{ "paper": { "school": "ACS Junior", "year": 2024, "level": "P6", "label": "Bite-Sized Assessment 2", "source_prefix": "ACS 2024 P6 Bite-Sized Assessment 2", "has_answer_key": false }, "questions": [ { "n": 1, "type_id": 1, "question": "In 4 978 512, which digit is in the ten thousands place?", "answer0": "5", "answer1": "7", "answer2": "8", "answer3": "9", "correct_answer": 1, "skill_id": 149, "difficulty_id": 1, "explanation": "Reading the place values of 4 978 512 from the right: 2 ones, 1 ten, 5 hundreds, 8 thousands, 7 ten thousands, 9 hundred thousands, 4 millions. The digit in the ten thousands place is 7.", "hints": ["Write the number with place-value labels: ones, tens, hundreds, thousands, ten thousands.", "Count four places in from the right (ones, tens, hundreds, thousands) then the next digit is the ten thousands."], "source": "ACS 2024 P6 Bite-Sized Assessment 2 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "no answer key — solved" }, { "n": 2, "type_id": 1, "question": "The radius of the quadrant is 14 cm. Find the perimeter of the quadrant. Take \\(\\pi = \\dfrac{22}{7}\\).", "answer0": "44 cm", "answer1": "50 cm", "answer2": "72 cm", "answer3": "116 cm", "correct_answer": 1, "skill_id": 221, "difficulty_id": 2, "explanation": "Perimeter of a quadrant = two radii + a quarter of the circle's circumference. Arc = \\(\\dfrac{1}{4}\\times 2\\times\\dfrac{22}{7}\\times 14 = \\dfrac{1}{4}\\times 88 = 22\\) cm. Perimeter = 14 + 14 + 22 = 50 cm.", "hints": ["A quadrant's boundary is made of two straight radii plus the curved arc.", "The arc is one quarter of the full circumference \\(2\\pi r\\)."], "source": "ACS 2024 P6 Bite-Sized Assessment 2 Q2", "image_needed": true, "image_options": false, "image_file": "q2.png", "image_page": 2, "image_bbox": [0.46, 0.60, 0.66, 0.70], "image_loc": "small quarter-circle (quadrant) diagram to the right of the question, with a 14 cm label on the right edge", "notes": "no answer key — solved" }, { "n": 3, "type_id": 1, "question": "Jackson had $20. He spent $8 on a burger.
What percentage of his money did he spend on the burger?", "answer0": "20%", "answer1": "28%", "answer2": "40%", "answer3": "75%", "correct_answer": 2, "skill_id": 171, "difficulty_id": 1, "explanation": "Fraction spent = \\(\\dfrac{8}{20}\\). As a percentage: \\(\\dfrac{8}{20}\\times 100\\% = 40\\%\\).", "hints": ["Percentage = (amount spent ÷ total amount) × 100%.", "Simplify \\(\\dfrac{8}{20}\\) to \\(\\dfrac{2}{5}\\) then multiply by 100%."], "source": "ACS 2024 P6 Bite-Sized Assessment 2 Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "no answer key — solved" }, { "n": 4, "type_id": 1, "question": "A bakery sold curry buns from 0800 to 1200. The line graph shows the amount of curry buns left in the shop from 0800 to 1200.
During which one-hour period were the sales of curry bun the most?", "answer0": "0800 to 0900", "answer1": "0900 to 1000", "answer2": "1000 to 1100", "answer3": "1100 to 1200", "correct_answer": 1, "skill_id": 147, "difficulty_id": 2, "explanation": "Sales in each hour = drop in the number of buns left. 0800→0900: 100 to 80 (20 sold); 0900→1000: 80 to about 35 (about 45 sold); 1000→1100: about 35 to 10 (about 25 sold); 1100→1200: about 10 to 5 (about 5 sold). The steepest fall, hence the most sales, is from 0900 to 1000.", "hints": ["Sales in an hour equal how much the line drops over that hour.", "Look for the steepest downward segment of the graph."], "source": "ACS 2024 P6 Bite-Sized Assessment 2 Q4", "image_needed": true, "image_options": false, "image_file": "q4.png", "image_page": 3, "image_bbox": [0.20, 0.34, 0.86, 0.56], "image_loc": "line graph: Number of Curry buns (y, 0-120) vs Time (h) 0800-1200, decreasing line", "notes": "no answer key — solved; graph reading is approximate but 0900-1000 is clearly the steepest fall" }, { "n": 5, "type_id": 1, "question": "A number when divided by 20 gives a remainder of 9. Which of the following can be added to the number to change it to a multiple of 5?", "answer0": "5", "answer1": "6", "answer2": "3", "answer3": "4", "correct_answer": 1, "skill_id": 114, "difficulty_id": 2, "explanation": "A number that leaves remainder 9 when divided by 20 ends in the digit 9 (e.g. 9, 29, 49). A multiple of 5 must end in 0 or 5. Adding 6 makes it end in 5 (e.g. 9+6=15, 29+6=35), which is a multiple of 5. So 6 can be added.", "hints": ["Such a number always ends in the digit 9.", "A multiple of 5 ends in 0 or 5 — what must you add to a number ending in 9 to reach the next 5?"], "source": "ACS 2024 P6 Bite-Sized Assessment 2 Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "no answer key — solved" }, { "n": 6, "type_id": 1, "question": "Dickson participated in a stair-climbing competition. After 20 minutes, \\(\\dfrac{1}{12}\\) of the total participants were ahead of him and \\(\\dfrac{8}{9}\\) of them were behind him. One of the participants dropped out of the competition. How many people participated in the competition at the beginning?", "answer0": "36", "answer1": "72", "answer2": "108", "answer3": "144", "correct_answer": 1, "skill_id": 209, "difficulty_id": 3, "explanation": "Let the total at the start be N. Ahead = \\(\\dfrac{1}{12}N\\), behind = \\(\\dfrac{8}{9}N\\). Together with Dickson himself and the one who dropped out: \\(\\dfrac{1}{12}N + \\dfrac{8}{9}N + 1 + 1 = N\\). Since \\(\\dfrac{1}{12}+\\dfrac{8}{9}=\\dfrac{35}{36}\\), we get \\(2 = \\dfrac{1}{36}N\\), so N = 72. Check: ahead = 6, behind = 64, plus Dickson plus dropout = 6+64+1+1 = 72.", "hints": ["The fractions ahead and behind, plus Dickson, plus the one who dropped out, must make up the whole.", "\\(\\dfrac{1}{12}+\\dfrac{8}{9}=\\dfrac{35}{36}\\); the remaining \\(\\dfrac{1}{36}\\) accounts for Dickson and the drop-out (2 people)."], "source": "ACS 2024 P6 Bite-Sized Assessment 2 Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "no answer key — solved" }, { "n": 7, "type_id": 1, "question": "ABCD is a square, CD = ED and \\(\\angle DCE = 65^\\circ\\). Find \\(\\angle DAE\\).", "answer0": "50°", "answer1": "55°", "answer2": "65°", "answer3": "70°", "correct_answer": 3, "skill_id": 230, "difficulty_id": 3, "explanation": "Triangle DCE is isosceles (CD = ED), so \\(\\angle DEC = \\angle DCE = 65^\\circ\\) and \\(\\angle CDE = 180^\\circ - 65^\\circ - 65^\\circ = 50^\\circ\\). In the square \\(\\angle ADC = 90^\\circ\\), so \\(\\angle ADE = 90^\\circ - 50^\\circ = 40^\\circ\\). Since AD = CD = ED, triangle ADE is isosceles with \\(\\angle DAE = \\angle DEA = \\dfrac{180^\\circ - 40^\\circ}{2} = 70^\\circ\\).", "hints": ["Use CD = ED to find the base angles, then the apex angle of triangle DCE.", "Subtract from the 90° corner of the square, then note AD = ED makes triangle ADE isosceles too."], "source": "ACS 2024 P6 Bite-Sized Assessment 2 Q7", "image_needed": true, "image_options": false, "image_file": "q7.png", "image_page": 4, "image_bbox": [0.38, 0.51, 0.66, 0.70], "image_loc": "square ABCD (A top-left, B top-right, C bottom-right, D bottom-left) with point E inside and 65° marked at C", "notes": "no answer key — solved" }, { "n": 8, "type_id": 2, "question": "The perimeter of the square is 80 cm, find the area of the circle. (Take \\(\\pi = 3.14\\)) [?]", "answer0": "314", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 220, "difficulty_id": 2, "explanation": "Side of square = 80 ÷ 4 = 20 cm. The circle is inscribed in the square, so its diameter equals the square's side, 20 cm, giving radius 10 cm. Area = \\(\\pi r^2 = 3.14 \\times 10^2 = 314\\) cm².", "hints": ["The circle fits exactly inside the square, so the circle's diameter equals the square's side.", "Find the side from the perimeter, halve it for the radius, then use \\(\\pi r^2\\)."], "source": "ACS 2024 P6 Bite-Sized Assessment 2 Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 5, "image_bbox": [0.55, 0.21, 0.78, 0.36], "image_loc": "a circle inscribed inside a square, to the right of the question", "notes": "no answer key — solved; answer in cm²" }, { "n": 9, "type_id": 1, "question": "Find \\(\\dfrac{4}{15} \\div \\dfrac{2}{5}\\).", "answer0": "\\(\\dfrac{2}{3}\\)", "answer1": "\\(\\dfrac{8}{75}\\)", "answer2": "\\(\\dfrac{2}{15}\\)", "answer3": "\\(\\dfrac{3}{2}\\)", "correct_answer": 0, "skill_id": 206, "difficulty_id": 2, "explanation": "Dividing by a fraction means multiplying by its reciprocal: \\(\\dfrac{4}{15} \\div \\dfrac{2}{5} = \\dfrac{4}{15} \\times \\dfrac{5}{2} = \\dfrac{20}{30} = \\dfrac{2}{3}\\).", "hints": ["To divide by a fraction, multiply by its reciprocal (flip the second fraction).", "Cancel common factors before multiplying to keep numbers small."], "source": "ACS 2024 P6 Bite-Sized Assessment 2 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "no answer key — solved; made MCQ because the answer 2/3 is a fraction (FIB is numeric only)" }, { "n": 10, "type_id": 2, "question": "A confectionery shop sold some candies on Monday. The graph shows the number of different candies sold.
How many candies did the confectionery shop sell in total? [?]", "answer0": "123", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 2, "explanation": "Read each bar: Chocolate = 42, Gummy = 24, Lollipop = 57. Total candies sold = 42 + 24 + 57 = 123.", "hints": ["Read the height of each bar against the y-axis (gridlines at 15, 30, 45, 60).", "Add the three bar values together."], "source": "ACS 2024 P6 Bite-Sized Assessment 2 Q10", "image_needed": true, "image_options": false, "image_file": "q10.png", "image_page": 6, "image_bbox": [0.15, 0.18, 0.84, 0.42], "image_loc": "bar graph 'Types of Candies': Chocolate, Gummy, Lollipop on x-axis, Number of Candies (0-60) on y-axis", "notes": "no answer key — solved; bar heights read as Chocolate 42, Gummy 24, Lollipop 57 (total 123) — verify exact heights against the crop" }, { "n": 11, "type_id": 2, "question": "Measure \\(\\angle ABC\\). [?]", "answer0": "50", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 140, "difficulty_id": 1, "explanation": "Using a protractor, place the centre at B with the base line along BA and read the angle to BC. The angle \\(\\angle ABC\\) measures about 50°.", "hints": ["Line up the protractor's centre on vertex B and its zero line along ray BA.", "Read where ray BC crosses the protractor scale."], "source": "ACS 2024 P6 Bite-Sized Assessment 2 Q11", "image_needed": true, "image_options": false, "image_file": "q11.png", "image_page": 6, "image_bbox": [0.18, 0.60, 0.62, 0.74], "image_loc": "an angle drawn with vertex B: ray BA going left (horizontal) and ray BC going up-right to C", "notes": "no answer key — protractor-measurement question; answer (~50°) must be confirmed by measuring the actual printed figure on the crop; answer in degrees" }, { "n": 12, "type_id": 1, "question": "40% of the fruits in a shop were oranges while the rest were apples. The ratio of the number of green apples to the number of red apples was 1 : 4. What is the ratio of the number of oranges to the number of green apples to the number of red apples?", "answer0": "10 : 3 : 12", "answer1": "2 : 1 : 4", "answer2": "40 : 1 : 4", "answer3": "5 : 1 : 4", "correct_answer": 0, "skill_id": 213, "difficulty_id": 3, "explanation": "Oranges = 40%, apples = 60%. Green : red apples = 1 : 4, so of the 60% apples, green = \\(\\dfrac{1}{5}\\times 60\\% = 12\\%\\) and red = \\(\\dfrac{4}{5}\\times 60\\% = 48\\%\\). Oranges : green : red = 40 : 12 : 48 = 10 : 3 : 12 (dividing by 4).", "hints": ["The apples make up 60%; split that 60% in the ratio 1 : 4 for green : red.", "Write oranges : green : red as percentages, then simplify the whole ratio."], "source": "ACS 2024 P6 Bite-Sized Assessment 2 Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "no answer key — solved; made MCQ because the answer is a ratio (FIB is numeric only)" }, { "n": 13, "type_id": 2, "question": "A clothing store has a sale. The original price of a pair of pants was $75. The price of the pair of pants during the sale was $60. Find the percentage decrease in price. [?]", "answer0": "20", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 208, "difficulty_id": 2, "explanation": "Decrease in price = $75 − $60 = $15. Percentage decrease = \\(\\dfrac{15}{75}\\times 100\\% = 20\\%\\).", "hints": ["Percentage decrease = (decrease ÷ original price) × 100%.", "The decrease is the original price minus the sale price."], "source": "ACS 2024 P6 Bite-Sized Assessment 2 Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "no answer key — solved; answer in %" }, { "n": 14, "type_id": 2, "question": "There are 44 students in a class. 25 of them play the violin and 32 of them play the piano. 7 of them do not play any instruments. How many students play both the violin and the piano? [?]", "answer0": "20", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 2, "explanation": "Students playing at least one instrument = 44 − 7 = 37. By the inclusion principle, violin + piano − both = at least one: 25 + 32 − both = 37, so both = 57 − 37 = 20.", "hints": ["First find how many play at least one instrument (44 − those who play none).", "violin + piano − both = number who play at least one instrument."], "source": "ACS 2024 P6 Bite-Sized Assessment 2 Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "no answer key — solved" }, { "n": 15, "type_id": 2, "question": "Figure 1 is a square made up of four identical shapes shown in Figure 2.
What is the area of the shape in Figure 2? [?]", "answer0": "16", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "Four identical L-shaped pieces tile the square in Figure 1 (a 4 by 4 grid of small unit squares = 16 units, so each piece is 4 unit squares). The 4 cm in Figure 2 spans 2 unit squares, so each unit square has side 2 cm and area 2 × 2 = 4 cm². The Figure 2 shape = 4 unit squares = 4 × 4 = 16 cm².", "hints": ["The big square is divided into four equal pieces, so each piece is one quarter of the square's area.", "Use the 4 cm mark to find the side of one small unit square, then count how many unit squares make up the Figure 2 shape."], "source": "ACS 2024 P6 Bite-Sized Assessment 2 Q15", "image_needed": true, "image_options": false, "image_file": "q15.png", "image_page": 9, "image_bbox": [0.28, 0.18, 0.66, 0.34], "image_loc": "two diagrams side by side: Figure 1 (a square grid divided into 4 identical pieces) and Figure 2 (one L-shaped piece with a 4 cm height marked)", "notes": "no answer key — solved; reading: 4 identical L-tetromino pieces tile a 4x4 unit-square grid, 4 cm = 2 units so unit side 2 cm, Figure 2 = 4 units = 16 cm². Verify the unit-square count and the 4 cm span against the crop; answer in cm²" }, { "n": 16, "type_id": 2, "question": "The diagram is not drawn to scale. CDE is a right-angled triangle. It is folded along DF, forming another triangle DFG. Find \\(\\angle FDG\\). [?]", "answer0": "29", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 3, "explanation": "CDE has the right angle at D, so \\(\\angle DCE = 180^\\circ - 90^\\circ - 70^\\circ = 20^\\circ\\). The 131° at F is \\(\\angle CFD\\) (exterior to triangle DFG along the fold). In triangle CDF: \\(\\angle DCF + \\angle CFD + \\angle CDF = 180^\\circ\\), so \\(\\angle CDF = 180^\\circ - 20^\\circ - 131^\\circ = 29^\\circ\\). Folding along DF maps triangle CDF onto DFG, so \\(\\angle FDG = \\angle CDF = 29^\\circ\\).", "hints": ["Folding along DF is a reflection, so \\(\\angle FDG = \\angle FDC\\) and the folded angle at C equals the angle at G.", "Find \\(\\angle DCE\\) first from the right angle and 70°, then use the angle sum of triangle CDF with the 131°."], "source": "ACS 2024 P6 Bite-Sized Assessment 2 Q16", "image_needed": true, "image_options": false, "image_file": "q16.png", "image_page": 9, "image_bbox": [0.10, 0.55, 0.62, 0.80], "image_loc": "triangle with C top, D bottom-left, E bottom-right; F on CE with 131° marked, 70° marked at E, G to the right of F", "notes": "no answer key — solved; diagram not to scale; right angle taken at D, fold maps C onto G so ∠FDG = ∠FDC = 29°; answer in degrees" }, { "n": 17, "type_id": 2, "question": "Grace and Brenda shared some stickers. \\(\\dfrac{2}{3}\\) of Grace's stickers was equal to \\(\\dfrac{2}{5}\\) of Brenda's stickers. Brenda had 14 stickers more than Grace. How many stickers did Brenda have? [?]", "answer0": "35", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "\\(\\dfrac{2}{3}\\) Grace = \\(\\dfrac{2}{5}\\) Brenda means \\(\\dfrac{1}{3}\\) Grace = \\(\\dfrac{1}{5}\\) Brenda, so Grace : Brenda = 3 : 5. The difference 5 − 3 = 2 units equals 14 stickers, so 1 unit = 7. Brenda = 5 units = 5 × 7 = 35 stickers.", "hints": ["From \\(\\dfrac{2}{3}\\) of Grace = \\(\\dfrac{2}{5}\\) of Brenda, work out the ratio Grace : Brenda.", "The 14-sticker difference is the difference between Brenda's units and Grace's units."], "source": "ACS 2024 P6 Bite-Sized Assessment 2 Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "no answer key — solved" }, { "n": 18, "type_id": 2, "question": "The number of students in two classes is shown.
Class 6A: 21 boys, 18 girls. Class 6B: 16 boys, 24 girls.
What percentage of the students in class 6B are girls? [?]", "answer0": "60", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 171, "difficulty_id": 2, "explanation": "Total students in 6B = 16 boys + 24 girls = 40. Percentage of girls = \\(\\dfrac{24}{40}\\times 100\\% = 60\\%\\).", "hints": ["Find the total number of students in class 6B first.", "Percentage of girls = (girls ÷ total in 6B) × 100%."], "source": "ACS 2024 P6 Bite-Sized Assessment 2 Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "no answer key — solved; table transcribed into the stem; answer in %" }, { "n": 19, "type_id": 2, "question": "A rectangular tank measures 23 cm by 13 cm by 18 cm. It is \\(\\dfrac{1}{3}\\) filled with water. Find the volume of water in the tank. Give your answer in litres. [?]", "answer0": "1.794", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 191, "difficulty_id": 2, "explanation": "Volume of tank = 23 × 13 × 18 = 5382 cm³. Water = \\(\\dfrac{1}{3}\\times 5382 = 1794\\) cm³. Since 1000 cm³ = 1 litre, 1794 cm³ = 1.794 litres.", "hints": ["Find the full volume of the tank (length × breadth × height) first.", "Take one third for the water, then convert cm³ to litres (1000 cm³ = 1 ℓ)."], "source": "ACS 2024 P6 Bite-Sized Assessment 2 Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "no answer key — solved; answer in litres" }, { "n": 20, "type_id": 2, "question": "The table shows the marks scored by 5 boys for an English test.
Ali: 81, Barney: 76, Chandra: 84, Dan: 79, Emmanuel: 88.
Find the average marks of the 5 boys. [?]", "answer0": "81.6", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 203, "difficulty_id": 1, "explanation": "Total marks = 81 + 76 + 84 + 79 + 88 = 408. Average = total ÷ number of boys = 408 ÷ 5 = 81.6.", "hints": ["Add up all five boys' marks to get the total.", "Average = total ÷ number of items (5 boys)."], "source": "ACS 2024 P6 Bite-Sized Assessment 2 Q20", "image_needed": false, "image_options": false, "image_file": null, "notes": "no answer key — solved; table transcribed into the stem" } ] }