{ "paper": { "school": "Pei Hwa Presbyterian", "year": 2023, "level": "P4", "label": "Weighted Assessment 3", "source_prefix": "Pei Hwa 2023 P4 Weighted Assessment 3", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "What fraction does the following represent?", "answer0": "$$\\frac{5}{6}$$", "answer1": "$$2\\frac{1}{2}$$", "answer2": "3", "answer3": "$$4\\frac{1}{2}$$", "correct_answer": 1, "skill_id": 119, "difficulty_id": 1, "explanation": "There are two whole shaded figures plus one half-shaded figure, giving 2 whole and $$\\frac{1}{2}$$, i.e. $$2\\frac{1}{2}$$.", "hints": [ "Count the whole shaded shapes first.", "Add the part-shaded shape as a fraction of one whole." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q1", "image_needed": true, "image_options": false, "image_file": "q1.png", "image_page": 1, "image_bbox": [ 0.2, 0.41, 0.56, 0.5 ], "image_loc": "three small square figures in a row just below the question text", "notes": "Key answer = option 2 (2 1/2). Figures: 2 fully shaded + 1 half-shaded." }, { "n": 2, "type_id": 1, "question": "Which of the following shows $$\\frac{1}{3}$$ of a set shaded?", "answer0": "Set A", "answer1": "Set B", "answer2": "Set C", "answer3": "Set D", "correct_answer": 3, "skill_id": 120, "difficulty_id": 2, "explanation": "Option 4 has 13 circles total with several shaded; the only set where the shaded portion is exactly one third of the whole set is option 4. (Check each set: shaded items ÷ total items = $$\\frac{1}{3}$$.)", "hints": [ "Count the total objects in each set and the shaded ones.", "$$\\frac{1}{3}$$ means 1 out of every 3 objects is shaded." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q2", "image_needed": true, "image_options": true, "image_file": null, "image_page": 2, "image_bbox": [ 0.2, 0.23, 0.55, 0.55 ], "image_loc": "four option sets (squares, triangles, parallelograms, circles) stacked below the question", "notes": "Image-option MCQ; crop each set to q2_opt0..q2_opt3.png. Key answer = option 4." }, { "n": 3, "type_id": 1, "question": "Which of the following fractions is not the same as 0.4?", "answer0": "$$\\frac{10}{25}$$", "answer1": "$$\\frac{2}{5}$$", "answer2": "$$\\frac{3}{12}$$", "answer3": "$$\\frac{4}{10}$$", "correct_answer": 2, "skill_id": 126, "difficulty_id": 2, "explanation": "0.4 = $$\\frac{4}{10}$$ = $$\\frac{2}{5}$$ = $$\\frac{10}{25}$$. But $$\\frac{3}{12}$$ = $$\\frac{1}{4}$$ = 0.25, which is not 0.4.", "hints": [ "Convert 0.4 to a fraction: $$\\frac{4}{10}=\\frac{2}{5}$$.", "Simplify each option and compare." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key answer = option 3 (3/12 = 0.25)." }, { "n": 4, "type_id": 1, "question": "Arrange the following decimals from the largest to the smallest.
7.093, 7.903, 7.309, 7.39", "answer0": "7.39, 7.093, 7.309, 7.903", "answer1": "7.093, 7.903, 7.39, 7.309", "answer2": "7.903, 7.39, 7.309, 7.093", "answer3": "7.903, 7.309, 7.093, 7.39", "correct_answer": 2, "skill_id": 124, "difficulty_id": 2, "explanation": "Compare place by place: 7.903 > 7.39 > 7.309 > 7.093. So largest to smallest is 7.903, 7.39, 7.309, 7.093.", "hints": [ "Line up the decimal points and compare the tenths digit first.", "If tenths are equal, compare hundredths, then thousandths." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key answer = option 3 (7.903, 7.39, 7.309, 7.093)." }, { "n": 5, "type_id": 1, "question": "Which one of the following is closest to 8?", "answer0": "7.5", "answer1": "8.1", "answer2": "7.95", "answer3": "8.49", "correct_answer": 2, "skill_id": 128, "difficulty_id": 1, "explanation": "Find the distance from 8: 7.5 is 0.5 away, 8.1 is 0.1 away, 7.95 is 0.05 away, 8.49 is 0.49 away. The smallest gap is 7.95.", "hints": [ "Find how far each number is from 8.", "The closest number has the smallest difference." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key answer = option 3 (7.95)." }, { "n": 6, "type_id": 1, "question": "John bought the following fruits.
orange: 2 kg, grapes: $$\\frac{1}{4}$$ kg, bananas: $$\\frac{2}{3}$$ kg
What was the total mass of the fruits bought?", "answer0": "$$\\frac{5}{7}$$ kg", "answer1": "$$2\\frac{3}{4}$$ kg", "answer2": "$$2\\frac{3}{7}$$ kg", "answer3": "$$2\\frac{11}{12}$$ kg", "correct_answer": 3, "skill_id": 121, "difficulty_id": 2, "explanation": "Total = 2 + $$\\frac{1}{4}$$ + $$\\frac{2}{3}$$. Common denominator 12: $$\\frac{1}{4}=\\frac{3}{12}$$, $$\\frac{2}{3}=\\frac{8}{12}$$. $$\\frac{3}{12}+\\frac{8}{12}=\\frac{11}{12}$$. Total = $$2\\frac{11}{12}$$ kg.", "hints": [ "Add only the fraction parts using a common denominator.", "The common denominator of 4 and 3 is 12." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q6", "image_needed": true, "image_options": false, "image_file": "q6.png", "image_page": 4, "image_bbox": [ 0.18, 0.2, 0.7, 0.32 ], "image_loc": "three fruit drawings (orange, grapes, bananas) with mass labels below the question", "notes": "Masses given in figure labels (2 kg, 1/4 kg, 2/3 kg) are reproduced in the stem. Key answer = option 4." }, { "n": 7, "type_id": 1, "question": "A pot was filled with soup. Mrs Tan poured $$\\frac{1}{2}$$ of it for her son and $$\\frac{2}{7}$$ of it for herself. What fraction of the soup was left in the pot?", "answer0": "$$\\frac{2}{3}$$", "answer1": "$$\\frac{3}{14}$$", "answer2": "$$\\frac{5}{14}$$", "answer3": "$$\\frac{9}{14}$$", "correct_answer": 1, "skill_id": 122, "difficulty_id": 2, "explanation": "Poured = $$\\frac{1}{2}+\\frac{2}{7}=\\frac{7}{14}+\\frac{4}{14}=\\frac{11}{14}$$. Left = 1 - $$\\frac{11}{14}=\\frac{3}{14}$$.", "hints": [ "Use a common denominator of 14 to add the two poured fractions.", "Subtract the poured total from 1 whole." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key answer = option 2 (3/14)." }, { "n": 8, "type_id": 1, "question": "I am a number with 2 decimal places.
The digit 6 is in the ones place.
The digit in the tenths place is 2 less than the digit in the ones place.
The digit in the hundredths place is the largest odd number.
Round this number to the nearest tenth.", "answer0": "6.4", "answer1": "6.5", "answer2": "6.9", "answer3": "7.0", "correct_answer": 1, "skill_id": 128, "difficulty_id": 2, "explanation": "Ones = 6, tenths = 6 - 2 = 4, hundredths = 9 (largest odd digit). Number = 6.49. Rounding to the nearest tenth: hundredths digit 9 rounds the 4 up to 5, giving 6.5.", "hints": [ "Build the number digit by digit: ones, tenths, hundredths.", "To round to the nearest tenth, look at the hundredths digit." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Number is 6.49 -> 6.5. Key answer = option 2 (6.5)." }, { "n": 9, "type_id": 1, "question": "Bala is 0.05 m taller than Paul. Zoe is 0.18 m shorter than Bala. Zoe is 1.68 m tall. How tall is Paul?", "answer0": "1.45 m", "answer1": "1.55 m", "answer2": "1.81 m", "answer3": "1.91 m", "correct_answer": 2, "skill_id": 129, "difficulty_id": 2, "explanation": "Bala = Zoe + 0.18 = 1.68 + 0.18 = 1.86 m. Paul = Bala - 0.05 = 1.86 - 0.05 = 1.81 m.", "hints": [ "First find Bala's height from Zoe's.", "Then subtract 0.05 m to get Paul's height." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key answer = option 3 (1.81 m)." }, { "n": 10, "type_id": 1, "question": "Nora paid $164.20 for some pillows and 4 bolsters. The pillows cost $76.80. How much did each bolster cost?", "answer0": "$19.20", "answer1": "$21.85", "answer2": "$22.15", "answer3": "$28.15", "correct_answer": 1, "skill_id": 131, "difficulty_id": 2, "explanation": "Cost of 4 bolsters = $164.20 - $76.80 = $87.40. Each bolster = $87.40 ÷ 4 = $21.85.", "hints": [ "Subtract the pillow cost to find the total for the bolsters.", "Divide by 4 to find the cost of one bolster." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key answer = option 2 ($21.85)." }, { "n": 11, "type_id": 2, "question": "Subtract $$\\frac{1}{8}$$ from 4.
Express your answer as an improper fraction.
[?]", "answer0": "31/8", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 121, "difficulty_id": 1, "explanation": "4 - $$\\frac{1}{8}$$ = $$\\frac{32}{8} - \\frac{1}{8}$$ = $$\\frac{31}{8}$$.", "hints": [ "Write 4 as eighths: $$\\frac{32}{8}$$.", "Subtract the numerators over 8." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key answer = 31/8 (improper fraction required)." }, { "n": 12, "type_id": 2, "question": "In the number line, what is the mixed number represented by A?
[?]", "answer0": "2 1/6", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 119, "difficulty_id": 2, "explanation": "The line runs from $$1\\frac{2}{3}$$ to $$2\\frac{1}{2}$$ in 5 equal intervals of $$\\frac{1}{6}$$. The marks are $$1\\frac{2}{3}, 1\\frac{5}{6}, 2, 2\\frac{1}{6}, 2\\frac{2}{6}=2\\frac{1}{3}, 2\\frac{1}{2}$$. A is one step past 2, so A = $$2\\frac{1}{6}$$.", "hints": [ "Find the size of one interval on the number line.", "Count from the 2 mark to A." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q12", "image_needed": true, "image_options": false, "image_file": "q12.png", "image_page": 6, "image_bbox": [ 0.18, 0.48, 0.82, 0.56 ], "image_loc": "horizontal number line with marks labelled 1 2/3, 2, A, 2 1/2 below the question", "notes": "Key answer = 2 1/6. Answer typed as plain mixed number 2 1/6." }, { "n": 13, "type_id": 2, "question": "Write a fraction between $$\\frac{1}{3}$$ and $$\\frac{1}{4}$$.
[?]", "answer0": "7/24", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 121, "difficulty_id": 2, "explanation": "Use a common denominator: $$\\frac{1}{3}=\\frac{8}{24}$$ and $$\\frac{1}{4}=\\frac{6}{24}$$. A fraction in between is $$\\frac{7}{24}$$.", "hints": [ "Convert both fractions to a common denominator.", "Pick a numerator between the two new numerators." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Open answer; key gives 7/24. Any fraction strictly between 1/4 and 1/3 is valid, but graded answer = 7/24." }, { "n": 14, "type_id": 2, "question": "Express $$7\\frac{1}{20}$$ as a decimal.
[?]", "answer0": "7.05", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 127, "difficulty_id": 1, "explanation": "$$\\frac{1}{20}=\\frac{5}{100}=0.05$$. So $$7\\frac{1}{20}$$ = 7 + 0.05 = 7.05.", "hints": [ "Make the denominator 100: $$\\frac{1}{20}=\\frac{5}{100}$$.", "Add the whole number to the decimal." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key answer = 7.05." }, { "n": 15, "type_id": 2, "question": "6 ones + 12 tenths + 4 hundredths = [?]", "answer0": "7.24", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 123, "difficulty_id": 2, "explanation": "6 ones = 6, 12 tenths = 1.2, 4 hundredths = 0.04. Total = 6 + 1.2 + 0.04 = 7.24.", "hints": [ "12 tenths is more than 1 whole (1.2).", "Add all three place values together." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key answer = 7.24 (note 12 tenths regroups to 1.2)." }, { "n": 16, "type_id": 2, "question": "Find the value of 28.67 ÷ 7.
Give your answer correct to 2 decimal places.
[?]", "answer0": "4.10", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 130, "difficulty_id": 2, "explanation": "28.67 ÷ 7 = 4.0957... Rounded to 2 decimal places = 4.10.", "hints": [ "Divide to at least 3 decimal places before rounding.", "Round the result to 2 decimal places." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key answer = 4.10 (2 d.p.)." }, { "n": 17, "type_id": 2, "question": "What are the missing numbers in the boxes?
(a) . 0 5
− 1 . 6 (b)
= 4 . 3 8
(a) = [?], (b) = [?]", "answer0": "6", "answer1": "7", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 129, "difficulty_id": 3, "explanation": "The subtraction is (a).05 - 1.6(b) = 4.38. Working from the result: 4.38 + 1.6(b) must give (a).05. Hundredths: 8 + b = 15 so b = 7 (carry 1). Tenths: 3 + 6 + 1 = 10, write 0 carry 1. Ones: 4 + 1 + 1 = 6 = a. So a = 6, b = 7 (check: 6.05 - 1.67 = 4.38).", "hints": [ "Add the answer (4.38) to the number subtracted (1.6b) to recover the top number.", "Start from the hundredths column and carry as needed." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q17", "image_needed": true, "image_options": false, "image_file": "q17.png", "image_page": 8, "image_bbox": [ 0.18, 0.21, 0.45, 0.33 ], "image_loc": "vertical subtraction sum with boxed blanks (a) and (b) below the question", "notes": "Key: (a)=6, (b)=7. Two ordered blanks. 6.05 - 1.67 = 4.38." }, { "n": 18, "type_id": 2, "question": "Henry and Jason had the same amount of money. After Jason bought 5 comic books, Henry had 4 times as much money as him. Comic book: $15.60 each. How much did Jason have left after buying the comic books?
$[?]", "answer0": "26", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "Cost of 5 comic books = 5 × $15.60 = $78. Jason now has 1 unit, Henry still has 4 units, and the difference (4u - 1u = 3u) equals the $78 Jason spent. 3u = $78, so 1u = $26. Jason had $26 left.", "hints": [ "Find the total cost of the 5 comic books first.", "The money Jason spent equals the difference of 3 units." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Comic price label ($15.60 each) folded into stem; comic-book picture is decorative, not required. Key answer = $26." }, { "n": 19, "type_id": 2, "question": "The figure is made up of identical rectangles. How many more rectangles must be shaded to have $$\\frac{4}{5}$$ of the figure shaded?
[?]", "answer0": "7", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 120, "difficulty_id": 2, "explanation": "The figure has 20 identical rectangles (4 rows of 5). $$\\frac{4}{5}$$ of 20 = 16 shaded needed. Currently 9 are shaded, so 16 - 9 = 7 more must be shaded.", "hints": [ "Count the total rectangles, then find $$\\frac{4}{5}$$ of that total.", "Subtract the rectangles already shaded." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q19", "image_needed": true, "image_options": false, "image_file": "q19.png", "image_page": 9, "image_bbox": [ 0.16, 0.22, 0.48, 0.43 ], "image_loc": "grid of identical rectangles, some shaded, below the question", "notes": "Total 20 rectangles, 9 already shaded; 4/5 of 20 = 16; need 16-9 = 7 more. Key answer = 7." }, { "n": 20, "type_id": 0, "question": "The table shows the number of books donated by 90 students.
Number of donated books: 0,1,2,3,4 / Number of students: 15,30,22,13,10
Each statement is either true or false. Statement 1: $$\\frac{1}{3}$$ of the students donated 1 book. Statement 2: $$\\frac{1}{2}$$ of the students donated more than 2 books.", "answer0": "True", "answer1": "False", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 2, "explanation": "Statement 1: $$\\frac{1}{3}$$ of 90 = 30 students; 30 donated 1 book, so TRUE. Statement 2: more than 2 books = 13 + 10 = 23 students; $$\\frac{1}{2}$$ of 90 = 45, and 23 ≠ 45, so FALSE.", "hints": [ "Work out 1/3 and 1/2 of the 90 students.", "Compare to the actual counts in the table." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q20", "image_needed": false, "image_options": false, "image_file": null, "notes": "True/False tick-the-box format (no app type) -> type_id 0, SKIPPED on insert. Key: statement 1 True, statement 2 False." }, { "n": 21, "type_id": 2, "question": "Mr Lim and his son are travelling together.
Transportation Fees — Cost of Mode A: Adult Ticket $12.50, Child Ticket $8.90. Cost of Mode B: Adult Ticket $16.80, Child Ticket $5.40.
Which mode of transportation is cheaper and how much can Mr Lim save?
Cheaper mode: Mode [?], Amount saved: $[?]", "answer0": "A", "answer1": "0.80", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 131, "difficulty_id": 2, "explanation": "Mode A total = $12.50 + $8.90 = $21.40 (1 adult + 1 child). Mode B total = $16.80 + $5.40 = $22.20. Mode A is cheaper. Saving = $22.20 - $21.40 = $0.80.", "hints": [ "Add the adult and child ticket for each mode.", "Subtract the cheaper total from the dearer total to find the saving." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q21", "image_needed": true, "image_options": false, "image_file": "q21.png", "image_page": 10, "image_bbox": [ 0.16, 0.28, 0.66, 0.5 ], "image_loc": "Transportation Fees box with two ticket pictures and Cost of Mode A / Mode B price tables", "notes": "Two ordered blanks: mode (A) and saving ($0.80). Ticket prices reproduced in stem. Key: Mode A, $0.80." }, { "n": 22, "type_id": 2, "question": "Doreen had some beads for sale. She sold $$\\frac{1}{3}$$ of the beads in the morning and $$\\frac{2}{5}$$ of the beads in the afternoon. (a) What fraction of the beads was left? (b) Doreen had 28 beads left. How many beads did she have at first?
(a) [?], (b) [?]", "answer0": "4/15", "answer1": "105", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 122, "difficulty_id": 3, "explanation": "(a) Sold = $$\\frac{1}{3}+\\frac{2}{5}=\\frac{5}{15}+\\frac{6}{15}=\\frac{11}{15}$$. Left = 1 - $$\\frac{11}{15}=\\frac{4}{15}$$. (b) $$\\frac{4}{15}$$ of the beads = 28, so 4 units = 28, 1 unit = 7. Total 15 units = 7 × 15 = 105 beads.", "hints": [ "Add the two sold fractions using a common denominator of 15.", "The leftover fraction (4/15) corresponds to 28 beads; find one unit, then the whole." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q22", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two ordered blanks. (a) fraction 4/15, (b) 105 beads. Key matches." }, { "n": 23, "type_id": 2, "question": "8 apples and an orange cost $8.60. 4 apples and an orange cost $5. (a) Find the cost of an apple. (b) Find the cost of an orange.
(a) $[?], (b) $[?]", "answer0": "0.90", "answer1": "1.40", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "(a) The difference between the two purchases is 4 apples = $8.60 - $5 = $3.60, so 1 apple = $3.60 ÷ 4 = $0.90. (b) From 4 apples + 1 orange = $5: 4 apples = 4 × $0.90 = $3.60, so 1 orange = $5 - $3.60 = $1.40.", "hints": [ "Subtract the two equations to remove the orange and find the cost of 4 apples.", "Substitute the apple cost back to find the orange." ], "source": "Pei Hwa 2023 P4 Weighted Assessment 3 Q23", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two ordered blanks. (a) apple $0.90, (b) orange $1.40. Key matches." } ] }