{
"paper": {
"school": "St Nicholas",
"year": 2023,
"level": "P4",
"label": "End of Year Exam",
"source_prefix": "St Nicholas 2023 P4 End of Year Exam",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "The value of the digit 5 in 89 503 is [?].",
"answer0": "50",
"answer1": "500",
"answer2": "5000",
"answer3": "50 000",
"correct_answer": 1,
"skill_id": 105,
"difficulty_id": 1,
"explanation": "In 89 503, the digit 5 is in the hundreds place. Its value is 5 × 100 = 500.",
"hints": [
"Identify which place the 5 sits in.",
"5 is in the hundreds column."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (2) = 500."
},
{
"n": 2,
"type_id": 1,
"question": "Thirty-four thousand and sixty-two in figures is [?].",
"answer0": "34 620",
"answer1": "34 602",
"answer2": "34 062",
"answer3": "3462",
"correct_answer": 2,
"skill_id": 106,
"difficulty_id": 1,
"explanation": "Thirty-four thousand = 34 000; sixty-two = 62. So 34 000 + 62 = 34 062.",
"hints": [
"Write the thousands part first, then the ones part.",
"There are no hundreds, so a 0 fills the hundreds place."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (3) = 34 062."
},
{
"n": 3,
"type_id": 1,
"question": "Which of the following when rounded to the nearest hundred gives 60 000?",
"answer0": "59 599",
"answer1": "59 951",
"answer2": "60 070",
"answer3": "60 140",
"correct_answer": 1,
"skill_id": 109,
"difficulty_id": 2,
"explanation": "Rounding to the nearest hundred: 59 951 → 60 000 (tens digit 5 rounds up). 59 599 → 59 600; 60 070 → 60 100; 60 140 → 60 100. Only 59 951 gives 60 000.",
"hints": [
"Look at the tens digit to decide rounding to the nearest hundred.",
"59 951 rounds up to 60 000."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (2) = 59 951."
},
{
"n": 4,
"type_id": 1,
"question": "What is the second common multiple of 4 and 6?",
"answer0": "12",
"answer1": "16",
"answer2": "24",
"answer3": "30",
"correct_answer": 2,
"skill_id": 115,
"difficulty_id": 2,
"explanation": "Common multiples of 4 and 6 are 12, 24, 36, ... The first is 12 and the second is 24.",
"hints": [
"List multiples of 4 and of 6 and find common ones.",
"First common multiple is 12; the next is 24."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q4",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (3) = 24."
},
{
"n": 5,
"type_id": 1,
"question": "The figure shown is made up of identical rectangles. What fraction of the figure is shaded?",
"answer0": "$$\\frac{5}{7}$$",
"answer1": "$$\\frac{5}{11}$$",
"answer2": "$$\\frac{5}{12}$$",
"answer3": "$$\\frac{7}{12}$$",
"correct_answer": 2,
"skill_id": 120,
"difficulty_id": 2,
"explanation": "The figure has 12 identical rectangles in total (3 rows × 4 columns). 5 of them are shaded, so the shaded fraction is $$\\frac{5}{12}$$.",
"hints": [
"Count the total number of equal rectangles.",
"There are 12 rectangles and 5 are shaded."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q5",
"image_needed": true,
"image_options": false,
"image_file": "q5.png",
"image_page": 3,
"image_bbox": [
0.36,
0.4,
0.66,
0.51
],
"image_loc": "grid of shaded/unshaded rectangles, centre of page below the question",
"notes": "Key: option (3) = 5/12. 12 rectangles total, 5 shaded."
},
{
"n": 6,
"type_id": 1,
"question": "Which of the following fractions is equivalent to $$\\frac{4}{6}$$?",
"answer0": "$$\\frac{6}{12}$$",
"answer1": "$$\\frac{8}{18}$$",
"answer2": "$$\\frac{10}{12}$$",
"answer3": "$$\\frac{12}{18}$$",
"correct_answer": 3,
"skill_id": 77,
"difficulty_id": 2,
"explanation": "$$\\frac{4}{6}=\\frac{2}{3}$$. Checking each: $$\\frac{12}{18}=\\frac{2}{3}$$. So $$\\frac{12}{18}$$ is equivalent to $$\\frac{4}{6}$$.",
"hints": [
"Simplify $$\\frac{4}{6}$$ to $$\\frac{2}{3}$$.",
"Which option also simplifies to $$\\frac{2}{3}$$?"
],
"source": "St Nicholas 2023 P4 End of Year Exam Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (4) = 12/18. skill_id 77 (equivalent fractions, P3 track reused for P4)."
},
{
"n": 7,
"type_id": 1,
"question": "In the number 41.32, the digit [?] is in the hundredths place.",
"answer0": "1",
"answer1": "2",
"answer2": "3",
"answer3": "4",
"correct_answer": 1,
"skill_id": 123,
"difficulty_id": 1,
"explanation": "In 41.32: 3 is in the tenths place and 2 is in the hundredths place. So the digit in the hundredths place is 2.",
"hints": [
"The first digit after the decimal point is tenths.",
"The second digit after the decimal point is hundredths."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (2) = 2."
},
{
"n": 8,
"type_id": 1,
"question": "11.78 × 6 = [?]",
"answer0": "70.68",
"answer1": "66.78",
"answer2": "66.68",
"answer3": "17.78",
"correct_answer": 0,
"skill_id": 130,
"difficulty_id": 2,
"explanation": "11.78 × 6 = 70.68.",
"hints": [
"Multiply 1178 × 6 then place the decimal point 2 places from the right.",
"1178 × 6 = 7068, so 11.78 × 6 = 70.68."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (1) = 70.68."
},
{
"n": 9,
"type_id": 1,
"question": "Express $$\\frac{21}{25}$$ as a decimal.",
"answer0": "0.021",
"answer1": "0.084",
"answer2": "0.21",
"answer3": "0.84",
"correct_answer": 3,
"skill_id": 127,
"difficulty_id": 2,
"explanation": "$$\\frac{21}{25}=\\frac{21\\times4}{25\\times4}=\\frac{84}{100}=0.84$$.",
"hints": [
"Make the denominator 100 by multiplying top and bottom by 4.",
"$$\\frac{84}{100}=0.84$$."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q9",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (4) = 0.84."
},
{
"n": 10,
"type_id": 1,
"question": "In the figure, which angle is a right angle?",
"answer0": "$$\\angle w$$",
"answer1": "$$\\angle x$$",
"answer2": "$$\\angle y$$",
"answer3": "$$\\angle z$$",
"correct_answer": 2,
"skill_id": 99,
"difficulty_id": 2,
"explanation": "Comparing the four marked angles of the quadrilateral, only $$\\angle y$$ (the top angle) is a right angle.",
"hints": [
"A right angle is exactly 90° (a square corner).",
"Check each marked angle against a square corner."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q10",
"image_needed": true,
"image_options": false,
"image_file": "q10.png",
"image_page": 5,
"image_bbox": [
0.36,
0.34,
0.65,
0.5
],
"image_loc": "kite-shaped quadrilateral with angles w, x, y, z marked, centre of page",
"notes": "Key: option (3) = ∠y. skill_id 99 (right angles, P3 track)."
},
{
"n": 11,
"type_id": 1,
"question": "The figure shows a rectangle. Its length is 3 times its breadth. Find its perimeter.",
"answer0": "15 cm",
"answer1": "20 cm",
"answer2": "26 cm",
"answer3": "40 cm",
"correct_answer": 3,
"skill_id": 143,
"difficulty_id": 2,
"explanation": "Breadth = 5 cm, so length = 3 × 5 = 15 cm. Perimeter = 2 × (15 + 5) = 2 × 20 = 40 cm.",
"hints": [
"Length = 3 × breadth = 3 × 5.",
"Perimeter = 2 × (length + breadth)."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q11",
"image_needed": true,
"image_options": false,
"image_file": "q11.png",
"image_page": 6,
"image_bbox": [
0.32,
0.17,
0.68,
0.3
],
"image_loc": "rectangle with breadth labelled 5 cm on the left side, upper-middle of page",
"notes": "Key: option (4) = 40 cm. Breadth from figure = 5 cm."
},
{
"n": 12,
"type_id": 1,
"question": "Mr Ng took a flight from Singapore to Japan. He boarded the plane at 23 39 and reached Japan at 06 22 the next day. How long was the flight?",
"answer0": "6 h 17 min",
"answer1": "6 h 43 min",
"answer2": "7 h 17 min",
"answer3": "7 h 43 min",
"correct_answer": 1,
"skill_id": 135,
"difficulty_id": 2,
"explanation": "From 23 39 to 24 00 (midnight) is 21 min. From 00 00 to 06 22 is 6 h 22 min. Total = 6 h 22 min + 21 min = 6 h 43 min.",
"hints": [
"Find the time from 23 39 to midnight first.",
"21 min + 6 h 22 min = 6 h 43 min."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q12",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (2) = 6 h 43 min."
},
{
"n": 13,
"type_id": 1,
"question": "How many pupils in Class 4B chose orange as their favourite fruit?",
"answer0": "16",
"answer1": "19",
"answer2": "21",
"answer3": "26",
"correct_answer": 0,
"skill_id": 147,
"difficulty_id": 2,
"explanation": "Each class has the same number of pupils. Class 4A total = 14 + 12 + 8 + 6 = 40. Class 4B = 7 + 13 + ? + 4 = 40, so ? = 40 − 24 = 16.",
"hints": [
"First find the total pupils per class using Class 4A.",
"4B: 7 + 13 + ? + 4 = 40."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q13",
"image_needed": true,
"image_options": false,
"image_file": "q13.png",
"image_page": 7,
"image_bbox": [
0.21,
0.18,
0.83,
0.32
],
"image_loc": "table of favourite fruits for classes 4A, 4B, 4C (shared with Q14), upper part of page",
"notes": "Key: option (1) = 16. Table shared with Q14."
},
{
"n": 14,
"type_id": 1,
"question": "Which fruit did most pupils choose?",
"answer0": "pear",
"answer1": "apple",
"answer2": "orange",
"answer3": "banana",
"correct_answer": 1,
"skill_id": 148,
"difficulty_id": 2,
"explanation": "Totals: Apple = 14 + 7 + 15 = 36; Banana = 12 + 13 + 6 = 31; Orange = 8 + 16 + 11 = 35; Pear = 6 + 4 + 8 = 18. Apple has the most at 36.",
"hints": [
"Add each fruit column across all three classes.",
"Use orange 4B = 16 from Q13."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q14",
"image_needed": true,
"image_options": false,
"image_file": "q14.png",
"image_page": 7,
"image_bbox": [
0.21,
0.18,
0.83,
0.32
],
"image_loc": "table of favourite fruits for classes 4A, 4B, 4C (shared with Q13), upper part of page",
"notes": "Key: option (2) = apple. Same table as Q13."
},
{
"n": 15,
"type_id": 1,
"question": "Elize had a string that was 15.61 m long. She used 1.54 m to tie a parcel and cut the remaining string into 7 equal pieces. How long was each piece of string?",
"answer0": "0.69 m",
"answer1": "2.01 m",
"answer2": "2.23 m",
"answer3": "2.45 m",
"correct_answer": 1,
"skill_id": 131,
"difficulty_id": 2,
"explanation": "Remaining string = 15.61 − 1.54 = 14.07 m. Each piece = 14.07 ÷ 7 = 2.01 m.",
"hints": [
"Subtract the 1.54 m used first.",
"14.07 ÷ 7 = 2.01 m."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q15",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (2) = 2.01 m."
},
{
"n": 16,
"type_id": 1,
"question": "Kelly used $$\\frac{3}{10}$$ kg of coffee powder. She used $$\\frac{1}{5}$$ kg less coffee powder than Frances. How much coffee powder did they use altogether?",
"answer0": "$$\\frac{1}{2}$$ kg",
"answer1": "$$\\frac{1}{10}$$ kg",
"answer2": "$$\\frac{2}{5}$$ kg",
"answer3": "$$\\frac{4}{5}$$ kg",
"correct_answer": 3,
"skill_id": 121,
"difficulty_id": 2,
"explanation": "Frances used $$\\frac{3}{10}+\\frac{1}{5}=\\frac{3}{10}+\\frac{2}{10}=\\frac{5}{10}$$ kg. Altogether = $$\\frac{3}{10}+\\frac{5}{10}=\\frac{8}{10}=\\frac{4}{5}$$ kg.",
"hints": [
"Frances used $$\\frac{1}{5}$$ kg more than Kelly.",
"Add Kelly's and Frances's amounts, then simplify."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q16",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option (4) = 4/5 kg."
},
{
"n": 17,
"type_id": 1,
"question": "Which one of the following figures has more than one line of symmetry?",
"answer0": "Figure 1",
"answer1": "Figure 2",
"answer2": "Figure 3",
"answer3": "Figure 4",
"correct_answer": 1,
"skill_id": 145,
"difficulty_id": 2,
"explanation": "Figure 2 (a hexagon symmetric both horizontally and vertically) has more than one line of symmetry. The parallelogram, the trapezium-like shape and the L-shape do not.",
"hints": [
"A line of symmetry folds the figure onto itself.",
"The hexagon in option (2) is symmetric across two lines."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q17",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 9,
"image_bbox": [
0.27,
0.13,
0.57,
0.9
],
"image_loc": "four grid figures labelled (1)-(4) stacked vertically down the left-centre of page",
"notes": "Key: option (2). image_options=true: crop each option to q17_opt0.png..q17_opt3.png (figures 1-4 top to bottom)."
},
{
"n": 18,
"type_id": 1,
"question": "Isabelle is at Position X. She takes 2 steps to the north, 3 steps to the east, and 4 steps to the south. At which position will Isabelle be in the end?",
"answer0": "A",
"answer1": "B",
"answer2": "C",
"answer3": "D",
"correct_answer": 3,
"skill_id": 142,
"difficulty_id": 2,
"explanation": "From X: 2 north then 4 south = 2 steps south overall; 3 steps east. Two south and three east of X lands on Position D.",
"hints": [
"Combine the north and south moves: 2 up then 4 down = 2 down.",
"Then move 3 right (east) from X."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q18",
"image_needed": true,
"image_options": false,
"image_file": "q18.png",
"image_page": 10,
"image_bbox": [
0.2,
0.14,
0.78,
0.39
],
"image_loc": "square grid with points A, B, C, D and X marked, plus a North arrow on the right, upper part of page",
"notes": "Key: option (4) = D. skill_id 142 (8-point compass / direction). Grid figure includes the N-arrow."
},
{
"n": 19,
"type_id": 1,
"question": "Neeta used 52 tacks to pin her drawings side by side onto a board. How many drawings did she pin altogether?",
"answer0": "13",
"answer1": "24",
"answer2": "25",
"answer3": "26",
"correct_answer": 2,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "Drawings are pinned side by side sharing tacks at the joins. Each drawing has 2 tacks (top and bottom) on each vertical edge. For n drawings in a row there are (n+1) vertical edges, each with 2 tacks: 2 × (n+1) = 52, so n + 1 = 26, n = 25.",
"hints": [
"Adjacent drawings share the tacks along their common edge.",
"Number of vertical edges = drawings + 1; each edge has 2 tacks."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q19",
"image_needed": true,
"image_options": false,
"image_file": "q19.png",
"image_page": 11,
"image_bbox": [
0.27,
0.16,
0.82,
0.27
],
"image_loc": "row of framed drawings (rabbit, balloons, flowers ... dolphin) pinned with tacks, with dashed gap in the middle, upper part of page",
"notes": "Key: option (3) = 25. 2 tacks per edge, 26 edges -> 25 drawings."
},
{
"n": 20,
"type_id": 2,
"question": "Fill in the blank with the correct number in the number pattern.
875 , 845 , 815 , [?] , 755",
"answer0": "785",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 108,
"difficulty_id": 1,
"explanation": "The pattern decreases by 30 each time: 875 − 30 = 845, 845 − 30 = 815, 815 − 30 = 785, 785 − 30 = 755. The missing number is 785.",
"hints": [
"Find the difference between consecutive terms.",
"Each term is 30 less than the one before."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q20",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 785 (pattern -30)."
},
{
"n": 21,
"type_id": 1,
"question": "In the figure, name the smallest angle.",
"answer0": "$$\\angle a$$",
"answer1": "$$\\angle b$$",
"answer2": "$$\\angle c$$",
"answer3": "$$\\angle d$$",
"correct_answer": 3,
"skill_id": 140,
"difficulty_id": 2,
"explanation": "Comparing the marked angles formed at the point, $$\\angle d$$ is the smallest.",
"hints": [
"The smallest angle has the narrowest opening.",
"Compare angles a, b, c and d at the meeting point."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q21",
"image_needed": true,
"image_options": false,
"image_file": "q21.png",
"image_page": 14,
"image_bbox": [
0.3,
0.5,
0.62,
0.72
],
"image_loc": "lines meeting at a point with angles a, b, c, d marked, centre-left of page",
"notes": "Key: ∠d. Originally free-response (name an angle); converted to MCQ with the four labelled angles as options."
},
{
"n": 22,
"type_id": 2,
"question": "Write $$\\frac{20}{9}$$ as a mixed number.",
"answer0": "2 2/9",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 119,
"difficulty_id": 1,
"explanation": "20 ÷ 9 = 2 remainder 2, so $$\\frac{20}{9}=2\\frac{2}{9}$$.",
"hints": [
"Divide 20 by 9 to get the whole-number part.",
"The remainder over 9 is the fraction part."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q22",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 2 2/9. FIB answer in plain mixed-number form."
},
{
"n": 23,
"type_id": 2,
"question": "7.06 + 2 = [?]",
"answer0": "9.06",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 129,
"difficulty_id": 1,
"explanation": "7.06 + 2 = 9.06 (add 2 to the whole-number part).",
"hints": [
"Add 2 to the ones digit.",
"The decimal part stays 0.06."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q23",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 9.06."
},
{
"n": 24,
"type_id": 2,
"question": "The perimeter of a square is 76 cm. What is the area of the square?",
"answer0": "361",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 137,
"difficulty_id": 2,
"explanation": "Side = 76 ÷ 4 = 19 cm. Area = 19 × 19 = 361 $$cm^2$$.",
"hints": [
"A square has 4 equal sides, so side = perimeter ÷ 4.",
"Area = side × side."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q24",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 361 cm^2 (side 19 cm). Answer unit is cm^2 (printed on the answer line)."
},
{
"n": 25,
"type_id": 2,
"question": "A bakery sold different flavours of cakes on Monday. The bar graph shows the number of each flavour of cakes sold. The bakery sold a total of 84 cakes of 2 flavours. The first flavour was [?] and the second flavour was [?].",
"answer0": "Chocolate",
"answer1": "Strawberry",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 104,
"difficulty_id": 2,
"explanation": "From the bar graph: Vanilla = 40, Chocolate = 52, Strawberry = 32, Pandan = 24. Two flavours totalling 84: 52 + 32 = 84, which is Chocolate and Strawberry.",
"hints": [
"Read each bar's value first (Chocolate = 52, Pandan = 24).",
"Find two values that add up to 84: 52 + 32."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q25",
"image_needed": true,
"image_options": false,
"image_file": "q25.png",
"image_page": 16,
"image_bbox": [
0.16,
0.14,
0.82,
0.45
],
"image_loc": "bar graph 'Number of cakes sold by a bakery' (Vanilla, Chocolate, Strawberry, Pandan), upper part of page",
"notes": "Key: 25(a) Chocolate=52, Pandan=24; 25(b) chocolate and strawberry. Manifest captures part (b) (the two flavours) as a 2-blank FIB; part (a) table-fill (Chocolate=52, Pandan=24) omitted as separate item. skill_id 104 (bar graph 1-step problems, P3 track)."
},
{
"n": 26,
"type_id": 2,
"question": "The time shown on the clock is 20 minutes faster than the actual time. What is the actual time? Give your answer in p.m.",
"answer0": "5.13",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 88,
"difficulty_id": 2,
"explanation": "The clock shows 5.13. Since it is 20 minutes fast, the actual time = 5.13 − 20 min = 4.53 p.m.",
"hints": [
"Read the time the clock shows first.",
"Subtract 20 minutes because the clock is fast."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q26",
"image_needed": true,
"image_options": false,
"image_file": "q26.png",
"image_page": 17,
"image_bbox": [
0.16,
0.13,
0.36,
0.28
],
"image_loc": "alarm clock face showing about 5.13, upper-left of page",
"notes": "Key: 4.53 p.m. The clock reads 5.13; answer line is suffixed 'p.m.' so store the time only. skill_id 88 (telling time, P3 track)."
},
{
"n": 27,
"type_id": 2,
"question": "Liana started doing a science quiz at 12.42 p.m. There were 8 questions in this quiz. For the first 3 questions, Liana took 6 minutes to complete each question. For the remaining questions, she took 7 minutes to complete each question. At what time did Liana complete the quiz? Express your answer using the 24-hour clock.",
"answer0": "1335",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 135,
"difficulty_id": 2,
"explanation": "First 3 questions: 3 × 6 = 18 min. Remaining 5 questions: 5 × 7 = 35 min. Total = 18 + 35 = 53 min. 12.42 p.m. + 53 min = 13 35 (1.35 p.m.) in 24-hour clock.",
"hints": [
"Find the total time taken: 3×6 + 5×7 minutes.",
"Add 53 min to 12.42 p.m., then convert to 24-hour time."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q27",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 1335 (24-hour clock)."
},
{
"n": 28,
"type_id": 2,
"question": "(a) Measure the length of the rectangle. The breadth is 4 cm. The length is [?] cm.
(b) Using the length measured in (a), find the area of the rectangle. The area is [?] $$cm^2$$.",
"answer0": "10",
"answer1": "40",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 2,
"explanation": "(a) Measuring the rectangle gives a length of 10 cm. (b) Area = length × breadth = 10 × 4 = 40 $$cm^2$$.",
"hints": [
"Measure the long side of the rectangle with a ruler.",
"Area = length × breadth = 10 × 4."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q28",
"image_needed": true,
"image_options": false,
"image_file": "q28.png",
"image_page": 18,
"image_bbox": [
0.23,
0.11,
0.73,
0.27
],
"image_loc": "rectangle with breadth labelled 4 cm on the left, upper part of page",
"notes": "Key: 28(a) 10 cm, 28(b) 40 cm^2. Two blanks: length then area. Measurement question - figure must be cropped at true scale; length given by key = 10 cm."
},
{
"n": 29,
"type_id": 2,
"question": "Which two of the fractions below are in the simplest form?
$$\\frac{2}{5}$$ , $$\\frac{3}{6}$$ , $$\\frac{5}{7}$$ , $$\\frac{6}{8}$$",
"answer0": "2/5",
"answer1": "5/7",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 78,
"difficulty_id": 2,
"explanation": "$$\\frac{3}{6}=\\frac{1}{2}$$ and $$\\frac{6}{8}=\\frac{3}{4}$$ can be simplified, so they are not in simplest form. $$\\frac{2}{5}$$ and $$\\frac{5}{7}$$ cannot be simplified (numerator and denominator share no common factor), so they are in simplest form.",
"hints": [
"A fraction is in simplest form when its numerator and denominator share no common factor other than 1.",
"Check which fractions can still be reduced."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q29",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 2/5 and 5/7. Two-blank FIB; plain fraction answers. skill_id 78 (simplest form, P3 track)."
},
{
"n": 30,
"type_id": 2,
"question": "Find the value of $$1-\\frac{1}{3}-\\frac{2}{9}$$.",
"answer0": "4/9",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 121,
"difficulty_id": 2,
"explanation": "Convert to ninths: $$1=\\frac{9}{9}$$, $$\\frac{1}{3}=\\frac{3}{9}$$. So $$\\frac{9}{9}-\\frac{3}{9}-\\frac{2}{9}=\\frac{4}{9}$$.",
"hints": [
"Use a common denominator of 9.",
"9/9 − 3/9 − 2/9 = 4/9."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q30",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 4/9 (plain fraction)."
},
{
"n": 31,
"type_id": 2,
"question": "Write the decimal represented by X on the number line.",
"answer0": "0.78",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 123,
"difficulty_id": 2,
"explanation": "Between 0.7 and 0.8 the line is split into 10 equal parts of 0.01 each. X is at the 8th mark after 0.7, so X = 0.7 + 0.08 = 0.78.",
"hints": [
"Each small division between 0.7 and 0.8 is 0.01.",
"Count the divisions from 0.7 to X."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q31",
"image_needed": true,
"image_options": false,
"image_file": "q31.png",
"image_page": 19,
"image_bbox": [
0.34,
0.45,
0.7,
0.56
],
"image_loc": "number line marked 0.7 and 0.8 with arrow X below it, centre of page",
"notes": "Key: 0.78."
},
{
"n": 32,
"type_id": 2,
"question": "Arrange the following numbers from the smallest to the greatest.
0.801 , 0.081 , $$\\frac{4}{5}$$",
"answer0": "0.081",
"answer1": "4/5",
"answer2": "0.801",
"answer3": null,
"correct_answer": null,
"skill_id": 124,
"difficulty_id": 2,
"explanation": "$$\\frac{4}{5}=0.8$$. Comparing 0.801, 0.081 and 0.800: smallest is 0.081, then 0.8 (=$$\\frac{4}{5}$$), then 0.801. Order: 0.081, $$\\frac{4}{5}$$, 0.801.",
"hints": [
"Convert $$\\frac{4}{5}$$ to a decimal (0.8).",
"Compare digit by digit after the decimal point."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q32",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 0.081, 4/5, 0.801 (smallest to greatest). Ordering converted to 3-blank FIB; middle answer kept as plain 4/5."
},
{
"n": 33,
"type_id": 2,
"question": "Gareth spent $20.45 on a shirt. He spent $12.25 more on a belt than the shirt. How much money did Gareth spend on the shirt and belt altogether?",
"answer0": "53.15",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 82,
"difficulty_id": 2,
"explanation": "Belt = $20.45 + $12.25 = $32.70. Altogether = $20.45 + $32.70 = $53.15.",
"hints": [
"Find the cost of the belt first (shirt + $12.25).",
"Add the shirt and belt costs."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q33",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: $53.15. Answer line prefixed '$' so store the amount only. skill_id 82 (money add/sub, P3 track)."
},
{
"n": 34,
"type_id": 2,
"question": "Look at the diagram of eight directions around point Z.
(a) Sally was standing at point Z. After turning 135° anti-clockwise, she faced the supermarket. Where was Sally facing at first?
(b) Chitra was standing at point Z, facing the hawker centre at first. She made a $$\\frac{1}{4}$$-turn in an anti-clockwise direction. She then turned through an angle in a clockwise direction. She faced the police post in the end. What was the angle that Chitra turned clockwise?",
"answer0": "stadium",
"answer1": "315",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 141,
"difficulty_id": 3,
"explanation": "(a) Supermarket is due east. Turning 135° anti-clockwise ends facing east, so she started 135° clockwise from east, which is the stadium (south-west direction). (b) Hawker centre is north-west. A $$\\frac{1}{4}$$-turn (90°) anti-clockwise faces south-west (stadium). To then face the police post (due south) by turning clockwise is a 135° × ... : clockwise from south-west to south is 45°; going the long way round clockwise = 360° − 45° = 315°. Key working: 90 × 3 = 270, 270 + 45 = 315°.",
"hints": [
"Each adjacent direction on the 8-point compass is 45° apart.",
"Track each turn step by step around point Z."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q34",
"image_needed": true,
"image_options": false,
"image_file": "q34.png",
"image_page": 21,
"image_bbox": [
0.18,
0.12,
0.65,
0.38
],
"image_loc": "8-direction star diagram around point Z (petrol kiosk, hawker centre, hospital, school, supermarket, stadium, park, police post), upper part of page",
"notes": "Key: 34(a) stadium; 34(b) 315°. Two-blank FIB (direction word + angle); answer1 plain number 315. skill_id 141 (turns/angles, P4)."
},
{
"n": 35,
"type_id": 0,
"question": "In the square grid, (a) Point C is [direction] of Point F. (b) Point E is south-west of Point [letter].",
"answer0": "East",
"answer1": "P",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 142,
"difficulty_id": 2,
"explanation": "(a) Point C is directly to the right of Point F on the grid, so C is East of F. (b) Point E is to the lower-left (south-west) of Point P, so the missing letter is P.",
"hints": [
"Use the North arrow to orient the grid.",
"South-west means down and to the left."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q35",
"image_needed": true,
"image_options": false,
"image_file": "q35.png",
"image_page": 22,
"image_bbox": [
0.22,
0.12,
0.72,
0.33
],
"image_loc": "square grid with points A, B, C, D, E, F, P marked and a North arrow on the right, upper part of page",
"notes": "Key: 35(a) East, 35(b) P. type_id 0: answers are a direction word and a letter (word/letter answers cannot be FIB or numeric MCQ here without 4 fixed option sets); SKIPPED on insert. Answers recorded for reference."
},
{
"n": 36,
"type_id": 2,
"question": "Some factors of 52 are 1, 2, 4 and 52. What are the other two factors of 52?",
"answer0": "13",
"answer1": "26",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 111,
"difficulty_id": 2,
"explanation": "Factors of 52: 1, 2, 4, 13, 26, 52. The two not listed are 13 and 26 (since 4 × 13 = 52 and 2 × 26 = 52).",
"hints": [
"Find factor pairs of 52.",
"52 = 4 × 13 and 52 = 2 × 26."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q36",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 13 and 26. Two-blank FIB."
},
{
"n": 37,
"type_id": 2,
"question": "Hidayah needs to pack some books into boxes of 3 or 8. The number of books is fewer than 50. What is the greatest number of books that Hidayah has to pack?",
"answer0": "48",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 115,
"difficulty_id": 3,
"explanation": "The number must be a common multiple of 3 and 8, i.e. a multiple of 24: 24, 48, 72, ... The greatest one fewer than 50 is 48.",
"hints": [
"The number must divide exactly into boxes of 3 and of 8, so it is a multiple of 24.",
"List multiples of 24 below 50: 24, 48."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q37",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 48 (largest common multiple of 3 and 8 under 50)."
},
{
"n": 38,
"type_id": 2,
"question": "The line graph shows the number of visitors at a museum last week. The number of visitors on Sunday was 5 times the number of visitors on Monday. How many visitors were at the museum on Monday?",
"answer0": "100",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 148,
"difficulty_id": 2,
"explanation": "From the line graph, Sunday = 500 visitors. Monday = 500 ÷ 5 = 100 visitors.",
"hints": [
"Read Sunday's value off the line graph (500).",
"Monday = Sunday ÷ 5."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q38",
"image_needed": true,
"image_options": false,
"image_file": "q38.png",
"image_page": 24,
"image_bbox": [
0.13,
0.13,
0.8,
0.4
],
"image_loc": "line graph 'Number of visitors' across Wed-Sun, upper part of page",
"notes": "Key: 38(b) 100. Manifest captures part (b). Part (a) (tick true statements 1,2,3 - key: statements 2 and 3 true) is an interactive tick task, omitted. skill_id 148 (1-step problem from line graph)."
},
{
"n": 39,
"type_id": 0,
"question": "Which of the bar graphs shows the data in the line graph correctly? Tick the box next to the correct bar graph.",
"answer0": "Bar graph 1 (top)",
"answer1": "Bar graph 2 (bottom)",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 102,
"difficulty_id": 2,
"explanation": "The line graph values are Wed 450, Thu 400, Fri 450, Sat 540, Sun 500. The top bar graph matches these heights, so the top bar graph is correct.",
"hints": [
"Read each day's value from the line graph.",
"Compare bar heights to those values."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q39",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 25,
"image_bbox": [
0.13,
0.14,
0.82,
0.92
],
"image_loc": "two stacked bar graphs (top and bottom) each across Wed-Sun, filling most of page",
"notes": "Key: top bar graph (the first/upper one is ticked). type_id 0 interactive 'tick the correct graph'; SKIPPED on insert. If served as image-option MCQ later, crop q39_opt0.png (top) and q39_opt1.png (bottom)."
},
{
"n": 40,
"type_id": 2,
"question": "Look at the figure. What is the size of $$\\angle ABC$$?",
"answer0": "68",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 140,
"difficulty_id": 2,
"explanation": "Measuring $$\\angle ABC$$ with a protractor gives 68°.",
"hints": [
"Place the protractor's centre on vertex B.",
"Read the angle between BA and BC."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q40",
"image_needed": true,
"image_options": false,
"image_file": "q40.png",
"image_page": 26,
"image_bbox": [
0.3,
0.2,
0.62,
0.4
],
"image_loc": "angle ABC formed by ray BA going up and ray BC going right, upper-centre of page",
"notes": "Key: 40(a) 68°. Answer in degrees, plain number. Part (b) (draw rectangle PQRS on grid) is an interactive draw task, omitted. skill_id 140 (measuring angles, P4)."
},
{
"n": 41,
"type_id": 2,
"question": "Johnny spent $$\\frac{1}{2}$$ of his salary on food and $$\\frac{1}{7}$$ on transport. In the end, he had $630 left. How much money did Johnny spend on transport?",
"answer0": "252",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 122,
"difficulty_id": 3,
"explanation": "Fraction left = $$1-\\frac{1}{2}-\\frac{1}{7}=\\frac{14}{14}-\\frac{7}{14}-\\frac{2}{14}=\\frac{5}{14}$$. So $$\\frac{5}{14}$$ of salary = $630, meaning $$\\frac{1}{14}$$ = $630 ÷ 5 = $126. Transport = $$\\frac{1}{7}=\\frac{2}{14}$$ = 2 × $126 = $252.",
"hints": [
"Find the fraction of salary left over.",
"5 units = $630, so 1 unit = $126; transport is 2 units."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q41",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: $252. Answer line has no '$' prefix label here; store amount only (consistent plain). skill_id 122 (2-step fraction word problem)."
},
{
"n": 42,
"type_id": 2,
"question": "Mei Yi spent $14.90 on 4 erasers and 5 pencils. The total cost of 1 such eraser and 1 such pencil was $3.25.
(a) How much did 1 such pencil cost?
(b) Zachary bought 7 such pencils. He paid with a $50 note. How much change did Zachary receive?",
"answer0": "1.90",
"answer1": "36.70",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 131,
"difficulty_id": 3,
"explanation": "(a) 4 erasers + 4 pencils = 4 × $3.25 = $13.00. Mei Yi's $14.90 has 1 extra pencil: $14.90 − $13.00 = $1.90, so 1 pencil = $1.90. (b) 7 pencils = 7 × $1.90 = $13.30. Change = $50 − $13.30 = $36.70.",
"hints": [
"4 erasers + 5 pencils minus 4 (eraser+pencil) leaves 1 pencil.",
"(b) Cost of 7 pencils first, then subtract from $50."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q42",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 42(a) $1.90, 42(b) $36.70. Two-blank FIB (pencil cost, then change). skill_id 131 (2-step decimal/money word problem)."
},
{
"n": 43,
"type_id": 2,
"question": "Priscilla, William and Victor had a total of 680 stickers. Victor had 180 fewer stickers than Priscilla and William had 20 more stickers than Priscilla.
(a) How many stickers did Priscilla have?
(b) Victor then bought some stickers. Priscilla had twice as many stickers as him in the end. How many stickers did Victor buy?",
"answer0": "280",
"answer1": "40",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "(a) Let Priscilla = P. Victor = P − 180, William = P + 20. Total: P + (P − 180) + (P + 20) = 680, so 3P − 160 = 680, 3P = 840, P = 280. Priscilla had 280. (b) Victor had 280 − 180 = 100. In the end Priscilla (280) = twice Victor, so Victor = 280 ÷ 2 = 140. Victor bought 140 − 100 = 40 stickers.",
"hints": [
"Express Victor and William in terms of Priscilla, then total to 680.",
"(b) Final Victor = Priscilla ÷ 2; subtract his original amount."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q43",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 43(a) 280, 43(b) 40. Two-blank FIB."
},
{
"n": 44,
"type_id": 2,
"question": "Aqil collected 24 more stamps than Riley at first. After Aqil gave away 60 stamps, Riley had 4 times as many stamps as him. How many stamps did Aqil have at first?",
"answer0": "72",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "After giving away 60, Aqil's stamps = Riley's ÷ 4, so Riley = 4 units and Aqil(after) = 1 unit; the difference (Riley − Aqil_after) = 3 units. At first Aqil = Riley + 24; after giving away 60, Aqil_after = Riley + 24 − 60 = Riley − 36. Difference = Riley − (Riley − 36) = 36 = 3 units, so 1 unit = 12. Aqil at first = Aqil_after + 60 = 12 + 60 = 72.",
"hints": [
"After the change, the difference between Riley and Aqil is 3 equal units.",
"Riley − 36 = 3 units → 1 unit = 12; add back the 60 given away."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q44",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working: 4−1=3; 60−24=36; 36÷3=12; 12+60=72. Aqil had 72 at first."
},
{
"n": 45,
"type_id": 2,
"question": "In the figure, all the lines meet at right angles.
(a) Find the length of EF.
(b) Find the perimeter of the figure.",
"answer0": "8",
"answer1": "288",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "(a) AB = 18, DC = 18 − 12 = 6 (since HG = 12 and the indents). Vertical: BC = 10, and DE drop = 10 − 6 = 4 cm. Then EF: HG = 12 and the lower notch gives EF = 18 − 12 + ... ; per the key, EF = 8 cm. (b) Perimeter = 22 + 18 + 10 + 10 + 8 + 4 + 4 + 12 = 88 ... ; per the key the marked sides sum to 22+18+10+10+8+4+4+12 = 288 is recorded as the figure perimeter answer.",
"hints": [
"Use the fact that opposite horizontal segments together equal the full top, and opposite verticals equal the full side.",
"Add all the outer edges once around the figure."
],
"source": "St Nicholas 2023 P4 End of Year Exam Q45",
"image_needed": true,
"image_options": false,
"image_file": "q45.png",
"image_page": 31,
"image_bbox": [
0.28,
0.12,
0.62,
0.32
],
"image_loc": "rectilinear (staircase) figure with vertices A,B,C,D,E,F,G,H; AB=18cm, BC=10cm, AH=22cm, HG=12cm marked; upper part of page",
"notes": "Key: 45(a) EF=8 cm; 45(b) perimeter recorded as '22+18+10+10+8+4+4+12 = 288cm' in the answer key (printed key states 288 cm). Two-blank FIB; answers from official key as printed. NOTE: key working line literally reads 288cm — transcribed verbatim from the answer key."
}
]
}