{
"paper": {
"school": "Anglo-Chinese School (Junior)",
"year": 2022,
"level": "P5",
"label": "Weighted Assessment 3",
"source_prefix": "ACS 2022 P5 Weighted Assessment 3",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "Express 2.5% as a decimal.",
"answer0": "0.025",
"answer1": "0.25",
"answer2": "2.5",
"answer3": "25.0",
"correct_answer": 0,
"skill_id": 173,
"difficulty_id": 1,
"explanation": "To convert a percentage to a decimal, divide by 100. \\(2.5\\% = 2.5 \\div 100 = 0.025\\). Answer: 0.025.",
"hints": ["A percentage means 'out of 100', so divide by 100.", "Move the decimal point two places to the left: 2.5 -> 0.025."],
"source": "ACS 2022 P5 Weighted Assessment 3 Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: Q1 = option 1 (0.025)."
},
{
"n": 2,
"type_id": 1,
"question": "Express \\(\\dfrac{3}{4}\\) as a percentage.",
"answer0": "3.4%",
"answer1": "34%",
"answer2": "7.5%",
"answer3": "75%",
"correct_answer": 3,
"skill_id": 173,
"difficulty_id": 1,
"explanation": "To write a fraction as a percentage, multiply by 100%. \\(\\dfrac{3}{4} \\times 100\\% = 75\\%\\). Answer: 75%.",
"hints": ["Multiply the fraction by 100%.", "\\(\\dfrac{3}{4} = 0.75 = 75\\%\\)."],
"source": "ACS 2022 P5 Weighted Assessment 3 Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: Q2 = option 4 (75%)."
},
{
"n": 3,
"type_id": 1,
"question": "The table shows the local parcel delivery charges. What is the delivery charge for delivering a parcel with a mass of 5.5 kg?",
"answer0": "$50",
"answer1": "$52",
"answer2": "$60",
"answer3": "$78",
"correct_answer": 0,
"skill_id": 152,
"difficulty_id": 2,
"explanation": "Up to 5 kg costs $42. The extra mass above 5 kg is 0.5 kg, which is charged as 1 full additional step (per 1 kg or part thereof) = $8. Total = $42 + $8 = $50. Answer: $50.",
"hints": ["Find the charge for the first 5 kg from the table.", "Any part of an extra 1 kg step counts as a full step, so 0.5 kg = 1 step = $8."],
"source": "ACS 2022 P5 Weighted Assessment 3 Q3",
"image_needed": true,
"image_options": false,
"image_file": "q3.png",
"image_page": 2,
"image_bbox": [0.19, 0.66, 0.86, 0.76],
"image_loc": "charge table in the middle of the page, below the question text",
"notes": "Key: Q3 = option 1 ($50). Table is required to answer."
},
{
"n": 4,
"type_id": 1,
"question": "A wire measuring 624 m was cut by a machine into 600 equal pieces. What was the total length of 10 pieces?",
"answer0": "0.14 m",
"answer1": "1.04 m",
"answer2": "10.4 m",
"answer3": "104 m",
"correct_answer": 2,
"skill_id": 167,
"difficulty_id": 2,
"explanation": "Length of 1 piece = \\(624 \\div 600 = 1.04\\) m. Length of 10 pieces = \\(1.04 \\times 10 = 10.4\\) m. Answer: 10.4 m.",
"hints": ["First find the length of one piece by dividing 624 m by 600.", "Then multiply that length by 10."],
"source": "ACS 2022 P5 Weighted Assessment 3 Q4",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: Q4 = option 3 (10.4 m)."
},
{
"n": 5,
"type_id": 1,
"question": "The average mass of 4 girls is 36 kg and the average mass of 2 boys is 54 kg. What is the average mass of these 6 children?",
"answer0": "90 kg",
"answer1": "47 kg",
"answer2": "42 kg",
"answer3": "30 kg",
"correct_answer": 2,
"skill_id": 152,
"difficulty_id": 2,
"explanation": "Total mass of girls = \\(4 \\times 36 = 144\\) kg. Total mass of boys = \\(2 \\times 54 = 108\\) kg. Total mass = \\(144 + 108 = 252\\) kg. Average = \\(252 \\div 6 = 42\\) kg. Answer: 42 kg.",
"hints": ["Find the total mass of the girls and the total mass of the boys separately.", "Add the totals, then divide by the total number of children (6)."],
"source": "ACS 2022 P5 Weighted Assessment 3 Q5",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: Q5 = option 3 (42 kg)."
},
{
"n": 6,
"type_id": 2,
"question": "Find the value of \\(0.002 \\times 5000\\). [?]",
"answer0": "10",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 166,
"difficulty_id": 1,
"explanation": "\\(0.002 \\times 5000 = 0.001 \\times 5000 \\times 2 = 5 \\times 2 = 10\\). Answer: 10.",
"hints": ["First find \\(0.001 \\times 5000 = 5\\).", "Then multiply by 2."],
"source": "ACS 2022 P5 Weighted Assessment 3 Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working: 0.001 x 5000 = 5; 5 x 2 = 10."
},
{
"n": 7,
"type_id": 2,
"question": "The average mass of two boxes is 1054 g. What is the total mass of the boxes? Give your answer in kilograms. [?]",
"answer0": "2.108",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 184,
"difficulty_id": 1,
"explanation": "Total mass = \\(1054 \\times 2 = 2108\\) g. Convert to kg: \\(2108 \\div 1000 = 2.108\\) kg. Answer: 2.108 kg.",
"hints": ["Total = average x number of boxes = 1054 x 2.", "Divide grams by 1000 to convert to kilograms."],
"source": "ACS 2022 P5 Weighted Assessment 3 Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer in kg = 2.108 (printed key: 1054 x 2 = 2108 g = 2.108 kg)."
},
{
"n": 8,
"type_id": 2,
"question": "The average of two numbers is 37. One of the numbers is 14. What is the other number? [?]",
"answer0": "60",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 1,
"explanation": "Sum of the two numbers = \\(37 \\times 2 = 74\\). Other number = \\(74 - 14 = 60\\). Answer: 60.",
"hints": ["The sum of the two numbers is the average times 2.", "Subtract the known number from the total."],
"source": "ACS 2022 P5 Weighted Assessment 3 Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working: 37 x 2 = 74; 74 - 14 = 60."
},
{
"n": 9,
"type_id": 2,
"question": "The figure ABCD is made up of squares and rectangles. What percentage of ABCD is shaded? [?]",
"answer0": "25",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 171,
"difficulty_id": 2,
"explanation": "Counting unit squares, the shaded area is 4 out of 16 equal parts. \\(\\dfrac{4}{16} = 0.25 = 25\\%\\). Answer: 25%.",
"hints": ["Count how many equal unit squares are shaded out of the total.", "Write the fraction shaded and convert it to a percentage."],
"source": "ACS 2022 P5 Weighted Assessment 3 Q9",
"image_needed": true,
"image_options": false,
"image_file": "q9.png",
"image_page": 5,
"image_bbox": [0.27, 0.18, 0.52, 0.34],
"image_loc": "shaded grid figure ABCD below the question, upper-left area of the page",
"notes": "Answer entry is a percentage value; blank = 25 (the % sign is printed on the answer line). Key working: 4/16 = 0.25 = 25%. Figure required to count shaded squares."
},
{
"n": 10,
"type_id": 2,
"question": "Kayel nailed Plank P, Q, R and S to make a frame. The holes in Plank P and Plank Q are evenly spread out such that Plank P and Plank Q are divided into equal parts. The holes in Plank P are 0.75 m apart. What is the length of Plank Q? Give your answer in centimetres. [?]",
"answer0": "125",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 184,
"difficulty_id": 3,
"explanation": "Plank P is divided into 3 equal parts by its holes, so 1 part = \\(0.75 \\div 3 = 0.25\\) m. Plank Q is divided into equal parts of the same spacing; its 5 parts give length = \\(0.25 \\times 5 = 1.25\\) m = 125 cm. Answer: 125 cm.",
"hints": ["Find the length of one equal part on Plank P: 0.75 m divided by the number of gaps.", "Multiply one part by the number of parts in Plank Q, then convert metres to centimetres (x100)."],
"source": "ACS 2022 P5 Weighted Assessment 3 Q10",
"image_needed": true,
"image_options": false,
"image_file": "q10.png",
"image_page": 5,
"image_bbox": [0.2, 0.5, 0.78, 0.66],
"image_loc": "frame diagram of Planks P, Q, R, S below the question text, middle of the page",
"notes": "Answer in cm = 125. Key working: 0.75/3 = 0.25; 0.25 x 5 = 1.25 m = 125 cm. Diagram required to see how many equal parts each plank is divided into."
},
{
"n": 11,
"type_id": 2,
"question": "The table shows the amount that the library charges for each library book that is overdue. Raees borrowed a few books from the library. The books were 9 days overdue when he returned them. He paid a total of $12 for the overdue books. How many books were overdue? [?]",
"answer0": "6",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "Cost for one book overdue 9 days: first 7 days = \\(0.20 \\times 7 = \\$1.40\\); last 2 days = \\(0.30 \\times 2 = \\$0.60\\); total per book = \\(1.40 + 0.60 = \\$2\\). Number of books = \\(12 \\div 2 = 6\\). Answer: 6 books.",
"hints": ["Work out the overdue charge for ONE book kept 9 days (7 days at 20 cents, then 2 days at 30 cents).", "Divide the total $12 by the cost of one book."],
"source": "ACS 2022 P5 Weighted Assessment 3 Q11",
"image_needed": true,
"image_options": false,
"image_file": "q11.png",
"image_page": 6,
"image_bbox": [0.24, 0.31, 0.61, 0.39],
"image_loc": "'Charges for each overdue book' table below the question text, upper portion of the page",
"notes": "Key working: 0.20 x 7 = 1.40; 0.30 x 2 = 0.60; per book = 2; 12/2 = 6 books. Charges table required."
},
{
"n": 12,
"type_id": 2,
"question": "There were 120 beads in a box. 60% of the beads are red and the rest are blue.
(a) How many red beads are there in the box? [?]
(b) After 21 red beads and some blue beads were removed from the box, there were 3 times as many red beads as blue beads left. How many blue beads were removed from the box? [?]",
"answer0": "72",
"answer1": "31",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 175,
"difficulty_id": 3,
"explanation": "(a) Red beads = \\(\\dfrac{60}{100} \\times 120 = 72\\). (b) Blue beads at start = \\(120 - 72 = 48\\). Red left after removing 21 = \\(72 - 21 = 51\\). Since red left is 3 times blue left, blue left = \\(51 \\div 3 = 17\\). Blue removed = \\(48 - 17 = 31\\). Answers: (a) 72, (b) 31.",
"hints": ["(a) Find 60% of 120.", "(b) After removing 21 red, the red beads (51) equal 3 units; one unit is the blue beads left. Subtract blue left from the original 48 blue beads."],
"source": "ACS 2022 P5 Weighted Assessment 3 Q12",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Two-part question, two blanks. Key: (a) 72 red beads; (b) 31 blue beads removed."
},
{
"n": 13,
"type_id": 2,
"question": "At a fruit stall, a fruit seller packed and sold these fruits at the prices shown. The fruit seller sold an equal number of kiwis and pears. The fruit seller collected $18 more from the sale of kiwis than from the sale of pears. How many kiwis were sold? [?]",
"answer0": "54",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "Take a common batch of 6 fruits. 6 kiwis cost \\(2 \\times \\$3.25 = \\$6.50\\) (3 for $3.25). 6 pears cost \\(3 \\times \\$1.50 = \\$4.50\\) (2 for $1.50). Difference per 6 fruits = \\(6.50 - 4.50 = \\$2\\). Number of such batches = \\(18 \\div 2 = 9\\). Kiwis sold = \\(9 \\times 6 = 54\\). Answer: 54 kiwis.",
"hints": ["Find a batch size (6) for which both kiwi and pear prices work out evenly, then find the cost of that batch for each fruit.", "Each batch of 6 gives a $2 difference; divide $18 by $2, then multiply by 6."],
"source": "ACS 2022 P5 Weighted Assessment 3 Q13",
"image_needed": true,
"image_options": false,
"image_file": "q13.png",
"image_page": 8,
"image_bbox": [0.32, 0.18, 0.62, 0.24],
"image_loc": "Kiwis / Pears price table below the question intro, upper portion of the page",
"notes": "Key working: 6 kiwis = $6.50, 6 pears = $4.50, diff $2 per 6; 18/2 = 9; 9 x 6 = 54 kiwis. Price table required."
}
]
}