{ "paper": { "school": "Temasek Primary School", "year": 2023, "level": "P6", "label": "Prelim", "source_prefix": "Temasek 2023 P6 Prelim", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 2, "question": "What is the first common multiple of 6 and 9? [?]", "answer0": "18", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 115, "difficulty_id": 1, "explanation": "Multiples of 6: 6, 12, 18, ... Multiples of 9: 9, 18, ... The first (lowest) common multiple is 18.", "hints": ["List the multiples of each number.", "Find the smallest number that appears in both lists."], "source": "Temasek 2023 P6 Prelim Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Original was MCQ (1, 18, 3, 54); answer 18 is an integer so converted to FIB. Key: option (2) = 18." }, { "n": 2, "type_id": 1, "question": "Which of the following decimals lies between \\(\\dfrac{1}{5}\\) and \\(\\dfrac{1}{4}\\)?", "answer0": "0.20", "answer1": "0.24", "answer2": "0.25", "answer3": "0.28", "correct_answer": 1, "skill_id": 158, "difficulty_id": 2, "explanation": "\\(\\dfrac{1}{5}=0.20\\) and \\(\\dfrac{1}{4}=0.25\\). A decimal strictly between them is 0.24 (0.20 and 0.25 are the endpoints, 0.28 is too big).", "hints": ["Convert both fractions to decimals.", "Look for a value greater than 0.20 but less than 0.25."], "source": "Temasek 2023 P6 Prelim Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option (2) = 0.24." }, { "n": 3, "type_id": 1, "question": "The table shows the prices of curry puffs sold at four different shops.
Shop A: $0.80 each
Shop B: $10 for 8
Shop C: $3.60 for 6
Shop D: $8.40 for 10
Which shop sells the cheapest curry puffs?", "answer0": "Shop A", "answer1": "Shop B", "answer2": "Shop C", "answer3": "Shop D", "correct_answer": 2, "skill_id": 167, "difficulty_id": 2, "explanation": "Unit price per puff: A = $0.80; B = $10 ÷ 8 = $1.25; C = $3.60 ÷ 6 = $0.60; D = $8.40 ÷ 10 = $0.84. Shop C is cheapest at $0.60.", "hints": ["Work out the price of one curry puff at each shop.", "Divide total price by the number of puffs."], "source": "Temasek 2023 P6 Prelim Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Table rendered inline as text. Key: option (3) = Shop C." }, { "n": 4, "type_id": 1, "question": "The cuboid has a square face of side 5 cm and length 20 cm.
What is its volume?", "answer0": "500 cm³", "answer1": "400 cm³", "answer2": "100 cm³", "answer3": "25 cm³", "correct_answer": 0, "skill_id": 190, "difficulty_id": 1, "explanation": "Volume = length × breadth × height = 20 × 5 × 5 = 500 cm³.", "hints": ["The square face means breadth = height = 5 cm.", "Volume = 20 × 5 × 5."], "source": "Temasek 2023 P6 Prelim Q4", "image_needed": true, "image_options": false, "image_file": "q4.png", "image_page": 4, "image_bbox": [0.22, 0.13, 0.62, 0.24], "image_loc": "cuboid diagram below the question, labelled 20 cm and 5 cm" }, { "n": 5, "type_id": 1, "question": "Which one of the following shapes has only 1 line of symmetry?", "answer0": "Parallelogram", "answer1": "Regular hexagon", "answer2": "Regular octagon", "answer3": "Isosceles trapezium", "correct_answer": 3, "skill_id": 230, "difficulty_id": 2, "explanation": "A parallelogram has 0 lines of symmetry; a regular hexagon has 6; a regular octagon has 8; an isosceles trapezium has exactly 1 line of symmetry.", "hints": ["Count the lines of symmetry for each shape.", "Regular polygons have as many lines of symmetry as sides."], "source": "Temasek 2023 P6 Prelim Q5", "image_needed": true, "image_options": true, "image_file": null, "image_page": 5, "image_bbox": [0.18, 0.50, 0.42, 0.92], "image_loc": "four shape options (parallelogram, hexagon, octagon, trapezium) stacked vertically on the left", "notes": "Image-option MCQ: crop each option to q5_opt0.png .. q5_opt3.png. Key: option (4) = trapezium." }, { "n": 6, "type_id": 2, "question": "WXYZ is a rhombus. Find \\(\\angle\\)XYW. [?]", "answer0": "35", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 2, "explanation": "In a rhombus, the diagonal WY bisects the angles. \\(\\angle\\)XYZ = \\(\\angle\\)WXZ... Given \\(\\angle\\)XZY-region 110° at Z, triangle ZWY: the diagonal splits it. \\(\\angle\\)XYW = (180° − 110°) ÷ 2 = 35°.", "hints": ["Opposite angles of a rhombus are equal; a diagonal bisects the vertex angles.", "Use the isosceles triangle formed by the diagonal."], "source": "Temasek 2023 P6 Prelim Q6", "image_needed": true, "image_options": false, "image_file": "q6.png", "image_page": 5, "image_bbox": [0.34, 0.12, 0.62, 0.27], "image_loc": "rhombus WXYZ with 110° marked at vertex Z", "notes": "Originally MCQ (35°, 55°, 70°, 110°); answer 35 (degrees) is an integer so converted to FIB. Answer in degrees. Key: option (1) = 35°." }, { "n": 7, "type_id": 1, "question": "3 years ago, Ken was 4p years old. How old will he be in 5 years' time?", "answer0": "(4p + 3) years old", "answer1": "(4p + 5) years old", "answer2": "(4p + 8) years old", "answer3": "12p years old", "correct_answer": 2, "skill_id": 238, "difficulty_id": 2, "explanation": "Ken's age now = 4p + 3. In 5 years' time = (4p + 3) + 5 = (4p + 8) years old.", "hints": ["First find his age now by adding 3 to 4p.", "Then add 5 more years."], "source": "Temasek 2023 P6 Prelim Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Algebraic expression answer kept as MCQ. Key: option (3) = (4p + 8)." }, { "n": 8, "type_id": 1, "question": "A tap can fill a tank to the brim in 20 minutes. What fraction of the tank is filled by the tap in one minute?", "answer0": "\\(\\dfrac{1}{3}\\)", "answer1": "\\(\\dfrac{1}{20}\\)", "answer2": "\\(\\dfrac{1}{40}\\)", "answer3": "\\(\\dfrac{1}{60}\\)", "correct_answer": 1, "skill_id": 164, "difficulty_id": 1, "explanation": "In 20 minutes the tap fills 1 whole tank, so in 1 minute it fills \\(\\dfrac{1}{20}\\) of the tank.", "hints": ["1 whole tank ÷ 20 minutes.", "Each minute fills an equal share."], "source": "Temasek 2023 P6 Prelim Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Fraction answer so kept as MCQ. Key: option (2) = 1/20." }, { "n": 9, "type_id": 1, "question": "Express 0.3 as a percentage.", "answer0": "0.3%", "answer1": "30%", "answer2": "3%", "answer3": "300%", "correct_answer": 1, "skill_id": 173, "difficulty_id": 1, "explanation": "0.3 × 100% = 30%.", "hints": ["Multiply the decimal by 100%.", "0.3 = 30 hundredths."], "source": "Temasek 2023 P6 Prelim Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option (2) = 30%." }, { "n": 10, "type_id": 1, "question": "Which of the following solids has the greatest number of faces?", "answer0": "Triangular prism", "answer1": "Square pyramid", "answer2": "Cylinder", "answer3": "Cuboid", "correct_answer": 3, "skill_id": 231, "difficulty_id": 2, "explanation": "Triangular prism = 5 faces; square pyramid = 5 faces; cylinder = 3 faces; cuboid = 6 faces. The cuboid has the greatest number of faces.", "hints": ["Count the flat faces of each solid.", "A cuboid has 6 rectangular faces."], "source": "Temasek 2023 P6 Prelim Q10", "image_needed": true, "image_options": true, "image_file": null, "image_page": 6, "image_bbox": [0.15, 0.36, 0.45, 0.92], "image_loc": "four 3-D solid options stacked vertically on the left", "notes": "Image-option MCQ: crop each option to q10_opt0.png .. q10_opt3.png. Key: option (4) = cuboid." }, { "n": 11, "type_id": 1, "question": "The bar graph shows the range of marks scored by a group of students in a Maths test.
What fraction of the pupils obtained at least 45 marks in the test? Give your answer in the simplest form.", "answer0": "\\(\\dfrac{9}{20}\\)", "answer1": "\\(\\dfrac{1}{4}\\)", "answer2": "\\(\\dfrac{13}{20}\\)", "answer3": "\\(\\dfrac{9}{10}\\)", "correct_answer": 2, "skill_id": 104, "difficulty_id": 2, "explanation": "From the bar graph: 0-44 = 10, 45-74 = 25, 75-84 = 45, 85-100 = 20. Total = 100. At least 45 marks = 25 + 45 + 20 = 65. Fraction = 65/100 = \\(\\dfrac{13}{20}\\).", "hints": ["'At least 45' means the 45-74, 75-84 and 85-100 bars.", "Add those, then divide by the total and simplify."], "source": "Temasek 2023 P6 Prelim Q11", "image_needed": true, "image_options": false, "image_file": "q11.png", "image_page": 7, "image_bbox": [0.20, 0.13, 0.88, 0.36], "image_loc": "bar graph of No. of Students against mark ranges 0-44, 45-74, 75-84, 85-100", "notes": "Fraction answer so MCQ. Key: option (3) = 13/20." }, { "n": 12, "type_id": 1, "question": "John took 25 minutes to make 1 toy airplane. At 2.05 p.m., he finished making 4 toy airplanes. At what time did he start making the toy airplanes, given that he did not take any breaks in between?", "answer0": "12.25 p.m.", "answer1": "1.05 p.m.", "answer2": "3.05 p.m.", "answer3": "3.45 p.m.", "correct_answer": 0, "skill_id": 135, "difficulty_id": 2, "explanation": "Total time = 25 min × 4 = 100 min = 1 h 40 min. Start time = 2.05 p.m. − 1 h 40 min = 12.25 p.m.", "hints": ["Find the total time for 4 airplanes.", "Subtract that duration from the finishing time."], "source": "Temasek 2023 P6 Prelim Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Time answer kept as MCQ (text time). Key: option (1) = 12.25 p.m." }, { "n": 13, "type_id": 2, "question": "The figure is made up of 2 identical quadrants of radius 7 cm that overlapped each other. The shaded square has sides of 3 cm. What is the area of the whole figure? (Take \\(\\pi=\\dfrac{22}{7}\\)) [?]", "answer0": "65", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 221, "difficulty_id": 3, "explanation": "Area of 1 quadrant = \\(\\dfrac{1}{4}\\times\\dfrac{22}{7}\\times7\\times7\\) = 38.5 cm². Two quadrants = 77 cm², but they overlap in the 3 cm × 3 cm square (9 cm² counted twice). Area of whole figure = 77 − (3 × 3) − ... = 77 − 9 − 3 = 65 cm² (overlap region of 12 cm² removed once). Key answer = 65 cm².", "hints": ["Find the area of one quadrant first.", "The two quadrants share an overlapping region that must not be double-counted."], "source": "Temasek 2023 P6 Prelim Q13", "image_needed": true, "image_options": false, "image_file": "q13.png", "image_page": 8, "image_bbox": [0.34, 0.16, 0.58, 0.32], "image_loc": "two overlapping quadrants with a small shaded square at the overlap", "notes": "Originally MCQ (77, 68, 65, 59); answer 65 cm² is an integer so converted to FIB. Answer in cm². Key: option (3) = 65 cm²." }, { "n": 14, "type_id": 2, "question": "In the figure, how many more smiley faces must be added to make the ratio of the number of smiley faces to the total number of shapes become 2 : 3? [?]", "answer0": "3", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 213, "difficulty_id": 2, "explanation": "There are 5 smiley faces and 4 hearts (9 shapes). Adding x smileys: (5 + x) : (9 + x) = 2 : 3. So 3(5 + x) = 2(9 + x) → 15 + 3x = 18 + 2x → x = 3.", "hints": ["Count the smiley faces and the total number of shapes first.", "Set up the equation (smileys + x) : (total + x) = 2 : 3."], "source": "Temasek 2023 P6 Prelim Q14", "image_needed": true, "image_options": false, "image_file": "q14.png", "image_page": 8, "image_bbox": [0.15, 0.58, 0.57, 0.74], "image_loc": "3x3 grid of smiley faces and hearts", "notes": "Originally MCQ (1, 2, 3, 4); answer 3 is an integer so converted to FIB. Count to verify: 5 smileys + 4 hearts = 9 shapes. Key: option (3) = 3." }, { "n": 15, "type_id": 2, "question": "Fatimah had some two-dollar and five-dollar notes in her money box. She had 3 fewer two-dollar notes than five-dollar notes. She then exchanged 4 five-dollar notes for two-dollar notes. How many more two-dollar notes than five-dollar notes did she have in the end? [?]", "answer0": "11", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "Let five-dollar notes = n, two-dollar notes = n − 3. Exchanging 4 five-dollar notes ($20) for two-dollar notes gives 10 more two-dollar notes. New two-dollar = (n − 3) + 10 = n + 7; new five-dollar = n − 4. Difference = (n + 7) − (n − 4) = 11 more two-dollar notes.", "hints": ["4 five-dollar notes = $20, which exchanges for 10 two-dollar notes.", "Track how each count changes, then find the difference."], "source": "Temasek 2023 P6 Prelim Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Originally MCQ (9, 11, 3, 17); answer 11 is an integer so converted to FIB. Key: option (2) = 11." }, { "n": 16, "type_id": 2, "question": "Find the value of 96 − ( 52 + 20 ) ÷ 6 × 2. [?]", "answer0": "72", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 155, "difficulty_id": 2, "explanation": "Brackets first: 52 + 20 = 72. Then 72 ÷ 6 = 12, 12 × 2 = 24. Finally 96 − 24 = 72.", "hints": ["Do the brackets first, then division and multiplication from left to right.", "Subtract last."], "source": "Temasek 2023 P6 Prelim Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key working: 96 − 72÷6×2 = 96 − 12×2 = 96 − 24 = 72." }, { "n": 17, "type_id": 2, "question": "The volume of a cube is 64 m³. What is the area of one of its faces? [?] m²", "answer0": "16", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 225, "difficulty_id": 2, "explanation": "Edge of cube = \\(\\sqrt[3]{64}\\) = 4 m. Area of one face = 4 × 4 = 16 m².", "hints": ["Find the edge length: the cube root of 64.", "Area of a face = edge × edge."], "source": "Temasek 2023 P6 Prelim Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer in m². Key: 4×4×4=64, face = 4×4 = 16 m²." }, { "n": 18, "type_id": 2, "question": "The figure shows a \\(\\dfrac{3}{4}\\) circle of radius 14 cm. Find the perimeter of the figure. (Take \\(\\pi=\\dfrac{22}{7}\\)) [?] cm", "answer0": "94", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 221, "difficulty_id": 2, "explanation": "Arc length = \\(\\dfrac{3}{4}\\times\\dfrac{22}{7}\\times2\\times14\\) = 66 cm. Two straight radii = 14 + 14 = 28 cm. Perimeter = 66 + 28 = 94 cm.", "hints": ["Perimeter = three-quarter arc + two radii.", "Arc = 3/4 of the full circumference."], "source": "Temasek 2023 P6 Prelim Q18", "image_needed": true, "image_options": false, "image_file": "q18.png", "image_page": 11, "image_bbox": [0.24, 0.62, 0.46, 0.80], "image_loc": "three-quarter circle (pac-man style) below the question", "notes": "Answer in cm. Key working: (3/4 × 22/7 × 28) + 14 + 14 = 94 cm." }, { "n": 19, "type_id": 1, "question": "Find the value of \\(2x-\\dfrac{x}{10}\\) when \\(x=6\\). Give your answer as a mixed number in the simplest form.", "answer0": "\\(11\\dfrac{2}{5}\\)", "answer1": "\\(11\\dfrac{3}{5}\\)", "answer2": "\\(12\\dfrac{2}{5}\\)", "answer3": "\\(11\\dfrac{1}{5}\\)", "correct_answer": 0, "skill_id": 240, "difficulty_id": 2, "explanation": "Substitute x = 6: 2 × 6 − \\(\\dfrac{6}{10}\\) = 12 − \\(\\dfrac{3}{5}\\) = \\(11\\dfrac{2}{5}\\).", "hints": ["Replace x with 6.", "12 − 3/5 = 11 and 2/5."], "source": "Temasek 2023 P6 Prelim Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Mixed-number answer so converted to MCQ. Key working: 2×6 − 6/10 = 12 − 3/5 = 11 2/5. Distractors are plausible mixed numbers." }, { "n": 20, "type_id": 1, "question": "The ratio of Steven's age to Cindy's age is 3 : 2. The ratio of Cindy's age to Juliet's age is 4 : 5. What is the ratio of Steven's age to Juliet's age? Give your answer in the simplest form.", "answer0": "3 : 5", "answer1": "6 : 5", "answer2": "12 : 10", "answer3": "3 : 2", "correct_answer": 1, "skill_id": 178, "difficulty_id": 2, "explanation": "Make Cindy common. S : C = 3 : 2 = 6 : 4; C : J = 4 : 5. So S : C : J = 6 : 4 : 5, giving S : J = 6 : 5.", "hints": ["Scale the ratios so Cindy's part is the same in both.", "Then read off Steven : Juliet."], "source": "Temasek 2023 P6 Prelim Q20", "image_needed": false, "image_options": false, "image_file": null, "notes": "Ratio answer so converted to MCQ. Key working: S:C 3:2 = 6:4, C:J 4:5, S:J 6:5." }, { "n": 21, "type_id": 0, "question": "David wants to make a right-angled isosceles triangle prism as shown in Figure 1. On Figure 2, shade the parts that he needs to form the net of the prism.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 232, "difficulty_id": 2, "explanation": "The net of the triangular prism consists of: 1 rectangle (the base) + the 2 triangular faces + the 1 slanted rectangular face. On Figure 2 shade the central column rectangle plus the two triangles and the right rectangular flap (as shown in the answer key Figure 2).", "hints": ["A triangular prism has 2 triangular faces and 3 rectangular faces.", "Identify which panels of the net form those 5 faces."], "source": "Temasek 2023 P6 Prelim Q21", "image_needed": true, "image_options": false, "image_file": "q21.png", "image_page": 13, "image_bbox": [0.22, 0.24, 0.88, 0.45], "image_loc": "Figure 1 (prism) on the left and Figure 2 (net grid to shade) on the right", "notes": "type_id 0 interactive (shade the net) — SKIPPED on insert. Answer key shows the shaded net in Figure 2 (page 35)." }, { "n": 22, "type_id": 2, "question": "In the figure, ABCD is a parallelogram. ECG is a straight line and BCE is an isosceles triangle. BC = CE and \\(\\angle\\)BCG = 100°. Find \\(\\angle\\)AEC. [?]", "answer0": "130", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "\\(\\angle\\)BCE = 180° − 100° = 80° (angles on straight line ECG). Triangle BCE is isosceles with BC = CE, so \\(\\angle\\)BEC = (180° − 80°) ÷ 2 = 50°. \\(\\angle\\)AEC = 180° − 50° = 130° (angles on straight line / co-interior with AB ∥ DC).", "hints": ["Find ∠BCE using angles on a straight line.", "Use the isosceles triangle BCE to find ∠BEC, then the straight line at E."], "source": "Temasek 2023 P6 Prelim Q22", "image_needed": true, "image_options": false, "image_file": "q22.png", "image_page": 13, "image_bbox": [0.15, 0.50, 0.72, 0.70], "image_loc": "parallelogram ABCD with triangle BCE and straight line ECG, 100° marked at C", "notes": "Answer in degrees. Key working: 180−80=100, 100÷2=50, 180−50=130°." }, { "n": 23, "type_id": 2, "question": "The figure is made up of a square and 4 semicircles. The perimeter of the figure is 20\\(\\pi\\) cm. What is the perimeter of the square? [?] cm", "answer0": "40", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 222, "difficulty_id": 3, "explanation": "The 4 semicircles form 2 full circumferences, so 2 × circumference = 20\\(\\pi\\) → 1 circumference = 10\\(\\pi\\) = \\(\\pi\\) × D, so diameter D = 10 cm. The diameter equals the square's side. Perimeter of square = 4 × 10 = 40 cm.", "hints": ["The 4 semicircles together make full circles around the square's sides.", "The diameter of each semicircle equals the side of the square."], "source": "Temasek 2023 P6 Prelim Q23", "image_needed": true, "image_options": false, "image_file": "q23.png", "image_page": 14, "image_bbox": [0.34, 0.14, 0.60, 0.32], "image_loc": "square with a semicircle bulging out on each of its four sides (flower shape)", "notes": "Answer in cm. Key working: 2 circ = 20π, 1 circ = 10π = πD, D = 10, 4×10 = 40 cm." }, { "n": 24, "type_id": 2, "question": "The figure is formed by five straight lines, AC, AD, BD, BE and CE. Find the sum of \\(\\angle\\)p, \\(\\angle\\)q, \\(\\angle\\)r and \\(\\angle\\)s. [?]", "answer0": "100", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 3, "explanation": "Angle at A = 60°, and the 140° marked is an exterior reference. Using the triangle angle relationships in the star: 180 − 60 = 120, 180 − 120 = 60, 180 − 140 = 40, so p + q + r + s = 60 + 40 = 100°.", "hints": ["Use the angle sum of the triangles and angles on a straight line.", "Relate the marked 60° and 140° to the four unknown angles."], "source": "Temasek 2023 P6 Prelim Q24", "image_needed": true, "image_options": false, "image_file": "q24.png", "image_page": 14, "image_bbox": [0.28, 0.52, 0.66, 0.76], "image_loc": "five-pointed star figure with angles p, q, r, s and marked 60° and 140°", "notes": "Answer in degrees. Key working: 180−60=120, 180−120=60, 180−140=40, 60+40=100°." }, { "n": 25, "type_id": 1, "question": "Jason left Town C for Town D at 12.50 p.m. He travelled at an average speed of 60 km/h. At 1.30 p.m., Peter left Town C for Town D, travelling along the same route at an average speed of 90 km/h. At what time did Peter overtake Jason?", "answer0": "2.50 p.m.", "answer1": "2.10 p.m.", "answer2": "3.10 p.m.", "answer3": "2.30 p.m.", "correct_answer": 0, "skill_id": 219, "difficulty_id": 3, "explanation": "By 1.30 p.m. Jason has travelled 40 min at 60 km/h = 40 km head start. Peter gains 90 − 60 = 30 km/h. Time to close 40 km = 40 ÷ 30 = 4/3 h = 1 h 20 min. 1.30 p.m. + 1 h 20 min = 2.50 p.m.", "hints": ["Find Jason's head-start distance when Peter starts at 1.30 p.m.", "Peter catches up at a rate of (90 − 60) km/h."], "source": "Temasek 2023 P6 Prelim Q25", "image_needed": false, "image_options": false, "image_file": null, "notes": "Time answer kept as MCQ (clock time). Key working gives 2.50 p.m. Distractors are plausible times." }, { "n": 26, "type_id": 0, "question": "The average mass of Bags W and X is 25 kg. The average mass of Bag X and Bag Y is 30 kg. The average mass of Bag Y and Bag Z is 28 kg. 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.
(a) The total mass of the 4 bags is 166 kg.
(b) The average mass of Bag W and Bag Z is 46 kg.
(c) Mass of Bag Z is 21 kg.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 202, "difficulty_id": 3, "explanation": "W+X = 50, X+Y = 60, Y+Z = 56. (a) Total W+X+Y+Z cannot be found uniquely (X and Y unknown individually) → False per key (W+X+Y+Z = 50+56 = 106, not 166). (b) W+Z: W = 50−X, Z = 56−Y; W+Z = 106 − (X+Y) = 106 − 60 = 46, so average = 23 kg, statement says 46 → False. (c) Z alone cannot be determined → Not possible to tell.", "hints": ["Write each pair-sum: W+X=50, X+Y=60, Y+Z=56.", "See which quantities can be found exactly and which cannot."], "source": "Temasek 2023 P6 Prelim Q26", "image_needed": false, "image_options": false, "image_file": null, "notes": "type_id 0: true/false/not-possible-to-tell tick-table — SKIPPED on insert. Answer key: (a) False, (b) False, (c) Not possible to tell." }, { "n": 27, "type_id": 0, "question": "A parallelogram WXYZ is drawn on a square grid. (a) Using the line AB, draw a triangle ABC such that it has the same perimeter as WXYZ and AB = BC. (b) Find the ratio of area of WXYZ to the area of ABC.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 199, "difficulty_id": 3, "explanation": "(a) is a drawing task on the grid (interactive). (b) From the answer key, the ratio of area of WXYZ to area of ABC is 1 : 1.", "hints": ["Part (a) requires constructing the triangle on the grid.", "Compare the area of the parallelogram with the constructed triangle."], "source": "Temasek 2023 P6 Prelim Q27", "image_needed": true, "image_options": false, "image_file": "q27.png", "image_page": 16, "image_bbox": [0.20, 0.12, 0.82, 0.36], "image_loc": "square grid with parallelogram WXYZ and line AB drawn", "notes": "type_id 0: part (a) is a draw-on-grid task — SKIPPED on insert. Answer key: (b) ratio = 1 : 1." }, { "n": 28, "type_id": 2, "question": "Sin Ling had 360 blue, green and white beads at first. After using \\(\\dfrac{1}{4}\\) of the blue beads, \\(\\dfrac{2}{3}\\) of the green beads and \\(\\dfrac{8}{9}\\) of the white beads, she had an equal number of each coloured beads left. Find the number of blue beads left. [?]", "answer0": "27", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Blue left = 3/4, green left = 1/3, white left = 1/9 of each colour. For equal beads left, express each colour total in units: blue 1:3:4 (used:left:total), green 2:1:3 → 6:3:9, white 8:1:9 → 24:3:27. Totals 4 + 9 + 27 = 40 units = 360, so 1 unit = 9. Blue left = 3 units = 3 × 9 = 27.", "hints": ["Let the equal beads left be the same number for all three colours.", "Express each colour's total as units and sum to 360."], "source": "Temasek 2023 P6 Prelim Q28", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key working: totals in units 4:9:27 = 40 units = 360, 1u = 9, blue left = 3u = 27." }, { "n": 29, "type_id": 2, "question": "At a shop, the price of 5 identical hats and 14 identical belts is the same as the price of 1 hat and 26 belts. Each hat costs $24 more than each belt. Find the cost of a hat. [?]", "answer0": "36", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 241, "difficulty_id": 3, "explanation": "5 hats + 14 belts = 1 hat + 26 belts → 4 hats = 12 belts → 1 hat = 3 belts (by value). Let 1 belt = 1 unit, 1 hat = 1 unit + $24. Then 1 unit + 24 = 3 units → 2 units = 24 → 1 unit = $12 (belt). Cost of a hat = $12 + $24 = $36.", "hints": ["Cancel the common items: subtract 1 hat and 14 belts from both sides.", "Use 'hat = belt + $24' with the value relationship."], "source": "Temasek 2023 P6 Prelim Q29", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer is in dollars (cost of a hat = $36). Key working: 8 units = $96, 1u = $12, hat = $12 + $24 = $36." }, { "n": 30, "type_id": 2, "question": "A group of boys scored an average of 58 points in a game. When 2 girls each scoring 64 points and 70 points respectively joined the group of boys, the average became 61. How many boys were there? [?]", "answer0": "4", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 205, "difficulty_id": 3, "explanation": "Each girl's score above the new average 61: (64 − 61) + (70 − 61) = 3 + 9 = 12 extra points. These raise the boys' average from 58 to 61, i.e. by 3 each. Number of boys = 12 ÷ 3 = 4.", "hints": ["Find how many points the two girls scored above the new average.", "Those extra points raised each boy's average by 3."], "source": "Temasek 2023 P6 Prelim Q30", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key working: (70−61)+(64−61) = 12, 12 ÷ (61−58) = 12 ÷ 3 = 4 boys." }, { "n": 31, "type_id": 0, "question": "The pie chart and bar graph show the number of different types of flowers sold in a particular week. The number of flowers sold is not shown on the scale. Draw the bar representing the number of stalks of carnations that were sold in that week in the bar graph above.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 236, "difficulty_id": 2, "explanation": "Draw-on-graph task. From the pie chart, Sunflowers = 1/8 and the Roses+Carnations sector is a right angle (1/4). Carnations = the remaining quarter minus sunflowers' portion; the carnation bar should be drawn to the height matching its share read from Roses (since Roses and Carnations share the upper-right quarter, carnations bar height should match the deduced count).", "hints": ["Use the pie chart fractions to compare carnations against the known bars.", "Carnations occupy part of the right-angle sector with roses."], "source": "Temasek 2023 P6 Prelim P2 Q1", "image_needed": true, "image_options": false, "image_file": "p2q1.png", "image_page": 19, "image_bbox": [0.20, 0.22, 0.88, 0.78], "image_loc": "pie chart (Orchids, Roses, Sunflowers 1/8, Carnations) above a bar graph for Roses, Carnations, Sunflowers, Orchids", "notes": "type_id 0: draw-the-bar task — SKIPPED on insert. This is Paper 2 Q1." }, { "n": 32, "type_id": 2, "question": "Mrs Tan bought 24 identical packets of nuts for $30. After the price of each packet of nuts had increased, she could only buy 20 packets with the same amount of money. What was the percentage increase in the price of each packet of nuts? [?] %", "answer0": "20", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 208, "difficulty_id": 3, "explanation": "Old price = $30 ÷ 24 = $1.25. New price = $30 ÷ 20 = $1.50. Increase = $0.25. Percentage increase = \\(\\dfrac{0.25}{1.25}\\times100\\)% = 20%.", "hints": ["Find the old and new price per packet.", "Percentage increase = increase ÷ original price × 100%."], "source": "Temasek 2023 P6 Prelim P2 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer in %. Paper 2 Q2. Key: 30÷24=$1.25, 30÷20=$1.50, 0.25/1.25 = 20%." }, { "n": 33, "type_id": 2, "question": "At first, 15 lamp posts were arranged in a row at an equal distance from point P to Q. The distance between 2 lamp posts is 26.6 m. Then, 5 more lamp posts were added. The lamp posts were rearranged at a new equal distance from point P to Q. Find the new distance between two lamp posts. [?] m", "answer0": "19.6", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 3, "explanation": "Total distance P to Q = 26.6 × (15 − 1) = 26.6 × 14 = 372.4 m. With 20 lamp posts there are 19 gaps. New distance = 372.4 ÷ 19 = 19.6 m.", "hints": ["15 posts means 14 gaps; find the total length PQ.", "20 posts means 19 gaps; divide the total by 19."], "source": "Temasek 2023 P6 Prelim P2 Q3", "image_needed": true, "image_options": false, "image_file": "p2q3.png", "image_page": 20, "image_bbox": [0.18, 0.56, 0.82, 0.70], "image_loc": "row of lamp posts from P to Q with 26.6 m gap marked between 1st and 2nd", "notes": "Answer in m. Paper 2 Q3. Key: 26.6×14 = 372.4 ÷ 19 = 19.6 m." }, { "n": 34, "type_id": 1, "question": "In an Art Club, \\(\\dfrac{5}{8}\\) of the members are girls. \\(\\dfrac{3}{4}\\) of the girls and \\(\\dfrac{1}{2}\\) of the boys are in Primary 6. What fraction of the members in the Art Club is not in Primary 6? Give your answer in its simplest form.", "answer0": "\\(\\dfrac{11}{32}\\)", "answer1": "\\(\\dfrac{21}{32}\\)", "answer2": "\\(\\dfrac{5}{16}\\)", "answer3": "\\(\\dfrac{3}{8}\\)", "correct_answer": 0, "skill_id": 165, "difficulty_id": 3, "explanation": "Girls = 5/8, boys = 3/8. Girls NOT in P6 = 1/4 × 5/8 = 5/32. Boys NOT in P6 = 1/2 × 3/8 = 3/16 = 6/32. Total not in P6 = 5/32 + 6/32 = 11/32.", "hints": ["Find the fraction of girls and boys not in Primary 6 separately.", "Add them using a common denominator of 32."], "source": "Temasek 2023 P6 Prelim P2 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Fraction answer so MCQ. Paper 2 Q4. Key: (1/4 × 5/8) + (1/2 × 3/8) = 5/32 + 6/32 = 11/32." }, { "n": 35, "type_id": 2, "question": "The figure shows taps A and B and an empty tank with dimensions 25 cm, 30 cm and 60 cm. At 1.30 p.m., only tap A was turned on. Water flowed into the tank from tap A at a rate of 1.8 litres per minute. After 20 minutes, tap B was turned on. At 2 p.m., the tank was half-filled with water. How much water flowed out from tap B in one minute? [?] \\(\\ell\\)", "answer0": "3.1", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 193, "difficulty_id": 3, "explanation": "Tank volume = 60 × 25 × 30 = 45 000 cm³ = 45 L; half = 22.5 L. From 1.30 to 2 p.m. is 30 min; tap A added 1.8 × 30 = 54 L. Tap B was on for 30 − 20 = 10 min. Water in tank at 2 p.m. = 22.5 L, so water out via B = 54 − 22.5 = 31.5 L over 10 min = 3.15 ≈ 3.1 L per minute.", "hints": ["Find the tank's half-full volume in litres.", "Tap A inflow minus what remains = total outflow; divide by the minutes B was open."], "source": "Temasek 2023 P6 Prelim P2 Q5", "image_needed": true, "image_options": false, "image_file": "p2q5.png", "image_page": 21, "image_bbox": [0.20, 0.36, 0.74, 0.58], "image_loc": "rectangular tank with Tap A on top, Tap B on the side, dims 25 cm, 30 cm, 60 cm", "notes": "Answer in litres. Paper 2 Q5. Key working: 60×25×30 = 45000 cm³ = 45L, half = 22.5L; 1.8×30 = 54L; out over 10 min = 54 − 22.5 = 31.5 ÷ 10 = 3.15 ≈ 3.1 L/min. Key shows '3.1'." }, { "n": 36, "type_id": 1, "question": "The figure is made up of three rectangles. A straight line drawn across the rectangles divides the figure into two parts: shaded and unshaded. Heights are 2 cm, 7 cm, 3 cm, 2 cm and base widths are 9 cm, 6 cm and x cm. (a) Find the total area of the figure in terms of x.", "answer0": "(138 + 2x) cm²", "answer1": "(108 + 2x) cm²", "answer2": "(138 + x) cm²", "answer3": "(120 + 2x) cm²", "correct_answer": 0, "skill_id": 239, "difficulty_id": 3, "explanation": "Three rectangles: 9 × 12 = 108 cm² (left, full height 7+... per key 12 cm), 6 × 5 = 30 cm² (middle), x × 2 = 2x cm² (right). Total = 108 + 30 + 2x = (138 + 2x) cm².", "hints": ["Split into three rectangles and find each area.", "The right rectangle has area x × 2 = 2x."], "source": "Temasek 2023 P6 Prelim P2 Q6a", "image_needed": true, "image_options": false, "image_file": "p2q6.png", "image_page": 22, "image_bbox": [0.22, 0.22, 0.72, 0.44], "image_loc": "staircase of three rectangles with a diagonal line, dims 2,7,3,2 cm and 9,6,x cm", "notes": "Algebraic-expression answer so MCQ. Paper 2 Q6(a). Key working: x×2=2x, 6×5=30, 12×9=108, total (138+2x) cm². Part (b) [area when x=2 = 85 cm²] omitted as it depends on the same figure; could be added as a separate FIB if needed." }, { "n": 37, "type_id": 2, "question": "Benedict and Samuel began jogging from the same starting point but in opposite directions along a straight line. They each jogged for half an hour. At the end of the jog, they were 10.5 km apart. Benedict's average speed was 120 m/min.
(a) How many kilometres did Benedict jog? [?] km
(b) What was Samuel's average speed in m/min? [?] m/min", "answer0": "3.6", "answer1": "230", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 219, "difficulty_id": 3, "explanation": "(a) Benedict: 120 m/min × 30 min = 3600 m = 3.6 km. (b) Samuel's distance = 10.5 − 3.6 = 6.9 km = 6900 m; speed = 6900 ÷ 30 = 230 m/min.", "hints": ["Half an hour = 30 minutes.", "Samuel's distance = 10.5 km − Benedict's distance."], "source": "Temasek 2023 P6 Prelim P2 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two FIB blanks: (a) 3.6 km, (b) 230 m/min. Paper 2 Q7. Key: 120×30=3600m=3.6km; 10.5−3.6=6.9km, 6.9÷30=0.23km=230 m/min." }, { "n": 38, "type_id": 2, "question": "During a game, Eng Soon, Fauzi and Harish scored an average of 68.5 points. Gary joined the game and the average score of the four children became 70.
(a) How many points did Gary score? [?]
(b) What percentage of the total score did Gary score? Round your answer to the nearest whole number. [?] %", "answer0": "74.5", "answer1": "27", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 205, "difficulty_id": 3, "explanation": "(a) Total of 3 = 68.5 × 3 = 205.5. Total of 4 = 70 × 4 = 280. Gary = 280 − 205.5 = 74.5 points. (b) \\(\\dfrac{74.5}{280}\\times100\\)% = 26.6% ≈ 27%.", "hints": ["Total = average × number of children.", "Gary's % = his points ÷ total of 4 × 100%."], "source": "Temasek 2023 P6 Prelim P2 Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two FIB blanks: (a) 74.5 points, (b) 27 %. Paper 2 Q8. Key: 68.5×3=205.5, 70×4=280, Gary=74.5; 74.5/280×100=26.61%≈27%." }, { "n": 39, "type_id": 2, "question": "The table shows the number of books read by 42 students. Two of the numbers in the table are accidentally painted over. The number of students reading 0, 1, 2 books are 0, 10, 9 respectively; the numbers for 3 and 4 books are hidden.
(a) On average, each student read 2.5 books. What was the total number of books read by all the students? [?]
(b) How many students read 4 books each? [?]", "answer0": "105", "answer1": "8", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 205, "difficulty_id": 3, "explanation": "(a) Total books = 2.5 × 42 = 105. (b) Students reading 3 or 4 books = 42 − (0 + 10 + 9) = 23. Books from 0,1,2 readers = 0 + 10 + 18 = 28, so books from 3 and 4 readers = 105 − 28 = 77. Let students reading 4 = f, reading 3 = 23 − f: 3(23 − f) + 4f = 77 → 69 + f = 77 → f = 8.", "hints": ["Total books = average × number of students.", "Set up an equation: 3-book and 4-book students total 23 and contribute the remaining books."], "source": "Temasek 2023 P6 Prelim P2 Q9", "image_needed": true, "image_options": false, "image_file": "p2q9.png", "image_page": 25, "image_bbox": [0.18, 0.13, 0.82, 0.22], "image_loc": "frequency table: books read 0-4 vs number of students, with 3 and 4 columns smudged", "notes": "Two FIB blanks: (a) 105 books, (b) 8 students. Paper 2 Q9. Key: 2.5×42=105; 42−19=23, 105−10−18=77, solving gives 8 students read 4 books." }, { "n": 40, "type_id": 2, "question": "In the figure, a piece of paper PQRS in the shape of a parallelogram is folded along 2 dotted lines, TS and UR. In Figure 2, \\(\\angle\\)PST = 32° and \\(\\angle\\)QRS = 14°.
(a) Find \\(\\angle\\)UQR in Figure 2. [?]
(b) Find \\(\\angle\\)QRU in Figure 2. [?]", "answer0": "122", "answer1": "22", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "(a) \\(\\angle\\)UQR: 90 − 32 = 58; 32 + 90 = 122°. (b) 180 − 90 − 32 = 58; 58 − 14 = 44; 44 ÷ 2 = 22°.", "hints": ["Use the folded right angles and the given 32° and 14°.", "Look for isosceles triangles created by the fold."], "source": "Temasek 2023 P6 Prelim P2 Q10", "image_needed": true, "image_options": false, "image_file": "p2q10.png", "image_page": 26, "image_bbox": [0.12, 0.14, 0.92, 0.32], "image_loc": "Figure 1 (parallelogram PQRS with fold lines TS, UR) and Figure 2 (folded result) with 32° and 14° marked", "notes": "Two FIB blanks (degrees): (a) 122°, (b) 22°. Paper 2 Q10. Key: (a) 90−32=58, 32+90=122°; (b) 180−90−32=58, 58−14=44, 44÷2=22°." }, { "n": 41, "type_id": 2, "question": "Elyse spent \\(\\dfrac{2}{5}\\) of her money and an additional $50 on a pair of shoes. She spent \\(\\dfrac{3}{5}\\) of the remainder and an additional $86 on a handbag. She spent half of the money that was left on food for $25. How much money did she have at first? [?]", "answer0": "650", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Working backwards: food $25 was half of what was left, so after handbag $50 was left. Before handbag: spent 3/5 of remainder + $86, leaving $50, so 2/5 of remainder = 50 + 86 = $136, remainder = $136 ÷ 2 × 5 = $340. Before shoes: 3/5 of money − $50 = $340, so 3/5 of money = $390, money = $390 ÷ 3 × 5 = $650.", "hints": ["Work backwards from the $25 spent on food.", "Each step: undo the 'additional $' then undo the fraction."], "source": "Temasek 2023 P6 Prelim P2 Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer in dollars ($650). Paper 2 Q11. Key working: 25×2=50, 50+86=136, 136÷2=68, 68×5=340, 340+50=390, 390÷3=130, 130×5=650." }, { "n": 42, "type_id": 2, "question": "In the figure, EFGH is a rhombus and FGJK is a trapezium. EH and KF are straight lines. \\(\\angle\\)KLH = 55° and \\(\\angle\\)HEF = 110°.
(a) Find \\(\\angle\\)KFH. [?]
(b) Find \\(\\angle\\)HGJ. [?]", "answer0": "20", "answer1": "15", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "(a) In rhombus EFGH, \\(\\angle\\)EHF = (180 − 110) ÷ 2 = 35°. \\(\\angle\\)KFH = 180 − 35 − 125 = 20° (using straight line and angle at L of 55°). (b) \\(\\angle\\)FGH = 110° (opposite angle of rhombus); using trapezium FGJK angle relationships: 360 − 55 − 55 = 250, 250 ÷ 2 = 125, 125 − 110 = 15°.", "hints": ["Use rhombus properties: opposite angles equal, diagonals bisect angles.", "Use the trapezium and straight-line angles for part (b)."], "source": "Temasek 2023 P6 Prelim P2 Q12", "image_needed": true, "image_options": false, "image_file": "p2q12.png", "image_page": 28, "image_bbox": [0.24, 0.13, 0.72, 0.32], "image_loc": "rhombus EFGH joined to trapezium FGJK, with 110° at E and 55° at L marked", "notes": "Two FIB blanks (degrees): (a) 20°, (b) 15°. Paper 2 Q12. Key: (a) 180−110=70, 70÷2=35, 180−35−125=20°; (b) 360−55−55=250, 250÷2=125, 125−110=15°." }, { "n": 43, "type_id": 2, "question": "Containers X and Y are rectangular containers. The base area of Container X is 30 cm² and the base area of Container Y is 100 cm². Container X contained water to a height of 120 cm and Container Y is empty.
(a) Find the volume of water in Container X. [?] cm³
(b) John then poured some water from Container X into Container Y without spilling. After that, the height of water level in Container X is twice the height of water level in Container Y. How much water did John pour into Container Y? [?] cm³", "answer0": "3600", "answer1": "2250", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 191, "difficulty_id": 3, "explanation": "(a) Volume in X = 30 × 120 = 3600 cm³. (b) Let height in Y = h, then height in X = 2h. 30 × 2h + 100 × h = 3600 → 60h + 100h = 3600 → 160h = 3600 → h = 22.5 cm. Water poured into Y = 100 × 22.5 = 2250 cm³.", "hints": ["Volume = base area × height.", "Set water in Y as height h, water in X as 2h, and the total volume is conserved."], "source": "Temasek 2023 P6 Prelim P2 Q13", "image_needed": true, "image_options": false, "image_file": "p2q13.png", "image_page": 29, "image_bbox": [0.34, 0.15, 0.84, 0.36], "image_loc": "two rectangular containers X (tall, 120 cm water) and Y (empty)", "notes": "Two FIB blanks: (a) 3600 cm³, (b) 2250 cm³. Paper 2 Q13. Key: (a) 30×120=3600; (b) 3600/160=22.5cm, 22.5×100=2250 cm³." }, { "n": 44, "type_id": 2, "question": "At a concert, 80% of the people were adults. 75% of the children at the concert were boys. There were 130 fewer boys than adults.
(a) What percentage of the people at the concert were boys? [?] %
(b) The price of a child's ticket was 40% of an adult ticket. A total of $2640 was collected at the concert. How much did an adult ticket cost? [?]", "answer0": "15", "answer1": "15", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 3, "explanation": "(a) Children = 20% of people; boys = 75% × 20% = 15% of all people. (b) Boys = 15%, adults = 80%, difference = 65% = 130 people → 1% = 2, so adults = 160, children = 40. Child : adult ticket value = 2 : 5. Total = (40 × 2u) + (160 × 5u) = 80u + 800u = 880u = $2640 → 1u = $3. Adult ticket = 5 × $3 = $15.", "hints": ["Boys = 75% of the 20% who are children.", "Use the 130-fewer relationship to find the number of people, then split the ticket money."], "source": "Temasek 2023 P6 Prelim P2 Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two FIB blanks: (a) 15 %, (b) $15. Paper 2 Q14. Key: (a) 75/100×20=15%; (b) 80−15=65% → 130, 1%→2, 80%→160 adults, 20%→40 children, ratio C:A 2:5, 880 units = $2640, 1u=$3, adult ticket 5×3 = $15." }, { "n": 45, "type_id": 2, "question": "The figure shows 2 identical semicircles and a rectangle. O and N are the centres of the semicircles. The length and breadth of the rectangle are 34 cm and 24 cm respectively. (Take \\(\\pi=3.14\\))
(a) Find the perimeter of total shaded area. [?] cm
(b) Find the total shaded area. [?] cm²", "answer0": "157.36", "answer1": "616.32", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 222, "difficulty_id": 3, "explanation": "(a) r = 24 cm (semicircle radius = breadth), diameter = 48 cm. Perimeter = quarter arc of radius 48 + 34 + 24 − 24 = (1/2 × 3.14 × 48) + 72 + 10 = 75.36 + 72 + 10 = 157.36 cm (per key working). (b) Half area = (1/4 × 3.14 × 24 × 24) + (1/2 × 24 × 24) = 164.16 cm²; total shaded = (1/4 × 3.14 × 24 × 24) + 164.16 = 616.32 cm².", "hints": ["The semicircle radius equals the breadth of the rectangle.", "Build the perimeter from the arcs and straight edges; build area from quarter-circle and triangle pieces."], "source": "Temasek 2023 P6 Prelim P2 Q15", "image_needed": true, "image_options": false, "image_file": "p2q15.png", "image_page": 31, "image_bbox": [0.30, 0.13, 0.78, 0.36], "image_loc": "two identical semicircles (centres O, N) overlapping a rectangle, 34 cm and 24 cm marked", "notes": "Two FIB blanks: (a) 157.36 cm, (b) 616.32 cm². Paper 2 Q15. Key working transcribed from page 39: (a) = 75.36 + 72 + 10 = 157.36 cm; (b) = 616.32 cm²." }, { "n": 46, "type_id": 2, "question": "Benedict had 130 more toy cars than Samuel in the beginning. Each of them gave Caleb some of their toy cars. The number of toy cars Benedict gave to Caleb was \\(\\dfrac{3}{4}\\) of the number of toy cars Samuel had at first. The number of toy cars Samuel gave to Caleb was 40% of the number of toy cars Benedict had at first. Both had an equal number of toy cars left. How many toy cars did Benedict have at first? [?]", "answer0": "650", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 3, "explanation": "Let Samuel at first = S (100 units), Benedict at first = B. 3/4 of S = 75 units. 40% of B = 40 units (taking B in same unit base). Benedict left = B − 75 units; Samuel left = S − 40 units. Setting equal and using B = S + 130: 52 units + 130 = 60 units − 52 ... solving (per key) 35 units = 182, 1 unit = 5.2, B = (5.2 × 100) + 130 = 650. Benedict had 650 toy cars at first.", "hints": ["Express both 'gave' amounts in the same unit base.", "Use 'Benedict = Samuel + 130' and 'left amounts equal' to solve."], "source": "Temasek 2023 P6 Prelim P2 Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer = 650 toy cars. Paper 2 Q16. Key working (page 39): 3/4×100=75 units, 40%×100=40 units, 52u+130 = 60u−52, 35 units = 182, 1u = 5.2, B = (5.2×100)+130 = 650." }, { "n": 47, "type_id": 2, "question": "Hasif uses white and black sticks to form figures that follow a pattern. The first five figures use white sticks 2, 2, 8, 8, 18 and black sticks 0, 4, 4, 12, 12 (totals 2, 6, 12, 20, 30).
(a) Complete the table for Figure 6: number of white sticks (i) [?], number of black sticks (ii) [?], total number of sticks (iii) [?].
(b) Which figure number has a total of 650 sticks? Figure [?].", "answer0": "18", "answer1": "24", "answer2": "42", "answer3": "25", "correct_answer": null, "skill_id": 239, "difficulty_id": 3, "explanation": "(a) Figure 6: white sticks (i) = 18, black sticks (ii) = 24, total (iii) = 18 + 24 = 42. (b) The totals 2, 6, 12, 20, 30 are products n(n+1) of consecutive integers. For total = 650, since 25 × 26 = 650, it is Figure 25 (per key: 24 × 25 = 600, 25 × 25 = 650).", "hints": ["Look for the pattern in the totals to extend to Figure 6.", "For part (b), test values near √650 (about 25)."], "source": "Temasek 2023 P6 Prelim P2 Q17", "image_needed": true, "image_options": false, "image_file": "p2q17.png", "image_page": 33, "image_bbox": [0.22, 0.10, 0.86, 0.26], "image_loc": "five figures (Figure 1-5) built from white and black sticks showing the growing pattern", "notes": "Four FIB blanks matching answer0..3: (a)(i)=18, (a)(ii)=24, (a)(iii)=42, (b)=Figure 25. Part (c) of the original paper [white sticks for Figure 15 = 128, key page 39] was dropped because the manifest schema only supports 4 answers; if a 5th-answer slot becomes available downstream, append (c)=128. Key (page 39): (i)18 (ii)24 (iii)42; (b) Fig 25; (c) 128." } ] }