{
"paper": {
"school": "Catholic High",
"year": 2022,
"level": "P5",
"label": "Semestral Assessment 2",
"source_prefix": "Catholic High 2022 P5 Semestral Assessment 2",
"has_answer_key": true,
"notes": "Paper titled End-of-Year Examination 2022. Comprises Paper 1 (Booklet A MCQ Q1-15, Booklet B short/structured Q16-30) and Paper 2 (Q1-17). Two independent question-number sequences each with its own answer key. Manifest numbers run 1-47; source labels keep original Paper-1/Paper-2 question identity."
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "Which of the following is four million, twenty-two thousand and twelve in numerals?",
"answer0": "4 022 012",
"answer1": "4 022 120",
"answer2": "4 220 012",
"answer3": "4 220 120",
"correct_answer": 0,
"skill_id": 149,
"difficulty_id": 1,
"explanation": "Four million = 4 000 000, twenty-two thousand = 22 000, twelve = 12. Sum = 4 022 012.",
"hints": ["Break the words into millions, thousands and ones.", "4 000 000 + 22 000 + 12."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 1 (index 0)."
},
{
"n": 2,
"type_id": 1,
"question": "What does the digit 7 in 6.871 stand for?",
"answer0": "7 ones",
"answer1": "7 tenths",
"answer2": "7 hundredths",
"answer3": "7 thousandths",
"correct_answer": 2,
"skill_id": 158,
"difficulty_id": 1,
"explanation": "In 6.871 the digit 7 is in the hundredths place, so it stands for 7 hundredths.",
"hints": ["After the decimal point the places are tenths, hundredths, thousandths.", "7 is the second digit after the point."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 3 (index 2)."
},
{
"n": 3,
"type_id": 1,
"question": "Which of the following is the same as 20 kg 95 g?",
"answer0": "2095 g",
"answer1": "2950 g",
"answer2": "20 095 g",
"answer3": "20 950 g",
"correct_answer": 2,
"skill_id": 184,
"difficulty_id": 1,
"explanation": "20 kg = 20 000 g. 20 000 g + 95 g = 20 095 g.",
"hints": ["1 kg = 1000 g.", "Convert 20 kg to grams then add 95 g."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 3 (index 2)."
},
{
"n": 4,
"type_id": 1,
"question": "Express 0.5 as a percentage.",
"answer0": "5%",
"answer1": "50%",
"answer2": "0.5%",
"answer3": "0.05%",
"correct_answer": 1,
"skill_id": 173,
"difficulty_id": 1,
"explanation": "0.5 \\(\\times\\) 100% = 50%.",
"hints": ["To convert a decimal to a percentage, multiply by 100%.", "0.5 = \\(\\dfrac{50}{100}\\)."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q4",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 2 (index 1)."
},
{
"n": 5,
"type_id": 1,
"question": "Sammy and Liting have 240 beads. Sammy has 60 beads. What is the ratio of Liting's beads to the total number of beads that Sammy and Liting have?",
"answer0": "1 : 3",
"answer1": "1 : 4",
"answer2": "3 : 1",
"answer3": "3 : 4",
"correct_answer": 3,
"skill_id": 180,
"difficulty_id": 2,
"explanation": "Liting's beads = 240 - 60 = 180. Liting : total = 180 : 240 = 3 : 4.",
"hints": ["Find Liting's beads first.", "Simplify 180 : 240 by dividing by 60."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q5",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 4 (index 3)."
},
{
"n": 6,
"type_id": 1,
"question": "Line AOB and line COD are straight lines. \\(\\angle\\)AOE = 14° and \\(\\angle\\)BOD = 30°. Find \\(\\angle\\)x.",
"answer0": "14°",
"answer1": "15°",
"answer2": "16°",
"answer3": "30°",
"correct_answer": 2,
"skill_id": 194,
"difficulty_id": 2,
"explanation": "\\(\\angle\\)AOC = \\(\\angle\\)BOD = 30° (vertically opposite). On straight line AOB, \\(\\angle\\)AOE + \\(\\angle\\)x + \\(\\angle\\)BOD = 180° is not used; rather \\(\\angle\\)x = \\(\\angle\\)AOC - \\(\\angle\\)AOE = 30° - 14° = 16°.",
"hints": ["\\(\\angle\\)AOC equals \\(\\angle\\)BOD because they are vertically opposite.", "x lies between OE and OC; subtract \\(\\angle\\)AOE from \\(\\angle\\)AOC."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q6",
"image_needed": true,
"image_options": false,
"image_file": "q6.png",
"image_page": 3,
"image_bbox": [0.18, 0.31, 0.68, 0.48],
"image_loc": "upper-middle of page, two crossing straight lines through O with labels A, B, C, D, E and angles 14 deg and 30 deg",
"notes": "Key: option 3 (index 2) = 16°. x is angle EOC."
},
{
"n": 7,
"type_id": 1,
"question": "Find the value of 10 ÷ 2000.",
"answer0": "20",
"answer1": "200",
"answer2": "0.05",
"answer3": "0.005",
"correct_answer": 3,
"skill_id": 166,
"difficulty_id": 1,
"explanation": "10 ÷ 2000 = 10 ÷ 2000 = 0.005.",
"hints": ["10 ÷ 1000 = 0.01.", "Then divide by another 2."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 4 (index 3)."
},
{
"n": 8,
"type_id": 1,
"question": "The table shows the marks attained by 3 girls in a test.
Alice 49, Betty 73, Carol 88.
What is the average marks of the 3 girls?",
"answer0": "61",
"answer1": "70",
"answer2": "105",
"answer3": "210",
"correct_answer": 1,
"skill_id": 203,
"difficulty_id": 1,
"explanation": "Total = 49 + 73 + 88 = 210. Average = 210 ÷ 3 = 70.",
"hints": ["Average = total ÷ number of items.", "Add the three marks then divide by 3."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Table data inlined into stem. Key: option 2 (index 1)."
},
{
"n": 9,
"type_id": 1,
"question": "Arrange the following volume in increasing order.
12 ℓ 4 mℓ , \\(12\\dfrac{4}{10}\\) ℓ , 1240 mℓ",
"answer0": "1240 mℓ , 12 ℓ 4 mℓ , \\(12\\dfrac{4}{10}\\) ℓ",
"answer1": "\\(12\\dfrac{4}{10}\\) ℓ , 12 ℓ 4 mℓ , 1240 mℓ",
"answer2": "1240 mℓ , \\(12\\dfrac{4}{10}\\) ℓ , 12 ℓ 4 mℓ",
"answer3": "12 ℓ 4 mℓ , 1240 mℓ , \\(12\\dfrac{4}{10}\\) ℓ",
"correct_answer": 0,
"skill_id": 184,
"difficulty_id": 3,
"explanation": "Convert all to mℓ: 12 ℓ 4 mℓ = 12 004 mℓ; \\(12\\dfrac{4}{10}\\) ℓ = 12.4 ℓ = 12 400 mℓ; 1240 mℓ = 1240 mℓ. Increasing order: 1240 mℓ , 12 ℓ 4 mℓ , \\(12\\dfrac{4}{10}\\) ℓ.",
"hints": ["Convert every quantity to the same unit (millilitres).", "1 ℓ = 1000 mℓ."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q9",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 1 (index 0). Options contain a fraction so kept as MCQ; fractions rendered inline."
},
{
"n": 10,
"type_id": 1,
"question": "FH is the base of triangle FGH. Which is the height of triangle FGH?",
"answer0": "FG",
"answer1": "HG",
"answer2": "KG",
"answer3": "HK",
"correct_answer": 2,
"skill_id": 185,
"difficulty_id": 2,
"explanation": "The height is the perpendicular distance from the opposite vertex G to the base line FH (extended). KG is drawn perpendicular to FH extended, so KG is the height.",
"hints": ["The height is perpendicular to the base.", "Find the segment from G that meets line FH at a right angle (mark at K)."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q10",
"image_needed": true,
"image_options": false,
"image_file": "q10.png",
"image_page": 5,
"image_bbox": [0.27, 0.13, 0.70, 0.30],
"image_loc": "top of page, triangle FGH with dashed perpendicular GK meeting base line extended at K (right-angle mark)",
"notes": "Key: option 3 (index 2) = KG."
},
{
"n": 11,
"type_id": 1,
"question": "At a cafe, the ratio of the number of tables to the number of chairs is 3 : 5. There is a total of 120 tables and chairs. How many more chairs than tables are there at the cafe?",
"answer0": "30",
"answer1": "45",
"answer2": "75",
"answer3": "80",
"correct_answer": 0,
"skill_id": 183,
"difficulty_id": 2,
"explanation": "Total units = 3 + 5 = 8. 1 unit = 120 ÷ 8 = 15. More chairs than tables = (5 - 3) units = 2 × 15 = 30.",
"hints": ["Add the ratio parts to find the total number of units.", "The difference is (5 - 3) units."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q11",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 1 (index 0)."
},
{
"n": 12,
"type_id": 1,
"question": "Huishan had $4000 in her bank account. The bank paid 2% interest at the end of each year. She did not withdraw her savings for 1 year. How much did she have in the bank at the end of 1 year?",
"answer0": "$80",
"answer1": "$800",
"answer2": "$4080",
"answer3": "$4200",
"correct_answer": 2,
"skill_id": 176,
"difficulty_id": 2,
"explanation": "Interest = 2% of $4000 = \\(\\dfrac{2}{100}\\) \\(\\times\\) 4000 = $80. Total = 4000 + 80 = $4080.",
"hints": ["Find 2% of $4000 first.", "Add the interest to the original amount."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q12",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 3 (index 2)."
},
{
"n": 13,
"type_id": 1,
"question": "Which of the following is closest to 1?",
"answer0": "\\(\\dfrac{3}{4}\\)",
"answer1": "\\(\\dfrac{3}{5}\\)",
"answer2": "\\(\\dfrac{5}{3}\\)",
"answer3": "\\(\\dfrac{7}{6}\\)",
"correct_answer": 3,
"skill_id": 158,
"difficulty_id": 2,
"explanation": "Differences from 1: \\(\\dfrac{3}{4}\\) is 0.25 away; \\(\\dfrac{3}{5}\\) is 0.4 away; \\(\\dfrac{5}{3}\\) is 0.667 away; \\(\\dfrac{7}{6}\\) is \\(\\dfrac{1}{6}\\) ≈ 0.167 away. \\(\\dfrac{7}{6}\\) is closest to 1.",
"hints": ["Compare how far each fraction is from 1.", "Convert each to a decimal or find |fraction - 1|."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q13",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 4 (index 3). Fraction options rendered inline."
},
{
"n": 14,
"type_id": 1,
"question": "Grandma had \\(\\dfrac{5}{9}\\) kg of sugar. She used \\(\\dfrac{1}{4}\\) of it to make desserts. How much sugar did she have left?",
"answer0": "\\(\\dfrac{3}{4}\\) kg",
"answer1": "\\(\\dfrac{5}{12}\\) kg",
"answer2": "\\(\\dfrac{5}{36}\\) kg",
"answer3": "\\(\\dfrac{11}{36}\\) kg",
"correct_answer": 1,
"skill_id": 165,
"difficulty_id": 2,
"explanation": "She has \\(1 - \\dfrac{1}{4} = \\dfrac{3}{4}\\) left. Sugar left = \\(\\dfrac{3}{4} \\times \\dfrac{5}{9} = \\dfrac{15}{36} = \\dfrac{5}{12}\\) kg.",
"hints": ["Fraction left = 1 - \\(\\dfrac{1}{4}\\).", "Multiply that by \\(\\dfrac{5}{9}\\) and simplify."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q14",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key in table printed as '2' but solution box gives option 2 (index 1) = 5/12. Fraction options inline."
},
{
"n": 15,
"type_id": 1,
"question": "The ratio of the perimeter of a square to the perimeter of a rectangle was 3 : 4. The perimeter of the rectangle was 48 cm. Find the length of one side of the square.",
"answer0": "6 cm",
"answer1": "9 cm",
"answer2": "12 cm",
"answer3": "36 cm",
"correct_answer": 1,
"skill_id": 183,
"difficulty_id": 2,
"explanation": "Square perimeter : rectangle perimeter = 3 : 4. 4 units = 48 cm so 1 unit = 12 cm; square perimeter = 3 units = 36 cm. One side = 36 ÷ 4 = 9 cm.",
"hints": ["Find the square's perimeter using the ratio.", "A square has 4 equal sides."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q15",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 2 (index 1) = 9 cm."
},
{
"n": 16,
"type_id": 2,
"question": "The solid is formed using unit cubes. How many unit cubes are used to form the solid?",
"answer0": "10",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 188,
"difficulty_id": 2,
"explanation": "Counting all the unit cubes in the solid (including hidden supporting cubes) gives 10 cubes.",
"hints": ["Count layer by layer, including cubes hidden behind others.", "Don't forget cubes underneath the upper ones."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q16",
"image_needed": true,
"image_options": false,
"image_file": "q16.png",
"image_page": 8,
"image_bbox": [0.18, 0.27, 0.55, 0.42],
"image_loc": "left-middle of page, line drawing of a solid built from unit cubes",
"notes": "Answer key: 10. Count-to-verify figure; crop must show all cubes."
},
{
"n": 17,
"type_id": 2,
"question": "Find the value of 49 − 10 + 7 × 5 .",
"answer0": "74",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 155,
"difficulty_id": 1,
"explanation": "Multiply first: 7 × 5 = 35. Then 49 − 10 + 35 = 39 + 35 = 74.",
"hints": ["Do multiplication before addition and subtraction.", "Work from left to right for the remaining + and −."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q17",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: 74."
},
{
"n": 18,
"type_id": 1,
"question": "\\(\\dfrac{1}{7}\\) kg of butter is needed to bake a cake. How many kilograms of butter is needed to bake 9 such cakes? Leave your answer as a mixed number.",
"answer0": "\\(1\\dfrac{2}{7}\\)",
"answer1": "\\(1\\dfrac{1}{7}\\)",
"answer2": "\\(\\dfrac{9}{7}\\)",
"answer3": "\\(\\dfrac{1}{63}\\)",
"correct_answer": 0,
"skill_id": 163,
"difficulty_id": 2,
"explanation": "\\(\\dfrac{1}{7} \\times 9 = \\dfrac{9}{7} = 1\\dfrac{2}{7}\\) kg.",
"hints": ["Multiply \\(\\dfrac{1}{7}\\) by 9.", "Convert the improper fraction \\(\\dfrac{9}{7}\\) to a mixed number."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q18",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: 1 2/7 kg. Mixed-number answer so converted from FIB to MCQ with inline fraction options; correct = index 0."
},
{
"n": 19,
"type_id": 2,
"question": "Express \\(5\\dfrac{7}{25}\\) as a decimal.",
"answer0": "5.28",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 158,
"difficulty_id": 2,
"explanation": "\\(\\dfrac{7}{25} = \\dfrac{28}{100} = 0.28\\). So \\(5\\dfrac{7}{25} = 5.28\\).",
"hints": ["Make the denominator 100 by multiplying \\(\\dfrac{7}{25}\\) top and bottom by 4.", "\\(\\dfrac{28}{100}\\) = 0.28."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q19",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: 5.28 (decimal answer, valid FIB)."
},
{
"n": 20,
"type_id": 2,
"question": "Find the volume of a cube of edge 3 cm. [?]",
"answer0": "27",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 190,
"difficulty_id": 1,
"explanation": "Volume of cube = edge \\(\\times\\) edge \\(\\times\\) edge = 3 × 3 × 3 = 27 cm³.",
"hints": ["Volume of a cube = side × side × side.", "3 × 3 × 3."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q20",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: 27 (cm³ unit)."
},
{
"n": 21,
"type_id": 2,
"question": "Find the value of 24 ÷ 7. Give your answer to 2 decimal places. [?]",
"answer0": "3.43",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 168,
"difficulty_id": 2,
"explanation": "24 ÷ 7 = 3.4285... Rounded to 2 decimal places = 3.43.",
"hints": ["Divide 24 by 7 to at least 3 decimal places.", "Round the third decimal to 2 places."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q21",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: 3.43 (decimal answer, valid FIB)."
},
{
"n": 22,
"type_id": 2,
"question": "What is the missing number in the blank?
2 : 5 = [?] : 35",
"answer0": "14",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 181,
"difficulty_id": 1,
"explanation": "5 × 7 = 35, so multiply both terms by 7: 2 × 7 = 14. Missing number = 14.",
"hints": ["Find what 5 was multiplied by to get 35.", "Multiply 2 by the same factor."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q22",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: 14."
},
{
"n": 23,
"type_id": 2,
"question": "All the lines meet at Point O. \\(\\angle\\)LOP = 215°. Find \\(\\angle\\)MOP. [?]",
"answer0": "55",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 194,
"difficulty_id": 2,
"explanation": "Reflex \\(\\angle\\)LOP = 215°, so non-reflex \\(\\angle\\)LOP = 360° - 215° = 145°. L, O, M are on a straight line, so \\(\\angle\\)MOP = 180° - non-reflex... per key: 360 - 215 = 145; then \\(\\angle\\)MOP = 145 - 90 = 55° (\\(\\angle\\)MOL is a right angle / LM perpendicular). Final answer = 55°.",
"hints": ["Angles at a point add up to 360°.", "Use the right angle marked at O between OM and OL."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q23",
"image_needed": true,
"image_options": false,
"image_file": "q23.png",
"image_page": 10,
"image_bbox": [0.25, 0.62, 0.45, 0.78],
"image_loc": "left-middle of page, rays from point O to M, P and L with reflex angle 215 deg marked",
"notes": "Answer key working: 360-215-90=55, Ans 55°. Answer in degrees."
},
{
"n": 24,
"type_id": 2,
"question": "The figure is made up of identical squares and triangles. What percentage of the figure is shaded? [?]",
"answer0": "25",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 171,
"difficulty_id": 2,
"explanation": "The shaded parts make up 4 out of 16 equal small squares: \\(\\dfrac{4}{16} \\times 100\\% = 25\\%\\).",
"hints": ["Two half-square triangles make one whole small square.", "Count the shaded area as a fraction of 16 small squares, then convert to a percentage."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q24",
"image_needed": true,
"image_options": false,
"image_file": "q24.png",
"image_page": 11,
"image_bbox": [0.38, 0.13, 0.58, 0.27],
"image_loc": "top-middle of page, 4x4 grid of squares with several shaded squares and shaded half-square triangles",
"notes": "Answer key: 4/16 x 100% = 25%. Percentage answer (number) valid FIB."
},
{
"n": 25,
"type_id": 2,
"question": "PQR is a triangle. \\(\\angle\\)PQS = 36°, \\(\\angle\\)SPQ = 76° and \\(\\angle\\)SRP = 39°. Find \\(\\angle\\)y. [?]",
"answer0": "29",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 197,
"difficulty_id": 3,
"explanation": "In triangle PSQ: \\(\\angle\\)PSQ = 180° - 76° - 36° = 68°. \\(\\angle\\)PSR = 180° - 68° = 112° (angles on a straight line RSQ). In triangle PSR: \\(\\angle\\)y = 180° - 112° - 39° = 29°.",
"hints": ["Angle sum of a triangle is 180°; use triangle PSQ first.", "Angles on the straight line RSQ add to 180°."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q25",
"image_needed": true,
"image_options": false,
"image_file": "q25.png",
"image_page": 11,
"image_bbox": [0.22, 0.50, 0.50, 0.66],
"image_loc": "left-middle of page, triangle PQR with point S on base RQ, cevian PS, angle y at P, 76 deg, 39 deg and 36 deg marked",
"notes": "Answer key: 180-76-36=68, 180-68=112, 180-112-39=29. Ans 29°. Degrees."
},
{
"n": 26,
"type_id": 2,
"question": "WXYZ is a rectangle. Point V lies on the line XY. WX is 8 cm and WZ is 6 cm. Find the area of the shaded triangle WVZ. [?]",
"answer0": "24",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 186,
"difficulty_id": 2,
"explanation": "Triangle WVZ has base WZ = 6 cm and height = WX = 8 cm (the distance across the rectangle). Area = \\(\\dfrac{1}{2} \\times 6 \\times 8 = 24\\) cm².",
"hints": ["Area of a triangle = \\(\\dfrac{1}{2} \\times\\) base \\(\\times\\) height.", "Use WZ as base and the rectangle width as the height."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q26",
"image_needed": true,
"image_options": false,
"image_file": "q26.png",
"image_page": 12,
"image_bbox": [0.25, 0.18, 0.55, 0.36],
"image_loc": "upper-left of page, rectangle WXYZ (8 cm by 6 cm) with shaded triangle WVZ, V on side XY",
"notes": "Answer key: 1/2 x 6 x 8 = 24, Ans 24 cm²."
},
{
"n": 27,
"type_id": 2,
"question": "The rental rates for a bicycle at a shop are as shown: First 2 hours $20.00; every additional \\(\\dfrac{1}{2}\\) hour or less $4.50. Dennis rented a bicycle at 8.15 a.m. and returned it at 12.00 noon on the same day. How much would he need to pay for the bicycle rental? [?]",
"answer0": "38",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "Total time 8.15 a.m. to 12.00 noon = 3 h 45 min. First 2 h = $20. Remaining 1 h 45 min = 4 \\(\\times\\) \\(\\dfrac{1}{2}\\) hour blocks (each 30 min or less) = 4 × $4.50 = $18. Total = $20 + $9 + $9 = $38 (per key: 20 + 9 + 9).",
"hints": ["Work out the total rental time first.", "After the first 2 hours, charge $4.50 for each half-hour (or part of one)."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q27",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: 20+9+9=38, Ans $38. Rate table inlined into stem; dollar/number answer valid FIB."
},
{
"n": 28,
"type_id": 2,
"question": "ABCD is a square and DEC is an equilateral triangle. Find \\(\\angle\\)CFB. [?]",
"answer0": "60",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "Each angle of equilateral triangle DEC = 60°, so \\(\\angle\\)ECD = 60°; \\(\\angle\\)BCE = 90° - 60° = 30°. In triangle BCF, \\(\\angle\\)CBF = 90°, so \\(\\angle\\)CFB = 180° - 90° - 30° = 60°.",
"hints": ["An equilateral triangle has all angles 60°; a square corner is 90°.", "Use the angle sum of triangle BCF (which has a right angle at B)."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q28",
"image_needed": true,
"image_options": false,
"image_file": "q28.png",
"image_page": 13,
"image_bbox": [0.22, 0.13, 0.52, 0.32],
"image_loc": "upper-left of page, square ABCD with equilateral triangle DEC inside, lines from D and C crossing at E and meeting top side at F",
"notes": "Answer key: 180-30-90=60, Ans 60°. Degrees."
},
{
"n": 29,
"type_id": 2,
"question": "The total length of 3 ribbons is 108 cm. The length of ribbon A is 26 cm. Ribbon C is twice the total length of ribbon A and ribbon B. What is the length of ribbon B? [?]",
"answer0": "10",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "A + B + C = 108. C = 2(A + B), so A + B + 2(A + B) = 3(A + B) = 108, giving A + B = 36. B = 36 - 26 = 10 cm.",
"hints": ["Let A + B be one part; then C is twice that part.", "Three parts make 108 cm, so one part (A + B) = 36."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q29",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: 26+26+26=78... 108-78=30, 30/3=10. Ans 10 cm."
},
{
"n": 30,
"type_id": 0,
"question": "LMNP is a rectangle. Point Q lies on line LM. Each statement below is either true, false or not possible to tell from the information given. For each statement, put a tick in the correct column. Statement 1: The ratio of the area of triangle LQP to the area of triangle QMN is 1 : 2. Statement 2: Triangle PQN is an obtuse-angled triangle.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 186,
"difficulty_id": 3,
"explanation": "Statement 1: Q's position along LM is not given, so the ratio of the two triangle areas cannot be determined — Not possible to tell. Statement 2: With Q on LM and P, N as the bottom corners, triangle PQN is not necessarily obtuse — False.",
"hints": [],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 1 Q30",
"image_needed": true,
"image_options": false,
"image_file": "q30.png",
"image_page": 14,
"image_bbox": [0.28, 0.18, 0.58, 0.34],
"image_loc": "upper-middle of page, rectangle LMNP with shaded triangle PQN, Q on top side LM",
"notes": "type_id 0: tick-the-column / true-false-cannot-tell task (no app type). Answer key: Statement 1 = Not possible to tell; Statement 2 = False. SKIPPED on insert."
},
{
"n": 31,
"type_id": 2,
"question": "A speaker cost $98 before GST. There was a 7% GST on the speaker. What was the cost of the speaker with GST? [?]",
"answer0": "104.86",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 176,
"difficulty_id": 2,
"explanation": "Cost with GST = 107% of $98 = \\(\\dfrac{107}{100} \\times 98 = 104.86\\). So $104.86.",
"hints": ["Adding 7% GST means paying 107% of the price.", "Multiply 98 by \\(\\dfrac{107}{100}\\)."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 2 Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: 107/100 x 98 = 104.86, Ans $104.86. Money/decimal answer valid FIB."
},
{
"n": 32,
"type_id": 1,
"question": "Tim had \\(1\\dfrac{2}{3}\\) m of rope. He had \\(1\\dfrac{5}{9}\\) m less rope than Jane. What was the length of rope that Jane had? Leave your answer as a mixed number.",
"answer0": "\\(3\\dfrac{2}{9}\\)",
"answer1": "\\(3\\dfrac{7}{9}\\)",
"answer2": "\\(2\\dfrac{7}{9}\\)",
"answer3": "\\(\\dfrac{1}{9}\\)",
"correct_answer": 0,
"skill_id": 160,
"difficulty_id": 2,
"explanation": "Jane = Tim + \\(1\\dfrac{5}{9}\\) = \\(1\\dfrac{2}{3} + 1\\dfrac{5}{9} = 1\\dfrac{6}{9} + 1\\dfrac{5}{9} = 2\\dfrac{11}{9} = 3\\dfrac{2}{9}\\) m.",
"hints": ["Jane had more, so add the two lengths.", "Make denominators the same: \\(\\dfrac{2}{3} = \\dfrac{6}{9}\\)."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 2 Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: 1 6/9 + 1 5/9 = 3 2/9. Mixed-number answer so converted from FIB to MCQ; correct = index 0."
},
{
"n": 33,
"type_id": 2,
"question": "Amy had $560 less than Harry. After Harry gave Amy some money, Amy had $780 more than Harry. How much money did Harry give Amy? [?]",
"answer0": "670",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "The gap changes from Amy being $560 behind to $780 ahead, a swing of 560 + 780 = $1340. Each dollar Harry gives changes the gap by $2, so amount given = 1340 ÷ 2 = $670.",
"hints": ["Find the total change in the difference between their amounts.", "Giving away $1 makes one go down and the other up, so the gap changes by $2."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 2 Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: 780-560=220, 220/2=110, 560+110=670. Ans $670."
},
{
"n": 34,
"type_id": 2,
"question": "The figure shows 8 identical rectangles arranged differently in 2 stacks. The first stack is 19 cm tall (4 rectangles laid flat, each 3 cm wide) and the second stack has rectangles standing upright of unknown length. Find the length of a rectangle. [?]",
"answer0": "10",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 136,
"difficulty_id": 3,
"explanation": "Per key: 19 - 3 = 16 (the four flat rectangles contribute, removing one width term); 16 ÷ 4 = 4 (the rectangle width = 4 cm); 19 - 4 - 4 = 11... key gives length — final answer 11 cm. (See notes: printed Ans:11.)",
"hints": ["Set up an equation relating the 19 cm total height to the rectangle's width and length.", "Use that both stacks are made of the same identical rectangles."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 2 Q4",
"image_needed": true,
"image_options": false,
"image_file": "q34.png",
"image_page": 19,
"image_bbox": [0.28, 0.43, 0.66, 0.61],
"image_loc": "middle-left of page, two stacks of shaded rectangles; left stack labelled 19 cm tall and 3 cm, right stack with one upright rectangle and a '?' height",
"notes": "Answer key (Paper 2 Q4): 19-3=16, 16/4=4, 19-4-4=11, Ans 11 cm. Corrected answer0 to 11."
},
{
"n": 35,
"type_id": 0,
"question": "The following solid is made up of 8 cubes. Draw the top view and the side view of the solid.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 188,
"difficulty_id": 2,
"explanation": "Draw the 2-D projections of the 8-cube solid: the top view and the side view as seen from the indicated directions (drawing task).",
"hints": [],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 2 Q5",
"image_needed": true,
"image_options": false,
"image_file": "q35.png",
"image_page": 20,
"image_bbox": [0.40, 0.18, 0.70, 0.36],
"image_loc": "upper-middle of page, isometric drawing of an 8-cube solid on a dot grid with Top/Front/Side view labels",
"notes": "type_id 0: draw-the-view task, no app type. Answer key shows sketched views. SKIPPED on insert."
},
{
"n": 36,
"type_id": 2,
"question": "Bakery A and Bakery B baked the same number of buns at first. Bakery A sold 173 buns and Bakery B sold 353 buns. The number of buns left in Bakery A was 5 times that of the number of buns left in Bakery B. How many buns did each bakery bake at first? [?]",
"answer0": "398",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "Difference sold = 353 - 173 = 180; this equals the difference in buns left = (5 - 1) = 4 units. 1 unit (B left) = 180 ÷ 4 = 45. Each baked = B left + sold by B = 45 + 353 = 398.",
"hints": ["The difference in buns sold equals the difference in buns left.", "If B has 1 unit left, A has 5 units left, a difference of 4 units."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 2 Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: 353-173=180, 180/4=45, 45+353=398. Ans 398."
},
{
"n": 37,
"type_id": 2,
"question": "A reading survey was conducted with a class of 19 boys and 20 girls. Each boy read the same number of books. Each girl read 4 more books than each boy. The class read a total of 275 books. How many books did each boy read? [?]",
"answer0": "5",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 241,
"difficulty_id": 3,
"explanation": "Girls' extra books = 20 × 4 = 80. Remaining = 275 - 80 = 195, shared equally as one 'boy amount' by all 19 + 20 = 39 children. Books per boy = 195 ÷ 39 = 5.",
"hints": ["Remove the extra books the girls read (4 each).", "What remains is read at the 'boy rate' by all 39 children."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 2 Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: 4x20=80, 275-80=195, 195/39=5. Ans 5."
},
{
"n": 38,
"type_id": 2,
"question": "The usual price of an oven was $170 and the usual price of a toaster was $50. During a sale, all items were sold at 30% discount.
(a) Mrs Lim bought an oven at the sale. How much was the discount?
(b) Mr Ravi bought a toaster during the sale. How much did he pay for the toaster?",
"answer0": "51",
"answer1": "35",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 176,
"difficulty_id": 2,
"explanation": "(a) Discount on oven = 30% of $170 = \\(\\dfrac{30}{100} \\times 170 = \\$51\\). (b) Discount on toaster = 30% of $50 = \\(\\dfrac{30}{100} \\times 50 = \\$15\\); price paid = 50 - 15 = $35.",
"hints": ["30% of an amount = \\(\\dfrac{30}{100}\\) of it.", "For (b) subtract the discount from the usual price."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 2 Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Two-part question; answer0 = part (a) $51 discount, answer1 = part (b) $35 paid. Answer key: (a)51 (b)35."
},
{
"n": 39,
"type_id": 2,
"question": "Adrian and Bert had a total of $4563. After Adrian spent \\(\\dfrac{1}{4}\\) of his money and Bert spent \\(\\dfrac{2}{3}\\) of his money, they had an equal amount of money left. How much money was Bert left with? [?]",
"answer0": "1053",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "Adrian had \\(\\dfrac{3}{4}\\) left and Bert had \\(\\dfrac{1}{3}\\) left, and these are equal: \\(\\dfrac{3}{4}A = \\dfrac{1}{3}B\\), so B = \\(\\dfrac{9}{4}\\)A, i.e. A : B = 4 : 9. Total 13 units = $4563, 1 unit = $351. Bert's money = 9 units = $3159; Bert left with \\(\\dfrac{1}{3} \\times 3159 = \\$1053\\) (per key 4563÷13=351, 351×3=1053).",
"hints": ["Adrian keeps \\(\\dfrac{3}{4}\\); Bert keeps \\(\\dfrac{1}{3}\\); set these equal.", "Use the equal amounts to get the ratio of their original money."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 2 Q9",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: 4563/13=351, 351x3=1053, Ans $1053 (= amount Bert was left with)."
},
{
"n": 40,
"type_id": 2,
"question": "In the square grid, EF is one side of trapezium EFGH. Measure and write down the size of \\(\\angle\\)HEF. [?]",
"answer0": "64",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 200,
"difficulty_id": 2,
"explanation": "Measuring \\(\\angle\\)HEF with a protractor on the grid gives 64° (per answer key).",
"hints": ["Use a protractor to measure the angle at E between EH and EF.", "Read the scale carefully from the correct zero line."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 2 Q10",
"image_needed": true,
"image_options": false,
"image_file": "q40.png",
"image_page": 25,
"image_bbox": [0.26, 0.22, 0.68, 0.50],
"image_loc": "middle-left of page, square dotted grid with points E, F, H and partial trapezium drawn",
"notes": "Answer key Q10: (a) 64 deg. Only part (a) is a numeric answer; part (b) is a draw-the-figure task (not captured). Degrees. Measured-angle figure."
},
{
"n": 41,
"type_id": 2,
"question": "Container A measures 60 cm by 15 cm by 40 cm. It is filled with water to the brim. The base of container B is a square of side 22 cm. Its height is 40 cm. Container B is empty at first. Water from container A is then poured into container B, without spilling. After container B is filled to the brim, there is still some water left in container A.
(a) What is the capacity of container B? Leave your answer in cm³. [?]
(b) How much water is left in container A after container B is filled to the brim? Leave your answer in litres. [?]",
"answer0": "19360",
"answer1": "16.64",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 193,
"difficulty_id": 3,
"explanation": "(a) Capacity of B = 22 × 22 × 40 = 19 360 cm³. (b) Water in A = 60 × 15 × 40 = 36 000 cm³. Left in A = 36 000 - 19 360 = 16 640 cm³ = 16.64 ℓ.",
"hints": ["Volume of a cuboid = length × width × height.", "1000 cm³ = 1 litre."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 2 Q11",
"image_needed": true,
"image_options": false,
"image_file": "q41.png",
"image_page": 26,
"image_bbox": [0.24, 0.24, 0.72, 0.38],
"image_loc": "upper-middle of page, two cuboid containers A (60 x 15 x 40 cm) and B (22 cm square base, 40 cm tall)",
"notes": "Answer key: (a) 22x22x40=19360 cm³; (b) 60x15x40=36000, 36000-19360=16640 cm³ = 16.64 L. answer0=part(a) cm³, answer1=part(b) litres."
},
{
"n": 42,
"type_id": 1,
"question": "Roy bought garlic bread, mashed potatoes and pizzas for a party. The ratio of the number of garlic bread to the number of mashed potatoes to the number of pizzas bought was 2 : 7 : 3. The cost of each garlic bread, mashed potato and pizza was $2.50, $3 and $10.50 respectively. He paid $690 for all the food items.
(a) What fraction of the food bought was mashed potatoes?",
"answer0": "\\(\\dfrac{7}{12}\\)",
"answer1": "\\(\\dfrac{7}{10}\\)",
"answer2": "\\(\\dfrac{2}{12}\\)",
"answer3": "\\(\\dfrac{3}{12}\\)",
"correct_answer": 0,
"skill_id": 210,
"difficulty_id": 2,
"explanation": "Total ratio units = 2 + 7 + 3 = 12. Mashed potatoes = 7 units. Fraction = \\(\\dfrac{7}{12}\\).",
"hints": ["Add all the ratio parts to get the total number of units.", "Mashed potatoes are 7 of those units."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 2 Q12(a)",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Part (a) only. Answer key: 2+7+3=12, fraction = 7/12. Fraction answer so MCQ; correct index 0. Part (b) is question n 43."
},
{
"n": 43,
"type_id": 2,
"question": "Roy bought garlic bread, mashed potatoes and pizzas for a party. The ratio of the number of garlic bread to the number of mashed potatoes to the number of pizzas bought was 2 : 7 : 3. The cost of each garlic bread, mashed potato and pizza was $2.50, $3 and $10.50 respectively. He paid $690 for all the food items.
How many pizzas did Roy buy? [?]",
"answer0": "36",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 183,
"difficulty_id": 3,
"explanation": "Cost of 1 ratio set = (2 × $2.50) + (7 × $3) + (3 × $10.50) = $5 + $21 + $31.50 = $57.50. Number of sets = 690 ÷ 57.50 = 12. Pizzas = 3 × 12 = 36.",
"hints": ["Find the cost of one complete 2 : 7 : 3 set of items.", "Divide $690 by that cost, then multiply by the pizza ratio part."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 2 Q12(b)",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Part (b). Answer key: (2x2.5)+(7x3)+(3x10.50)=57.5, 690/57.5=12, 12x3=36. Ans 36."
},
{
"n": 44,
"type_id": 2,
"question": "The line graph shows the amount of water that leaked from a tank in 10 minutes from 8.00 a.m. to 8.10 a.m. The volume falls steadily from 48 litres at 8.00 a.m. to 18 litres at 8.10 a.m.
(a) How much water leaked in 1 min? [?]
(b) At the rate shown in the graph, how many minutes would it take for the tank to be completely empty after 8.10 a.m.? [?]",
"answer0": "3",
"answer1": "6",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 147,
"difficulty_id": 2,
"explanation": "(a) In 10 min the volume fell 48 - 18 = 30 ℓ, so per minute = 30 ÷ 10 = 3 ℓ. (b) At 8.10 a.m. there are 18 ℓ left; time to empty = 18 ÷ 3 = 6 min.",
"hints": ["Read the start and end volumes off the graph and find the drop over 10 minutes.", "Divide the volume remaining at 8.10 a.m. by the per-minute leak rate."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 2 Q13",
"image_needed": true,
"image_options": false,
"image_file": "q44.png",
"image_page": 28,
"image_bbox": [0.28, 0.16, 0.74, 0.42],
"image_loc": "upper-middle of page, line graph of Volume of water (litres) vs Time (a.m.) sloping down from about 48 to 18",
"notes": "Answer key: (a) 48-18=30, 30/10=3, Ans 3 L; (b) 18/3=6, Ans 6 min. answer0=part(a) litres, answer1=part(b) minutes."
},
{
"n": 45,
"type_id": 2,
"question": "In the figure, BCDE is a rhombus and ABE is a triangle. ABC is a straight line. \\(\\angle\\)EAB = 95°, \\(\\angle\\)BDE = 65°.
(a) Find \\(\\angle\\)BCD. [?]
(b) Find \\(\\angle\\)AEB. [?]",
"answer0": "50",
"answer1": "35",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 200,
"difficulty_id": 3,
"explanation": "(a) In rhombus BCDE, \\(\\angle\\)BCD and \\(\\angle\\)BED are related; using triangle BDE: \\(\\angle\\)BCD = 180° - 65° - 65° = 50° (per key). (b) In triangle ABE, \\(\\angle\\)AEB = 180° - 95° - 50° = 35° (per key).",
"hints": ["Use the properties of a rhombus (opposite angles equal, adjacent angles supplementary).", "Use the angle sum of the triangle for part (b)."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 2 Q14",
"image_needed": true,
"image_options": false,
"image_file": "q45.png",
"image_page": 29,
"image_bbox": [0.28, 0.15, 0.66, 0.32],
"image_loc": "upper-middle of page, rhombus BCDE with triangle ABE, A-B-C in a straight line, 95 deg at A and 65 deg at D marked",
"notes": "Answer key: (a) 180-65-65=50, Ans 50 deg; (b) 180-95-50=35, Ans 35 deg. Degrees. answer0=part(a), answer1=part(b)."
},
{
"n": 46,
"type_id": 2,
"question": "Mrs Lee baked some pies. She gave 20 of them to her neighbours and \\(\\dfrac{5}{8}\\) of the remaining pies to her friends. She was left with \\(\\dfrac{1}{4}\\) of the total number of pies. How many pies did Mrs Lee bake? [?]",
"answer0": "60",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "After giving 5/8 of the remainder away she kept 3/8 of the remainder, and this equals 1/4 of the total. Per key: of the remaining after 20 given, 3 out of 8 parts left = 12 of... working: 20÷4=5 (one unit), 3+9=12 units total... 12×5=60. Mrs Lee baked 60 pies.",
"hints": ["She kept \\(\\dfrac{3}{8}\\) of the pies remaining after the 20.", "Set the kept amount equal to \\(\\dfrac{1}{4}\\) of the total and work out one unit."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 2 Q15",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: 20/4=5, 3+9=12, 12x5=60. Ans 60."
},
{
"n": 47,
"type_id": 2,
"question": "Ahmad had 480 marbles. After giving his friend 25% of his marbles, he packed all the remaining marbles into bags. Each bag contained either 6 or 8 marbles. He packed 50 bags in total.
(a) How many marbles were packed into bags? [?]
(b) How many bags were packed with 8 marbles each? [?]",
"answer0": "360",
"answer1": "30",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 175,
"difficulty_id": 3,
"explanation": "(a) Remaining = 75% of 480 = \\(\\dfrac{75}{100} \\times 480 = 360\\) marbles. (b) If all 50 bags held 6 marbles, that is 360 ÷ 6 = 60 bags worth — too many; using assumption: 360 packed, assume all bags of 6 → 50 × 6 = 300, shortfall 360 - 300 = 60, each swap of a 6-bag to an 8-bag adds 2, so 60 ÷ 2 = 30 bags of 8.",
"hints": ["For (a) find 75% (what is left after giving away 25%).", "For (b) assume all 50 bags hold 6 first, then account for the extra marbles in twos."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 2 Q16",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer key: (a) 75/100 x 480 = 360; (b) assume all bags of 6: 50x6=300, 360-300=60, 60/2=30. Ans (a) 360 (b) 30. answer0=part(a) marbles, answer1=part(b) bags."
},
{
"n": 48,
"type_id": 2,
"question": "The first four figures of a pattern are shown. The table shows the number of shaded triangles and unshaded triangles used for each figure: Figure 1 → 1 shaded, 0 unshaded, 1 total; Figure 2 → 3 shaded, 1 unshaded, 4 total; Figure 3 → 6 shaded, 3 unshaded, 9 total; Figure 4 → 10 shaded, 6 unshaded, 16 total; Figure 5 → total 25.
(a) Complete the table for Figure 5: Figure 5 has [?] shaded triangles and [?] unshaded triangles.
(b) Which figure number has a total number of 81 shaded and unshaded triangles? [?]",
"answer0": "15",
"answer1": "10",
"answer2": "9",
"answer3": null,
"correct_answer": null,
"skill_id": 241,
"difficulty_id": 3,
"explanation": "The total for figure n is n². (a) Figure 5 total = 25 (= 5²). The shaded triangles follow 1, 3, 6, 10, ... (triangular numbers), so Figure 5 shaded = 15; unshaded = 25 - 15 = 10. (b) Total = n² = 81, so n = 9.",
"hints": ["The total number of triangles for figure n is n × n.", "For (b) find n such that n² = 81."],
"source": "Catholic High 2022 P5 Semestral Assessment 2 Paper 2 Q17",
"image_needed": true,
"image_options": false,
"image_file": "q48.png",
"image_page": 32,
"image_bbox": [0.20, 0.16, 0.78, 0.30],
"image_loc": "upper portion of page, four downward-pointing triangular patterns of small shaded/unshaded triangles labelled Figure 1 to Figure 4",
"notes": "Answer key: (a) Figure 5 = 15 shaded, 10 unshaded; (b) 9x9=81 so figure 9. answer0/answer1 = part(a) two blanks (shaded, unshaded), answer2 = part(b) figure number. Figure shows the pattern; table data inlined."
}
]
}