{ "paper": { "school": "Rosyth School", "year": 2022, "level": "P5", "label": "Weighted Assessment 2", "source_prefix": "Rosyth School 2022 P5 Weighted Assessment 2", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "In 8 127 349, the value of digit 1 is [blank].", "answer0": "100", "answer1": "1000", "answer2": "10 000", "answer3": "100 000", "correct_answer": 3, "skill_id": 149, "difficulty_id": 1, "explanation": "In 8 127 349, the digit 1 is in the hundred-thousands place, so its value is 100 000.", "hints": ["Identify the place of the digit 1.", "It sits in the hundred-thousands column."], "source": "Rosyth School 2022 P5 Weighted Assessment 2 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Section A MCQ. Printed key: option 4 (100 000)." }, { "n": 2, "type_id": 1, "question": "Identify the base of triangle ABC given that BD is its height.", "answer0": "AC", "answer1": "EB", "answer2": "AE", "answer3": "BC", "correct_answer": 0, "skill_id": 186, "difficulty_id": 2, "explanation": "The base of a triangle is the side perpendicular to its height. Since BD is the height drawn perpendicular to AC (D lies on AC), the base is AC.", "hints": ["The base is the side at right angles to the height.", "BD meets AC at a right angle."], "source": "Rosyth School 2022 P5 Weighted Assessment 2 Q2", "image_needed": true, "image_options": false, "image_file": "q2.png", "image_page": 2, "image_bbox": [0.25, 0.40, 0.65, 0.55], "image_loc": "below the question, triangle ABC with height BD to AC, point E and dashed lines on the left", "notes": "Printed key: option 1 (AC)." }, { "n": 3, "type_id": 1, "question": "The table shows the number of cupcakes baked by Radziah. Butter: 24, Chocolate: 10, Strawberry: 22. Find the ratio of the number of butter cupcakes to the total number of chocolate and strawberry cupcakes that Radziah baked.", "answer0": "3 : 4", "answer1": "3 : 7", "answer2": "12 : 5", "answer3": "12 : 11", "correct_answer": 0, "skill_id": 179, "difficulty_id": 2, "explanation": "Chocolate + strawberry = 10 + 22 = 32. Ratio butter : (chocolate + strawberry) = 24 : 32 = 3 : 4 (dividing both by 8).", "hints": ["Add the chocolate and strawberry counts first.", "Simplify 24 : 32 by dividing by 8."], "source": "Rosyth School 2022 P5 Weighted Assessment 2 Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed key: option 1 (3 : 4). Table values stated in stem (no figure needed)." }, { "n": 4, "type_id": 1, "question": "What is the value of \\(\\dfrac{2}{3} \\times \\dfrac{5}{6}\\)?", "answer0": "\\(\\dfrac{7}{9}\\)", "answer1": "\\(\\dfrac{5}{9}\\)", "answer2": "\\(\\dfrac{4}{5}\\)", "answer3": "\\(\\dfrac{7}{18}\\)", "correct_answer": 1, "skill_id": 161, "difficulty_id": 1, "explanation": "$\\dfrac{2}{3}\\times\\dfrac{5}{6}=\\dfrac{2\\times 5}{3\\times 6}=\\dfrac{10}{18}=\\dfrac{5}{9}$.", "hints": ["Multiply the numerators and the denominators.", "Simplify $\\dfrac{10}{18}$ by dividing by 2."], "source": "Rosyth School 2022 P5 Weighted Assessment 2 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed key: option 2 ($\\dfrac{5}{9}$)." }, { "n": 5, "type_id": 1, "question": "What is the value of A as a decimal rounded to 2 decimal places?", "answer0": "4.47", "answer1": "4.74", "answer2": "4.57", "answer3": "4.58", "correct_answer": 2, "skill_id": 168, "difficulty_id": 2, "explanation": "On the number line from $3\\dfrac{6}{7}$ to 6, point A falls at the marked tick whose value, rounded to 2 decimal places, is 4.57.", "hints": ["Work out the size of each interval on the number line.", "Read off the position of A and round to 2 decimal places."], "source": "Rosyth School 2022 P5 Weighted Assessment 2 Q5", "image_needed": true, "image_options": false, "image_file": "q5.png", "image_page": 3, "image_bbox": [0.18, 0.66, 0.78, 0.78], "image_loc": "below the question, a number line marked from 3 6/7 to 6 with arrow at A", "notes": "Printed key: option 3 (4.57). Value of A must be read from the number-line figure." }, { "n": 6, "type_id": 2, "question": "What is the value of \\(2 \\times (20 - 5) \\div 3 + 2\\)? [?]", "answer0": "12", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 156, "difficulty_id": 2, "explanation": "Brackets first: 20 - 5 = 15. Then 2 \\(\\times\\) 15 = 30, 30 \\(\\div\\) 3 = 10, 10 + 2 = 12.", "hints": ["Do the bracket first.", "Then multiply and divide before adding."], "source": "Rosyth School 2022 P5 Weighted Assessment 2 Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Section B. Printed key: 2\\u00d715\\u00f73+2 = 12." }, { "n": 7, "type_id": 2, "question": "The ratio of Eddie's age to his mother's age now is 1 : 5. His mother is 65 years old. What is Eddie's age? [?]", "answer0": "13", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 182, "difficulty_id": 2, "explanation": "The mother's age is 5 units = 65, so 1 unit = 65 \\(\\div\\) 5 = 13. Eddie is 1 unit = 13 years old.", "hints": ["The mother's age is 5 units.", "Divide 65 by 5 to find one unit (Eddie's age)."], "source": "Rosyth School 2022 P5 Weighted Assessment 2 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed key: 65 \\u00f7 5 = 13 years old." }, { "n": 8, "type_id": 2, "question": "What is the area of the triangle ABC? [?]", "answer0": "20", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 2, "explanation": "Take base BC = 8 cm and height = 5 cm (the perpendicular height of the triangle). Area = $\\dfrac{1}{2}\\times 8\\times 5 = 20$ cm\\u00b2.", "hints": ["Use base BC = 8 cm and the perpendicular height 5 cm.", "Area = \\u00bd \\u00d7 base \\u00d7 height; the 4 cm and 12 cm are not needed."], "source": "Rosyth School 2022 P5 Weighted Assessment 2 Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 4, "image_bbox": [0.22, 0.58, 0.70, 0.78], "image_loc": "below the question, triangle ABC with 5 cm (height), 4 cm, BC = 8 cm and base span 12 cm marked", "notes": "Printed key: 5 \\u00d7 8 \\u00d7 \\u00bd = 20 cm\\u00b2. Answer requires units cm\\u00b2." }, { "n": 9, "type_id": 1, "question": "Linda has \\(2\\dfrac{1}{8}\\) m of ribbon. She has \\(1\\dfrac{3}{16}\\) m less ribbon than what Susan has. What is the total length of ribbon they have?", "answer0": "\\(5\\dfrac{7}{16}\\) m", "answer1": "\\(5\\dfrac{5}{16}\\) m", "answer2": "\\(3\\dfrac{5}{16}\\) m", "answer3": "\\(4\\dfrac{1}{4}\\) m", "correct_answer": 0, "skill_id": 160, "difficulty_id": 2, "explanation": "Linda = $2\\dfrac{1}{8}=2\\dfrac{2}{16}$ m. Susan has $1\\dfrac{3}{16}$ m more: $2\\dfrac{2}{16}+1\\dfrac{3}{16}=3\\dfrac{5}{16}$ m. Total = $2\\dfrac{2}{16}+3\\dfrac{5}{16}=5\\dfrac{7}{16}$ m.", "hints": ["Convert $2\\dfrac{1}{8}$ to sixteenths first.", "Find Susan's amount, then add both."], "source": "Rosyth School 2022 P5 Weighted Assessment 2 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed key: 2 1/8 = 2 2/16; Susan = 3 5/16; total = 5 7/16 m. Mixed-number answer \\u2192 MCQ per FIB-no-fraction rule." }, { "n": 10, "type_id": 2, "question": "Darian, Jaclyn and Ah Liang collected some stamps. Darian had 12 950 stamps. Jaclyn had 2750 stamps more than Darian. Ah Liang had 1650 stamps less than Jaclyn. How many stamps did Ah Liang have? [?]", "answer0": "14050", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 2, "explanation": "Jaclyn = 12 950 + 2750 = 15 700. Ah Liang = 15 700 - 1650 = 14 050 stamps.", "hints": ["First find Jaclyn's amount (Darian + 2750).", "Then subtract 1650 for Ah Liang."], "source": "Rosyth School 2022 P5 Weighted Assessment 2 Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed key: 12 950 + 2750 = 15 700; 15 700 \\u2212 1650 = 14 050." }, { "n": 11, "type_id": 2, "question": "There is a total of 918 students in a school. The ratio of the number of girls to the number of boys is 2 : 7. How many more boys than girls are there? [?]", "answer0": "510", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 183, "difficulty_id": 2, "explanation": "Total units = 2 + 7 = 9. 9 units = 918, so 1 unit = 918 \\(\\div\\) 9 = 102. More boys than girls = (7 - 2) units = 5 \\(\\times\\) 102 = 510.", "hints": ["Add the ratio parts to get 9 units.", "The difference is (7 \\u2212 2) = 5 units."], "source": "Rosyth School 2022 P5 Weighted Assessment 2 Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed key: 918 \\u00f7 9 = 102; 5 \\u00d7 102 = 510." }, { "n": 12, "type_id": 1, "question": "Siva bought some cookies. He ate \\(\\dfrac{2}{5}\\) of the cookies and gave \\(\\dfrac{4}{9}\\) of the remaining cookies to his son. What fraction of the cookies was given to his son? Give your answer in the simplest form.", "answer0": "\\(\\dfrac{4}{15}\\)", "answer1": "\\(\\dfrac{8}{45}\\)", "answer2": "\\(\\dfrac{4}{9}\\)", "answer3": "\\(\\dfrac{3}{5}\\)", "correct_answer": 0, "skill_id": 161, "difficulty_id": 2, "explanation": "Remaining after eating = $1-\\dfrac{2}{5}=\\dfrac{3}{5}$. Given to son = $\\dfrac{4}{9}\\times\\dfrac{3}{5}=\\dfrac{12}{45}=\\dfrac{4}{15}$.", "hints": ["Find the fraction remaining after he eats $\\dfrac{2}{5}$.", "Take $\\dfrac{4}{9}$ of that remainder and simplify."], "source": "Rosyth School 2022 P5 Weighted Assessment 2 Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed key: $\\dfrac{4}{15}$. Fraction answer \\u2192 MCQ per FIB-no-fraction rule." }, { "n": 13, "type_id": 2, "question": "Daryl wants to put 72 stalks of orchids and 45 stalks of carnations into identical vases. An equal number of each type of flower is put into each vase. What is the greatest number of vases that Daryl can use? [?]", "answer0": "9", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 156, "difficulty_id": 3, "explanation": "The greatest number of identical vases is the greatest common factor of 72 and 45. 72 = 8 \\(\\times\\) 9, 45 = 5 \\(\\times\\) 9, so the GCF is 9. Daryl can use 9 vases.", "hints": ["Find the largest number that divides both 72 and 45 exactly.", "List common factors of 72 and 45."], "source": "Rosyth School 2022 P5 Weighted Assessment 2 Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed key: 9 vases (greatest common factor of 72 and 45)." }, { "n": 14, "type_id": 2, "question": "Elena has a total of 4200 orange, red and green stickers. The ratio of the number of red stickers to the total number of stickers is 1 : 6. What is the total number of green and orange stickers that Elena has? [?]", "answer0": "3500", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 182, "difficulty_id": 2, "explanation": "Red : total = 1 : 6, so red = 4200 \\(\\div\\) 6 = 700. Green + orange = 4200 - 700 = 3500.", "hints": ["Total is 6 units; red is 1 unit.", "Subtract the red stickers from 4200."], "source": "Rosyth School 2022 P5 Weighted Assessment 2 Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed key: 4200 \\u00f7 6 = 700; 700 \\u00d7 5 = 3500." }, { "n": 15, "type_id": 2, "question": "Mr Chua and Miss Sally had the same amount of money. Mr Chua bought 3 muffins and had $13 left. Miss Sally wanted to buy 8 muffins but was short of $11. What was the cost of 1 muffin? [?]", "answer0": "4.80", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "The difference of 8 - 3 = 5 muffins corresponds to the money difference $13 (left over) + $11 (short) = $24. So 1 muffin = $24 \\(\\div\\) 5 = $4.80.", "hints": ["The 5 extra muffins account for $13 + $11.", "Divide $24 by 5 muffins."], "source": "Rosyth School 2022 P5 Weighted Assessment 2 Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Section C. Printed key: 5u = $13 + $11 = $24; 1 muffin = $24 \\u00f7 5 = $4.80. Money answer." }, { "n": 16, "type_id": 2, "question": "The figure shows a rectangle PQRS and three triangles PTS, PQT and QRT. The ratio of the area of triangle PTS to the area of triangle QRT is 3 : 1. If the area of PTS is 30 cm\\u00b2, find the length of QR. [?]", "answer0": "8", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 3, "explanation": "Area QRT = 30 \\(\\div\\) 3 = 10 cm\\u00b2. Let QR = PS = h (rectangle's width). Area PTS = $\\dfrac{1}{2}\\times ST\\times h = 30$, so ST \\(\\times\\) h = 60; area QRT = $\\dfrac{1}{2}\\times TR\\times h = 10$, so TR \\(\\times\\) h = 20. Adding: (ST + TR) \\(\\times\\) h = 80, and ST + TR = SR = 10 cm, so 10h = 80, giving h = QR = 8 cm.", "hints": ["Find the area of QRT from the 3 : 1 ratio.", "Add ST and TR (= SR = 10 cm) using the two triangle areas."], "source": "Rosyth School 2022 P5 Weighted Assessment 2 Q16", "image_needed": true, "image_options": false, "image_file": "q16.png", "image_page": 9, "image_bbox": [0.30, 0.20, 0.70, 0.38], "image_loc": "below the question, rectangle PQRS with T on SR; SR (bottom) = 10 cm marked", "notes": "Printed key: 30+10=40, 40\\u00d72=80, 80=8\\u00d710, QR = 8 cm. Answer requires units cm." }, { "n": 17, "type_id": 2, "question": "Seng bought some blue and red pens at a stationery shop. \\(\\dfrac{2}{3}\\) of the pens he bought were blue and the rest were red. He gave away \\(\\dfrac{1}{2}\\) of the red pens and had 100 red pens left. He then gave away \\(\\dfrac{2}{5}\\) of the blue pens. How many blue pens did he give away? [?]", "answer0": "160", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "He gave away half the red pens and had 100 left, so red pens = 100 \\(\\times\\) 2 = 200. Blue pens are $\\dfrac{2}{3}$ and red $\\dfrac{1}{3}$, so blue = 2 \\(\\times\\) red = 400. He gave away $\\dfrac{2}{5}$ of the blue pens = $\\dfrac{2}{5}\\times 400 = 160$.", "hints": ["Half the red pens equal 100, so find the total red pens.", "Blue is twice the red; take $\\dfrac{2}{5}$ of the blue."], "source": "Rosyth School 2022 P5 Weighted Assessment 2 Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed key: red = 100\\u00d72 = 200, blue = 400, gave away 400\\u00f75\\u00d72 = 160." }, { "n": 18, "type_id": 2, "question": "Yazid was given some money. He spent an equal amount of money each day. After 3 days, \\(\\dfrac{3}{4}\\) of his pocket money was left. He then continued to spend the same amount each day for the next 7 days and had $280 left. Find the amount of money that Yazid was given at first. [?]", "answer0": "1680", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "After 3 days $\\dfrac{1}{4}$ was spent, so the daily spending is $\\dfrac{1}{4}\\div 3 = \\dfrac{1}{12}$ per day. Over 10 days he spends $\\dfrac{10}{12}$, leaving $\\dfrac{2}{12}=\\dfrac{1}{6}$. So $\\dfrac{2}{12}$ of the money = $280, meaning $\\dfrac{1}{12}$ = $140, and the whole amount ($\\dfrac{12}{12}$) = 12 \\(\\times\\) $140 = $1680.", "hints": ["Find the fraction spent per day from the first 3 days.", "After 10 days, the leftover fraction equals $280."], "source": "Rosyth School 2022 P5 Weighted Assessment 2 Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed key: 1 day = 1/12, 10 days = 10/12, 280\\u00f72 = 140 (per 1/12), 140\\u00d712 = $1680. Money answer." }, { "n": 19, "type_id": 2, "question": "Steven had some boxes of pencils, each containing the same number of pencils. He took 21 pencils out from each box. As a result, the total number of pencils left in the 5 boxes of pencils was equal to the total number of pencils in 2 of the boxes of pencils at first. What was the total number of pencils in each box at first? [?]", "answer0": "35", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "Let each box have x pencils at first. After removing 21 from each of 5 boxes, pencils left = 5(x - 21). This equals 2 boxes at first = 2x. So 5(x - 21) = 2x, i.e. 5x - 105 = 2x, 3x = 105, x = 35.", "hints": ["Pencils left in 5 boxes = 5 \\u00d7 (x \\u2212 21).", "Set this equal to 2x and solve."], "source": "Rosyth School 2022 P5 Weighted Assessment 2 Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed key: 21\\u00d75 = 105, 105\\u00f73 = 35 pencils per box." } ] }