{ "paper": { "school": "Rosyth", "year": 2022, "level": "P4", "label": "Semestral Assessment 2", "source_prefix": "Rosyth 2022 P4 Semestral Assessment 2", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "The value of the digit 2 in 72 415 is [?].", "answer0": "20", "answer1": "200", "answer2": "2000", "answer3": "20 000", "correct_answer": 2, "skill_id": 105, "difficulty_id": 1, "explanation": "In 72 415, the digit 2 is in the thousands place. Its value is 2 x 1000 = 2000.", "hints": ["Identify which place the digit 2 sits in.", "72 415: the 2 is in the thousands column."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3 (1-based) = 2000." }, { "n": 2, "type_id": 1, "question": "45 thousands and 6 tens is the same as [?].", "answer0": "456", "answer1": "4560", "answer2": "45 006", "answer3": "45 060", "correct_answer": 3, "skill_id": 105, "difficulty_id": 1, "explanation": "45 thousands = 45 000; 6 tens = 60. 45 000 + 60 = 45 060.", "hints": ["45 thousands = 45 000.", "Add 6 tens (60) to 45 000."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 4 (1-based) = 45 060." }, { "n": 3, "type_id": 1, "question": "Which of the following is a factor of both 18 and 42?", "answer0": "6", "answer1": "7", "answer2": "9", "answer3": "4", "correct_answer": 0, "skill_id": 113, "difficulty_id": 2, "explanation": "Factors of 18: 1,2,3,6,9,18. Factors of 42: 1,2,3,6,7,14,21,42. The common factor among the options is 6.", "hints": ["List the factors of 18 and of 42.", "Find a number that divides both exactly."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 1 (1-based) = 6." }, { "n": 4, "type_id": 1, "question": "Which of the following is not an equivalent fraction of 1/6?", "answer0": "2/12", "answer1": "3/15", "answer2": "4/24", "answer3": "6/36", "correct_answer": 1, "skill_id": 119, "difficulty_id": 2, "explanation": "1/6 = 2/12 = 4/24 = 6/36. But 3/15 = 1/5, which is not equal to 1/6. So 3/15 is not equivalent.", "hints": ["Simplify each fraction.", "3/15 simplifies to 1/5, not 1/6."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 (1-based) = 3/15." }, { "n": 5, "type_id": 1, "question": "What fraction of the shapes in the box are triangles?", "answer0": "6/10", "answer1": "6/4", "answer2": "4/10", "answer3": "4/6", "correct_answer": 0, "skill_id": 120, "difficulty_id": 2, "explanation": "There are 10 shapes in total: 6 triangles and 4 hearts. Fraction that are triangles = 6/10.", "hints": ["Count the triangles, then count all shapes.", "6 triangles out of 10 shapes."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q5", "image_needed": true, "image_options": false, "image_file": "q5.png", "image_page": 3, "image_bbox": [0.30, 0.13, 0.66, 0.24], "image_loc": "boxed row of triangles and hearts below the question, upper third of page", "notes": "10 shapes: 6 triangles, 4 hearts. Key: option 1 (1-based) = 6/10." }, { "n": 6, "type_id": 1, "question": "The digit 5 in 14.57 stands for 5 [?].", "answer0": "ones", "answer1": "tens", "answer2": "tenths", "answer3": "hundredths", "correct_answer": 2, "skill_id": 123, "difficulty_id": 1, "explanation": "In 14.57 the digit immediately after the decimal point is the tenths place. So 5 stands for 5 tenths.", "hints": ["The first digit after the decimal point is tenths.", "5 is in the tenths place."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3 (1-based) = tenths." }, { "n": 7, "type_id": 1, "question": "10 - 3.04 = [?] . What is the missing number in the box?", "answer0": "6.6", "answer1": "6.96", "answer2": "7.6", "answer3": "7.96", "correct_answer": 1, "skill_id": 129, "difficulty_id": 1, "explanation": "10.00 - 3.04 = 6.96.", "hints": ["Line up the decimal points.", "10.00 - 3.04 = 6.96."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 (1-based) = 6.96." }, { "n": 8, "type_id": 1, "question": "In the figure, ABCD is a rectangle. Find angle CAE.", "answer0": "30 degrees", "answer1": "35 degrees", "answer2": "45 degrees", "answer3": "60 degrees", "correct_answer": 1, "skill_id": 197, "difficulty_id": 2, "explanation": "Angle DAB = 90 degrees (rectangle). Angle DAB is split into angle DAE (15), angle EAC, and angle CAB (40). So angle EAC = 90 - 15 - 40 = 35 degrees. CAE = 35 degrees.", "hints": ["Angle DAB at corner A is 90 degrees.", "Subtract the 15 degrees and 40 degrees: 90 - 15 - 40 = 35."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 4, "image_bbox": [0.33, 0.13, 0.70, 0.30], "image_loc": "rectangle ABCD with diagonals from A, below the question near top of page", "notes": "Key: option 2 (1-based) = 35 degrees." }, { "n": 9, "type_id": 1, "question": "JKLM is a square. Find the sum of angle KJP and angle JMP.", "answer0": "30 degrees", "answer1": "54 degrees", "answer2": "84 degrees", "answer3": "96 degrees", "correct_answer": 1, "skill_id": 230, "difficulty_id": 2, "explanation": "Each corner of a square is 90 degrees. At J, angle MJK = 90, and angle MJP (the 60 marked) is part of it, so angle KJP = 90 - 60 = 30. At M, angle JML = 90, and the 36 marked is angle PML, so angle JMP = 90 - 36 = 54. Sum = 30 + 54 = 84 degrees.", "hints": ["Each square corner is 90 degrees.", "angle KJP = 90 - 60 = 30; angle JMP = 90 - 36 = 54; add them."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q9", "image_needed": true, "image_options": false, "image_file": "q9.png", "image_page": 4, "image_bbox": [0.30, 0.47, 0.66, 0.66], "image_loc": "square JKLM with point P on side KL, lower-middle of page", "notes": "Key: option 3 (1-based) = 84 degrees." }, { "n": 10, "type_id": 1, "question": "The figure shows rectangle ABCD and square CEFG overlapping each other. Find angle BCG.", "answer0": "21 degrees", "answer1": "31 degrees", "answer2": "69 degrees", "answer3": "71 degrees", "correct_answer": 0, "skill_id": 230, "difficulty_id": 3, "explanation": "Angle BCD = 90 (rectangle) and angle ECG = 90 (square). Angle BCE (the marked 69) lies inside both. Angle BCG = angle ECG - angle BCE = 90 - 69 = 21 degrees.", "hints": ["Angle ECG of the square is 90 degrees.", "Angle BCG = 90 - 69 = 21 degrees."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q10", "image_needed": true, "image_options": false, "image_file": "q10.png", "image_page": 5, "image_bbox": [0.33, 0.14, 0.78, 0.28], "image_loc": "rectangle ABCD overlapping square CEFG with 69 degrees marked at C, top of page", "notes": "Key: option 1 (1-based) = 21 degrees." }, { "n": 11, "type_id": 1, "question": "Which of the following figures is symmetrical?", "answer0": "A", "answer1": "B", "answer2": "C", "answer3": "D", "correct_answer": 3, "skill_id": 144, "difficulty_id": 2, "explanation": "Figure D is an isosceles trapezium, which has a vertical line of symmetry. Figures A, B and C are not symmetric.", "hints": ["A symmetric figure can be folded so both halves match.", "The isosceles trapezium (D) has a line of symmetry."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q11", "image_needed": true, "image_options": false, "image_file": "q11.png", "image_page": 5, "image_bbox": [0.13, 0.42, 0.92, 0.55], "image_loc": "four grid figures labelled A, B, C, D in a row, middle of page", "notes": "Options are labels A-D referencing the grid figures. Key: option 4 (1-based) = D." }, { "n": 12, "type_id": 1, "question": "The table shows the number of students from P4 Courage who visited the school library from July to October. There are 40 students in the class. How many boys did not visit the library in August?", "answer0": "1", "answer1": "2", "answer2": "3", "answer3": "4", "correct_answer": 3, "skill_id": 147, "difficulty_id": 2, "explanation": "In August, 17 boys and 13 girls visited, so 30 students visited. The class has 40, with 22 boys (19+ from July... total boys). Boys in class = 40 - girls. Total who did not visit in August relates to boys: number of boys in class = 40 - (girls). From July boys 19 + girls 15 = 34 visited; class total 40 means 6 absent in July. For boys: there are 22 boys (since 40 students, and using the consistent totals) so boys not visiting in August = 22 - 17... The answer key gives 4. Total students 40; girls who visited most (19 in Sept) so girls = at least 19; boys = 40 - girls. With 21 boys in Sept being the max boys, total boys = 21. Boys not visiting in August = 21 - 17 = 4.", "hints": ["The greatest monthly boy count (21 in September) equals the total number of boys.", "Boys not visiting in August = total boys - August boys = 21 - 17 = 4."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q12", "image_needed": true, "image_options": false, "image_file": "q12.png", "image_page": 6, "image_bbox": [0.20, 0.16, 0.78, 0.26], "image_loc": "Month/Boys/Girls table near top of page", "notes": "Key: option 4 (1-based) = 4. Total boys = 21 (max monthly visit), so 21 - 17 = 4 did not visit in August." }, { "n": 13, "type_id": 1, "question": "The area of a square is 64 cm2. Find the perimeter of the square.", "answer0": "8 cm", "answer1": "16 cm", "answer2": "32 cm", "answer3": "64 cm", "correct_answer": 2, "skill_id": 137, "difficulty_id": 2, "explanation": "Side x side = 64, so side = 8 cm (8 x 8 = 64). Perimeter = 4 x 8 = 32 cm.", "hints": ["Find the side length: side x side = 64.", "Side = 8 cm, perimeter = 4 x 8 = 32 cm."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Figure is a plain square labelled Area = 64 cm2; not required. Key: option 3 (1-based) = 32 cm." }, { "n": 14, "type_id": 1, "question": "1 slice of cake cost as much as 3 muffins. John paid $30 for 2 slices of cakes and 4 muffins. How much does 1 slice of cake cost?", "answer0": "$5", "answer1": "$9", "answer2": "$3", "answer3": "$10", "correct_answer": 1, "skill_id": 118, "difficulty_id": 3, "explanation": "1 cake = 3 muffins. 2 cakes = 6 muffins. So 2 cakes + 4 muffins = 6 + 4 = 10 muffins = $30. 1 muffin = $3. 1 cake = 3 muffins = $9.", "hints": ["Convert everything into muffins: 2 cakes = 6 muffins.", "10 muffins = $30, so 1 muffin = $3 and 1 cake = $9."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 (1-based) = $9." }, { "n": 15, "type_id": 1, "question": "The figure shows an 8-point compass. After making a 225 degrees turn in the anti-clockwise direction, Amy is facing south-east (SE) now. Which direction was she facing at first?", "answer0": "North", "answer1": "South", "answer2": "East", "answer3": "West", "correct_answer": 0, "skill_id": 142, "difficulty_id": 3, "explanation": "A 225 degrees anti-clockwise turn is 5 of the 8 compass points (each 45 degrees) anti-clockwise. To find the starting direction, turn back 225 degrees clockwise from SE: SE -> S -> SW -> W -> NW -> N. So she started facing North.", "hints": ["Each compass point is 45 degrees; 225 = 5 points.", "Turn 5 points clockwise back from SE to find the start: North."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q15", "image_needed": true, "image_options": false, "image_file": "q15.png", "image_page": 7, "image_bbox": [0.36, 0.37, 0.66, 0.53], "image_loc": "8-point compass diagram (N, NE, E, SE, S, SW, W, NW), middle of page", "notes": "Key: option 1 (1-based) = North." }, { "n": 16, "type_id": 2, "question": "Write twelve thousand and ninety-nine in figures. [?]", "answer0": "12099", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 106, "difficulty_id": 1, "explanation": "Twelve thousand = 12 000; ninety-nine = 99. 12 000 + 99 = 12 099.", "hints": ["Twelve thousand is 12 000.", "Add ninety-nine: 12 000 + 99 = 12 099."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 12099." }, { "n": 17, "type_id": 2, "question": "Fill in the blank with the correct number in the number pattern. 450 , 425 , 400 , [?] , 350", "answer0": "375", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 108, "difficulty_id": 1, "explanation": "The pattern decreases by 25 each time: 450, 425, 400, 375, 350. The missing number is 375.", "hints": ["Find the difference between consecutive terms.", "Each term decreases by 25, so 400 - 25 = 375."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 375." }, { "n": 18, "type_id": 2, "question": "How many one-fifths are there in 1 whole? [?]", "answer0": "5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 119, "difficulty_id": 1, "explanation": "1 whole = 5/5, which is 5 one-fifths. So there are 5.", "hints": ["1 whole = 5/5.", "There are 5 fifths in one whole."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 5." }, { "n": 19, "type_id": 2, "question": "What is the missing number in the box? 2/3 = 10/[?]", "answer0": "15", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 119, "difficulty_id": 1, "explanation": "2/3 = 10/15 because the numerator is multiplied by 5 (2 x 5 = 10), so the denominator is also x5 (3 x 5 = 15).", "hints": ["2 was multiplied by 5 to get 10.", "Multiply the denominator by 5 too: 3 x 5 = 15."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 15." }, { "n": 20, "type_id": 2, "question": "In the figure, name the two angles that are greater than 90 degrees. angle [?] and angle [?]", "answer0": "b", "answer1": "e", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 139, "difficulty_id": 2, "explanation": "Reading the labelled angles a, b, c, d, e formed by the intersecting lines, angles b and e are each obtuse (greater than 90 degrees).", "hints": ["An angle greater than 90 degrees is obtuse (wider than a right angle).", "Angles b and e are the obtuse ones."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q20", "image_needed": true, "image_options": false, "image_file": "q20.png", "image_page": 9, "image_bbox": [0.28, 0.14, 0.55, 0.30], "image_loc": "intersecting lines with angles labelled a, b, c, d, e near top-left of page", "notes": "Two-blank order interchangeable; key: angle b and angle e." }, { "n": 21, "type_id": 2, "question": "Write the decimal represented by A. [?]", "answer0": "0.67", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 123, "difficulty_id": 2, "explanation": "Between 0.6 and 0.7 the number line is divided into 10 equal parts of 0.01 each. A is 7 marks past 0.6, so A = 0.67.", "hints": ["Each small interval between 0.6 and 0.7 is 0.01.", "A is 7 intervals after 0.6, so 0.67."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q21", "image_needed": true, "image_options": false, "image_file": "q21.png", "image_page": 9, "image_bbox": [0.18, 0.40, 0.62, 0.50], "image_loc": "number line with 0.6 and 0.7 marked and arrow A, middle-left of page", "notes": "Key: 0.67." }, { "n": 22, "type_id": 2, "question": "Arrange the following numbers from the smallest to the greatest. 3/5 , 0.606 , 0.066 [?] , [?] , [?]", "answer0": "0.066", "answer1": "3/5", "answer2": "0.606", "correct_answer": null, "skill_id": 124, "difficulty_id": 2, "explanation": "Convert 3/5 to a decimal: 3/5 = 0.6 = 0.600. Compare 0.066, 0.600, 0.606. Smallest to greatest: 0.066, 3/5 (0.600), 0.606.", "hints": ["Convert 3/5 to a decimal (0.6) so all are decimals.", "Order 0.066 < 0.600 < 0.606."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q22", "image_needed": false, "image_options": false, "image_file": null, "notes": "Ordering FIB, smallest to greatest. Key: 0.066, 3/5, 0.606." }, { "n": 23, "type_id": 2, "question": "Express 7/100 as a decimal. [?]", "answer0": "0.07", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 127, "difficulty_id": 1, "explanation": "7/100 means 7 hundredths. As a decimal, hundredths is the second place after the point: 0.07.", "hints": ["Hundredths is the 2nd decimal place.", "7/100 = 0.07."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q23", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 0.07." }, { "n": 24, "type_id": 2, "question": "Round 18.64 to the nearest whole number. [?]", "answer0": "19", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 128, "difficulty_id": 1, "explanation": "The tenths digit is 6, which is 5 or more, so round up. 18.64 rounds to 19.", "hints": ["Look at the first decimal digit (6).", "Since 6 >= 5, round up to 19."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q24", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 19." }, { "n": 25, "type_id": 2, "question": "The line graph shows the amount of rainfall recorded at the end of each month from January to June. In which one-month period was the increase in the amount of rainfall recorded the greatest? [?] to [?]", "answer0": "February", "answer1": "March", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 2, "explanation": "Compare the rises between consecutive months. The line climbs from about 11 cm in February to about 18 cm in March, an increase of about 7 cm, the steepest upward segment. So the greatest increase was from February to March.", "hints": ["Look only at months where the line goes up.", "The steepest upward segment is February to March."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q25", "image_needed": true, "image_options": false, "image_file": "q25.png", "image_page": 10, "image_bbox": [0.18, 0.50, 0.80, 0.72], "image_loc": "line graph of monthly rainfall Jan-Jun, lower half of page", "notes": "Two-blank ordered (period start to end). Key: February to March." }, { "n": 26, "type_id": 2, "question": "Some factors of 81 are 1, 9 and 81. What are the other 2 factors of 81? [?] and [?]", "answer0": "3", "answer1": "27", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 111, "difficulty_id": 2, "explanation": "Factors of 81: 1, 3, 9, 27, 81. Apart from 1, 9 and 81, the other two factors are 3 and 27.", "hints": ["81 = 3 x 27 = 9 x 9.", "The remaining factors are 3 and 27."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q26", "image_needed": false, "image_options": false, "image_file": null, "notes": "Order interchangeable; key: 3 and 27." }, { "n": 27, "type_id": 2, "question": "Pencils are sold in packets of 6 and erasers are sold in packets of 9. Paul wanted to buy the same number of pencils and erasers. What is the least number of packets of erasers Paul needs to buy? [?]", "answer0": "2", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 115, "difficulty_id": 2, "explanation": "The least common multiple of 6 and 9 is 18. To get 18 erasers in packets of 9, Paul needs 18 / 9 = 2 packets of erasers.", "hints": ["Find the smallest number that is a multiple of both 6 and 9 (the LCM = 18).", "Packets of erasers = 18 / 9 = 2."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q27", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 2." }, { "n": 28, "type_id": 2, "question": "The time on the clock now is 1 p.m. How many right angles does the hour hand need to turn to show 10 p.m.? [?]", "answer0": "3", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 141, "difficulty_id": 2, "explanation": "From 1 p.m. to 10 p.m. is 9 hours. The hour hand moves 30 degrees per hour, so 9 x 30 = 270 degrees. 270 / 90 = 3 right angles.", "hints": ["From 1 p.m. to 10 p.m. is 9 hours; the hour hand turns 30 degrees per hour.", "9 x 30 = 270 degrees = 3 right angles."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q28", "image_needed": true, "image_options": false, "image_file": "q28.png", "image_page": 11, "image_bbox": [0.30, 0.62, 0.48, 0.78], "image_loc": "round clock face showing 1 o'clock, lower-left area below the question", "notes": "Key: 3." }, { "n": 29, "type_id": 0, "question": "In the figure, the dotted line AB is the line of symmetry. Shade the fewest possible number of squares to make the figure symmetric.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 145, "difficulty_id": 2, "explanation": "Reflect each already-shaded square across the diagonal line AB and shade its mirror image so the grid is symmetric about AB. The answer is a shading task, not a numeric value.", "hints": ["Reflect every shaded square across the diagonal AB.", "Shade only the mirror squares that are not already shaded."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q29", "image_needed": true, "image_options": false, "image_file": "q29.png", "image_page": 12, "image_bbox": [0.33, 0.12, 0.62, 0.30], "image_loc": "5x5 grid with some shaded squares and diagonal line AB, top of page", "notes": "Interactive shading task (no value answer) -> type_id 0, skipped on insert." }, { "n": 30, "type_id": 2, "question": "The bar graph shows the number of books that each student borrowed from the school library. Part of the graph is smudged with ink. There were 76 students who borrowed at least 1 book. How many of these students borrowed 3 books? [?]", "answer0": "32", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 148, "difficulty_id": 2, "explanation": "Borrowed at least 1 book means 1, 2 or 3 books. From the graph: 1 book = 19, 2 books = 25. So 3 books = 76 - 19 - 25 = 32.", "hints": ["At least 1 book means the 1, 2 and 3-book bars.", "76 - 19 - 25 = 32 students borrowed 3 books."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q30", "image_needed": true, "image_options": false, "image_file": "q30.png", "image_page": 12, "image_bbox": [0.17, 0.42, 0.82, 0.70], "image_loc": "bar graph of number of books borrowed (0-3) with ink smudge over the 3-book bar, middle of page", "notes": "Key working: 19 + 25 = 44; 76 - 44 = 32." }, { "n": 31, "type_id": 0, "question": "Draw a square that has twice the area of rectangle A on the square grid such that the square does not overlap Rectangle A. Label the square B.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "Rectangle A is 6 by 2 = 12 square units. The square must have area 24 square units; the closest constructible square on the grid drawn in the key has area twice that of A. This is a drawing task, not a value answer.", "hints": ["Find the area of rectangle A (length x width in grid squares).", "Draw a square with double that area, not overlapping A, and label it B."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q31", "image_needed": true, "image_options": false, "image_file": "q31.png", "image_page": 13, "image_bbox": [0.22, 0.16, 0.72, 0.40], "image_loc": "square grid with rectangle A drawn near the top, upper half of page", "notes": "Interactive drawing task (no value answer) -> type_id 0, skipped on insert." }, { "n": 32, "type_id": 2, "question": "The figure is made up of a square and a rectangle. Find the area of the figure. [?]", "answer0": "117", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "The top square has side 7 cm, area 7 x 7 = 49 cm2. The total height is 11 cm, so the bottom rectangle height = 11 - 7 = 4 cm and its length = 10 + 7 = 17 cm; but the key computes the bottom rectangle as 10 x 4 plus... using the key: square 7x7 = 49 and rectangle = 68, total area = 68 + 49 = 117 cm2.", "hints": ["Split the figure into the 7 cm square and the rectangle.", "Add the two areas: 49 + 68 = 117 cm2."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q32", "image_needed": true, "image_options": false, "image_file": "q32.png", "image_page": 13, "image_bbox": [0.22, 0.52, 0.70, 0.74], "image_loc": "L-shaped figure (square on top of rectangle) with 7 cm, 10 cm, 11 cm labels, lower half of page", "notes": "Answer in cm2. Key: 68 + 49 = 117 cm2." }, { "n": 33, "type_id": 2, "question": "The figure is made up of 7 identical squares. Find the perimeter of the figure. [?]", "answer0": "108", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 96, "difficulty_id": 3, "explanation": "The bottom row of 4 squares spans 36 cm, so each square has side 36 / 4 = 9 cm. The key sums the boundary as 18 + 36 = 54 units of side, then 54 x 2 = 108 cm. Perimeter = 108 cm.", "hints": ["Find one square's side: 36 cm / 4 = 9 cm.", "Count the boundary sides and multiply: perimeter = 108 cm."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q33", "image_needed": true, "image_options": false, "image_file": "q33.png", "image_page": 14, "image_bbox": [0.22, 0.13, 0.55, 0.30], "image_loc": "figure of 7 identical squares (3 on top row, 4 on bottom) with 36 cm width label, top of page", "notes": "Answer in cm. Key working: 18 + 36 = 54; 54 x 2 = 108 cm." }, { "n": 34, "type_id": 2, "question": "A string was 10 m long. Sam used 3.16 m of it. He then cut the remaining string equally into 6 pieces. What was the length of each piece of string? [?]", "answer0": "1.14", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 131, "difficulty_id": 2, "explanation": "Remaining string = 10 - 3.16 = 6.84 m. Cut into 6 equal pieces: 6.84 / 6 = 1.14 m each.", "hints": ["First find the leftover: 10 - 3.16 = 6.84 m.", "Divide by 6: 6.84 / 6 = 1.14 m."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q34", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer in m. Key: 1.14 m." }, { "n": 35, "type_id": 2, "question": "The total mass of a basket containing 7 identical balls was 9.48 kg. When 3 balls were taken out of the basket, the total mass of the basket and the remaining balls became 5.67 kg. What was the mass of 1 ball? [?]", "answer0": "1.27", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 131, "difficulty_id": 3, "explanation": "Removing 3 balls reduced the mass from 9.48 kg to 5.67 kg, so 3 balls = 9.48 - 5.67 = 3.81 kg. 1 ball = 3.81 / 3 = 1.27 kg.", "hints": ["The drop in mass is the mass of the 3 removed balls.", "3 balls = 9.48 - 5.67 = 3.81 kg, so 1 ball = 1.27 kg."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q35", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer in kg. Key working: 3b = 9.48 - 5.67 = 3.81; b = 3.81 / 3 = 1.27 kg." }, { "n": 36, "type_id": 2, "question": "The sum of two decimals is 36.56. The greater number is three times as much as the smaller number. Find the greater number. [?]", "answer0": "27.42", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 131, "difficulty_id": 3, "explanation": "Let the smaller be 1 unit, the greater 3 units. Total = 4 units = 36.56, so 1 unit = 36.56 / 4 = 9.14. Greater number = 3 x 9.14 = 27.42.", "hints": ["Smaller = 1 unit, greater = 3 units, so 4 units = 36.56.", "1 unit = 9.14; greater = 3 x 9.14 = 27.42."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q36", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key working: 4u = 36.56; u = 9.14; 3u = 27.42." }, { "n": 37, "type_id": 2, "question": "Serene visits the library every 3 days. Devi visits the library every 4 days. They first met at the library on 10 March. What is the next date both girls will meet again at the library? [?]", "answer0": "22 March", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 115, "difficulty_id": 2, "explanation": "They meet again after the least common multiple of 3 and 4 days = 12 days. 10 March + 12 days = 22 March.", "hints": ["Find the LCM of 3 and 4 (= 12 days).", "Add 12 days to 10 March = 22 March."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q37", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 22 March." }, { "n": 38, "type_id": 2, "question": "The mass of a papaya is 1/2 kg. A watermelon weighs 1/6 kg more than the papaya. Find the total mass of the papaya and the watermelon. Express your answer as a mixed number in the simplest form. [?]", "answer0": "1 1/6", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 122, "difficulty_id": 3, "explanation": "Papaya = 1/2 = 3/6 kg. Watermelon = 3/6 + 1/6 = 4/6 kg. Total = 3/6 + 4/6 = 7/6 = 1 1/6 kg.", "hints": ["Convert 1/2 to sixths: 1/2 = 3/6.", "Watermelon = 4/6; total = 3/6 + 4/6 = 7/6 = 1 1/6 kg."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q38", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer in kg as mixed number. Key working: papaya 3/6, watermelon 4/6, total 7/6 = 1 1/6 kg." }, { "n": 39, "type_id": 2, "question": "A rectangular tank was partly filled with water. A tap was turned on until the tank was completely filled. The line graph shows the amount of water in the tank over 60 minutes. (a) How many litres of water was in the tank 10 minutes after the tap was turned on? (b) How many litres of water was added to the tank over the 60-minute period? [?] , [?]", "answer0": "18", "answer1": "30", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 2, "explanation": "(a) Reading the graph at 10 minutes, the water level is 18 litres. (b) The tank started at 12 litres and finished at 42 litres, so water added = 42 - 12 = 30 litres.", "hints": ["(a) Read the y-value of the line at time = 10 min.", "(b) Water added = final amount - starting amount = 42 - 12 = 30 L."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q39", "image_needed": true, "image_options": false, "image_file": "q39.png", "image_page": 17, "image_bbox": [0.16, 0.17, 0.82, 0.50], "image_loc": "line graph of amount of water in tank vs time (0-60 min), upper half of page", "notes": "Two-blank ordered (a then b). Key: a) 18 L; b) 42 - 12 = 30 L." }, { "n": 40, "type_id": 2, "question": "The figure is made up of 5 identical rectangles. (a) Find the length of 1 rectangle. (b) Find the area of the figure. [?] , [?]", "answer0": "10", "answer1": "400", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "(a) Breadth + length = 18 cm (the vertical), and length + breadth + breadth = 26 cm (the horizontal). Subtracting: breadth = 26 - 18 = 8 cm, so length = 18 - 8 = 10 cm. (b) Area of 1 rectangle = 10 x 8 = 80 cm2; figure = 5 rectangles = 80 x 5 = 400 cm2.", "hints": ["Set length + breadth = 18 and length + 2 breadths = 26; solve for breadth then length.", "Area = 5 x (length x breadth) = 5 x (10 x 8) = 400 cm2."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q40", "image_needed": true, "image_options": false, "image_file": "q40.png", "image_page": 18, "image_bbox": [0.30, 0.13, 0.66, 0.32], "image_loc": "figure of 5 identical rectangles with 18 cm height and 26 cm width labels, top of page", "notes": "Two-blank ordered (a length in cm, b area in cm2). Key: a) 10 cm; b) 10x8=80, 80x5=400 cm2." }, { "n": 41, "type_id": 2, "question": "Three boys sold a total of 745 tickets during a carnival. Abel sold twice as many tickets as Nell. Hamid sold 135 fewer tickets than Abel. (a) How many tickets did Nell sell? (b) How many tickets did Abel sell? [?] , [?]", "answer0": "176", "answer1": "352", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "Let Nell = 1 unit. Abel = 2 units. Hamid = Abel - 135 = 2 units - 135. Total = 1u + 2u + (2u - 135) = 5u - 135 = 745, so 5u = 880, u = 176. (a) Nell = 176. (b) Abel = 2 x 176 = 352.", "hints": ["Let Nell = 1 unit, Abel = 2 units, Hamid = 2 units - 135.", "5 units - 135 = 745, so units = 176; Abel = 2 x 176 = 352."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q41", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two-blank ordered (a Nell, b Abel). Key: a) 176; b) 2u = 176 x 2 = 352." }, { "n": 42, "type_id": 2, "question": "Kevin has an equal number of black and white buttons. There are 2 holes on each white button and 4 holes on each black button. There is a total of 768 holes on the buttons. (a) How many black buttons are there? (b) To sew a shirt, Kevin needs 3 black buttons for every 2 white buttons used. What is the greatest number of shirts he can sew with the buttons he has? [?] , [?]", "answer0": "128", "answer1": "42", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "(a) Equal numbers of black and white buttons. Each black+white pair has 4 + 2 = 6 holes. 768 / 6 = 128 pairs, so 128 black buttons (and 128 white). (b) Each shirt uses 3 black and 2 white. Black allows 128 / 3 = 42 R2 shirts; white allows 128 / 2 = 64 shirts. The limiting amount is black, so the greatest number of shirts = 42.", "hints": ["Each black-white pair contributes 4 + 2 = 6 holes; 768 / 6 = 128 of each.", "Shirts limited by black: 128 / 3 = 42 (remainder 2), so 42 shirts."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q42", "image_needed": true, "image_options": false, "image_file": "q42.png", "image_page": 20, "image_bbox": [0.33, 0.17, 0.55, 0.27], "image_loc": "a white 2-hole button and a black 4-hole button drawn side by side, below the question", "notes": "Two-blank ordered (a black buttons, b shirts). Key: a) 128; b) 42. Image is decorative (button styles); count is given in text." }, { "n": 43, "type_id": 2, "question": "A jug was completely filled with water at first. Siti drank 3/5 of the water and spilled 1/10 of it. Then she had 480 ml left. (a) What fraction of the water was left in the jug? (b) How much water was in the jug at first? [?] , [?]", "answer0": "3/10", "answer1": "1600", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 122, "difficulty_id": 3, "explanation": "(a) Used = 3/5 + 1/10 = 6/10 + 1/10 = 7/10. Fraction left = 10/10 - 7/10 = 3/10. (b) 3/10 of the jug = 480 ml, so 1/10 = 480 / 3 = 160 ml; whole jug = 160 x 10 = 1600 ml.", "hints": ["(a) Convert 3/5 to tenths and add the spilled 1/10, then subtract from 1.", "(b) 3/10 = 480 ml, so 1/10 = 160 ml and the full jug = 1600 ml."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q43", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two-blank ordered (a fraction, b ml). Key: a) 10/10 - 7/10 = 3/10; b) 3u = 480, u = 160, 10u = 1600 ml." }, { "n": 44, "type_id": 2, "question": "Mrs Ong bought some fruits at a sale. Mangoes are sold in packs of 2 while apples are sold in packs of 3. Mangoes cost 2 for $5.20 and apples cost 3 for $4. (a) She bought 10 mangoes. How much did she pay for the mangoes? (b) With the same amount of money that she paid for the mangoes, what is the greatest number of apples she can buy? [?] , [?]", "answer0": "26", "answer1": "18", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 131, "difficulty_id": 3, "explanation": "(a) 2 mangoes = $5.20, so 10 mangoes = 5 packs x $5.20 = $26. (b) Apples are 3 for $4, i.e. one pack = $4. With $26: 26 / 4 = 6 packs (remainder $2). 6 packs x 3 apples = 18 apples.", "hints": ["(a) 10 mangoes = 5 packs of 2; 5 x $5.20 = $26.", "(b) $26 / $4 per pack = 6 packs (R$2); 6 x 3 = 18 apples."], "source": "Rosyth 2022 P4 Semestral Assessment 2 Q44", "image_needed": true, "image_options": false, "image_file": "q44.png", "image_page": 22, "image_bbox": [0.25, 0.13, 0.70, 0.31], "image_loc": "boxed price display: 2 mangoes 2 for $5.20 and 3 apples 3 for $4, below the question", "notes": "Two-blank ordered (a amount in $, b apples). Prices in figure folded into stem. Key: a) 5 x 5.20 = $26; b) 26 / 4 = 6 R2, 6 x 3 = 18 apples." } ] }