{ "paper": { "school": "ACS Junior", "year": 2023, "level": "P4", "label": "Weighted Assessment 2", "source_prefix": "ACS Junior 2023 P4 Weighted Assessment 2", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "In the figure, which angle is greater than a right angle?", "answer0": "∠ABC", "answer1": "∠BAD", "answer2": "∠CDA", "answer3": "∠DCB", "correct_answer": 3, "skill_id": 139, "difficulty_id": 1, "explanation": "A right angle is 90°. Comparing the four angles of quadrilateral ABCD, ∠DCB is the angle that opens out wider than a square corner (90°), so it is greater than a right angle. The other three angles are 90° or smaller.", "hints": ["A right angle looks like the square corner of a book — exactly 90°.", "Check each marked vertex: an angle wider (more open) than that square corner is greater than a right angle."], "source": "ACS Junior 2023 P4 Weighted Assessment 2 Q1", "image_needed": true, "image_options": false, "image_file": "q1.png", "image_page": 2, "image_bbox": [0.32, 0.27, 0.62, 0.43], "image_loc": "quadrilateral ABCD figure, upper-middle of page, above the options", "notes": "Answer key: option 4 (∠DCB)." }, { "n": 2, "type_id": 1, "question": "Which of the following figures is a symmetric figure?", "answer0": "Figure 1", "answer1": "Figure 2", "answer2": "Figure 3", "answer3": "Figure 4", "correct_answer": 1, "skill_id": 144, "difficulty_id": 1, "explanation": "A symmetric figure can be folded along a line so the two halves match exactly. Figure 2 (the pentagon-like shape) has a line of symmetry; the arrow/zig-zag, wavy and slanted shapes do not. So the answer is Figure 2.", "hints": ["A symmetric figure has at least one line where both halves are mirror images.", "Imagine folding each figure in half — the symmetric one matches perfectly."], "source": "ACS Junior 2023 P4 Weighted Assessment 2 Q2", "image_needed": true, "image_options": true, "image_file": null, "image_page": 2, "image_bbox": [0.18, 0.58, 0.82, 0.90], "image_loc": "four labelled candidate figures (1-4) in a 2x2 grid in the lower half of the page", "notes": "Answer key: option 2. image_options=true — crop each option to q2_opt0.png..q2_opt3.png." }, { "n": 3, "type_id": 1, "question": "KLMN is a square. Find ∠e.", "answer0": "36°", "answer1": "46°", "answer2": "59°", "answer3": "67°", "correct_answer": 0, "skill_id": 197, "difficulty_id": 3, "explanation": "At vertex M the corner of the square is 90°. The 31° angle and ∠e and the 23° angle sit inside that corner: 90° − 31° − 23° = 36°. So ∠e = 36°.", "hints": ["Each corner of a square is a right angle (90°).", "The three angles at corner M (31°, ∠e and 23°) add up to 90°."], "source": "ACS Junior 2023 P4 Weighted Assessment 2 Q3", "image_needed": true, "image_options": false, "image_file": "q3.png", "image_page": 3, "image_bbox": [0.28, 0.12, 0.58, 0.30], "image_loc": "square KLMN with diagonals/lines and marked angles 23°, 31° and e, upper-left of page", "notes": "Answer key: option 1 (36°). Figure not drawn to scale." }, { "n": 4, "type_id": 1, "question": "John is facing south-west. When he turns through an angle of [?] in an anti-clockwise direction, he will be facing east.", "answer0": "45°", "answer1": "90°", "answer2": "135°", "answer3": "225°", "correct_answer": 2, "skill_id": 142, "difficulty_id": 2, "explanation": "On the 8-point compass, turning anti-clockwise from south-west: SW → S (45°) → SE (90°) → E (135°). Each step between compass points is 45°, and there are 3 steps from south-west to east going anti-clockwise, so the turn is 3 × 45° = 135°.", "hints": ["Adjacent points on an 8-point compass are 45° apart.", "Count the 45° steps from south-west to east turning anti-clockwise."], "source": "ACS Junior 2023 P4 Weighted Assessment 2 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 3 (135°). The small N-compass icon is decorative only; question is solvable from text. type_id kept as MCQ per the printed options; the [?] in the stem marks the missing value the options fill." }, { "n": 5, "type_id": 1, "question": "The figure is made up of 2 identical squares of side 4 cm, a rectangle A with breadth 5 cm and a square B. Find the length of rectangle A.", "answer0": "9 cm", "answer1": "17 cm", "answer2": "18 cm", "answer3": "22 cm", "correct_answer": 1, "skill_id": 138, "difficulty_id": 2, "explanation": "The 14 cm marked length runs from the left edge of square B to the right edge of rectangle A. Square B has side 4 cm (it lines up with the 4 cm squares). Length of A = total 14 cm + the two 4 cm squares overhang... reading the figure, A's length = 14 − 4 (square B) gives the start, plus the additional small squares; the answer key gives 17 cm.", "hints": ["Square B has the same 4 cm side as the small squares.", "Add and subtract the marked segments carefully to isolate the length of rectangle A."], "source": "ACS Junior 2023 P4 Weighted Assessment 2 Q5", "image_needed": true, "image_options": false, "image_file": "q5.png", "image_page": 4, "image_bbox": [0.28, 0.16, 0.70, 0.30], "image_loc": "composite figure: square B + rectangle A (5 cm) with 14 cm and 4 cm dimension lines, upper-middle of page", "notes": "Answer key: option 2 (17 cm). Geometry of the composite is the load-bearing part — crop must include all dimension labels (14 cm, 5 cm, 4 cm) and squares." }, { "n": 6, "type_id": 2, "question": "Use a protractor to measure ∠XYZ.", "answer0": "108", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 140, "difficulty_id": 1, "explanation": "Placing a protractor with its centre at Y and the baseline along one arm, the other arm reads 108°. So ∠XYZ = 108°.", "hints": ["Put the protractor's centre on the vertex Y and align the 0° line with one arm.", "Read the scale where the other arm crosses; this angle is obtuse (more than 90°)."], "source": "ACS Junior 2023 P4 Weighted Assessment 2 Q6", "image_needed": true, "image_options": false, "image_file": "q6.png", "image_page": 5, "image_bbox": [0.18, 0.22, 0.66, 0.43], "image_loc": "angle XYZ with vertex Y and arms to X and Z, middle of page", "notes": "Answer key: 108°. Answer unit is degrees; stored as plain 108." }, { "n": 7, "type_id": 2, "question": "What is the least number of squares that must be added so that AB is the line of symmetry for the figure.", "answer0": "3", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 145, "difficulty_id": 2, "explanation": "AB is the diagonal line of symmetry. For each shaded square, its mirror image across AB must also be shaded. Reflecting the existing shaded squares across AB, three of the required mirror-image squares are still empty, so 3 squares must be added.", "hints": ["A line of symmetry means each shaded square must have a matching shaded square on the other side of AB.", "Reflect each shaded square across the diagonal AB and count how many mirror positions are still empty."], "source": "ACS Junior 2023 P4 Weighted Assessment 2 Q7", "image_needed": true, "image_options": false, "image_file": "q7.png", "image_page": 5, "image_bbox": [0.30, 0.55, 0.62, 0.82], "image_loc": "5x5 grid with shaded squares and dashed diagonal AB, lower half of page", "notes": "Answer key: 3." }, { "n": 8, "type_id": 0, "question": "In the square grid, two sides of a rectangle have been drawn. Complete the drawing of the rectangle within the grid with the given lines.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 143, "difficulty_id": 2, "explanation": "Add the two remaining sides parallel to the given sides to close the rectangle on the grid, as shown in the answer key.", "hints": ["A rectangle has opposite sides equal and parallel.", "Each new side must be parallel and equal in length to the side opposite it."], "source": "ACS Junior 2023 P4 Weighted Assessment 2 Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 6, "image_bbox": [0.16, 0.16, 0.62, 0.42], "image_loc": "square grid with two sides of a rectangle drawn, upper half of page", "notes": "Draw/construct task (complete the rectangle) — no value answer, so type_id 0; SKIPPED on insert. Answer key shows the completed rectangle drawn on the grid." }, { "n": 9, "type_id": 2, "question": "EF is perpendicular FG and ∠p = ∠q. Find ∠p.", "answer0": "21", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 194, "difficulty_id": 2, "explanation": "EF is perpendicular to FG, so ∠EFG = 90°. This 90° is made up of ∠p, 48° and ∠q: ∠p + 48° + ∠q = 90°. Since ∠p = ∠q, the two equal angles share the remaining 90° − 48° = 42°, so ∠p = 42° ÷ 2 = 21°.", "hints": ["Perpendicular lines meet at 90°, so ∠EFG = 90°.", "Subtract the 48° first, then split the rest equally between the two equal angles p and q."], "source": "ACS Junior 2023 P4 Weighted Assessment 2 Q9", "image_needed": true, "image_options": false, "image_file": "q9.png", "image_page": 6, "image_bbox": [0.14, 0.50, 0.46, 0.72], "image_loc": "angle figure with vertex F, arms to E and G, marked p, 48° and q, lower-left of page", "notes": "Answer key: 90−48=42, 42÷2=21°. Figure not drawn to scale. Answer unit is degrees; stored as plain 21." }, { "n": 10, "type_id": 2, "question": "Perry was at a certain position. He walked 2 steps due north, 1 step due east, 4 steps due south and then 3 steps due west. He ended at Position X. What was his starting position?", "answer0": "Y", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 142, "difficulty_id": 3, "explanation": "Net displacement from start to X = 2 north + 4 south = 2 steps south, and 1 east + 3 west = 2 steps west. So X is 2 steps south and 2 steps west of the start. Reversing, the start is 2 steps north and 2 steps east of X — that point on the grid is Position Y.", "hints": ["Find the overall (net) move: combine the north/south steps and the east/west steps separately.", "Work backwards from X by the opposite of the net move to find the starting point."], "source": "ACS Junior 2023 P4 Weighted Assessment 2 Q10", "image_needed": true, "image_options": false, "image_file": "q10.png", "image_page": 7, "image_bbox": [0.22, 0.13, 0.66, 0.40], "image_loc": "5x5 grid with labelled points T, V, W, X, Y and a 1-step scale, upper half of page", "notes": "Answer key: Y. Answer is a labelled grid position (letter), kept as FIB single value matching the key." }, { "n": 11, "type_id": 2, "question": "Mr Lim had 528 mangoes. He sold all the mangoes at 6 for $14. How much money did he receive?", "answer0": "$1232", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 2, "explanation": "Number of groups of 6 mangoes = 528 ÷ 6 = 88 groups. Each group sells for $14, so total money = 88 × $14 = $1232. Mr Lim received $1232.", "hints": ["First find how many groups of 6 mangoes there are: 528 ÷ 6.", "Multiply the number of groups by $14."], "source": "ACS Junior 2023 P4 Weighted Assessment 2 Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 528÷6=88, 88×14=1232 → $1232." }, { "n": 12, "type_id": 2, "question": "Mrs Tan baked three times as many banana muffins as chocolate muffins. After she gave away 16 chocolate muffins, there were 5 times as many banana muffins as chocolate muffins. How many chocolate muffins did she bake at first?", "answer0": "40", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "Let chocolate at first = 3 units of banana, so banana = 3 × chocolate. After giving away 16 chocolate, banana = 5 × (new chocolate). Banana stays the same. Using units: original chocolate is 1 part of the banana's 3 parts; after removal it is 1 part of 5. The 16 removed muffins equal the difference: with 5 units → 1 unit banana, work out 1 unit = 16×3÷? Following the key: 2u → 16×3 = 48, 1u → 48÷2 = 24, chocolate at first = 24 + 16 = 40. She baked 40 chocolate muffins at first.", "hints": ["Banana muffins never change — use them as the fixed total.", "Write the before and after relationships in units of the fixed banana total, then the 16 given-away muffins fill the gap."], "source": "ACS Junior 2023 P4 Weighted Assessment 2 Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 2u→16×3=48, 1u→48÷2=24, 24+16=40 chocolate muffins at first." }, { "n": 13, "type_id": 2, "question": "Rina had 5 times as many red beads as blue beads at first. She then gave away 36 red beads and bought another 36 blue beads. She had the same number of red beads and blue beads in the end. How many red beads did she have in the end?", "answer0": "54", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "At first red = 5 units, blue = 1 unit. After giving away 36 red and buying 36 blue, the totals are equal. The difference at first was 5u − 1u = 4 units; the changes close a gap of 36 + 36 = 72, which equals 4 units, so 1 unit = 18. Following the key: 36 + 36 = 72 closes the gap of (5u−1u); 72÷4 = 18 per unit. Red in the end = 5×18 − 36 = 90 − 36 = 54. She had 54 red beads in the end.", "hints": ["Set red = 5 units and blue = 1 unit at the start; the gap is 4 units.", "Giving away red and buying blue both shrink the gap to zero — use that to find 1 unit, then compute the final red count."], "source": "ACS Junior 2023 P4 Weighted Assessment 2 Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key shows 36+2=18, 3×18=54 → 54 red beads in the end. (Key's terse working; final answer 54 verified: 1u=18, end red = 5×18−36 = 54.)" } ] }