{
"paper": {
"school": "ACS Primary",
"year": 2024,
"level": "P5",
"label": "End-of-Year Exam",
"source_prefix": "ACS Primary 2024 P5 End-of-Year Exam",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "Which one of the following is forty-eight thousand and five in numerals?",
"answer0": "485",
"answer1": "48 005",
"answer2": "48 050",
"answer3": "48 500",
"correct_answer": 1,
"skill_id": 149,
"difficulty_id": 1,
"explanation": "Forty-eight thousand = 48 000; and five = 5. So 48 000 + 5 = 48 005.",
"hints": ["Forty-eight thousand is 48 000.", "Then add 5 ones."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: option 2 (0-based index 1)."
},
{
"n": 2,
"type_id": 1,
"question": "Andy won $500 at story-writing competition. He gave $150 to his father. What percentage of his prize money did Andy give to his father?",
"answer0": "3%",
"answer1": "30%",
"answer2": "70%",
"answer3": "150%",
"correct_answer": 1,
"skill_id": 171,
"difficulty_id": 2,
"explanation": "Fraction given = \\(\\dfrac{150}{500}\\). As a percentage: \\(\\dfrac{150}{500} \\times 100\\% = 30\\%\\).",
"hints": ["Write the amount given as a fraction of the total.", "Multiply the fraction by 100% to get the percentage."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: option 2 (0-based index 1)."
},
{
"n": 3,
"type_id": 1,
"question": "Which of the following is equal to \\(2\\dfrac{2}{9}\\)?",
"answer0": "\\(\\dfrac{4}{9}\\)",
"answer1": "\\(\\dfrac{13}{9}\\)",
"answer2": "\\(\\dfrac{20}{9}\\)",
"answer3": "\\(\\dfrac{22}{9}\\)",
"correct_answer": 2,
"skill_id": 158,
"difficulty_id": 1,
"explanation": "Convert the mixed number to an improper fraction: \\(2\\dfrac{2}{9} = \\dfrac{2 \\times 9 + 2}{9} = \\dfrac{20}{9}\\).",
"hints": ["Multiply the whole number by the denominator.", "Add the numerator, then keep the same denominator."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: option 3 (0-based index 2). Options are fractions, so MCQ."
},
{
"n": 4,
"type_id": 1,
"question": "Given that ZW is the height of triangle VZX. Identify base that is related to the height ZW.",
"answer0": "VX",
"answer1": "VY",
"answer2": "ZX",
"answer3": "ZV",
"correct_answer": 0,
"skill_id": 186,
"difficulty_id": 2,
"explanation": "The height ZW is drawn from vertex Z perpendicular to the opposite side. ZW meets VX (extended) at W, so the base related to height ZW is VX.",
"hints": ["The base is the side the height meets at a right angle.", "ZW is perpendicular to VX at W."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q4",
"image_needed": true,
"image_options": false,
"image_file": "q4.png",
"image_page": 4,
"image_bbox": [0.33, 0.16, 0.62, 0.33],
"image_loc": "triangle VZX with dashed height ZW, upper-middle of page below the question",
"notes": "Answer key: option 1 (0-based index 0)."
},
{
"n": 5,
"type_id": 1,
"question": "30 000 + 800 + 50 + 4 = [ ]",
"answer0": "3 854",
"answer1": "30 854",
"answer2": "38 054",
"answer3": "38 540",
"correct_answer": 1,
"skill_id": 149,
"difficulty_id": 1,
"explanation": "Add by place value: 30 000 + 800 + 50 + 4 = 30 854.",
"hints": ["Line up the place values.", "There are no thousands besides 30 000, so the digit in the thousands group stays 30 8__."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q5",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: option 2 (0-based index 1). The printed box in the stem is a display placeholder for the answer being chosen, not an FIB blank — this is MCQ; rendered as [ ] (no [?])."
},
{
"n": 6,
"type_id": 1,
"question": "Jules worked \\(5\\dfrac{3}{4}\\) h each day. Verne worked twice the number of hours that Jules worked each day. How many hours did Vern work each day?",
"answer0": "\\(6\\dfrac{1}{2}\\) h",
"answer1": "\\(7\\dfrac{5}{6}\\) h",
"answer2": "\\(10\\dfrac{6}{8}\\) h",
"answer3": "\\(11\\dfrac{1}{2}\\) h",
"correct_answer": 3,
"skill_id": 163,
"difficulty_id": 2,
"explanation": "Twice Jules' time = \\(2 \\times 5\\dfrac{3}{4} = 2 \\times \\dfrac{23}{4} = \\dfrac{46}{4} = 11\\dfrac{1}{2}\\) h.",
"hints": ["Convert the mixed number to an improper fraction first.", "Multiply by 2, then convert back to a mixed number."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: option 4 (0-based index 3). Options are mixed numbers, so MCQ."
},
{
"n": 7,
"type_id": 1,
"question": "Arrange the following decimals from greatest to the smallest:
0.303, 0.33, 0.033",
"answer0": "0.033, 0.33, 0.303",
"answer1": "0.303, 0.33, 0.033",
"answer2": "0.33, 0.033, 0.303",
"answer3": "0.33, 0.303, 0.033",
"correct_answer": 3,
"skill_id": 158,
"difficulty_id": 2,
"explanation": "Compare by place value: 0.330 > 0.303 > 0.033. Greatest to smallest: 0.33, 0.303, 0.033.",
"hints": ["Add trailing zeros so all have the same number of decimal places: 0.303, 0.330, 0.033.", "Then compare the hundredths and thousandths digits."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: option 4 (0-based index 3). Ordering task with given option orderings, kept as MCQ."
},
{
"n": 8,
"type_id": 1,
"question": "PQ and RS are straight lines. Which of the following is true?",
"answer0": "\\(\\angle\\)RAV = \\(\\angle\\)PAS",
"answer1": "\\(\\angle\\)RAP = \\(\\angle\\)VAQ",
"answer2": "\\(\\angle\\)RAV + \\(\\angle\\)VAQ = 180°",
"answer3": "\\(\\angle\\)PAS + \\(\\angle\\)SAQ = 180°",
"correct_answer": 3,
"skill_id": 194,
"difficulty_id": 2,
"explanation": "PQ is a straight line through A, so the angles on one side sum to 180°. \\(\\angle\\)PAS and \\(\\angle\\)SAQ are adjacent angles on straight line PQ, so \\(\\angle\\)PAS + \\(\\angle\\)SAQ = 180°.",
"hints": ["Adjacent angles on a straight line add up to 180°.", "S, A and Q: check which angles sit on the same straight line PQ."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q8",
"image_needed": true,
"image_options": false,
"image_file": "q8.png",
"image_page": 6,
"image_bbox": [0.28, 0.18, 0.62, 0.33],
"image_loc": "rays from point A labelled R, P, V, Q, S, upper-middle of page",
"notes": "Answer key: option 4 (0-based index 3)."
},
{
"n": 9,
"type_id": 1,
"question": "Find \\(\\angle\\)k.",
"answer0": "34°",
"answer1": "66°",
"answer2": "100°",
"answer3": "166°",
"correct_answer": 3,
"skill_id": 194,
"difficulty_id": 2,
"explanation": "Angles at a point add to 360°. \\(\\angle\\)k = 360° − 80° − 114° = 166°.",
"hints": ["The three angles around the central point add up to 360°.", "Subtract the two known angles (80° and 114°) from 360°."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q9",
"image_needed": true,
"image_options": false,
"image_file": "q9.png",
"image_page": 6,
"image_bbox": [0.24, 0.52, 0.58, 0.66],
"image_loc": "three rays meeting at a point with angles 80°, 114° and k marked, middle of page",
"notes": "Answer key: option 4 (0-based index 3)."
},
{
"n": 10,
"type_id": 1,
"question": "In a class, there are 18 girls and 12 boys. What is the ratio of the number of boys to girls? Give your answer in its simplest form.",
"answer0": "2 : 1",
"answer1": "2 : 3",
"answer2": "2 : 5",
"answer3": "3 : 5",
"correct_answer": 1,
"skill_id": 179,
"difficulty_id": 1,
"explanation": "Boys : girls = 12 : 18. Divide both by 6: 12 : 18 = 2 : 3.",
"hints": ["Write boys first, then girls: 12 : 18.", "Divide both parts by their greatest common factor, 6."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q10",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: option 2 (0-based index 1). Ratio answer, so MCQ."
},
{
"n": 11,
"type_id": 1,
"question": "What is the volume of the cube?",
"answer0": "21 cm³",
"answer1": "49 cm³",
"answer2": "294 cm³",
"answer3": "343 cm³",
"correct_answer": 3,
"skill_id": 190,
"difficulty_id": 1,
"explanation": "Volume of a cube = edge³ = 7 × 7 × 7 = 343 cm³.",
"hints": ["All edges of a cube are equal, here 7 cm.", "Volume = side × side × side."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q11",
"image_needed": true,
"image_options": false,
"image_file": "q11.png",
"image_page": 7,
"image_bbox": [0.21, 0.36, 0.41, 0.45],
"image_loc": "drawing of a cube with edge marked 7 cm, left side below the question",
"notes": "Answer key: option 4 (0-based index 3)."
},
{
"n": 12,
"type_id": 1,
"question": "A recipe requires 12 bananas to bake 4 loaves of banana bread. If Mrs Tan wants to bake 24 loaves, how many bananas will she need?",
"answer0": "8",
"answer1": "16",
"answer2": "32",
"answer3": "72",
"correct_answer": 3,
"skill_id": 152,
"difficulty_id": 2,
"explanation": "12 bananas make 4 loaves, so 1 loaf needs 12 ÷ 4 = 3 bananas. For 24 loaves: 3 × 24 = 72 bananas.",
"hints": ["Find how many bananas are needed for 1 loaf.", "Multiply that by 24 loaves."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q12",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: option 4 (0-based index 3)."
},
{
"n": 13,
"type_id": 1,
"question": "Not drawn to scale, BE and CD are straight lines. Find \\(\\angle\\)CAD.",
"answer0": "60°",
"answer1": "73°",
"answer2": "107°",
"answer3": "133°",
"correct_answer": 1,
"skill_id": 197,
"difficulty_id": 3,
"explanation": "\\(\\angle\\)AEB = 180° − 133° = 47° (angles on straight line BE). In triangle ABE, \\(\\angle\\)BAE = 180° − 60° − 47° = 73°. \\(\\angle\\)CAD is the same as \\(\\angle\\)BAE = 73°.",
"hints": ["Use angles on a straight line at E to find \\(\\angle\\)AEB.", "Then use the angle sum of triangle ABE (180°)."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q13",
"image_needed": true,
"image_options": false,
"image_file": "q13.png",
"image_page": 8,
"image_bbox": [0.22, 0.18, 0.62, 0.34],
"image_loc": "triangle ACD with line BE inside, angles 60° at B and 133° at E, upper part of page",
"notes": "Answer key: option 2 (0-based index 1)."
},
{
"n": 14,
"type_id": 1,
"question": "The figure is divided into 20 equal parts. What percentage of the figure is unshaded?",
"answer0": "9%",
"answer1": "11%",
"answer2": "45%",
"answer3": "55%",
"correct_answer": 2,
"skill_id": 173,
"difficulty_id": 2,
"explanation": "There are 9 unshaded parts out of 20. \\(\\dfrac{9}{20} \\times 100\\% = 45\\%\\).",
"hints": ["Count the unshaded squares out of the 20 parts.", "Convert the fraction \\(\\dfrac{9}{20}\\) to a percentage."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q14",
"image_needed": true,
"image_options": false,
"image_file": "q14.png",
"image_page": 8,
"image_bbox": [0.22, 0.55, 0.43, 0.71],
"image_loc": "5x4 grid with some squares shaded, 9 unshaded; upper-middle of page below the question",
"notes": "Answer key: option 3 (0-based index 2). 9 unshaded of 20."
},
{
"n": 15,
"type_id": 1,
"question": "Find the sum of 10 + 12 + 14 + .... + 20 + 22 + 24.",
"answer0": "102",
"answer1": "126",
"answer2": "136",
"answer3": "204",
"correct_answer": 2,
"skill_id": 152,
"difficulty_id": 2,
"explanation": "The numbers are 10, 12, 14, 16, 18, 20, 22, 24 — eight terms. Sum = (10 + 24) × 8 ÷ 2 = 34 × 4 = 136.",
"hints": ["List all the even numbers from 10 to 24.", "Pair first + last and multiply by the number of pairs."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q15",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: option 3 (0-based index 2)."
},
{
"n": 16,
"type_id": 2,
"question": "What is the value of 30 − (5 + 4) ÷ 3 ? [?]",
"answer0": "27",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 156,
"difficulty_id": 1,
"explanation": "Brackets first: 5 + 4 = 9. Then divide: 9 ÷ 3 = 3. Then subtract: 30 − 3 = 27.",
"hints": ["Work out the brackets first.", "Do division before subtraction."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q16",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: 27."
},
{
"n": 17,
"type_id": 2,
"question": "Find the value of 20.12 − 8.09 [?]",
"answer0": "12.03",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 167,
"difficulty_id": 1,
"explanation": "Subtract the decimals: 20.12 − 8.09 = 12.03.",
"hints": ["Line up the decimal points.", "Subtract column by column, regrouping where needed."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q17",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: 12.03."
},
{
"n": 18,
"type_id": 1,
"question": "The figure is made up of 4 identical squares. One square is divided equally into 4 triangles. What fraction of the figure is unshaded? Give your answer in its simplest form.",
"answer0": "\\(\\dfrac{13}{16}\\)",
"answer1": "\\(\\dfrac{3}{4}\\)",
"answer2": "\\(\\dfrac{15}{16}\\)",
"answer3": "\\(\\dfrac{1}{4}\\)",
"correct_answer": 0,
"skill_id": 159,
"difficulty_id": 2,
"explanation": "Each square = \\(\\dfrac{4}{16}\\). One square split into 4 triangles, with 3 of them shaded = \\(\\dfrac{3}{16}\\) shaded. Unshaded = \\(1 - \\dfrac{3}{16} = \\dfrac{13}{16}\\).",
"hints": ["Split each square into 16ths of the whole figure.", "Find the shaded fraction, then subtract from 1."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q18",
"image_needed": true,
"image_options": false,
"image_file": "q18.png",
"image_page": 12,
"image_bbox": [0.33, 0.18, 0.52, 0.30],
"image_loc": "2x2 arrangement of 4 squares, top-left square divided into 4 triangles with 3 shaded; upper-middle of page",
"notes": "Answer key: 13/16. Fraction answer, so converted to MCQ."
},
{
"n": 19,
"type_id": 2,
"question": "Andy folds 6 paper cranes in 10 min. At this rate, how many paper cranes can Andy fold in 50 min? [?]",
"answer0": "30",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 1,
"explanation": "50 min is 5 times 10 min (10 × 5 = 50). So cranes = 6 × 5 = 30.",
"hints": ["How many 10-minute periods are in 50 minutes?", "Multiply the cranes per 10 min by that number."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q19",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: 6 x 5 = 30."
},
{
"n": 20,
"type_id": 2,
"question": "Find the value of 7402 ÷ 4. [?]",
"answer0": "1850.5",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 151,
"difficulty_id": 1,
"explanation": "7402 ÷ 4 = 1850 remainder 2, and 2 ÷ 4 = 0.5, so 7402 ÷ 4 = 1850.5.",
"hints": ["Do long division.", "The remainder 2 over 4 gives the decimal part 0.5."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q20",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: 1850.5."
},
{
"n": 21,
"type_id": 2,
"question": "A machine takes 3 minutes to print 8 posters. At the same rate, how long will it take to print 56 posters? [?] min",
"answer0": "21",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 2,
"explanation": "56 posters ÷ 8 posters = 7 sets. Each set takes 3 min, so 7 × 3 = 21 min.",
"hints": ["How many groups of 8 posters are in 56?", "Multiply the number of groups by 3 minutes."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q21",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: 56 ÷ 8 = 7; 7 x 3 = 21 min."
},
{
"n": 22,
"type_id": 2,
"question": "Mr Tan gave $60 to Steve and Andy in the ratio 2 : 3. How much did Andy get? $[?]",
"answer0": "36",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 182,
"difficulty_id": 2,
"explanation": "Total units = 2 + 3 = 5. 1 unit = $60 ÷ 5 = $12. Andy has 3 units = 3 × $12 = $36.",
"hints": ["Add the ratio parts to find total units.", "Find the value of 1 unit, then multiply by Andy's 3 units."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q22",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: 1u = 12, 3u = $36."
},
{
"n": 23,
"type_id": 2,
"question": "Siti, Betty and Matilda each has some stamps. Siti has twice as many stamps as Betty. Siti has 4 times as many stamps as Matilda. If Betty has 908 stamps, how many more stamps does Siti have than Matilda? [?]",
"answer0": "1362",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "Siti = 2 × Betty = 2 × 908 = 1816. Matilda = Siti ÷ 4 = 1816 ÷ 4 = 454. Difference = 1816 − 454 = 1362.",
"hints": ["Find Siti's stamps from Betty's.", "Find Matilda's stamps, then subtract from Siti's."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q23",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: Siti 1816, Matilda 454, difference 1362."
},
{
"n": 24,
"type_id": 2,
"question": "AFD and BFC are straight lines. \\(\\angle\\)ABC = 37° and \\(\\angle\\)BAF = 72°. Find \\(\\angle\\)y. [?]°",
"answer0": "71",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 197,
"difficulty_id": 2,
"explanation": "In triangle ABF, \\(\\angle\\)AFB = 180° − 37° − 72° = 71°. \\(\\angle\\)y = \\(\\angle\\)DFC is vertically opposite \\(\\angle\\)AFB, so \\(\\angle\\)y = 71°.",
"hints": ["Use the angle sum of triangle ABF to find \\(\\angle\\)AFB.", "\\(\\angle\\)y is vertically opposite \\(\\angle\\)AFB."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q24",
"image_needed": true,
"image_options": false,
"image_file": "q24.png",
"image_page": 15,
"image_bbox": [0.22, 0.49, 0.66, 0.66],
"image_loc": "two crossing straight lines AFD and BFC forming triangles, angles 37° at B, 72° at A, y at F; middle of page",
"notes": "Answer key: 180 − (72 + 37) = 71°. Vertically opposite angle."
},
{
"n": 25,
"type_id": 2,
"question": "Chun Ming and Naomi had $13 and $45 respectively. They were given an equal amount of money. Naomi had twice as much money as Chun Ming in the end. How much money did each of them receive? $[?]",
"answer0": "19",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "Let each receive x. End: Naomi = 45 + x, Chun Ming = 13 + x, with 45 + x = 2(13 + x). 45 + x = 26 + 2x, so x = 19. Each received $19.",
"hints": ["Write expressions for each person's final amount after adding x.", "Set Naomi's amount equal to twice Chun Ming's amount and solve."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q25",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: $19 (check: 13+19=32, 45+19=64 = 2x32)."
},
{
"n": 26,
"type_id": 2,
"question": "The average of a set of two numbers is 12.6. The average of another set of two numbers is 19.9. What is the average of all the four numbers? [?]",
"answer0": "16.25",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 167,
"difficulty_id": 2,
"explanation": "First set total = 12.6 × 2 = 25.2. Second set total = 19.9 × 2 = 39.8. All four total = 25.2 + 39.8 = 65. Average = 65 ÷ 4 = 16.25.",
"hints": ["Average × count = total, for each set of two.", "Add the two totals and divide by 4."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q26",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key shows 12.6 x 2 = 25.5 (typo; correct is 25.2) and totals to 65.3 ÷ 4 = 16.325. Correct value: 25.2 + 39.8 = 65, 65 ÷ 4 = 16.25. Used mathematically correct 16.25; flagged printed key arithmetic typo."
},
{
"n": 27,
"type_id": 2,
"question": "The figure is made up of 2 identical trapezium. What is the value of \\(\\angle\\)a + \\(\\angle\\)b + \\(\\angle\\)c + \\(\\angle\\)d? [?]°",
"answer0": "360",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 200,
"difficulty_id": 3,
"explanation": "Each trapezium has two right angles, so its other two angles sum to 360° − 90° − 90° = 180°. With 2 identical trapeziums, \\(\\angle\\)a + \\(\\angle\\)b + \\(\\angle\\)c + \\(\\angle\\)d = 180° × 2 = 360°.",
"hints": ["The four angles of a trapezium add up to 360°.", "Subtract the two right angles, then account for both trapeziums."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q27",
"image_needed": true,
"image_options": false,
"image_file": "q27.png",
"image_page": 17,
"image_bbox": [0.22, 0.15, 0.52, 0.34],
"image_loc": "two identical trapeziums joined, angles a, b, c, d marked; upper-left of page below the question",
"notes": "Answer key: 360 − 90 − 90 = 180; 180 x 2 = 360°."
},
{
"n": 28,
"type_id": 1,
"question": "Danny is 11 years old now. Eric is thrice as old as Danny. What was the ratio of Danny's age to Eric's age three years ago? Give your answer in its simplest form.",
"answer0": "8 : 30",
"answer1": "4 : 15",
"answer2": "11 : 33",
"answer3": "1 : 3",
"correct_answer": 1,
"skill_id": 179,
"difficulty_id": 2,
"explanation": "Eric now = 3 × 11 = 33. Three years ago: Danny = 11 − 3 = 8, Eric = 33 − 3 = 30. Ratio = 8 : 30 = 4 : 15.",
"hints": ["Find each person's age three years ago.", "Write the ratio and simplify by dividing both parts by 2."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q28",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: Danny 8, Eric 30, simplest form 4:15. Ratio answer, so converted to MCQ."
},
{
"n": 29,
"type_id": 2,
"question": "ABC, CFE and BFD are straight lines. \\(\\angle\\)ABF = 157° and \\(\\angle\\)BCE = 120°. Find \\(\\angle\\)CFD. [?]°",
"answer0": "143",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 197,
"difficulty_id": 3,
"explanation": "\\(\\angle\\)FBC = 180° − 157° = 23° (straight line ABC). In triangle BFC, \\(\\angle\\)BFC = 180° − 23° − 120° = 37°. \\(\\angle\\)CFD = 180° − 37° = 143° (straight line BFD).",
"hints": ["Find \\(\\angle\\)FBC using the straight line at B.", "Use triangle BFC angle sum, then the straight line at F."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q29",
"image_needed": true,
"image_options": false,
"image_file": "q29.png",
"image_page": 18,
"image_bbox": [0.14, 0.15, 0.72, 0.34],
"image_loc": "straight line ABC with rays to E, F, D; angles 157° at B and 120° at C; upper part of page",
"notes": "Answer key: 143°."
},
{
"n": 30,
"type_id": 2,
"question": "PQRS is a rectangle. The area of rectangle PQRS is 392 cm². W and X are points on PQ and Y and Z are points on RS. Find the total area of the shaded parts. [?] cm²",
"answer0": "196",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 186,
"difficulty_id": 3,
"explanation": "Each shaded triangle has its base on one long side of the rectangle and its apex on the opposite side, so each triangle's area = \\(\\dfrac{1}{2}\\) × base × height. The triangles' bases together span the full width and their height equals the rectangle's height, so the total shaded area = \\(\\dfrac{1}{2}\\) × area of rectangle = 392 ÷ 2 = 196 cm².",
"hints": ["Each triangle has the same height as the rectangle.", "The bases of the triangles add up to the full width, so the total area is half the rectangle."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q30",
"image_needed": true,
"image_options": false,
"image_file": "q30.png",
"image_page": 19,
"image_bbox": [0.16, 0.18, 0.78, 0.37],
"image_loc": "rectangle PQRS with three shaded triangles standing on the base; W, X on top side and Y, Z on bottom side; upper part of page",
"notes": "Answer key: 392 ÷ 2 = 196 cm²."
},
{
"n": 31,
"type_id": 2,
"question": "8000 ml of water was poured into 5 containers equally. How many litres of water were there in one container? [?] ℓ",
"answer0": "1.6",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 192,
"difficulty_id": 1,
"explanation": "8000 ml = 8 ℓ. Divide equally: 8 ÷ 5 = 1.6 ℓ in one container.",
"hints": ["Convert 8000 ml to litres (1000 ml = 1 ℓ).", "Divide by 5 containers."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q31",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q1. Answer key: 8 ÷ 5 = 1.6 L."
},
{
"n": 32,
"type_id": 2,
"question": "A six-sided die has a number from 1 to 6 on each side. The die was rolled three times and the number on the top of the die was recorded. The product of the three numbers was 96. What were the three numbers recorded? [?], [?], [?]",
"answer0": "6",
"answer1": "4",
"answer2": "4",
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 2,
"explanation": "Find three numbers from 1–6 whose product is 96. Since 96 = 6 × 16 = 6 × 4 × 4, the three numbers are 6, 4 and 4.",
"hints": ["Break 96 into factors that are each between 1 and 6.", "96 = 6 × 4 × 4."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q32",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q2. Answer key: 6, 4, 4 (order interchangeable). Three blanks for the three numbers."
},
{
"n": 33,
"type_id": 0,
"question": "Draw the side view of the solid on the square grid.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 187,
"difficulty_id": 2,
"explanation": "Draw the side view of the stacked-cube solid as seen from the indicated direction (an L-shaped outline: two cubes high on one column, with a single cube extending to the side at the base).",
"hints": ["Look at the solid from the side-view arrow direction.", "Sketch the outline of the cubes you would see, ignoring depth."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q33",
"image_needed": true,
"image_options": false,
"image_file": "q33.png",
"image_page": 22,
"image_bbox": [0.30, 0.18, 0.68, 0.36],
"image_loc": "isometric drawing of stacked unit cubes with a 'Side View' arrow; upper-middle of page",
"notes": "Paper 2 Q3. Interactive draw-on-grid task with no definite numeric/sequence answer — type_id 0, skipped on insert. No printed answer (drawing)."
},
{
"n": 34,
"type_id": 2,
"question": "The table shows the parking charges at a car park.
6 a.m. – 12 p.m.: $0.60 per 30 minutes or part thereof
12 p.m. – 2 p.m.: $1.20 per 30 minutes or part thereof
2 p.m. – 6 p.m.: $0.60 per 30 minutes or part thereof
6 p.m. – 6 a.m.: $8 per entry
Mr Ho parked his car from 11 a.m. to 2.15 p.m. How much did he pay for the parking? $[?]",
"answer0": "6.60",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 167,
"difficulty_id": 3,
"explanation": "11 a.m.–12 p.m. (1 h) at $0.60/30 min = 2 × $0.60 = $1.20. 12 p.m.–2 p.m. (2 h) at $1.20/30 min = 4 × $1.20 = $4.80. 2 p.m.–2.15 p.m. (part of 30 min) at $0.60 = $0.60. Total = $1.20 + $4.80 + $0.60 = $6.60.",
"hints": ["Split the parking time across the different rate periods.", "Charge each 30-minute block (or part of one) at the right rate, then add."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q34",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q4. Answer key: 1.20 + 4.80 + 0.60 = $6.60. Table transcribed into stem text."
},
{
"n": 35,
"type_id": 2,
"question": "Ali had some money at first. He gave \\(\\dfrac{2}{7}\\) of his money to his mother and \\(\\dfrac{1}{5}\\) of the remainder to his sister. He had $216 left. How much money did he have at first? $[?]",
"answer0": "378",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "After mother, remainder = \\(\\dfrac{5}{7}\\). Sister gets \\(\\dfrac{1}{5}\\) of that, leaving \\(\\dfrac{4}{5}\\) of the remainder = \\(\\dfrac{4}{5} \\times \\dfrac{5}{7} = \\dfrac{4}{7}\\) of the original = $216. So \\(\\dfrac{1}{7}\\) = $54, and the whole = 7 × $54 = $378.",
"hints": ["After giving to mother, \\(\\dfrac{5}{7}\\) remains.", "Sister takes \\(\\dfrac{1}{5}\\) of the remainder, so $216 is \\(\\dfrac{4}{7}\\) of the original."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q35",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q5. Answer key: 4u = 216, 1u = 54, 7u = $378."
},
{
"n": 36,
"type_id": 2,
"question": "ABCD is a rhombus. \\(\\angle\\)BAD = 110°. Find \\(\\angle\\)BDC. [?]°",
"answer0": "35",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 200,
"difficulty_id": 2,
"explanation": "Opposite angles of a rhombus are equal, so \\(\\angle\\)BCD = \\(\\angle\\)BAD = 110°. Triangle BCD is isosceles (CB = CD), so \\(\\angle\\)BDC = (180° − 110°) ÷ 2 = 35°.",
"hints": ["Opposite angles of a rhombus are equal.", "Triangle BCD is isosceles, so the two base angles are equal."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q36",
"image_needed": true,
"image_options": false,
"image_file": "q36.png",
"image_page": 24,
"image_bbox": [0.12, 0.27, 0.45, 0.46],
"image_loc": "rhombus ABCD with diagonal BD drawn, angle 110° marked at A; left-middle of page",
"notes": "Paper 2 Q6. Answer key: (180-110) ÷ 2 = 35°."
},
{
"n": 37,
"type_id": 2,
"question": "Leon worked \\(6\\dfrac{1}{5}\\) h daily from Monday to Friday. He worked \\(4\\dfrac{2}{3}\\) h on Saturday. He did not work on Sunday. How many weeks must he work to have worked 535 hours? [?]",
"answer0": "15",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "Weekday hours = \\(6\\dfrac{1}{5} \\times 5 = 31\\) h. Add Saturday: \\(31 + 4\\dfrac{2}{3} = 35\\dfrac{2}{3} = \\dfrac{107}{3}\\) h per week. Weeks = \\(535 \\div \\dfrac{107}{3} = 535 \\times \\dfrac{3}{107} = 15\\) weeks.",
"hints": ["Find the total hours Leon works in one week.", "Divide 535 by the weekly hours."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q37",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q7. Answer key: weekly = 107/3 h; 535 ÷ 107/3 = 15 weeks."
},
{
"n": 38,
"type_id": 2,
"question": "Tiffany and Leila had the same amount of money at first. Tiffany spent all her money to buy 1 dress and 6 identical skirts. Leila bought 1 such dress and a blouse and had $72 left. The blouse cost $8 more than the skirt. What was the cost of the blouse? $[?]",
"answer0": "24",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "Both start equal. Tiffany: dress + 6 skirts. Leila: dress + blouse + $72 left. So 6 skirts = blouse + $72. Blouse = skirt + $8, so 6 skirts = skirt + 8 + 72, giving 5 skirts = 80, skirt = $16. Blouse = 16 + 8 = $24.",
"hints": ["Both spent the same total; set Tiffany's spending equal to Leila's spending plus $72.", "The dress cancels; solve for the skirt, then add $8 for the blouse."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q38",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q8. Answer key: skirt $16, blouse = 16 + 8 = $24."
},
{
"n": 39,
"type_id": 2,
"question": "A triangle is drawn in rectangle ABCE. Find the area of triangle ADF. [?] cm²",
"answer0": "60",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 186,
"difficulty_id": 3,
"explanation": "Area of triangle ADB (base AB = 24, height = 14) = \\(\\dfrac{1}{2} \\times 24 \\times 14 = 168\\) cm². F is 5 cm below the top, so triangle ABF has height 14 − 5 = 9: area = \\(\\dfrac{1}{2} \\times 24 \\times 9 = 108\\) cm². Area of triangle ADF = 168 − 108 = 60 cm².",
"hints": ["Find the area of the large triangle ADB using base 24 and height 14.", "Subtract triangle ABF (height 14 − 5 = 9)."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q39",
"image_needed": true,
"image_options": false,
"image_file": "q39.png",
"image_page": 25,
"image_bbox": [0.14, 0.50, 0.58, 0.72],
"image_loc": "rectangle ABCE (14 cm by 24 cm) with shaded triangle ADF and point F marked 5 cm from top; lower-left of page",
"notes": "Paper 2 Q9. Answer key: 168 − 108 = 60 cm² (printed unit '60cm' is a typo; correct is cm²)."
},
{
"n": 40,
"type_id": 1,
"question": "The bar graph shows the distance travelled by a car from Monday to Friday. Which day did the car travel the furthest?",
"answer0": "Monday",
"answer1": "Tuesday",
"answer2": "Wednesday",
"answer3": "Thursday",
"correct_answer": 1,
"skill_id": 152,
"difficulty_id": 1,
"explanation": "Reading the bar graph, Tuesday's bar is tallest at 300 km, the greatest distance.",
"hints": ["Find the tallest bar on the graph.", "Read off the day below it."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q40",
"image_needed": true,
"image_options": false,
"image_file": "q40.png",
"image_page": 26,
"image_bbox": [0.18, 0.15, 0.72, 0.39],
"image_loc": "bar graph 'Distance Travelled by a Car' with bars Mon 250, Tue 300, Wed 200, Thu 250, Fri 150; upper part of page",
"notes": "Paper 2 Q10(a). Answer key: Tuesday = 300km. Word answer, so converted to MCQ; index 1 = Tuesday."
},
{
"n": 41,
"type_id": 2,
"question": "The bar graph shows the distance travelled by a car from Monday to Friday. If the average distance travelled by the car on Saturday and Sunday is 290 km, what is the average distance travelled by the car from Monday to Sunday? Correct your answer to the nearest tenth. [?] km",
"answer0": "247.1",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 168,
"difficulty_id": 3,
"explanation": "Mon–Fri total = 250 + 300 + 200 + 250 + 150 = 1150 km. Sat + Sun = 290 × 2 = 580 km. Total Mon–Sun = 1150 + 580 = 1730 km. Average = 1730 ÷ 7 ≈ 247.1 km.",
"hints": ["Add the five weekday distances from the graph.", "Add Saturday and Sunday (2 × 290), then divide the grand total by 7."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q41",
"image_needed": true,
"image_options": false,
"image_file": "q41.png",
"image_page": 26,
"image_bbox": [0.18, 0.15, 0.72, 0.39],
"image_loc": "same bar graph 'Distance Travelled by a Car'; upper part of page",
"notes": "Paper 2 Q10(b). Answer key: 1730 ÷ 7 = 247.1 km (to nearest tenth)."
},
{
"n": 42,
"type_id": 2,
"question": "Mrs Tan wanted to fill up her car with $60 worth of petrol. Petrol Kiosk A was offering a 12% discount, while Petrol Kiosk B was offering a cash discount of $2 on top of a 10% discount.
Find the difference in the discounts offered by the 2 petrol kiosks. $[?]",
"answer0": "0.80",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 176,
"difficulty_id": 3,
"explanation": "Kiosk A discount = 12% of $60 = $7.20. Kiosk B discount = 10% of $60 + $2 = $6 + $2 = $8. Difference = $8 − $7.20 = $0.80.",
"hints": ["Work out each kiosk's total discount in dollars.", "Kiosk B is 10% of $60 plus the extra $2; then find the difference."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q42",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q11(a). Answer key: A $7.20, B $8, difference $0.80."
},
{
"n": 43,
"type_id": 2,
"question": "Mrs Tan wanted to fill up her car with $60 worth of petrol. Petrol Kiosk B was offering a cash discount of $2 on top of a 10% discount. Mrs Tan decided to fill up her car at Petrol Kiosk B. How much did Mrs Tan pay inclusive of 9% GST? $[?]",
"answer0": "56.68",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 176,
"difficulty_id": 3,
"explanation": "Price after Kiosk B discount = $60 − $8 = $52. GST = 9% of $52 = $4.68. Amount paid = $52 + $4.68 = $56.68.",
"hints": ["Subtract Kiosk B's total discount of $8 from $60.", "Add 9% GST on the discounted price."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q43",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q11(b). Answer key: 52 + 4.68 = $56.68."
},
{
"n": 44,
"type_id": 2,
"question": "Mrs Teo baked a total of 612 chocolate and strawberry cupcakes at first. She sold half of the chocolate cupcakes and baked another 48 strawberry cupcakes. In the end, she had an equal number of chocolate and strawberry cupcakes.
How many strawberry cupcakes did she have in the end? [?]",
"answer0": "220",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "In the end the new total = 612 − (half the chocolate sold) ... using the key's method: 612 + 48 = 660, and since end chocolate = end strawberry, divide the adjusted equal-share total: 660 ÷ 3 = 220 strawberry cupcakes in the end.",
"hints": ["Let the original chocolate be 2 units (half is sold).", "Set end chocolate equal to end strawberry and use the total."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q44",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q12(a). Answer key: 612 + 48 = 660; 660 ÷ 3 = 220."
},
{
"n": 45,
"type_id": 2,
"question": "Mrs Teo baked a total of 612 chocolate and strawberry cupcakes at first. She sold half of the chocolate cupcakes and baked another 48 strawberry cupcakes. In the end, she had an equal number of chocolate and strawberry cupcakes.
How many more chocolate cupcakes than strawberry cupcakes did she have at first? [?]",
"answer0": "268",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "End each = 220. Original chocolate = 2 × 220 = 440 (since half was sold to reach 220). Original strawberry = 220 − 48 = 172. Difference at first = 440 − 172 = 268.",
"hints": ["End chocolate 220 was half the original chocolate, so double it.", "Original strawberry = end strawberry minus the 48 baked later; then subtract."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q45",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q12(b). Answer key: chocolate 440, strawberry 172, difference 268."
},
{
"n": 46,
"type_id": 2,
"question": "A fruit seller had some fruits. \\(\\dfrac{1}{5}\\) of the fruits were apples and the rest were oranges. She sold \\(\\dfrac{4}{7}\\) of the apples and 51 of the oranges. She then had \\(\\dfrac{2}{5}\\) of the fruits left. How many fruits did she have at first? [?]",
"answer0": "105",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "Apples sold = \\(\\dfrac{1}{5} \\times \\dfrac{4}{7} = \\dfrac{4}{35}\\) of all fruits, leaving \\(\\dfrac{31}{35}\\) before selling oranges. Final left = \\(\\dfrac{2}{5} = \\dfrac{14}{35}\\). So oranges sold = \\(\\dfrac{31}{35} - \\dfrac{14}{35} = \\dfrac{17}{35}\\) of all fruits = 51. Thus \\(\\dfrac{1}{35}\\) = 51 ÷ 17 = 3, and total = 3 × 35 = 105 fruits.",
"hints": ["Express the apples sold as a fraction of all the fruits.", "The 51 oranges sold equal the difference between fractions left; use it to find 1 unit."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q46",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q13. Answer key: 17/35 = 51, 1u = 3, total = 105."
},
{
"n": 47,
"type_id": 2,
"question": "The usual price of a kilogram of flour is $1.80. During a sale, each kilogram of flour cost 30 cents cheaper.
How much did Karen pay for 31 kg of flour during the sale? $[?]",
"answer0": "46.50",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 167,
"difficulty_id": 2,
"explanation": "Sale price = $1.80 − $0.30 = $1.50 per kg. For 31 kg: $1.50 × 31 = $46.50.",
"hints": ["Find the sale price per kilogram first.", "Multiply by 31 kg."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q47",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q14(a). Answer key: 1.5 x 31 = $46.50."
},
{
"n": 48,
"type_id": 2,
"question": "The usual price of a kilogram of flour is $1.80. During a sale, each kilogram of flour cost 30 cents cheaper.
If Karen paid $23.40 to buy some flour at the usual price, how much more flour can she buy during the sale? [?] kg",
"answer0": "2.6",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 167,
"difficulty_id": 3,
"explanation": "At usual price: $23.40 ÷ $1.80 = 13 kg. At sale price: $23.40 ÷ $1.50 = 15.6 kg. More flour = 15.6 − 13 = 2.6 kg.",
"hints": ["Find how many kg $23.40 buys at $1.80/kg.", "Find how many kg the same money buys at $1.50/kg, then subtract."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q48",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q14(b). Answer key: 15.6 − 13 = 2.6 kg."
},
{
"n": 49,
"type_id": 2,
"question": "James poured 4 buckets of water into an empty rectangular tank measuring 60 cm long, 40 cm wide and 70 cm high. Each bucket had a capacity of 8 ℓ. How much more water did James need to fill the tank to a depth of 18 cm? Give your answer in litres. [?] ℓ",
"answer0": "11.2",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 193,
"difficulty_id": 3,
"explanation": "Water needed at 18 cm depth = 60 × 40 × 18 = 43 200 cm³ = 43.2 ℓ. Poured = 4 × 8 ℓ = 32 ℓ. More needed = 43.2 − 32 = 11.2 ℓ.",
"hints": ["Volume to depth 18 cm = 60 × 40 × 18 cm³ (1000 cm³ = 1 ℓ).", "Subtract the 4 × 8 ℓ already poured."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q49",
"image_needed": true,
"image_options": false,
"image_file": "q49.png",
"image_page": 31,
"image_bbox": [0.10, 0.25, 0.85, 0.54],
"image_loc": "rectangular tank (60 cm x 40 cm x 70 cm) with 4 buckets of 8 ℓ each; middle of page",
"notes": "Paper 2 Q15. Answer key: 43200 cm³ = 43.2 L; 43.2 − 32 = 11.2 L."
},
{
"n": 50,
"type_id": 2,
"question": "The line graph shows Cynthia's savings from March to July. What was Cynthia's average monthly savings from March to July? $[?]",
"answer0": "60",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 167,
"difficulty_id": 2,
"explanation": "Readings: Mar 50, Apr 70, May 60, Jun 40, Jul 80. Total = 50 + 70 + 60 + 40 + 80 = 300. Average = 300 ÷ 5 = $60.",
"hints": ["Read each month's savings off the line graph.", "Add all five and divide by 5."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q50",
"image_needed": true,
"image_options": false,
"image_file": "q50.png",
"image_page": 32,
"image_bbox": [0.16, 0.14, 0.78, 0.40],
"image_loc": "line graph 'Monthly Savings ($)' from Mar to July; upper part of page",
"notes": "Paper 2 Q16(a). Answer key: 300 ÷ 5 = $60."
},
{
"n": 51,
"type_id": 2,
"question": "The line graph shows Cynthia's savings from March to July. Cynthia's average monthly savings from March to August is $75. How much was his savings in August? $[?]",
"answer0": "150",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 167,
"difficulty_id": 3,
"explanation": "Mar–Aug is 6 months. Total = 75 × 6 = $450. Mar–Jul total = $300. August = 450 − 300 = $150.",
"hints": ["Average × 6 months gives the Mar–Aug total.", "Subtract the Mar–Jul total of $300."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q51",
"image_needed": true,
"image_options": false,
"image_file": "q51.png",
"image_page": 32,
"image_bbox": [0.16, 0.14, 0.78, 0.40],
"image_loc": "same line graph 'Monthly Savings ($)' from Mar to July; upper part of page",
"notes": "Paper 2 Q16(b). Answer key: 75 x 6 = 450; 450 − 300 = $150."
},
{
"n": 52,
"type_id": 2,
"question": "Circles and triangles are used to form figures that follow a pattern. The number of triangles used in Figures 1 to 4 are 4, 7, 10, 13 and the number of circles are 4, 8, 12, 16. In Figure 9, 28 triangles are used and the total of triangles and circles is 64. Complete the table: how many circles are used in Figure 9? [?]",
"answer0": "36",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 2,
"explanation": "Circles increase by 4 each figure: 4, 8, 12, 16, ... so Figure n has 4n circles. Figure 9: 4 × 9 = 36 circles. (Check: 28 triangles + 36 circles = 64.)",
"hints": ["The number of circles goes up by 4 each figure.", "Figure 9 circles = 4 × 9, or 64 − 28."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q52",
"image_needed": true,
"image_options": false,
"image_file": "q52.png",
"image_page": 33,
"image_bbox": [0.16, 0.12, 0.80, 0.30],
"image_loc": "pattern Figures 1-4 made of triangles and circles; upper part of page above the table",
"notes": "Paper 2 Q17(a). Answer key: 36 circles in Figure 9."
},
{
"n": 53,
"type_id": 2,
"question": "Circles and triangles are used to form figures that follow a pattern. The number of triangles used in Figures 1 to 4 are 4, 7, 10, 13. In Figure 50, how many triangles were used? [?]",
"answer0": "151",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "Triangles: 4, 7, 10, 13, ... increasing by 3, so Figure n has 3n + 1 triangles. Figure 50: 3 × 50 + 1 = 150 + 1 = 151.",
"hints": ["The number of triangles goes up by 3 each figure.", "Figure n triangles = 3 × n + 1."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q53",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q17(b). Answer key: 50 x 3 = 150; 150 + 1 = 151."
},
{
"n": 54,
"type_id": 2,
"question": "Circles and triangles are used to form figures that follow a pattern. Triangles in Figures 1 to 4 are 4, 7, 10, 13 and circles are 4, 8, 12, 16. Find the total number of circles and triangles in Figure 99. [?]",
"answer0": "694",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "Totals: 8, 15, 22, 29, ... increasing by 7, so Figure n total = 7n + 1. Figure 99: 7 × 99 + 1 = 693 + 1 = 694.",
"hints": ["The total (triangles + circles) goes up by 7 each figure.", "Figure n total = 7 × n + 1."],
"source": "ACS Primary 2024 P5 End-of-Year Exam Q54",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q17(c). Answer key: 99 x 7 + 1 = 694."
}
]
}