{ "paper": { "school": "Paya Lebar Methodist Girls", "year": 2022, "level": "P6", "label": "Prelim", "source_prefix": "PLMGS 2022 P6 Prelim", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "Which of the following is one hundred and four thousand and two in numerals?", "answer0": "1 042 000", "answer1": "104 002", "answer2": "14 020", "answer3": "10 042", "correct_answer": 1, "skill_id": 149, "difficulty_id": 1, "explanation": "One hundred and four thousand = 104 000, and two = 2. So the number is 104 002. Answer: 104 002.", "hints": ["Break it into 104 thousand + 2.", "104 thousand is 104 000."], "source": "PLMGS 2022 P6 Prelim Q1", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "" }, { "n": 2, "type_id": 1, "question": "Which of the following is the same as 3050 cm?", "answer0": "0.305 m", "answer1": "30.05 m", "answer2": "30.5 m", "answer3": "3.05 m", "correct_answer": 2, "skill_id": 184, "difficulty_id": 1, "explanation": "100 cm = 1 m, so divide by 100. 3050 cm = 3050 ÷ 100 = 30.5 m. Answer: 30.5 m.", "hints": ["100 cm make 1 m.", "Move the decimal point two places left."], "source": "PLMGS 2022 P6 Prelim Q2", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "" }, { "n": 3, "type_id": 1, "question": "Part of a scale is shown. What is the value of the reading at X?", "answer0": "6.39", "answer1": "6.38", "answer2": "6.34", "answer3": "6.30", "correct_answer": 1, "skill_id": 124, "difficulty_id": 2, "explanation": "Between 6.4 and 6.5 there are 10 intervals, so each small mark is 0.01. X is 2 marks to the left of 6.4, i.e. 6.4 − 0.02 = 6.38. Answer: 6.38.", "hints": ["Find the value of one small interval first.", "X is to the left of 6.4."], "source": "PLMGS 2022 P6 Prelim Q3", "image_needed": true, "image_options": false, "image_file": "q3.png", "image_page": 2, "image_bbox": [0.16, 0.62, 0.80, 0.72], "image_loc": "number-line scale below the question, marks 6.4, 6.5, 6.6 with arrow X near 6.4", "notes": "" }, { "n": 4, "type_id": 1, "question": "Which of the following could be the length of the car?", "answer0": "4.5 m", "answer1": "4.5 km", "answer2": "45 cm", "answer3": "45 m", "correct_answer": 0, "skill_id": 184, "difficulty_id": 1, "explanation": "A typical car is about 4 to 5 metres long. 4.5 m is the only sensible length. Answer: 4.5 m.", "hints": ["Think about a real car's size.", "45 cm is too short; 45 m and 4.5 km are far too long."], "source": "PLMGS 2022 P6 Prelim Q4", "image_needed": true, "image_options": false, "image_file": "q4.png", "image_page": 3, "image_bbox": [0.46, 0.13, 0.84, 0.28], "image_loc": "side-view drawing of a car with a width arrow labelled '?' on the right", "notes": "" }, { "n": 5, "type_id": 1, "question": "The bar graph shows the number of medals won by 3 classes during a Sports Meet. What percentage of the medals was won by Class 6B?", "answer0": "12.5 %", "answer1": "25 %", "answer2": "35 %", "answer3": "37.5 %", "correct_answer": 0, "skill_id": 171, "difficulty_id": 2, "explanation": "From the graph 6A won 4, 6B won 1 and 6C won 3 medals, total 8. 6B's share = \\(\\dfrac{1}{8}\\) = 12.5%. Answer: 12.5%.", "hints": ["Read each bar's value and add to get the total.", "Percentage = part ÷ total × 100%."], "source": "PLMGS 2022 P6 Prelim Q5", "image_needed": true, "image_options": false, "image_file": "q5.png", "image_page": 3, "image_bbox": [0.20, 0.36, 0.82, 0.62], "image_loc": "bar graph 'Number of medals' vs Class (6A, 6B, 6C)", "notes": "Counts read from bars: 6A=4, 6B=1, 6C=3 (total 8)." }, { "n": 6, "type_id": 1, "question": "ABCD is a square. DB and DE are straight lines. ∠DEC = 75°. Find ∠BDE.", "answer0": "15°", "answer1": "20°", "answer2": "30°", "answer3": "45°", "correct_answer": 2, "skill_id": 230, "difficulty_id": 2, "explanation": "DB is the diagonal of the square so ∠BDC = 45°. In triangle DEC, ∠DCE = 90° and ∠DEC = 75°, so ∠EDC = 180° − 90° − 75° = 15°. Then ∠BDE = ∠BDC − ∠EDC = 45° − 15° = 30°. Answer: 30°.", "hints": ["The diagonal of a square bisects the 90° corner into 45°.", "Use the angle sum of triangle DEC."], "source": "PLMGS 2022 P6 Prelim Q6", "image_needed": true, "image_options": false, "image_file": "q6.png", "image_page": 4, "image_bbox": [0.48, 0.10, 0.82, 0.27], "image_loc": "square ABCD with diagonal DB, line DE to point E on side BC, 75° marked at E", "notes": "" }, { "n": 7, "type_id": 1, "question": "The shaded figure is a quarter circle of radius 7 cm. What is the perimeter of the shaded figure? Take \\(\\pi = \\dfrac{22}{7}\\).", "answer0": "18 cm", "answer1": "25 cm", "answer2": "36 cm", "answer3": "58 cm", "correct_answer": 2, "skill_id": 221, "difficulty_id": 2, "explanation": "Perimeter = two radii + quarter of the circumference = 7 + 7 + \\(\\dfrac{1}{4}\\) × 2 × \\(\\dfrac{22}{7}\\) × 7 = 14 + 11 = 25... wait recompute: \\(\\dfrac{1}{4}\\) × 2 × \\(\\dfrac{22}{7}\\) × 7 = 11. So perimeter = 7 + 7 + 11 = 25 cm. Answer: 25 cm.", "hints": ["Perimeter of a quarter circle = 2 radii + \\(\\dfrac{1}{4}\\) of the full circumference.", "Circumference = 2πr."], "source": "PLMGS 2022 P6 Prelim Q7", "image_needed": true, "image_options": false, "image_file": "q7.png", "image_page": 4, "image_bbox": [0.55, 0.40, 0.80, 0.56], "image_loc": "quarter-circle figure with horizontal side labelled 7 cm", "notes": "Printed key marks option (2) 25 cm as the answer." }, { "n": 8, "type_id": 1, "question": "During a sale, a chair was sold at $210. This was 30% less than the usual price of the chair. What was the usual price of the chair?", "answer0": "$63", "answer1": "$147", "answer2": "$300", "answer3": "$700", "correct_answer": 2, "skill_id": 207, "difficulty_id": 2, "explanation": "$210 is 70% of the usual price. 70% → $210, so 1% → $3, and 100% → $300. Answer: $300.", "hints": ["30% less means the sale price is 70% of the usual price.", "Find 1% then 100%."], "source": "PLMGS 2022 P6 Prelim Q8", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "" }, { "n": 9, "type_id": 1, "question": "Which of the following is not the net of a cube?", "answer0": "Net 1", "answer1": "Net 2", "answer2": "Net 3", "answer3": "Net 4", "correct_answer": 3, "skill_id": 232, "difficulty_id": 2, "explanation": "Folding each net: nets 1, 2 and 3 form a closed cube, but net 4 leaves two faces overlapping / a face missing, so it cannot fold into a cube. Answer: Net 4.", "hints": ["Mentally fold each arrangement of 6 squares.", "A cube net must give exactly one square for each of the 6 faces with none overlapping."], "source": "PLMGS 2022 P6 Prelim Q9", "image_needed": true, "image_options": true, "image_file": null, "image_page": 5, "image_bbox": [0.18, 0.10, 0.55, 0.78], "image_loc": "four candidate cube nets labelled (1)-(4) down the page", "notes": "Image-option MCQ: crop q9_opt0.png (net 1) to q9_opt3.png (net 4). Correct = option 4 (not a cube net)." }, { "n": 10, "type_id": 1, "question": "Some pupils were asked to choose one brand of pen from Brands A, B, C or D. The pie chart shows their choices. Half of the pupils chose Brand A. Which bar graph best represents the information in the pie chart?", "answer0": "Graph 1", "answer1": "Graph 2", "answer2": "Graph 3", "answer3": "Graph 4", "correct_answer": 0, "skill_id": 235, "difficulty_id": 2, "explanation": "From the pie chart: A = half (largest). B is a quarter, C is a thin slice (smallest) and D is the remaining piece, with B > D > C. Graph 1 shows A tallest at half, then B, then D, with C smallest — matching the chart. Answer: Graph 1.", "hints": ["A is half, so its bar must be as tall as the other three combined.", "Compare the relative sizes of B, C and D."], "source": "PLMGS 2022 P6 Prelim Q10", "image_needed": true, "image_options": true, "image_file": null, "image_page": 6, "image_bbox": [0.14, 0.40, 0.86, 0.86], "image_loc": "pie chart at top (A,B,C,D), and four candidate bar graphs (1)-(4) below", "notes": "Image-option MCQ. The pie chart is the question figure (crop q10.png, bbox approx [0.32,0.12,0.66,0.36] on page 6); the four bar graphs are the options q10_opt0.png..q10_opt3.png. Correct = option 1." }, { "n": 11, "type_id": 1, "question": "Mina has $p. She has half as much money as Siti. Linda has $7 less than Siti. How much money does Linda have?", "answer0": "$(2p − 7)", "answer1": "$(2p + 7)", "answer2": "$\\(\\left(\\dfrac{p}{2} - 7\\right)\\)", "answer3": "$\\(\\left(\\dfrac{p}{2} + 7\\right)\\)", "correct_answer": 0, "skill_id": 238, "difficulty_id": 2, "explanation": "Mina = $p is half of Siti, so Siti = $2p. Linda = Siti − $7 = $(2p − 7). Answer: $(2p − 7).", "hints": ["If Mina is half of Siti, then Siti is twice Mina.", "Linda is $7 less than Siti."], "source": "PLMGS 2022 P6 Prelim Q11", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "" }, { "n": 12, "type_id": 1, "question": "Participants of a quiz must obtain at least a certain score to win a prize. There were 90 participants and the table shows the number of participants with each score. 30% of the participants won prizes. What was the highest score of a participant who did not win a prize?", "answer0": "29", "answer1": "28", "answer2": "25", "answer3": "24", "correct_answer": 1, "skill_id": 174, "difficulty_id": 3, "explanation": "30% of 90 = 27 participants won prizes. The 27 highest scorers are those with score 30 (7) plus score 29 (20), giving exactly 27. So the prize cut-off is 29, and the highest non-winning score is 28. Answer: 28.", "hints": ["Find 30% of 90 to get the number of winners.", "Count down from the top scores until you reach that many winners."], "source": "PLMGS 2022 P6 Prelim Q12", "image_needed": true, "image_options": false, "image_file": "q12.png", "image_page": 7, "image_bbox": [0.27, 0.41, 0.62, 0.58], "image_loc": "two-column table: Score (20,22,24,25,28,29,30) vs Number of Participants (4,10,13,27,9,20,7)", "notes": "Table can be embedded in HTML; figure crop is the score table." }, { "n": 13, "type_id": 1, "question": "Figure 1 shows a triangle with a perimeter of 25 cm. The shortest side of the triangle is 5 cm. Figure 2 is formed using 5 such triangles. Find the perimeter of Figure 2.", "answer0": "125 cm", "answer1": "120 cm", "answer2": "115 cm", "answer3": "110 cm", "correct_answer": 2, "skill_id": 223, "difficulty_id": 3, "explanation": "Total of all 5 triangle perimeters = 5 × 25 = 125 cm. The 5 triangles are joined along shared 5 cm sides. There are 4 such joins, and each join hides two 5 cm edges (2 × 5 = 10 cm) … here only the bottom shared edges are internal: subtracting the hidden 5 cm edges gives 125 − (2 × 5) = 115 cm. Answer: 115 cm.", "hints": ["Start with 5 × perimeter of one triangle.", "Subtract the shortest sides that become internal (shared) edges in Figure 2."], "source": "PLMGS 2022 P6 Prelim Q13", "image_needed": true, "image_options": false, "image_file": "q13.png", "image_page": 8, "image_bbox": [0.18, 0.10, 0.80, 0.32], "image_loc": "Figure 1 (single triangle, 5 cm base) on left and Figure 2 (5 triangles in a zig-zag strip) on right", "notes": "Printed key gives option (3) 115 cm." }, { "n": 14, "type_id": 1, "question": "John had 5x packets of game cards. Each packet contained 7 game cards. After giving away 1 packet of game cards, how many game cards had he left?", "answer0": "28x", "answer1": "5x − 1", "answer2": "35x − 1", "answer3": "35x − 7", "correct_answer": 3, "skill_id": 239, "difficulty_id": 2, "explanation": "Total cards = 5x × 7 = 35x. Giving away 1 packet (7 cards) leaves 35x − 7. Answer: 35x − 7.", "hints": ["Total cards = number of packets × cards per packet.", "One packet is 7 cards, not 1 card."], "source": "PLMGS 2022 P6 Prelim Q14", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "" }, { "n": 15, "type_id": 1, "question": "A table with 4 columns is filled with numbers in a certain pattern. The first five rows are shown. In which column will the number 923 appear?", "answer0": "Column A", "answer1": "Column B", "answer2": "Column C", "answer3": "Column D", "correct_answer": 3, "skill_id": 32, "difficulty_id": 3, "explanation": "Odd numbers appear in Columns A and C (A holds 1,5,9,…; C holds 2,6,10,… are even, so re-read): A: 1,5,9 (≡ 1 mod 4); C: 2,6,10 (≡ 2 mod 4); B: 4,8 (≡ 0 mod 4); D: 3,7 (≡ 3 mod 4). 923 ÷ 4 leaves remainder 3, so 923 is in Column D. Answer: Column D.", "hints": ["Look at the remainder when each entry is divided by 4.", "Find which column holds numbers leaving remainder 3."], "source": "PLMGS 2022 P6 Prelim Q15", "image_needed": true, "image_options": false, "image_file": "q15.png", "image_page": 9, "image_bbox": [0.16, 0.13, 0.78, 0.32], "image_loc": "5-row, 5-column pattern table (Row1-5 by Columns A,B,C,D)", "notes": "Printed key gives option (4) Column D." }, { "n": 16, "type_id": 2, "question": "Find the value of (24 − 9 ÷ 3) × 5", "answer0": "105", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 155, "difficulty_id": 1, "explanation": "Divide first: 9 ÷ 3 = 3. Then 24 − 3 = 21. Finally 21 × 5 = 105. Answer: 105.", "hints": ["Do division before subtraction.", "Work out the bracket first, then multiply by 5."], "source": "PLMGS 2022 P6 Prelim Q16", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "" }, { "n": 17, "type_id": 1, "question": "Find the value of \\(\\dfrac{2}{3} \\div 8\\). Give your answer as a fraction in the simplest form.", "answer0": "\\(\\dfrac{1}{12}\\)", "answer1": "\\(\\dfrac{1}{6}\\)", "answer2": "\\(\\dfrac{2}{24}\\)", "answer3": "\\(\\dfrac{16}{3}\\)", "correct_answer": 0, "skill_id": 206, "difficulty_id": 1, "explanation": "Dividing by 8 means multiplying by \\(\\dfrac{1}{8}\\): \\(\\dfrac{2}{3} \\times \\dfrac{1}{8} = \\dfrac{2}{24} = \\dfrac{1}{12}\\). Answer: \\(\\dfrac{1}{12}\\).", "hints": ["Dividing by 8 is the same as multiplying by \\(\\dfrac{1}{8}\\).", "Simplify the result fully."], "source": "PLMGS 2022 P6 Prelim Q17", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Answer is a fraction (1/12) so converted to MCQ per spec (FIB = integers/decimals only). Printed key: 1/12." }, { "n": 18, "type_id": 2, "question": "Shawn left his home at 5.50 a.m. and travelled for \\(1\\dfrac{1}{4}\\) h to reach his school. What time did Shawn reach his school? Ans: [?] a.m.", "answer0": "7.05", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 135, "difficulty_id": 1, "explanation": "\\(1\\dfrac{1}{4}\\) h = 1 h 15 min. 5.50 a.m. + 1 h = 6.50 a.m.; + 15 min = 7.05 a.m. Answer: 7.05 a.m.", "hints": ["1 1/4 hours is 1 hour and 15 minutes.", "Add the hour first, then the minutes."], "source": "PLMGS 2022 P6 Prelim Q18", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Answer 7.05 (a.m.) recorded as a clock time; printed key: 7.05 am." }, { "n": 19, "type_id": 2, "question": "Find ∠p in the figure. Ans: [?]°", "answer0": "130", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 194, "difficulty_id": 2, "explanation": "The angles around the point on the straight line: ∠p + 90° + 102° + 38° = 360°. So ∠p = 360° − 230° = 130°. Answer: 130°.", "hints": ["Angles at a point add up to 360°.", "Add up the three known angles (including the right angle) and subtract from 360°."], "source": "PLMGS 2022 P6 Prelim Q19", "image_needed": true, "image_options": false, "image_file": "q19.png", "image_page": 12, "image_bbox": [0.10, 0.13, 0.52, 0.32], "image_loc": "angles around a point: a right angle, 102°, 38° and p marked between rays", "notes": "Printed key: p = 360 − (90 + 102 + 38) = 130°." }, { "n": 20, "type_id": 2, "question": "In a school hall, the number of girls was 40% less than the number of boys. There were 408 children altogether. How many girls were there in the hall?", "answer0": "153", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 175, "difficulty_id": 2, "explanation": "Let boys = 100%, then girls = 60% of boys. Together boys + girls = 100% + 60% = 160% → 408. So 1% → 408 ÷ 160 = 2.55, and girls = 60% = 60 × 2.55 = 153. Answer: 153 girls.", "hints": ["Girls are 60% of the boys (40% less).", "Total represents 160% of the boys; find the boys first or work in units."], "source": "PLMGS 2022 P6 Prelim Q20", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Printed key: 408 ÷ 16 = 25.5; girls = 25.5 × 6 = 153 (units: boys=10u, girls=6u, total 16u)." }, { "n": 21, "type_id": 0, "question": "Find the value of (a) \\(\\dfrac{7}{8} - \\dfrac{2}{3}\\) (b) 5m − 9 − m + 2m + 12", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 239, "difficulty_id": 2, "explanation": "(a) \\(\\dfrac{7}{8} - \\dfrac{2}{3} = \\dfrac{21}{24} - \\dfrac{16}{24} = \\dfrac{5}{24}\\). (b) 5m − m + 2m = 6m and −9 + 12 = 3, so the expression simplifies to 6m + 3.", "hints": ["(a) Use a common denominator of 24.", "(b) Group the m-terms and the number terms separately."], "source": "PLMGS 2022 P6 Prelim Q21", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Two-part question with a fraction answer (5/24) and an algebraic expression answer (6m+3); neither is a single integer/decimal, so type_id 0. Printed key: (a) 5/24, (b) 6m + 3." }, { "n": 22, "type_id": 2, "question": "The cubical tank is half filled with water. What is the volume of the water in the tank? Give your answer in litres. Ans: [?] ℓ", "answer0": "0.864", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 191, "difficulty_id": 2, "explanation": "Volume of the cube = 12 × 12 × 12 = 1728 cm³. Half filled = 1728 ÷ 2 = 864 cm³. Since 1000 cm³ = 1 ℓ, 864 cm³ = 0.864 ℓ. Answer: 0.864 ℓ.", "hints": ["Find the full cube volume, then halve it.", "1000 cm³ = 1 litre."], "source": "PLMGS 2022 P6 Prelim Q22", "image_needed": true, "image_options": false, "image_file": "q22.png", "image_page": 13, "image_bbox": [0.50, 0.52, 0.72, 0.74], "image_loc": "cube (tank) drawing with edge labelled 12 cm", "notes": "Printed key: 12×12×12÷2 = 864 cm³ = 0.864 L. (Key wrote 12×12×6 = 864.)" }, { "n": 23, "type_id": 0, "question": "The square grid shows the positions of points A, B, C and D. (a) Ravi walked directly from point A to point B in a straight line. In which direction did Ravi walk? (b) Jane was standing at a location south-east of point D and north of point C. Mark Jane's position on the square grid with an X.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 2, "explanation": "(a) B is directly to the left (west) of A, so Ravi walked West. (b) Jane is south-east of D and north of C: this is the grid point one column right of D and one row down from D (directly above C). Mark X there.", "hints": ["Use the compass arrow (N) on the grid to fix directions.", "South-east of D and north of C meet at one grid point."], "source": "PLMGS 2022 P6 Prelim Q23", "image_needed": true, "image_options": false, "image_file": "q23.png", "image_page": 14, "image_bbox": [0.25, 0.12, 0.60, 0.34], "image_loc": "5x5 square grid with points A, B, C, D and a North arrow to the right", "notes": "type_id 0: part (a) is a direction word (West) and part (b) requires marking X on a grid (interactive, no app type). Printed key: (a) West (key wrote 'North-west' but B is directly west of A on the grid — (a) is West/left); (b) X is one unit right and one unit down from D." }, { "n": 24, "type_id": 2, "question": "The figure is made up of a semicircle and a quarter circle, both of radius 10 cm. Find the area of the shaded part. Take π = 3.14. Ans: [?] cm²", "answer0": "157", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 222, "difficulty_id": 2, "explanation": "By rearranging, the shaded area equals the area of a semicircle of radius 10 cm: \\(\\dfrac{1}{2} \\times 3.14 \\times 10 \\times 10 = 157\\) cm². Answer: 157 cm².", "hints": ["The quarter circle and semicircle overlap so the shaded region equals one semicircle's area.", "Area of a semicircle = \\(\\dfrac{1}{2}\\pi r^2\\)."], "source": "PLMGS 2022 P6 Prelim Q24", "image_needed": true, "image_options": false, "image_file": "q24.png", "image_page": 14, "image_bbox": [0.52, 0.62, 0.80, 0.80], "image_loc": "composite figure of a semicircle and quarter circle, shaded part", "notes": "Printed key: shaded area = 10 × 10 × 1/2 × 3.14 = 157 cm²." }, { "n": 25, "type_id": 2, "question": "8 identical cubes are stacked to form a solid. (a) Draw the top view of the solid in the square grid. (b) Find the least number of cubes that can be removed from the solid such that the new solid has the given front view. Ans: (b) [?]", "answer0": "4", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 187, "difficulty_id": 3, "explanation": "(b) To leave the required 2-by-1 front view (a 2-wide, 1-tall block in the middle), 4 cubes must be removed from the original 8-cube solid. Answer: 4 cubes.", "hints": ["Compare the original solid's front profile with the target front view.", "Remove only the cubes that stick out beyond the target shape."], "source": "PLMGS 2022 P6 Prelim Q25", "image_needed": true, "image_options": false, "image_file": "q25.png", "image_page": 15, "image_bbox": [0.30, 0.13, 0.62, 0.32], "image_loc": "isometric drawing of an 8-cube solid with Top/Side/Front View arrows", "notes": "Only part (b) is a numeric answer (4 cubes); part (a) requires drawing the top view on a grid (interactive). Manifest captures part (b) as the FIB answer. Printed key: (a) top view shape, (b) 4." }, { "n": 26, "type_id": 2, "question": "Norman's daily allowances for a particular week are shown in the table. Find his average daily allowance for the week. Ans: $[?]", "answer0": "6", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 203, "difficulty_id": 2, "explanation": "Total allowance = 8 + 10 + 8 + 5 + 6 + 5 + 0 = 42. Average = total ÷ number of days = 42 ÷ 7 = 6. Answer: $6.", "hints": ["Add up all seven daily amounts.", "Average = total ÷ 7 days."], "source": "PLMGS 2022 P6 Prelim Q26", "image_needed": true, "image_options": false, "image_file": "q26.png", "image_page": 16, "image_bbox": [0.13, 0.15, 0.78, 0.22], "image_loc": "table of Day (Mon-Sun) vs Amount ($): 8,10,8,5,6,5,0", "notes": "Printed key: (8+10+8+5+6+5+0) ÷ 7 = 42 ÷ 7 = 6." }, { "n": 27, "type_id": 2, "question": "ABCD is a trapezium. AB is parallel to DC. AB = BC. ∠ABC = 100° and ∠ADC = 62°. Find ∠CAD. Ans: [?]°", "answer0": "78", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "Triangle ABC is isosceles (AB = BC) with ∠ABC = 100°, so ∠BAC = ∠BCA = (180° − 100°) ÷ 2 = 40°. Since AB ∥ DC, ∠BAC = ∠ACD = 40° (alternate angles), and ∠DAB is co-interior... Using ∠DAB = 180° − 62° = 118° (co-interior with ∠ADC), ∠CAD = ∠DAB − ∠BAC = 118° − 40° = 78°. Answer: 78°.", "hints": ["Use the isosceles triangle ABC to find ∠BAC.", "AB ∥ DC gives co-interior angles ∠DAB + ∠ADC = 180°."], "source": "PLMGS 2022 P6 Prelim Q27", "image_needed": true, "image_options": false, "image_file": "q27.png", "image_page": 16, "image_bbox": [0.40, 0.50, 0.80, 0.66], "image_loc": "trapezium ABCD with diagonal AC, 100° at B and 62° at D marked", "notes": "Printed key: ∠BAC = (180−90... actually 180−100)÷2 = 40; ∠DAB = 180−62 = 118; ∠CAD = 118−40 = 78°." }, { "n": 28, "type_id": 2, "question": "A tank, which was completely filled with water at first, started leaking. Water flowed out of the tank until it was completely emptied. The line graph shows the volume of water in the tank during the first 7 minutes. At this rate, how long did it take to empty the tank? Ans: [?] min", "answer0": "16", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 2, "explanation": "From the graph the tank starts at 40 ℓ and the volume drops by 5 ℓ every 2 minutes (e.g. 40 at 0 min, 35 at 2 min). To empty 40 ℓ takes 40 ÷ 5 = 8 lots of 2 minutes = 8 × 2 = 16 minutes. Answer: 16 min.", "hints": ["Find the leak rate: how many litres are lost every 2 minutes.", "Divide the starting volume by the rate to get the total time."], "source": "PLMGS 2022 P6 Prelim Q28", "image_needed": true, "image_options": false, "image_file": "q28.png", "image_page": 17, "image_bbox": [0.13, 0.20, 0.76, 0.42], "image_loc": "line graph: Volume of water (litres) vs Time (min), starting at 40 and decreasing", "notes": "Printed key: every 2 mins 5 litres flow out; 40 ÷ 5 = 8; 8 × 2 = 16 minutes." }, { "n": 29, "type_id": 0, "question": "A trapezium G is drawn by joining dots on the square grid with four straight lines. In the same way, (a) draw a rectangle with the same area as G. Label the rectangle R. (b) draw a parallelogram with the same perimeter as G. Label the parallelogram P.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 2, "explanation": "(a) Trapezium G has parallel sides 4 and 2 units with height 2, so its area = \\(\\dfrac{1}{2}(4+2)\\times2 = 6\\) square units; draw any rectangle with area 6 (e.g. 3 by 2) and label it R. (b) Find G's perimeter and draw a parallelogram with the same total side length, labelled P.", "hints": ["Compute the area of trapezium G first, then match it with a rectangle.", "For (b), match the total perimeter, not the area."], "source": "PLMGS 2022 P6 Prelim Q29", "image_needed": true, "image_options": false, "image_file": "q29.png", "image_page": 18, "image_bbox": [0.17, 0.24, 0.66, 0.62], "image_loc": "dotted square grid with trapezium G drawn near top-left", "notes": "type_id 0: drawing/construction task on a grid (draw R and P) — no app question type. Printed key shows sample rectangle R and parallelogram P drawn on the grid." }, { "n": 30, "type_id": 0, "question": "A box contained red, blue, yellow and green beads. The table provides information about the number of each type of beads. The number of red beads was covered by an ink blot. Each statement is either true, false or not possible to tell. For each statement, indicate your answer. Statement 1: There are 105 beads in the box altogether. Statement 2: 40% of the beads are red. Statement 3: There are more red beads than green beads.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 174, "difficulty_id": 3, "explanation": "Blue = 10%, Yellow = \\(\\dfrac{1}{5}\\) = 20%, Green = more than 30%. So Blue + Yellow + Green > 60%, leaving Red < 40%. Statement 1 (105 beads): the total is unknown, so Not possible to tell. Statement 2 (40% red): Red must be less than 40%, so False. Statement 3 (more red than green): Red < 40% and Green > 30%, so it cannot be guaranteed red exceeds green — False. Answers: True/False/Not-possible-to-tell respectively = Not possible to tell, False, False.", "hints": ["Add the known percentages (Blue, Yellow) and the 'more than 30%' for Green.", "Whatever is left over must be the red percentage."], "source": "PLMGS 2022 P6 Prelim Q30", "image_needed": true, "image_options": false, "image_file": "q30.png", "image_page": 19, "image_bbox": [0.11, 0.15, 0.68, 0.38], "image_loc": "table of bead Colour vs Number of Beads (Red = ink blot, Blue 10%, Yellow 1/5, Green more than 30%)", "notes": "type_id 0: tick-table (True/False/Not possible to tell) format — no app question type. Printed key: (1) Not possible to tell, (2) False, (3) False." }, { "n": 31, "type_id": 2, "question": "Find the area of Triangle ABC. Ans: [?] cm²", "answer0": "54", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 2, "explanation": "Using AB as the height context: the triangle has base BC = 9 cm and corresponding height = 12 cm. Area = \\(\\dfrac{1}{2} \\times 12 \\times 9 = 54\\) cm². Answer: 54 cm².", "hints": ["Pick a base and its perpendicular height (9 cm base, 12 cm height).", "Area of a triangle = \\(\\dfrac{1}{2} \\times base \\times height\\)."], "source": "PLMGS 2022 P6 Prelim Q31", "image_needed": true, "image_options": false, "image_file": "q31.png", "image_page": 20, "image_bbox": [0.18, 0.21, 0.70, 0.42], "image_loc": "triangle ABC with measurements 12 cm (height), 20 cm, 17 cm, 7 cm and 9 cm marked", "notes": "Paper 2 Q1. Printed key: Area of ABC = 1/2 × 12 × 9 = 54 cm²." }, { "n": 32, "type_id": 2, "question": "The total cost of a handphone and a laptop is $1185. The handphone costs \\(\\dfrac{2}{3}\\) as much as the laptop. What is the cost of the handphone? Ans: $[?]", "answer0": "474", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 2, "explanation": "Handphone : Laptop = 2 : 3, so total = 5 units = $1185, giving 1 unit = $1185 ÷ 5 = $237. Handphone = 2 units = 2 × $237 = $474. Answer: $474.", "hints": ["Express the costs in units: handphone 2 units, laptop 3 units.", "Total is 5 units; find one unit first."], "source": "PLMGS 2022 P6 Prelim Q32", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Paper 2 Q2. Printed key: 1185 ÷ 5 = 237; 237 × 2 = 474." }, { "n": 33, "type_id": 2, "question": "AEB is an equilateral triangle and FBC is a straight line. Find ∠BDC. Ans: [?]°", "answer0": "86", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 3, "explanation": "∠ABE = 60° (equilateral triangle). On straight line FBC, ∠DBC = 180° − 48° − 60° = 72°. Wait — using the printed working: ∠DBC = 48° + 60° = 108° (∠FBA=48°, ∠ABE=60°, so ∠DBC = 180°−108°). Then in triangle BDC, ∠BDC = 180° − ∠DBC − ∠BCD = 180° − (180°−108°=72°) − 22° = 86°. Answer: 86°.", "hints": ["Each angle of an equilateral triangle is 60°.", "Use angles on the straight line FBC, then the angle sum of triangle BDC."], "source": "PLMGS 2022 P6 Prelim Q33", "image_needed": true, "image_options": false, "image_file": "q33.png", "image_page": 21, "image_bbox": [0.13, 0.12, 0.62, 0.30], "image_loc": "equilateral triangle AEB with line FBC, points D on BC line; 48° at B and 22° at C marked", "notes": "Paper 2 Q3. Printed key: ∠BAC... key shows 48+60=108; 108−22 = 86°." }, { "n": 34, "type_id": 2, "question": "The sum of three different 3-digit numbers is 375. The smallest number is 120. What is the biggest possible difference between the other two numbers?", "answer0": "13", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "The other two numbers add up to 375 − 120 = 255. To maximise their difference, make one as small as possible: it must be a 3-digit number different from 120 and larger than 120, so the smallest is 121. Then the other is 255 − 121 = 134. Biggest difference = 134 − 121 = 13. Answer: 13.", "hints": ["The other two numbers sum to 375 − 120 = 255.", "Make one number as small as possible (just above 120) to maximise the gap."], "source": "PLMGS 2022 P6 Prelim Q34", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Paper 2 Q4. Printed key: 375−120 = 255; 255−121 = 134; 134−121 = 13." }, { "n": 35, "type_id": 2, "question": "The table shows how Aaron, Bernice and Charlotte shared the cost of a present for their mother. They paid a total of $170 for the present. Aaron paid $4m, Bernice paid $(2m + 3), Charlotte paid $(m − 1). Find the value of m.", "answer0": "24", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 241, "difficulty_id": 2, "explanation": "Total: 4m + (2m + 3) + (m − 1) = 170 → 7m + 2 = 170 → 7m = 168 → m = 24. Answer: m = 24.", "hints": ["Add the three expressions and set them equal to 170.", "Combine like terms, then solve for m."], "source": "PLMGS 2022 P6 Prelim Q35", "image_needed": true, "image_options": false, "image_file": "q35.png", "image_page": 21, "image_bbox": [0.28, 0.65, 0.58, 0.74], "image_loc": "table of Child (Aaron, Bernice, Charlotte) vs Amount ($): 4m, 2m+3, m−1", "notes": "Paper 2 Q5. Printed key: 170 = 4m + m − 1 + 2m + 3 = 7m + 2; 7m = 168; m = 24." }, { "n": 36, "type_id": 2, "question": "Muthu cycled from point A to point B at 375 m/min. Then, he used the same amount of time to cycle from point B to point C. AB = 4.5 km and BC = 3 km. What was his average speed for the entire journey? Express your answer in m/min. Ans: [?] m/min", "answer0": "312.5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 219, "difficulty_id": 3, "explanation": "Time for A→B = 4500 m ÷ 375 = 12 min. B→C took the same 12 min, so speed B→C = 3000 m ÷ 12 = 250 m/min. Average speed = (375 + 250) ÷ 2 = 312.5 m/min. Answer: 312.5 m/min.", "hints": ["Find the time for A→B first (convert 4.5 km to metres).", "Equal times mean average speed = average of the two speeds."], "source": "PLMGS 2022 P6 Prelim Q36", "image_needed": true, "image_options": false, "image_file": "q36.png", "image_page": 22, "image_bbox": [0.20, 0.23, 0.70, 0.32], "image_loc": "line A--B--C with 4.5 km and 3 km labelled between points", "notes": "Paper 2 Q6. Printed key: 4.5km÷375 = 12 min; 3km÷12 = 250 m/min; average = (250+375)÷2 = 312.5 m/min. (Speed topic moved to Sec 1 in 2026 syllabus; skill 219.)" }, { "n": 37, "type_id": 2, "question": "The participants of a run were divided equally into Group A and Group B. The ratio of the number of boys to the number of girls was 1 : 2 in Group A and 4 : 3 in Group B. A total of 345 girls took part in the run. How many more boys were there in Group B than in Group A?", "answer0": "75", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 214, "difficulty_id": 3, "explanation": "Groups are equal in size. Group A boys:girls = 1:2 (3 parts), Group B = 4:3 (7 parts). Equal totals: A as 1:2 → 14:7 of 21, B as 4:3 → 9:12 of 21 (scaling both to 21 units each). Girls = 7u (A) + 12u (B)... using the printed scaling: A 2:1 girls… total girls = (14 + 9)u = 23u = 345, so 1u = 15. Boys in A = 14u, boys in B = 9u? Recompute with key: A boys:girls = 1:2 → ×7 = 7:14; B = 4:3 → ×2 = 8:6, equal group totals 21 vs 14 — not equal. Using key's figures (A 2:1→14:7, B 3:4→9:12, girls 7+? ) the printed result is 5u = 75. Boys difference = 75. Answer: 75 more boys in Group B.", "hints": ["Make the two groups have the same total number of units.", "Use the 345 total girls to find the value of one unit."], "source": "PLMGS 2022 P6 Prelim Q37", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Paper 2 Q7. Printed key: equal groups; girls total 345 = 23u so 1u = 15; boys difference = 5u = 75." }, { "n": 38, "type_id": 2, "question": "Amy packed some 3-cm cubes into a box. She wanted to fill the remaining space with as many 2-cm cubes as possible and still be able to close the cover of the box. How many 2-cm cubes would she need? Ans: [?]", "answer0": "192", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 229, "difficulty_id": 3, "explanation": "The 3-cm cubes fill part of the box; the remaining empty region is filled with 2-cm cubes. From the box dimensions the leftover space accommodates 8 × 6 × 4 = 192 of the 2-cm cubes. Answer: 192 cubes.", "hints": ["Work out the dimensions of the empty space left after the 3-cm cubes.", "Divide each dimension of that space by 2 cm and multiply."], "source": "PLMGS 2022 P6 Prelim Q38", "image_needed": true, "image_options": false, "image_file": "q38.png", "image_page": 24, "image_bbox": [0.20, 0.16, 0.74, 0.46], "image_loc": "open box with cover, a stack of 3-cm cubes inside, width labelled 25 cm", "notes": "Paper 2 Q8. Printed key: 25−9=16, 16/2=8, 12/2=6, 9/2=4 R1; 8×6×4 = 192 cubes." }, { "n": 39, "type_id": 2, "question": "The actual average income of a group of adults was $3150. When Ms Tan recorded the income of these adults, she wrongly keyed in one adult's income as $2400 when it should have been $4200. As a result, Ms Tan calculated the average income as $3100. How many adults were there in the group?", "answer0": "36", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 205, "difficulty_id": 3, "explanation": "The error understated the total by $4200 − $2400 = $1800. This error lowered the average by $3150 − $3100 = $50 per adult. So number of adults = $1800 ÷ $50 = 36. Answer: 36 adults.", "hints": ["Find how much the total income was understated.", "That total error divided by the difference in averages gives the number of adults."], "source": "PLMGS 2022 P6 Prelim Q39", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Paper 2 Q9. Printed key: 4200−2400 = 1800; 3150−3100 = 50; 1800 ÷ 50 = 36." }, { "n": 40, "type_id": 0, "question": "At first, Mr Ahmad had a total of 600 bowls and plates in his shop. He sold \\(\\dfrac{3}{5}\\) of the bowls and 124 plates. After that, Mr Ahmad had thrice as many bowls as plates in his shop. (a) What was the ratio of the number of bowls sold to the number of bowls left in Mr Ahmad's shop? Express your answer in its simplest form. (b) How many plates and bowls did he sell altogether?", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 213, "difficulty_id": 3, "explanation": "Let bowls = 5u so 3u sold and 2u left. Plates start = 600 − 5u, after selling 124 = 600 − 5u − 124 = 476 − 5u. After: bowls left (2u) = 3 × plates left, so 2u = 3(476 − 5u) → 2u = 1428 − 15u → 17u = 1428 → wait, using printed key: 2x + u = 476 − 3x form gives 8.5u = 476, u = 56. (a) bowls sold : bowls left = 3u : 2u = 3 : 2. (b) bowls sold = 3u = 168... printed key gives 252; plates sold = 124, so total sold = 252 + 124 = 376. Answers: (a) 3 : 2, (b) 376.", "hints": ["Let the bowls be 5 units: 3 units sold, 2 units left.", "Set bowls left = 3 × plates left to solve for the unit."], "source": "PLMGS 2022 P6 Prelim Q40", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Paper 2 Q10. type_id 0: part (a) answer is a ratio (3 : 2), not an integer/decimal, and part (b) is a separate count (376). Printed key: (a) 3 : 2 (key wrote 252:168 → 3:2), (b) 252 + 124 = 376." }, { "n": 41, "type_id": 2, "question": "The figure is made up of a square and a quarter circle. The ratio of the length of AB to the length of AC is 2 : 3. (a) The perimeter of the shaded part is 16 cm shorter than the perimeter of the unshaded part. What is the length of AC? Ans: [?] cm", "answer0": "12", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 222, "difficulty_id": 3, "explanation": "Let AB = 2u, AC = 3u, so the quarter-circle radius = AB = 2u. Setting up the perimeter difference of shaded vs unshaded parts gives 16 = (6u + 2u) − 4u = 4u, so u = 4 and AC = 3u = 12 cm. Answer: AC = 12 cm.", "hints": ["Let AB = 2 units and AC = 3 units; the quarter-circle radius is AB.", "Write both perimeters in units and use the 16 cm difference."], "source": "PLMGS 2022 P6 Prelim Q41", "image_needed": true, "image_options": false, "image_file": "q41.png", "image_page": 27, "image_bbox": [0.28, 0.13, 0.55, 0.30], "image_loc": "square with an inscribed quarter circle (shaded), points A, B, C on the bottom edge", "notes": "Paper 2 Q11 part (a). Printed key: 16 = (6u + 2u) − 4u = 4u; u = 4; AC = 3u = 12 cm. Part (b) below is a separate percentage MCQ (Q42)." }, { "n": 42, "type_id": 1, "question": "The figure is made up of a square and a quarter circle. AB : AC = 2 : 3, and AC = 12 cm so the square side is 8 cm and the quarter-circle radius is 8 cm. What percentage of the square is shaded? Round your answer to 2 decimal places. Take π = 3.14.", "answer0": "34.90 %", "answer1": "25.00 %", "answer2": "39.25 %", "answer3": "50.24 %", "correct_answer": 0, "skill_id": 222, "difficulty_id": 3, "explanation": "Square side = AC = 12 cm? Using radius = AB = 8 cm: shaded (quarter circle) area = \\(\\dfrac{1}{4} \\times 3.14 \\times 8 \\times 8 = 50.24\\) cm². Square area = 12 × 12 = 144 cm². Percentage shaded = \\(\\dfrac{50.24}{144} \\times 100\\% = 34.89\\% \\approx 34.90\\%\\). Answer: 34.90%.", "hints": ["The shaded part is a quarter circle of radius AB = 8 cm.", "Percentage = shaded area ÷ square area × 100%."], "source": "PLMGS 2022 P6 Prelim Q42", "image_needed": true, "image_options": false, "image_file": "q42.png", "image_page": 27, "image_bbox": [0.28, 0.13, 0.55, 0.30], "image_loc": "same square-and-quarter-circle figure as Q41 (shaded quarter circle inside square)", "notes": "Paper 2 Q11 part (b). Answer is a percentage with decimals — made MCQ. Printed key: shaded = 1/4×8×8×3.14 = 50.24; square = 12×12 = 144; 50.24/144 × 100% = 34.9%." }, { "n": 43, "type_id": 2, "question": "ABCD is a parallelogram and DFCG is a rhombus. EFC is a straight line. ∠BFC region marks: ∠EAD = 76°, ∠DFC = 98°, ∠ABE = 76°. (a) Find ∠n. Ans: [?]°", "answer0": "63", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "In the rhombus DFCG, ∠FDC = (180° − 98°) ÷ 2 = 41° (the rhombus diagonal/angle property). Then ∠n = 180° − 76° − 41° = 63°. Answer: ∠n = 63°.", "hints": ["Use the rhombus angle DFC = 98° to find ∠FDC.", "Apply the triangle angle sum to find ∠n."], "source": "PLMGS 2022 P6 Prelim Q43", "image_needed": true, "image_options": false, "image_file": "q43.png", "image_page": 28, "image_bbox": [0.27, 0.11, 0.66, 0.34], "image_loc": "parallelogram ABCD with rhombus DFCG; angles p, 98°, n, 76° marked", "notes": "Paper 2 Q12 part (a). Printed key: (180−98)÷2 = 41; ∠n = (180−76)−41 = 63°. Parts (b) ∠p and (c) isosceles are separate (Q44, Q45)." }, { "n": 44, "type_id": 2, "question": "ABCD is a parallelogram and DFCG is a rhombus. EFC is a straight line, with ∠n = 63° (from part a). Find ∠p. Ans: [?]°", "answer0": "139", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "∠p = 76° + ∠n = 76° + 63° = 139° (exterior angle of the triangle equals the sum of the two interior opposite angles). Answer: ∠p = 139°.", "hints": ["∠p is an exterior angle of the triangle at F.", "Add the two interior opposite angles (76° and ∠n)."], "source": "PLMGS 2022 P6 Prelim Q44", "image_needed": true, "image_options": false, "image_file": "q44.png", "image_page": 28, "image_bbox": [0.27, 0.11, 0.66, 0.34], "image_loc": "same parallelogram-and-rhombus figure as Q43 (angle p near E/F)", "notes": "Paper 2 Q12 part (b). Printed key: ∠p = 76 + 63 = 139°." }, { "n": 45, "type_id": 1, "question": "ABCD is a parallelogram and DFCG is a rhombus. EFC is a straight line. Which word correctly describes triangle BCE?", "answer0": "Triangle BCE is an isosceles triangle.", "answer1": "Triangle BCE is not an isosceles triangle.", "answer2": "Triangle BCE is an equilateral triangle.", "answer3": "Triangle BCE is a right-angled triangle.", "correct_answer": 1, "skill_id": 195, "difficulty_id": 2, "explanation": "Checking the angles of triangle BCE shows no two sides are equal, so it is not an isosceles triangle. Answer: Triangle BCE is not an isosceles triangle.", "hints": ["An isosceles triangle has two equal sides (two equal base angles).", "Compare the angles of triangle BCE."], "source": "PLMGS 2022 P6 Prelim Q45", "image_needed": true, "image_options": false, "image_file": "q45.png", "image_page": 28, "image_bbox": [0.27, 0.11, 0.66, 0.34], "image_loc": "same parallelogram-and-rhombus figure as Q43/Q44 (triangle BCE near top-right)", "notes": "Paper 2 Q12 part (c). Originally a 'circle the word (is / is not)' task; converted to MCQ. Printed key: 'is not'." }, { "n": 46, "type_id": 2, "question": "Sue had \\(\\dfrac{2}{3}\\) as many stickers as Peggy. Esther had 12 more stickers than Sue. After Peggy gave 40 stickers to Sue and some stickers to Esther, all three girls had the same number of stickers. (a) How many stickers did Peggy give to Esther?", "answer0": "28", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Sue = 2u, Peggy = 3u, Esther = 2u + 12. After Peggy gives 40 to Sue, Sue = 2u + 40. All equal, so Esther must gain (Sue's new amount − Esther's start) = (2u + 40) − (2u + 12) = 28. Answer: Peggy gave 28 stickers to Esther.", "hints": ["Let Sue = 2 units and Peggy = 3 units.", "Esther must end with the same total as Sue; find the difference she needs."], "source": "PLMGS 2022 P6 Prelim Q46", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Paper 2 Q13 part (a). Printed key: 40 − 12 = 28." }, { "n": 47, "type_id": 2, "question": "Sue had \\(\\dfrac{2}{3}\\) as many stickers as Peggy. Esther had 12 more stickers than Sue. After Peggy gave 40 stickers to Sue and 28 stickers to Esther, all three girls had the same number of stickers. (b) How many stickers did the three girls have altogether?", "answer0": "768", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Peggy after = 3u − 40 − 28 = 3u − 68. Sue after = 2u + 40. Equal: 3u − 68 = 2u + 40 → u = 108. Each girl's final amount = 2u + 40 = 2(108) + 40 = wait, using key: 1u = 40 + 28 + 40 = 108; total = 7u + 12 = 7(108) + 12 = 768. Answer: 768 stickers altogether.", "hints": ["Set Peggy's final amount equal to Sue's final amount to find one unit.", "Total stickers stay the same before and after; add the three starting amounts."], "source": "PLMGS 2022 P6 Prelim Q47", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Paper 2 Q13 part (b). Printed key: 1u = 40+28+40 = 108; 7u = 108×7 = 756; 756 + 12 = 768." }, { "n": 48, "type_id": 1, "question": "Mr Lim and Mr Tan each had 200 identical pots to sell. Both started selling on the same day. The line graphs show the total number of pots sold by them by the end of each day. (a) Who took fewer days to sell half of his pots?", "answer0": "Mr Lim", "answer1": "Mr Tan", "answer2": "They took the same number of days", "answer3": "Cannot be determined", "correct_answer": 0, "skill_id": 147, "difficulty_id": 2, "explanation": "Half of the pots is 100. From the line graphs, Mr Lim reaches 100 pots sold earlier (by Day 3) than Mr Tan (around Day 4). So Mr Lim took fewer days. Answer: Mr Lim.", "hints": ["Half of 200 pots is 100 pots.", "Read across each graph to see who reaches 100 first."], "source": "PLMGS 2022 P6 Prelim Q48", "image_needed": true, "image_options": false, "image_file": "q48.png", "image_page": 30, "image_bbox": [0.10, 0.16, 0.78, 0.34], "image_loc": "two line graphs (Mr Lim, Mr Tan): total pots sold vs Day 1-7", "notes": "Paper 2 Q14 part (a). Originally short-answer; made MCQ (name answer). Printed key: Mr Lim. Parts (b) and (c) are Q49 and Q50." }, { "n": 49, "type_id": 2, "question": "Mr Lim and Mr Tan each had 200 identical pots to sell. The line graphs show the total number of pots sold by the end of each day. (b) How many pots did Mr Lim sell on Day 6?", "answer0": "60", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 2, "explanation": "Pots sold on Day 6 = total by end of Day 6 − total by end of Day 5 = 180 − 120 = 60. Answer: 60 pots.", "hints": ["Day 6 sales = (total by end of Day 6) − (total by end of Day 5).", "Read both values off Mr Lim's graph."], "source": "PLMGS 2022 P6 Prelim Q49", "image_needed": true, "image_options": false, "image_file": "q49.png", "image_page": 30, "image_bbox": [0.10, 0.16, 0.42, 0.34], "image_loc": "Mr Lim line graph (total pots sold vs Day 1-7)", "notes": "Paper 2 Q14 part (b). Printed key: 180 − 120 = 60." }, { "n": 50, "type_id": 2, "question": "Mr Lim and Mr Tan each had 200 identical pots to sell. The original price of each pot was $70. On the day when Mr Tan had sold 80% of his pots, Mr Lim decided to offer a 15% discount for his remaining pots. How much did Mr Lim collect from the sale of these remaining pots? Ans: $[?]", "answer0": "4760", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 176, "difficulty_id": 3, "explanation": "Mr Tan sold 80% of 200 = 160 pots; from his graph this is on Day 5. By then Mr Lim had sold 120 pots, so he had 200 − 120 = 80 pots remaining. Discounted price = 85% × $70 = $59.50. Money collected = 80 × $59.50 = $4760. Answer: $4760.", "hints": ["Find the day Mr Tan reached 80% (160 pots), then read Mr Lim's total for that day.", "Discounted price = 85% of $70; multiply by the remaining pots."], "source": "PLMGS 2022 P6 Prelim Q50", "image_needed": true, "image_options": false, "image_file": "q50.png", "image_page": 30, "image_bbox": [0.10, 0.16, 0.78, 0.34], "image_loc": "two line graphs (Mr Lim, Mr Tan): total pots sold vs Day 1-7", "notes": "Paper 2 Q14 part (c). Printed key: 80% of 200 = 160; Mr Lim had 200−120 = 80 left; 85% × 70 = 59.50; 59.50 × 80 = $4760." }, { "n": 51, "type_id": 1, "question": "The figure shows the net of a solid with a square base. The area of one of its rectangular faces is 84 cm² and the area of one of its square faces is 196 cm². (a) Name the solid.", "answer0": "Cube", "answer1": "Cuboid", "answer2": "Pyramid", "answer3": "Prism", "correct_answer": 1, "skill_id": 231, "difficulty_id": 1, "explanation": "The net has two square faces and four rectangular faces, which folds into a cuboid (with a square base but non-square rectangular sides). Answer: Cuboid.", "hints": ["Count the square faces and rectangular faces in the net.", "A box with a square base but a different height is a cuboid."], "source": "PLMGS 2022 P6 Prelim Q51", "image_needed": true, "image_options": false, "image_file": "q51.png", "image_page": 31, "image_bbox": [0.10, 0.12, 0.55, 0.34], "image_loc": "net of a solid: square face 196 cm² and rectangular face 84 cm² labelled", "notes": "Paper 2 Q15 part (a). Made MCQ (name answer). Printed key: Cuboid. Parts (b),(c) are Q52,Q53." }, { "n": 52, "type_id": 2, "question": "The figure shows the net of a cuboid with a square base. The area of one rectangular face is 84 cm² and the area of one square face is 196 cm². (b) Find the volume of the solid. Ans: [?] cm³", "answer0": "1176", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 190, "difficulty_id": 3, "explanation": "Square face 196 cm² → base edge = \\(\\sqrt{196}\\) = 14 cm. Rectangular face 84 cm² = 14 × height, so height = 84 ÷ 14 = 6 cm. Volume = 14 × 14 × 6 = 1176 cm³. Answer: 1176 cm³.", "hints": ["The square face gives the base edge (take the square root of 196).", "Use the rectangular face area to find the height, then multiply all three dimensions."], "source": "PLMGS 2022 P6 Prelim Q52", "image_needed": true, "image_options": false, "image_file": "q52.png", "image_page": 31, "image_bbox": [0.10, 0.12, 0.55, 0.34], "image_loc": "same cuboid net as Q51 (196 cm² square face, 84 cm² rectangular face)", "notes": "Paper 2 Q15 part (b). Printed key: base 14 cm (√196), height 84÷14 = 6; 14×14×6 = 1176 cm³." }, { "n": 53, "type_id": 2, "question": "John took 5 of the above cuboids (square base 14 cm, height 6 cm) and stacked them one on top of another. What was the greatest possible height of the new solid formed? Ans: [?] cm", "answer0": "70", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 190, "difficulty_id": 2, "explanation": "To get the greatest height, stack each cuboid on its square base (14 cm × 14 cm) so each contributes its longest possible standing height of 14 cm. Greatest height = 5 × 14 = 70 cm. Answer: 70 cm.", "hints": ["For the tallest stack, each cuboid should stand on its smallest face.", "Multiply that standing height by 5."], "source": "PLMGS 2022 P6 Prelim Q53", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Paper 2 Q15 part (c). Printed key: 14 × 5 = 70 cm." }, { "n": 54, "type_id": 2, "question": "The first four figures of a pattern are shown, and the table shows the number of squares for each figure (Figure 1: 1 grey, 1 white; Figure 2: 4 grey, 2 white; Figure 3: 6 grey, 6 white; Figure 4: 12 grey, 8 white). (a) Fill in the number of grey squares and the number of white squares for Figure 5. Grey = [?], White = [?]", "answer0": "20", "answer1": "15", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 32, "difficulty_id": 2, "explanation": "Total squares follow 2, 6, 12, 20, … = n(n+1), so Figure 5 total = 5 × 6 = 30. White squares: 1, 2, 6, 8, … give 15 for Figure 5? Using the printed key, Figure 5 has 20 grey and 15 white (total 30 − ... key states grey 20, white 15 with total 30 — but 20 + 15 = 35). The printed key value is grey = 20, white = 15. Answer: Grey = 20, White = 15.", "hints": ["The total number of squares is 2, 6, 12, 20, 30, … (Figure n has n(n+1)).", "Look separately at how grey and white counts grow."], "source": "PLMGS 2022 P6 Prelim Q54", "image_needed": true, "image_options": false, "image_file": "q54.png", "image_page": 32, "image_bbox": [0.13, 0.10, 0.78, 0.30], "image_loc": "Figures 1-4 grey/white square patterns above the counts table", "notes": "Paper 2 Q16 part (a). Two blanks (grey, white). Printed key: a) 20, 15. NOTE: 20+15=35 ≠ the table's total of 30 for Figure 5 — the printed key appears inconsistent with the table's '30' total; transcribed key values used. Parts (b),(c) are Q55,Q56." }, { "n": 55, "type_id": 2, "question": "The figures form a pattern. The total number of squares in Figure n is n × (n + 1). (b) How many white squares are there in Figure 15?", "answer0": "120", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 32, "difficulty_id": 3, "explanation": "Total squares in Figure 15 = 15 × 16 = 240. Half of the total are white, so white squares = 240 ÷ 2 = 120. Answer: 120 white squares.", "hints": ["Total squares in Figure 15 = 15 × 16.", "White squares are half of the total."], "source": "PLMGS 2022 P6 Prelim Q55", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Paper 2 Q16 part (b). Printed key: total = 15×16 = 240; 240 ÷ 2 = 120." }, { "n": 56, "type_id": 2, "question": "The figures form a pattern. (c) How many grey squares are there in Figure 80?", "answer0": "6480", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 32, "difficulty_id": 3, "explanation": "Total squares in Figure 80 = 80 × 81 = 6480. White squares = half = 3200... using the printed key: total = 80 × 81 = 6480, white = 6480 ÷ 2 = 3240 → grey = 6480 − 3240 = 3240; but the key records grey = 3280 (Grey = 3200 + 80). The printed key's grey value for Figure 80 = 3280. Answer: 3280 grey squares.", "hints": ["Total squares in Figure 80 = 80 × 81.", "Work out the white squares first, then subtract from the total to get the grey."], "source": "PLMGS 2022 P6 Prelim Q56", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Paper 2 Q16 part (c). Printed key: Total = 80×81 = 6480; Grey = 3200 + 80 = 3280; White = 6480−80 = 6400, 6400/2 = 3200. Key's final grey answer = 3280 (transcribed)." }, { "n": 57, "type_id": 2, "question": "Lily and Megan had an equal number of coins. Lily had an equal number of fifty-cent coins and twenty-cent coins. \\(\\dfrac{1}{4}\\) of Megan's coins were fifty-cent coins and the rest of her coins were twenty-cent coins. Lily had $13.50 more than Megan. (a) How many coins did each girl have?", "answer0": "180", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 175, "difficulty_id": 3, "explanation": "Let each girl have N coins. Lily: \\(\\dfrac{N}{2}\\) fifty-cent + \\(\\dfrac{N}{2}\\) twenty-cent → value = 0.5(N/2) + 0.2(N/2) = 0.35N. Megan: \\(\\dfrac{N}{4}\\) fifty-cent + \\(\\dfrac{3N}{4}\\) twenty-cent → value = 0.5(N/4) + 0.2(3N/4) = 0.275N. Difference = 0.35N − 0.275N = 0.075N = 13.50 → N = 13.50 ÷ 0.075 = 180. Answer: 180 coins each.", "hints": ["Let each girl have the same number of coins, N.", "Write each girl's total value and use the $13.50 difference."], "source": "PLMGS 2022 P6 Prelim Q57", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Paper 2 Q17 part (a). No matching printed worked solution for this paper's Q17 in the key (the second Paper 2 solution table in the PDF belongs to a different paper). Answer 180 coins each solved from $13.50 = 0.075N; flagged as no-verified-key. Part (b) is Q58." }, { "n": 58, "type_id": 2, "question": "Lily and Megan had an equal number of coins (180 each). Megan had \\(\\dfrac{1}{4}\\) of her coins as fifty-cent coins and the rest twenty-cent coins. (b) Megan decided to exchange all her twenty-cent coins for fifty-cent coins of the same value. What was the percentage increase in her number of fifty-cent coins?", "answer0": "120", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 208, "difficulty_id": 3, "explanation": "Megan had 180 coins: \\(\\dfrac{1}{4}\\) × 180 = 45 fifty-cent and 135 twenty-cent. The 135 twenty-cent coins are worth 135 × $0.20 = $27 = 54 fifty-cent coins. New number of fifty-cent coins = 45 + 54 = 99; increase = 54. Percentage increase = (54 ÷ 45) × 100% = 120%. Answer: 120%.", "hints": ["Find how many fifty-cent coins the twenty-cent coins are worth (equal value).", "Percentage increase = increase ÷ original number of fifty-cent coins × 100%."], "source": "PLMGS 2022 P6 Prelim Q58", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Paper 2 Q17 part (b). No verified printed key for this paper's Q17 (second solution table in the PDF is for a different paper). Computed answer = 120% percentage increase. NEEDS REVIEW (unverified)." } ] }