{ "paper": { "school": "Nan Hua", "year": 2023, "level": "P6", "label": "Weighted Assessment 1", "source_prefix": "Nan Hua 2023 P6 Weighted Assessment 1", "has_answer_key": true, "notes": "Single assessment contains Paper 1 (Q1-13) and Paper 2 (Q1-9). Paper 1 questions sourced as 'Q', Paper 2 as 'P2 Q' to keep sources unique. Answer key on PDF pages 17-18." }, "questions": [ { "n": 1, "type_id": 1, "question": "Arrange the following fractions from the greatest to the smallest.
\\(\\dfrac{5}{9}\\), \\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{6}\\)", "answer0": "\\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{9}\\), \\(\\dfrac{5}{6}\\)", "answer1": "\\(\\dfrac{5}{6}\\), \\(\\dfrac{5}{9}\\), \\(\\dfrac{1}{2}\\)", "answer2": "\\(\\dfrac{5}{6}\\), \\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{9}\\)", "answer3": "\\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{6}\\), \\(\\dfrac{5}{9}\\)", "correct_answer": 1, "skill_id": 206, "difficulty_id": 2, "explanation": "Convert to compare: \\(\\dfrac{5}{6}\\approx0.833\\), \\(\\dfrac{5}{9}\\approx0.556\\), \\(\\dfrac{1}{2}=0.5\\). Greatest to smallest: \\(\\dfrac{5}{6}\\), \\(\\dfrac{5}{9}\\), \\(\\dfrac{1}{2}\\).", "hints": ["Find a common denominator or convert each fraction to a decimal.", "Order the decimal values from largest to smallest."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q1 = option 2 (1-based) -> 0-based index 1." }, { "n": 2, "type_id": 1, "question": "Which one of the following is a common factor of 16 and 36?", "answer0": "144", "answer1": "8", "answer2": "6", "answer3": "4", "correct_answer": 3, "skill_id": 206, "difficulty_id": 1, "explanation": "Factors of 16: 1, 2, 4, 8, 16. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The common factor among the options is 4.", "hints": ["List the factors of 16 and the factors of 36.", "A common factor must divide both numbers exactly."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q2 = option 4 (1-based) -> 0-based index 3. Skill 206 is closest available P6 number/operations skill." }, { "n": 3, "type_id": 1, "question": "What is the value of \\(360 + (60 - 6) \\div 6\\)?", "answer0": "69", "answer1": "359", "answer2": "369", "answer3": "419", "correct_answer": 2, "skill_id": 206, "difficulty_id": 1, "explanation": "Order of operations: \\((60-6)\\div6 = 54\\div6 = 9\\). Then \\(360 + 9 = 369\\).", "hints": ["Work out the brackets first, then the division.", "Add the result to 360 last."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q3 = option 3 (1-based) -> 0-based index 2." }, { "n": 4, "type_id": 1, "question": "A bag cost $200. Kate bought it at a 25% discount. How much did she pay for the bag after adding 8% GST?", "answer0": "$162", "answer1": "$150", "answer2": "$138", "answer3": "$134", "correct_answer": 0, "skill_id": 209, "difficulty_id": 2, "explanation": "Discounted price = $200 \\(\\times\\) 75% = $150. Add 8% GST: $150 \\(\\times\\) 1.08 = $162.", "hints": ["A 25% discount means she pays 75% of $200.", "Then add 8% GST to the discounted price."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q4 = option 1 (1-based) -> 0-based index 0." }, { "n": 5, "type_id": 1, "question": "AC and DF are straight lines. Find \\(\\angle CBF\\).", "answer0": "160°", "answer1": "155°", "answer2": "100°", "answer3": "80°", "correct_answer": 1, "skill_id": 230, "difficulty_id": 2, "explanation": "\\(\\angle ABF = 25^\\circ\\) lies on straight line AC. \\(\\angle CBF\\) and \\(\\angle ABF\\) are angles on a straight line, so \\(\\angle CBF = 180^\\circ - 25^\\circ = 155^\\circ\\).", "hints": ["AC is a straight line, so angles ABF and CBF add to 180°.", "Subtract the 25° angle from 180°."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 Q5", "image_needed": true, "image_options": false, "image_file": "q5.png", "image_page": 3, "image_bbox": [0.18, 0.14, 0.62, 0.36], "image_loc": "upper-left of page, intersecting straight lines AC and DF crossing at B with labelled angles 25° and 75°", "notes": "Key Q5 = option 2 (1-based) -> 0-based index 1." }, { "n": 6, "type_id": 1, "question": "Shanice had 350 marbles. She gave some of the marbles to her friends and had 280 marbles left. What was the percentage decrease in the number of marbles?", "answer0": "20%", "answer1": "25%", "answer2": "70%", "answer3": "80%", "correct_answer": 0, "skill_id": 208, "difficulty_id": 2, "explanation": "Decrease = 350 - 280 = 70 marbles. Percentage decrease = \\(\\dfrac{70}{350}\\times100\\% = 20\\%\\).", "hints": ["Find how many marbles were given away.", "Percentage decrease = decrease ÷ original amount × 100%."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q6 = option 1 (1-based) -> 0-based index 0." }, { "n": 7, "type_id": 2, "question": "Express \\(2\\dfrac{3}{8}\\) as a decimal. [?]", "answer0": "2.375", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 206, "difficulty_id": 1, "explanation": "\\(\\dfrac{3}{8} = 0.375\\), so \\(2\\dfrac{3}{8} = 2 + 0.375 = 2.375\\).", "hints": ["Divide 3 by 8 to convert the fraction part.", "Add the whole number 2 to the decimal."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q7 = 2.375 (decimal, FIB)." }, { "n": 8, "type_id": 2, "question": "A cuboid has a height of 8 cm and a square base of edge 5 cm. What is its volume? [?]", "answer0": "200", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 229, "difficulty_id": 1, "explanation": "Volume = base area × height = (5 × 5) × 8 = 25 × 8 = 200 cm³.", "hints": ["Base area = edge × edge for a square base.", "Volume = base area × height."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 4, "image_bbox": [0.14, 0.55, 0.42, 0.78], "image_loc": "left side of page, 3D cuboid sketch with 8 cm height and 5 cm base edge labelled", "notes": "Key Q8 = 200 cm³. Answer in cm³." }, { "n": 9, "type_id": 1, "question": "A poster has an area of \\(\\dfrac{3}{4}\\) m². Its length is \\(\\dfrac{7}{8}\\) m. Find its breadth.", "answer0": "\\(\\dfrac{6}{7}\\) m", "answer1": "\\(\\dfrac{21}{32}\\) m", "answer2": "\\(\\dfrac{7}{6}\\) m", "answer3": "\\(\\dfrac{3}{4}\\) m", "correct_answer": 0, "skill_id": 206, "difficulty_id": 2, "explanation": "Breadth = area ÷ length = \\(\\dfrac{3}{4} \\div \\dfrac{7}{8} = \\dfrac{3}{4} \\times \\dfrac{8}{7} = \\dfrac{24}{28} = \\dfrac{6}{7}\\) m.", "hints": ["Breadth = area ÷ length.", "Dividing by a fraction means multiplying by its reciprocal."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q9 = 6/7 m (fraction) -> made MCQ per spec; correct option index 0." }, { "n": 10, "type_id": 2, "question": "Sam has some 1-dollar and 20-cent coins in the ratio 2 : 5. The total value of the coins is $21. How many 20-cent coins does he have? [?]", "answer0": "35", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 213, "difficulty_id": 2, "explanation": "Let units be 2u of $1 coins and 5u of 20-cent coins. Value = 2u × $1 + 5u × $0.20 = $2u + $1u = $3u. $3u = $21, so u = 7. 20-cent coins = 5u = 35.", "hints": ["Value of $1 coins = 2u × $1; value of 20-cent coins = 5u × $0.20.", "Add the values, set equal to $21, then solve for one unit."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q10 = 35 (integer count, FIB)." }, { "n": 11, "type_id": 2, "question": "The table shows Macy's savings from January to March. Her average savings for the 3 months was $52. How much did she save in March?
January: $28
February: $70
March: ? [?]", "answer0": "58", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 204, "difficulty_id": 2, "explanation": "Total for 3 months = average × 3 = $52 × 3 = $156. March = $156 - $28 - $70 = $58.", "hints": ["Total savings = average × number of months.", "Subtract January and February savings from the total."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q11 = $58 (table transcribed inline into stem; answer in dollars). Directional 'below' stripped." }, { "n": 12, "type_id": 1, "question": "Suzy packed 13 kg of flour into small packets. Each packet contained \\(\\dfrac{2}{3}\\) kg of flour. How much flour was left in the packet that was not completely filled?", "answer0": "\\(\\dfrac{1}{3}\\) kg", "answer1": "\\(\\dfrac{2}{3}\\) kg", "answer2": "\\(\\dfrac{1}{2}\\) kg", "answer3": "\\(\\dfrac{1}{6}\\) kg", "correct_answer": 0, "skill_id": 206, "difficulty_id": 3, "explanation": "Number of full packets = \\(13 \\div \\dfrac{2}{3} = 13 \\times \\dfrac{3}{2} = \\dfrac{39}{2} = 19\\dfrac{1}{2}\\), so 19 full packets are filled. Flour used = \\(19 \\times \\dfrac{2}{3} = \\dfrac{38}{3} = 12\\dfrac{2}{3}\\) kg. Left over = \\(13 - 12\\dfrac{2}{3} = \\dfrac{1}{3}\\) kg.", "hints": ["Divide 13 by 2/3 to find how many full packets there are.", "Multiply the number of full packets by 2/3, then subtract from 13."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q12 = 1/3 kg (fraction) -> made MCQ per spec; correct option index 0." }, { "n": 13, "type_id": 2, "question": "In the figure, ABCH is a square and DEGH is a rectangle. Given that the area of the shaded triangle is 35 cm², find the length of DE. [?]", "answer0": "9", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 223, "difficulty_id": 3, "explanation": "Shaded triangle has base AB = 5 cm (top of square) and its area is 35 cm². Triangle area = \\(\\dfrac{1}{2}\\times\\)base\\(\\times\\)height, so \\(35 = \\dfrac{1}{2}\\times5\\times\\)height, giving height = 14 cm. This height spans from AB down to F. Square side = 5 cm (so HC = 5). The triangle's full height to F = 14, with 5 inside the square, so the part below HC is 14 - 5 = 9 cm. DE equals the rectangle's height = 9 cm.", "hints": ["Use area of triangle = ½ × base × height to find the triangle's height.", "DE is the height of rectangle DEGH; relate it to the triangle height below the square."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 Q13", "image_needed": true, "image_options": false, "image_file": "q13.png", "image_page": 7, "image_bbox": [0.12, 0.16, 0.55, 0.42], "image_loc": "upper-left of page, composite figure: square ABCH with shaded triangle and adjoining rectangle DEGH; 5 cm and 15 cm dimensions labelled", "notes": "Key Q13 = 9 cm. Answer in cm." }, { "n": 14, "type_id": 2, "question": "Simon has some peanuts. He wants to pack 28 packets of peanuts. Each packet contains 0.8 kg of peanuts. He has 620 g of peanuts left. How many kilograms of peanuts did he have at first? [?]", "answer0": "23.02", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 2, "explanation": "0.8 kg = 800 g. Peanuts packed = 800 g × 28 = 22400 g. Add leftover: 22400 + 620 = 23020 g = 23.02 kg.", "hints": ["Convert 0.8 kg to grams, then multiply by 28 packets.", "Add the 620 g left, then convert the total back to kilograms."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 P2 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q1. Key = 23.02 kg (decimal, FIB). Answer in kg." }, { "n": 15, "type_id": 1, "question": "A sum of money was shared between Ali and John in the ratio 2 : 5. John gave \\(\\dfrac{1}{4}\\) of his share to Ali. What is the new ratio of Ali's share to John's share of the money?", "answer0": "13 : 15", "answer1": "2 : 5", "answer2": "3 : 4", "answer3": "7 : 8", "correct_answer": 0, "skill_id": 214, "difficulty_id": 2, "explanation": "Ali : John = 2 : 5. Make John divisible by 4: multiply by 4 → Ali : John = 8 : 20. John gives \\(\\dfrac{1}{4}\\) of 20 = 5 to Ali. New Ali = 8 + 5 = 13, new John = 20 - 5 = 15. New ratio = 13 : 15.", "hints": ["Scale the ratio so John's share is divisible by 4.", "Move one quarter of John's units to Ali, then write the new ratio."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 P2 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q2. Key = 13:15 (ratio) -> made MCQ per spec; correct option index 0." }, { "n": 16, "type_id": 2, "question": "Andy packed 168 beads into 3 bags, A, B and C. The ratio of the number of beads in Bag A to the number of beads in Bag B to the number of beads in Bag C was 3 : 15 : 10. How many beads were there in Bag C? [?]", "answer0": "60", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 213, "difficulty_id": 2, "explanation": "Total units = 3 + 15 + 10 = 28u. 28u = 168, so 1u = 6. Bag C = 10u = 10 × 6 = 60 beads.", "hints": ["Add the ratio parts to find the total number of units.", "Find the value of 1 unit, then multiply by Bag C's units."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 P2 Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q3. Key = 60 (integer, FIB)." }, { "n": 17, "type_id": 2, "question": "In the figure, ABCD is a trapezium and BCD is an isosceles triangle. Find \\(\\angle x\\). [?]", "answer0": "43", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "AB is parallel to DC. \\(\\angle BDC = \\angle ABD\\)... using the trapezium and isosceles triangle BCD: \\(\\angle BDC = 32^\\circ\\). In triangle BCD, \\(\\angle BDC = \\angle BCD\\) (isosceles), so the working gives \\(\\angle x = 180^\\circ - 105^\\circ - 32^\\circ = 43^\\circ\\).", "hints": ["Use the parallel sides of the trapezium to find equal angles.", "BCD is isosceles — two of its angles are equal; angles in a triangle sum to 180°."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 P2 Q4", "image_needed": true, "image_options": false, "image_file": "q17.png", "image_page": 11, "image_bbox": [0.13, 0.18, 0.56, 0.33], "image_loc": "upper-left of page, trapezium ABCD with isosceles triangle BCD; angles 105°, 32° and unknown x labelled", "notes": "Paper 2 Q4. Key working = 180 - 105 - 32 = 43°. Answer in degrees (integer, FIB)." }, { "n": 18, "type_id": 2, "question": "Macy had $270 less than Lindy. After Macy gave Lindy some money, Lindy had 4 times as much money as Macy. If Macy had $520 left, how much money did she have at first? [?]", "answer0": "1165", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 241, "difficulty_id": 3, "explanation": "After: Macy = $520, Lindy = 4 × $520 = $2080. Total = $520 + $2080 = $2600 (unchanged). Before: Macy had $270 less than Lindy, so Macy = (2600 - 270) ÷ 2 = $1165.", "hints": ["The total money is unchanged when Macy gives money to Lindy.", "Use 'Macy had $270 less than Lindy' with the constant total to split it."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 P2 Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q5. Key = $1165 (integer dollars, FIB). Stem printed 'Macy had $270 less and Lindy' — read as '$270 less than Lindy'." }, { "n": 19, "type_id": 2, "question": "An empty rectangular tank measures 52 cm by 45 cm by 40 cm. A tap was turned on and water flowed at a rate of 5.2 litres per minute. How long would it take for the tank to be \\(\\dfrac{1}{2}\\)-filled? [?]", "answer0": "9", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 229, "difficulty_id": 2, "explanation": "Full volume = 52 × 45 × 40 = 93600 cm³. Half = 46800 cm³ = 46800 ml = 46.8 L. Time = 46.8 ÷ 5.2 = 9 minutes.", "hints": ["Find the tank's volume in cm³, then halve it.", "1000 cm³ = 1 litre; divide the half-volume by the flow rate."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 P2 Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q6. Key = 9 minutes (integer, FIB). Answer in minutes." }, { "n": 20, "type_id": 2, "question": "Ashton, Bryan and Charles were given the same number of funfair tickets to sell. Charles sold 92 tickets. Bryan had twice as many tickets left unsold as Ashton's. Charles' number of tickets left unsold was 14 fewer than Bryan's. There was a total of 491 unsold tickets. How many tickets did each of them have to sell? [?]", "answer0": "280", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 241, "difficulty_id": 3, "explanation": "Let Ashton's unsold = 1u. Bryan's unsold = 2u. Charles' unsold = 2u - 14. Total unsold: 1u + 2u + (2u - 14) = 491, so 5u - 14 = 491, 5u = 505, 1u = 101. Charles' unsold = 2(101) - 14 = 188. Each was given Charles' sold + Charles' unsold = 92 + 188 = 280 tickets.", "hints": ["Write each person's unsold tickets in units of Ashton's unsold (1u).", "Solve 5u - 14 = 491; each person's total = Charles sold + Charles unsold."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 P2 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q7. Printed key's last line '188 + 92 = 208' is an arithmetic typo; 188 + 92 = 280. Each was given 280 tickets (integer, FIB). Flagged per spec." }, { "n": 21, "type_id": 2, "question": "Fatimah spent \\(\\dfrac{1}{4}\\) of her money on 8 cookies and 2 muffins. A muffin cost three times as much as a cookie. She bought some more cookies with \\(\\dfrac{2}{7}\\) of her remaining money. How many cookies did Fatimah buy altogether? [?]", "answer0": "20", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 3, "explanation": "8 cookies + 2 muffins, muffin = 3 cookies, so cost = 8 + 2×3 = 14 cookie-units = \\(\\dfrac{1}{4}\\) of money. Remaining money = \\(\\dfrac{3}{4}\\). Money spent on more cookies = \\(\\dfrac{2}{7}\\times\\dfrac{3}{4} = \\dfrac{6}{28}\\) of total. Since \\(\\dfrac{1}{4} = \\dfrac{7}{28}\\) buys 14 cookie-units, \\(\\dfrac{1}{28}\\) buys 2 cookies, so \\(\\dfrac{6}{28}\\) buys 12 cookies. Total cookies = 8 + 12 = 20.", "hints": ["Express the muffin cost in terms of a cookie's cost (1 muffin = 3 cookies).", "Find how many cookies one '1/28 of the money' buys, then scale to 6/28."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 P2 Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q8. Key = 20 cookies altogether (integer, FIB)." }, { "n": 22, "type_id": 2, "question": "Danny had 880 cards in his collection. 25% of the cards were football cards and the rest were basketball cards.
(a) How many more basketball cards than football cards did he have in his collection? [?]
(b) How many more football cards must Danny buy if he wanted to increase the number of football cards in his collection to 45%? [?]", "answer0": "440", "answer1": "320", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 3, "explanation": "(a) Football = 25% of 880 = 220. Basketball = 880 - 220 = 660. Difference = 660 - 220 = 440. (b) Basketball stays 660 = 100% - 45% = 55% of the new total. 55% = 660, so 1% = 12 and 45% = 540 football cards needed. Must buy 540 - 220 = 320 more.", "hints": ["(a) 25% are football; the rest (75%) are basketball. Subtract.", "(b) Basketball count is fixed (660) and becomes 55%; find the new football count (45%) and subtract the 220 he already has."], "source": "Nan Hua 2023 P6 Weighted Assessment 1 P2 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q9, two parts. (a) = 440, (b) = 320; both integers in order (answer0=part a, answer1=part b), FIB with one [?] per part." } ] }