: 50, 60, 70, 80, 90
Number of pupils: 25, 34, 19, ?, ?
How many pupils in total collected 80 and 90 stickers?
[?]",
"answer0": "68",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 147,
"difficulty_id": 2,
"explanation": "'At least 70 stickers' means the 70, 80 and 90 columns together = 87 pupils. The 70 column has 19 pupils, so the 80 and 90 columns together = 87 − 19 = 68 pupils. Answer: 68.",
"hints": [
"'At least 70' includes the 70, 80 and 90 groups.",
"Subtract the 19 pupils in the 70 column from 87."
],
"source": "PLMGS 2023 P4 End of Year Exam Q34",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 87 - 19 = 68. Table data transcribed into the stem; covered cells shown as ?."
},
{
"n": 35,
"type_id": 0,
"question": "Complete the figure on the grid such that it has only one line of symmetry. The completed figure is made up of a square and a rectangle.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 145,
"difficulty_id": 2,
"explanation": "Reflect the given part of the figure so that the finished shape (a square joined to a rectangle) has exactly one line of symmetry. The added squares mirror the existing ones across that single axis.",
"hints": [
"A line of symmetry folds the figure exactly onto itself.",
"Draw the mirror image of the given shaded cells across one axis only."
],
"source": "PLMGS 2023 P4 End of Year Exam Q35",
"image_needed": true,
"image_options": false,
"image_file": "q35.png",
"image_page": 18,
"image_bbox": [
0.34,
0.5,
0.66,
0.8
],
"image_loc": "square grid with partial figure, lower half of page",
"notes": "Drawing/completion task (complete the symmetric figure on a grid) — interactive, no app question type, set type_id 0. SKIPPED on insert."
},
{
"n": 36,
"type_id": 2,
"question": "The figure is made up of 5 identical rectangles. The perimeter of each rectangle is 48 cm. Find the length of AD.
Ans: [?] $$cm$$",
"answer0": "30",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Looking across the figure, the long side AB equals 3 short sides + ... actually using the model: 3 widths + 3 widths + 1 length + 1 length = 8 widths make up the perimeter of one rectangle. So 8 units = 48 cm, giving 1 unit = 48 ÷ 8 = 6 cm. AD is made of 5 such units: AD = 6 × 5 = 30 cm. Answer: 30 cm.",
"hints": [
"Express the perimeter of one rectangle in equal 'units' from the figure.",
"Find one unit, then count how many units make up AD."
],
"source": "PLMGS 2023 P4 End of Year Exam Q36",
"image_needed": true,
"image_options": false,
"image_file": "q36.png",
"image_page": 19,
"image_bbox": [
0.32,
0.16,
0.6,
0.42
],
"image_loc": "figure of 5 identical rectangles with corners A, B, C, D, upper part of page",
"notes": "Key: 8 units = 48 cm, 1 unit = 6 cm, AD = 5 units = 30 cm."
},
{
"n": 37,
"type_id": 2,
"question": "A pair of trousers cost $132. It cost $27 more than a shirt. Mr Lee bought a pair of trousers and 4 shirts.
(a) How much did a shirt cost?
(b) How much did Mr Lee pay for a pair of trousers and 4 shirts altogether?
(a) $[?]
(b) $[?]",
"answer0": "105",
"answer1": "552",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 2,
"explanation": "(a) A shirt costs $27 less than the trousers: $132 − $27 = $105. (b) Cost of 4 shirts = 4 × $105 = $420. Total = $132 + $420 = $552. Answers: (a) $105 (b) $552.",
"hints": [
"The shirt is $27 cheaper than the $132 trousers.",
"Multiply the shirt price by 4, then add the trousers."
],
"source": "PLMGS 2023 P4 End of Year Exam Q37",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (a) 132 - 27 = 105; (b) 132 + 4 x 105 = 552. Two-part FIB; blank0 = (a), blank1 = (b)."
},
{
"n": 38,
"type_id": 2,
"question": "Study the figures. They follow a pattern where Figure number 1, 2, 3, 4, 5 have grey squares 3, 4, 5, 6, 7 and white squares 1, 2, 3, 4, ?, with total squares 4, 6, 8, 10, ?.
(a) Complete the table for Figure 5: the number of white squares and the total number of squares.
(b) How many grey squares will there be in Figure 8?
(c) How many squares are needed to form Figure 15?
White squares in Figure 5 = [?]; total squares in Figure 5 = [?]; grey squares in Figure 8 = [?]; total squares in Figure 15 = [?]",
"answer0": "5",
"answer1": "12",
"answer2": "10",
"answer3": "32",
"correct_answer": null,
"skill_id": 108,
"difficulty_id": 2,
"explanation": "White squares equal the figure number, so Figure 5 has 5 white squares. Grey squares = figure number + 2, so total = (figure number) + (figure number + 2) = 2 × figure number + 2; Figure 5 total = 2 × 5 + 2 = 12. (b) Grey squares in Figure 8 = 8 + 2 = 10. (c) Total squares in Figure 15 = 2 × 15 + 2 = 32. Answers: (a)(i) 5 (ii) 12, (b) 10, (c) 32.",
"hints": [
"White squares match the figure number; grey squares are 2 more than the figure number.",
"Total = grey + white = 2 × figure number + 2."
],
"source": "PLMGS 2023 P4 End of Year Exam Q38",
"image_needed": true,
"image_options": false,
"image_file": "q38.png",
"image_page": 21,
"image_bbox": [
0.15,
0.13,
0.7,
0.27
],
"image_loc": "row of four grey/white square patterns labelled Figure 1 to Figure 4, top of page",
"notes": "Key: (a)(i) 5 (ii) 12, (b) 8+2=10, (c) (15+2)+15=32. Four blanks in order: white5, total5, grey8, total15. Figure shows the pattern (grey = n+2, white = n)."
},
{
"n": 39,
"type_id": 2,
"question": "There were some stickers in a box. Mariam took $$\\frac{3}{8}$$ of the stickers and Amy took the rest. Mariam took 36 fewer stickers than Amy.
(a) What fraction of the stickers did Amy take?
(b) How many stickers were in the box in total?
(a) [?]
(b) [?]",
"answer0": "5/8",
"answer1": "144",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 122,
"difficulty_id": 3,
"explanation": "(a) Amy took the rest: $$1-\\frac{3}{8}=\\frac{5}{8}$$. (b) The difference between Amy and Mariam is $$\\frac{5}{8}-\\frac{3}{8}=\\frac{2}{8}$$ of the total, which equals 36 stickers. So $$\\frac{2}{8}$$ = 36 means $$\\frac{1}{8}$$ = 18, and the total $$\\frac{8}{8}$$ = 18 × 8 = 144 stickers. Answers: (a) $$\\frac{5}{8}$$ (b) 144.",
"hints": [
"Amy's fraction is 1 minus Mariam's fraction.",
"The difference in their fractions equals the 36-sticker difference; find one unit, then the whole."
],
"source": "PLMGS 2023 P4 End of Year Exam Q39",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (a) 1 - 3/8 = 5/8; (b) 2u = 36, 8u = 36 x 4 = 144. Two-part FIB; blank0 = (a) fraction (plain), blank1 = (b) total."
},
{
"n": 40,
"type_id": 2,
"question": "Peter has a string 130.5 cm long. He tied stars on the string. The distance between 2 stars is 9 cm.
(a) What is the length of the string between the 1st and 6th star?
(b) Find the most number of stars Peter can tie on the string.
(a) [?] $$cm$$
(b) [?]",
"answer0": "45",
"answer1": "15",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "(a) Between the 1st and 6th star there are 6 − 1 = 5 gaps, each 9 cm: 5 × 9 = 45 cm. (b) Number of gaps that fit in 130.5 cm = 130.5 ÷ 9 = 14.5, so 14 whole gaps. The number of stars = number of gaps + 1 = 14 + 1 = 15. Answers: (a) 45 cm (b) 15.",
"hints": [
"The number of gaps between stars is one less than the number of stars.",
"Divide the string length by 9 to find the whole gaps, then add 1 for the stars."
],
"source": "PLMGS 2023 P4 End of Year Exam Q40",
"image_needed": true,
"image_options": false,
"image_file": "q40.png",
"image_page": 23,
"image_bbox": [
0.15,
0.16,
0.78,
0.27
],
"image_loc": "row of 6 stars with 9 cm gap marked, 1st and 6th labelled, below the question",
"notes": "Key: (a) (6-1) x 9 = 45; (b) 130.5/9 = 14.5 -> 14, 14+1 = 15. Two-part FIB; blank0 = (a) cm, blank1 = (b) stars."
},
{
"n": 41,
"type_id": 2,
"question": "Ahmad and Jack had the same amount of money at first. After Ahmad had spent $37 and Jack had received $15, Jack had 3 times as much money as Ahmad in the end.
(a) How much more money did Jack have than Ahmad in the end?
(b) How much money did Jack have at first?
(a) $[?]
(b) $[?]",
"answer0": "52",
"answer1": "63",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "(a) They started equal. Ahmad spent $37 and Jack received $15, so the difference between them in the end is $37 + $15 = $52. (b) In the end Jack = 3 × Ahmad, so the difference of $52 equals 2 units (3 − 1). 1 unit = $52 ÷ 2 = $26 (Ahmad's end amount); Jack's end amount = 3 × $26 = $78. Jack at first = $78 − $15 = $63. Answers: (a) $52 (b) $63.",
"hints": [
"Each dollar Ahmad spends and Jack receives widens the gap between them.",
"Use the 3-times relationship: the gap is 2 units; find one unit, then work back to Jack's starting amount."
],
"source": "PLMGS 2023 P4 End of Year Exam Q41",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (a) 37 + 15 = 52; (b) 2u = 52/2 = 26, 3u = 78, 78 - 15 = 63. Two-part FIB; blank0 = (a), blank1 = (b)."
},
{
"n": 42,
"type_id": 2,
"question": "Tina saved some money from Monday to Friday. Each day, she saved $1 more than the previous day. At the end of Wednesday, she saved a total of $38.70.
(a) How much money did Tina save on Wednesday?
(b) How much money did she save on Friday?
(a) $[?]
(b) $[?]",
"answer0": "13.90",
"answer1": "15.90",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "(a) Let Wednesday's saving be W. Monday = W − $2 and Tuesday = W − $1. Their total: (W − 2) + (W − 1) + W = 3W − 3 = $38.70, so 3W = $41.70 and W = $13.90. (b) Thursday = $13.90 + $1 = $14.90; Friday = $14.90 + $1 = $15.90. Answers: (a) $13.90 (b) $15.90.",
"hints": [
"Write Monday and Tuesday in terms of Wednesday's amount.",
"Their three-day total is $38.70; once you have Wednesday, add $1 twice for Friday."
],
"source": "PLMGS 2023 P4 End of Year Exam Q42",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (a) Mon+Tue+Wed: (38.70 - 3)/3 = 11.90 = Mon; Wed = 11.90 + 2 = 13.90; (b) Fri = 13.90 + 2 = 15.90. Two-part FIB; blank0 = (a), blank1 = (b)."
},
{
"n": 43,
"type_id": 2,
"question": "The figure is made up of Rectangle P, Rectangle Q, Rectangle R and Square S. The perimeter of Rectangle Q is 40 cm. The perimeter of the figure is 72 cm.
(a) Find the length of AB.
(b) Find the area of Square S.
(a) [?] $$cm$$
(b) [?] $$cm^2$$",
"answer0": "8",
"answer1": "64",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "(a) The figure's outer perimeter (72 cm) is the outer rectangle: 2 × (length + AB). Rectangle Q's perimeter is 40 cm; using the layout, the figure length is shared so AB (the right-hand height) works out from 72 − 40 = 32, then 32 ÷ 4 = 8 cm. AB = 8 cm. (b) Square S has the same side as AB region; side = 8 cm, so area = 8 × 8 = 64 cm². Answers: (a) 8 cm (b) 64 cm².",
"hints": [
"Combine the given perimeters (72 cm figure and 40 cm Rectangle Q) to find the short side.",
"Square S has side equal to AB, so its area is side × side."
],
"source": "PLMGS 2023 P4 End of Year Exam Q43",
"image_needed": true,
"image_options": false,
"image_file": "q43.png",
"image_page": 26,
"image_bbox": [
0.25,
0.14,
0.66,
0.3
],
"image_loc": "rectangle divided into P, Q, R, S with A and B marking the right side, below the question",
"notes": "Key: (a) 72 - 40 = 32, 32/4 = 8 cm; (b) 8 x 8 = 64 cm2. Two-part FIB; blank0 = (a) AB length, blank1 = (b) area."
}
]
}