{ "paper": { "school": "CHIJ St Nicholas Girls' School (Primary)", "year": 2025, "level": "P4", "label": "End-of-Year Exam", "source_prefix": "St Nicholas 2025 P4 End-of-Year Exam", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "The value of the digit 5 in 89 503 is [?].", "answer0": "50", "answer1": "500", "answer2": "5000", "answer3": "50 000", "correct_answer": 1, "skill_id": 105, "difficulty_id": 1, "explanation": "In 89 503 the digit 5 is in the hundreds place, so its value is $$5 \\times 100 = 500$$.", "hints": ["Identify the place of the digit 5.", "5 sits in the hundreds column."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 (500)." }, { "n": 2, "type_id": 1, "question": "Thirty-four thousand and sixty-two in figures is [?].", "answer0": "34 620", "answer1": "34 602", "answer2": "34 062", "answer3": "3462", "correct_answer": 2, "skill_id": 106, "difficulty_id": 1, "explanation": "Thirty-four thousand = 34 000; sixty-two = 62. Together: $$34\\,000 + 62 = 34\\,062$$.", "hints": ["Write the thousands part first.", "Add sixty-two to 34 000."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3 (34 062)." }, { "n": 3, "type_id": 1, "question": "Which of the following when rounded to the nearest hundred gives 60 000?", "answer0": "59 599", "answer1": "59 951", "answer2": "60 070", "answer3": "60 140", "correct_answer": 1, "skill_id": 109, "difficulty_id": 2, "explanation": "Rounding to the nearest hundred: 59 951 rounds to 60 000 (the tens digit 5 rounds up). 59 599 rounds to 59 600; 60 070 rounds to 60 100; 60 140 rounds to 60 100.", "hints": ["Look at the tens digit to decide rounding.", "Which value is between 59 950 and 60 049?"], "source": "St Nicholas 2025 P4 End-of-Year Exam Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 (59 951)." }, { "n": 4, "type_id": 1, "question": "What is the second common multiple of 4 and 6?", "answer0": "12", "answer1": "16", "answer2": "24", "answer3": "30", "correct_answer": 2, "skill_id": 115, "difficulty_id": 2, "explanation": "Common multiples of 4 and 6 are 12, 24, 36, ... The first is 12 and the second is 24.", "hints": ["List the multiples of 4 and of 6.", "The first common multiple is 12."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3 (24)." }, { "n": 5, "type_id": 1, "question": "The figure is made up of identical rectangles. What fraction of the figure is shaded?", "answer0": "$$\\frac{5}{7}$$", "answer1": "$$\\frac{5}{11}$$", "answer2": "$$\\frac{5}{12}$$", "answer3": "$$\\frac{7}{12}$$", "correct_answer": 2, "skill_id": 120, "difficulty_id": 2, "explanation": "The grid has 3 rows by 4 columns = 12 identical rectangles. 5 of them are shaded, so the shaded fraction is $$\\frac{5}{12}$$.", "hints": ["Count the total number of rectangles.", "Count the shaded ones over the total."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q5", "image_needed": true, "image_options": false, "image_file": "q5.png", "image_page": 3, "image_bbox": [0.34, 0.39, 0.66, 0.52], "image_loc": "middle of page: 3-row by 4-column grid of rectangles with 5 cells shaded", "notes": "Key: option 3 (5/12). 12 cells, 5 shaded." }, { "n": 6, "type_id": 1, "question": "Which of the following fractions is equivalent to $$\\frac{4}{6}$$?", "answer0": "$$\\frac{6}{12}$$", "answer1": "$$\\frac{8}{18}$$", "answer2": "$$\\frac{10}{12}$$", "answer3": "$$\\frac{12}{18}$$", "correct_answer": 3, "skill_id": 119, "difficulty_id": 2, "explanation": "$$\\frac{4}{6} = \\frac{2}{3}$$. Checking: $$\\frac{12}{18} = \\frac{2}{3}$$, so it is equivalent.", "hints": ["Simplify 4/6 to 2/3.", "Which option also simplifies to 2/3?"], "source": "St Nicholas 2025 P4 End-of-Year Exam Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 4 (12/18). Skill 119 (equivalent fractions); closest P4 entry." }, { "n": 7, "type_id": 1, "question": "In the number 41.32, the digit [?] is in the hundredths place.", "answer0": "1", "answer1": "2", "answer2": "3", "answer3": "4", "correct_answer": 1, "skill_id": 123, "difficulty_id": 1, "explanation": "In 41.32, the first decimal place (tenths) is 3 and the second (hundredths) is 2. So the digit in the hundredths place is 2.", "hints": ["Tenths is the first decimal place.", "Hundredths is the second decimal place."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 (2)." }, { "n": 8, "type_id": 1, "question": "$$11.78 \\times 6 = $$ [?]", "answer0": "70.68", "answer1": "66.78", "answer2": "66.68", "answer3": "17.78", "correct_answer": 0, "skill_id": 130, "difficulty_id": 2, "explanation": "$$11.78 \\times 6 = 70.68$$.", "hints": ["Multiply 1178 by 6 then place the decimal point.", "1178 × 6 = 7068."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 1 (70.68). Stem shown verbatim; the printed blank is the MCQ answer." }, { "n": 9, "type_id": 1, "question": "Express $$\\frac{21}{25}$$ as a decimal.", "answer0": "0.021", "answer1": "0.084", "answer2": "0.21", "answer3": "0.84", "correct_answer": 3, "skill_id": 127, "difficulty_id": 2, "explanation": "Make the denominator 100: $$\\frac{21}{25} = \\frac{84}{100} = 0.84$$.", "hints": ["Multiply numerator and denominator by 4.", "84 over 100 is 0.84."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 4 (0.84)." }, { "n": 10, "type_id": 1, "question": "In the figure, which angle is a right angle?", "answer0": "$$\\angle w$$", "answer1": "$$\\angle x$$", "answer2": "$$\\angle y$$", "answer3": "$$\\angle z$$", "correct_answer": 2, "skill_id": 140, "difficulty_id": 2, "explanation": "Of the four angles in the quadrilateral, angle y is the one that forms a right angle (90 degrees).", "hints": ["A right angle looks like a square corner.", "Compare each marked angle to 90 degrees."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q10", "image_needed": true, "image_options": false, "image_file": "q10.png", "image_page": 5, "image_bbox": [0.33, 0.36, 0.65, 0.52], "image_loc": "middle of page: a quadrilateral (kite-like) with angles labelled w, x, y, z", "notes": "Key: option 3 (angle y)." }, { "n": 11, "type_id": 1, "question": "The figure shows a rectangle. Its length is 3 times its breadth. Find its perimeter.", "answer0": "$$15\\ cm$$", "answer1": "$$20\\ cm$$", "answer2": "$$26\\ cm$$", "answer3": "$$40\\ cm$$", "correct_answer": 3, "skill_id": 143, "difficulty_id": 2, "explanation": "Breadth = 5 cm, so length = $$3 \\times 5 = 15$$ cm. Perimeter = $$2 \\times (15 + 5) = 40$$ cm.", "hints": ["Length = 3 × breadth.", "Perimeter = 2 × (length + breadth)."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q11", "image_needed": true, "image_options": false, "image_file": "q11.png", "image_page": 6, "image_bbox": [0.30, 0.16, 0.67, 0.29], "image_loc": "upper-middle: a rectangle with the breadth labelled 5 cm on its left side", "notes": "Key: option 4 (40 cm). Breadth 5 cm from figure." }, { "n": 12, "type_id": 1, "question": "Mr Ng took a flight from Singapore to Japan. He boarded the plane at 23 39 and reached Japan at 06 22 the next day. How long was the flight?", "answer0": "6 h 17 min", "answer1": "6 h 43 min", "answer2": "7 h 17 min", "answer3": "7 h 43 min", "correct_answer": 1, "skill_id": 135, "difficulty_id": 2, "explanation": "From 23 39 to 24 00 is 21 min. From 00 00 to 06 22 is 6 h 22 min. Total: $$6\\ h\\ 22\\ min + 21\\ min = 6\\ h\\ 43\\ min$$.", "hints": ["Find the time to midnight first.", "Add the time after midnight."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 (6 h 43 min)." }, { "n": 13, "type_id": 1, "question": "How many pupils in Class 4B chose orange as their favourite fruit?", "answer0": "16", "answer1": "19", "answer2": "21", "answer3": "26", "correct_answer": 0, "skill_id": 147, "difficulty_id": 2, "explanation": "Each class has the same number of pupils. Class 4A total = $$14+12+8+6 = 40$$. So 4B total = 40. 4B = $$7+13+?+4 = 24 + ?$$, so orange = $$40 - 24 = 16$$.", "hints": ["Total each class to the same number.", "Class 4A totals 40 pupils."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q13", "image_needed": true, "image_options": false, "image_file": "q13.png", "image_page": 7, "image_bbox": [0.18, 0.18, 0.78, 0.31], "image_loc": "upper portion: table of favourite fruits (Class / Apple / Banana / Orange / Pear) for 4A, 4B, 4C", "notes": "Key: option 1 (16). Table shared by Q13 and Q14." }, { "n": 14, "type_id": 1, "question": "Which fruit did most pupils choose?", "answer0": "pear", "answer1": "apple", "answer2": "orange", "answer3": "banana", "correct_answer": 1, "skill_id": 147, "difficulty_id": 2, "explanation": "Totals across all classes: Apple = $$14+7+15 = 36$$, Banana = $$12+13+6 = 31$$, Orange = $$8+16+11 = 35$$, Pear = $$6+4+8 = 18$$. Apple has the most (36).", "hints": ["Add each fruit column across all three classes.", "Use 16 for 4B orange from Q13."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q14", "image_needed": true, "image_options": false, "image_file": "q14.png", "image_page": 7, "image_bbox": [0.18, 0.18, 0.78, 0.31], "image_loc": "upper portion: table of favourite fruits (Class / Apple / Banana / Orange / Pear) for 4A, 4B, 4C", "notes": "Key: option 2 (apple). Same table as Q13." }, { "n": 15, "type_id": 1, "question": "Elize had a string that was 15.61 m long. She used 1.54 m to tie a parcel and cut the remaining string into 7 equal pieces. How long was each piece of string?", "answer0": "0.69 m", "answer1": "2.01 m", "answer2": "2.23 m", "answer3": "2.45 m", "correct_answer": 1, "skill_id": 131, "difficulty_id": 2, "explanation": "Remaining string = $$15.61 - 1.54 = 14.07$$ m. Each piece = $$14.07 \\div 7 = 2.01$$ m.", "hints": ["Subtract the part used first.", "Divide the remainder by 7."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 (2.01 m)." }, { "n": 16, "type_id": 1, "question": "Kelly used $$\\frac{3}{10}$$ kg of coffee powder. She used $$\\frac{1}{5}$$ kg less coffee powder than Frances. How much coffee powder did they use altogether?", "answer0": "$$\\frac{1}{2}$$ kg", "answer1": "$$\\frac{1}{10}$$ kg", "answer2": "$$\\frac{2}{5}$$ kg", "answer3": "$$\\frac{4}{5}$$ kg", "correct_answer": 3, "skill_id": 122, "difficulty_id": 3, "explanation": "Frances = $$\\frac{3}{10} + \\frac{1}{5} = \\frac{3}{10} + \\frac{2}{10} = \\frac{5}{10} = \\frac{1}{2}$$ kg. Altogether = $$\\frac{3}{10} + \\frac{5}{10} = \\frac{8}{10} = \\frac{4}{5}$$ kg.", "hints": ["Find Frances's amount first (Kelly used 1/5 kg less).", "Add Kelly's and Frances's amounts."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 4 (4/5 kg)." }, { "n": 17, "type_id": 1, "question": "Which one of the following figures has more than one line of symmetry?", "answer0": "Figure 1 (parallelogram)", "answer1": "Figure 2 (hexagon)", "answer2": "Figure 3 (trapezium shape)", "answer3": "Figure 4 (L-shape)", "correct_answer": 1, "skill_id": 145, "difficulty_id": 2, "explanation": "The regular-looking hexagon in Figure 2 has both a horizontal and a vertical line of symmetry (more than one). The parallelogram has none; the others have at most one.", "hints": ["Try folding each shape along a line.", "Look for a shape symmetric both vertically and horizontally."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q17", "image_needed": true, "image_options": true, "image_file": null, "image_page": 9, "image_bbox": [0.20, 0.13, 0.55, 0.92], "image_loc": "four grid figures stacked vertically labelled (1) parallelogram, (2) hexagon, (3) trapezium, (4) L-shape", "notes": "Key: option 2 (the hexagon). Crop each option to q17_opt0..3.png." }, { "n": 18, "type_id": 1, "question": "Isabelle is at Position X. She takes 2 steps to the north, 3 steps to the east, and 4 steps to the south. At which position will Isabelle be in the end?", "answer0": "A", "answer1": "B", "answer2": "C", "answer3": "D", "correct_answer": 3, "skill_id": 142, "difficulty_id": 2, "explanation": "Net vertical move = 2 north then 4 south = 2 steps south of X. Net horizontal move = 3 steps east. From X this lands on position D.", "hints": ["Combine the north and south steps first.", "Then apply the eastward steps."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q18", "image_needed": true, "image_options": false, "image_file": "q18.png", "image_page": 10, "image_bbox": [0.22, 0.14, 0.78, 0.38], "image_loc": "upper portion: a grid of 1-step squares with points A, B, X, C, D marked and a North arrow", "notes": "Key: option 4 (D)." }, { "n": 19, "type_id": 1, "question": "Neeta used 52 tacks to pin her drawings side by side onto a board. How many drawings did she pin altogether?", "answer0": "13", "answer1": "24", "answer2": "25", "answer3": "26", "correct_answer": 2, "skill_id": 108, "difficulty_id": 3, "explanation": "Drawings are pinned side by side sharing tacks. Each drawing uses 2 tacks at its corners on top and bottom, but adjacent drawings share the in-between tacks. With the shared-tack pattern shown, 52 tacks pin 25 drawings.", "hints": ["Adjacent drawings share tacks between them.", "Work out how many tacks one extra drawing adds."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q19", "image_needed": true, "image_options": false, "image_file": "q19.png", "image_page": 11, "image_bbox": [0.22, 0.18, 0.78, 0.30], "image_loc": "row of pinned drawings (rabbit, balloons, flowers, dolphin) with tacks at the corners, dashed continuation", "notes": "Key: option 3 (25). Shared-tack pattern." }, { "n": 20, "type_id": 2, "question": "Fill in the blank with the correct number in the number pattern below.
875 , 845 , 815 , [?] , 755", "answer0": "785", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 108, "difficulty_id": 1, "explanation": "The pattern decreases by 30 each time: $$875 - 845 = 30$$. So the missing term is $$815 - 30 = 785$$ (and $$785 - 30 = 755$$ checks).", "hints": ["Find the difference between consecutive terms.", "Subtract 30 from 815."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q20", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 785." }, { "n": 21, "type_id": 1, "question": "In the figure, name the smallest angle.", "answer0": "$$\\angle a$$", "answer1": "$$\\angle b$$", "answer2": "$$\\angle c$$", "answer3": "$$\\angle d$$", "correct_answer": 3, "skill_id": 140, "difficulty_id": 2, "explanation": "Comparing the four marked angles around the point, angle d is the smallest (narrowest opening).", "hints": ["The smallest angle has the narrowest opening.", "Compare the sizes of angles a, b, c and d."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q21", "image_needed": true, "image_options": false, "image_file": "q21.png", "image_page": 13, "image_bbox": [0.30, 0.50, 0.62, 0.72], "image_loc": "middle: lines crossing at a point with angles a, b, c, d marked around it", "notes": "Key: d. Converted to MCQ (angle-naming word answer)." }, { "n": 22, "type_id": 2, "question": "Write $$\\frac{20}{9}$$ as a mixed number. [?]", "answer0": "2 2/9", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 119, "difficulty_id": 1, "explanation": "$$20 \\div 9 = 2$$ remainder $$2$$, so $$\\frac{20}{9} = 2\\frac{2}{9}$$.", "hints": ["Divide 20 by 9.", "Whole part is the quotient, remainder over 9 is the fraction part."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q22", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 2 2/9. FIB answer kept plain as a typed mixed number." }, { "n": 23, "type_id": 2, "question": "$$7.06 + 2 = $$ [?]", "answer0": "9.06", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 129, "difficulty_id": 1, "explanation": "$$7.06 + 2 = 9.06$$ (add to the whole-number part).", "hints": ["Add 2 to the whole-number part.", "The decimal part stays 0.06."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q23", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 9.06." }, { "n": 24, "type_id": 2, "question": "The perimeter of a square is 76 cm. What is the area of the square? [?]", "answer0": "361", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 137, "difficulty_id": 2, "explanation": "Side = $$76 \\div 4 = 19$$ cm. Area = $$19 \\times 19 = 361$$ cm². Answer in $$cm^2$$.", "hints": ["A square has 4 equal sides.", "Side = perimeter ÷ 4, then area = side × side."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q24", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 361 cm². Answer entered in cm²." }, { "n": 25, "type_id": 2, "question": "A bakery sold different flavours of cakes on Monday. The bar graph shows the number of each flavour of cakes sold.
(a) Use the data from the graph to complete the table: Chocolate = [?] , Pandan = [?].
(b) The bakery sold a total of 84 cakes of 2 flavours. Which were the 2 flavours? [?] and [?]", "answer0": "52", "answer1": "24", "answer2": "chocolate", "answer3": "strawberry", "correct_answer": null, "skill_id": 104, "difficulty_id": 2, "explanation": "From the bar graph: Vanilla = 40, Chocolate = 52, Strawberry = 32, Pandan = 24. (b) Two flavours totalling 84: $$52 + 32 = 84$$, so chocolate and strawberry.", "hints": ["Read each bar height from the graph.", "Find the pair of flavours that sum to 84."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q25", "image_needed": true, "image_options": false, "image_file": "q25.png", "image_page": 15, "image_bbox": [0.16, 0.16, 0.80, 0.45], "image_loc": "upper portion: bar graph 'Number of cakes sold by a bakery' with bars Vanilla, Chocolate, Strawberry, Pandan (y-axis 0-60)", "notes": "Key: Chocolate 52, Pandan 24; (b) chocolate and strawberry. Four real blanks." }, { "n": 26, "type_id": 2, "question": "The time shown on the clock is 20 minutes faster than the actual time. What is the actual time? [?] p.m.", "answer0": "4.53", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 92, "difficulty_id": 2, "explanation": "The clock shows 5.13 p.m. The actual time is 20 minutes earlier: $$5.13 - 20\\ min = 4.53$$ p.m.", "hints": ["Read the time on the clock face.", "Subtract 20 minutes because the clock is fast."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q26", "image_needed": true, "image_options": false, "image_file": "q26.png", "image_page": 16, "image_bbox": [0.14, 0.13, 0.34, 0.27], "image_loc": "left side: an alarm clock face showing about 5.13", "notes": "Key: 4.53 p.m. Clock reads 5.13 p.m. Answer entered before the printed 'p.m.'. Skill 92 (P3 time problems) is the closest match; P4 has no plain clock-reading skill." }, { "n": 27, "type_id": 2, "question": "Liana started doing a science quiz at 12.42 p.m. There were 8 questions in this quiz. For the first 3 questions, Liana took 6 minutes to complete each question. For the remaining questions, she took 7 minutes to complete each question. At what time did Liana complete the quiz? Express your answer using the 24-hour clock. [?]", "answer0": "1335", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 135, "difficulty_id": 3, "explanation": "First 3 questions: $$3 \\times 6 = 18$$ min. Remaining $$8 - 3 = 5$$ questions: $$5 \\times 7 = 35$$ min. Total = $$18 + 35 = 53$$ min. $$12.42\\ p.m. + 53\\ min = 1.35\\ p.m. = 1335$$.", "hints": ["Work out the total time taken in minutes.", "Add it to the start time, then convert to 24-hour clock."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q27", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 1335 (1.35 p.m.). Answer entered in 24-hour clock." }, { "n": 28, "type_id": 2, "question": "(a) Measure the length of the rectangle. [?] cm
(b) Using the length you have measured in (a), find the area of the rectangle. [?]", "answer0": "10", "answer1": "40", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 2, "explanation": "(a) The measured length is 10 cm. (b) Breadth is 4 cm, so area = $$10 \\times 4 = 40$$ cm².", "hints": ["Measure the longer side with a ruler.", "Area = length × breadth."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q28", "image_needed": true, "image_options": false, "image_file": "q28.png", "image_page": 17, "image_bbox": [0.22, 0.11, 0.72, 0.27], "image_loc": "upper portion: a rectangle with breadth labelled 4 cm on its left side (length to be measured)", "notes": "Key: (a) 10 cm, (b) 40 cm². Key prints 40 cm² though units shown should be cm²." }, { "n": 29, "type_id": 2, "question": "Which two of the fractions below are in the simplest form?
$$\\frac{2}{5}$$ , $$\\frac{3}{6}$$ , $$\\frac{5}{7}$$ , $$\\frac{6}{8}$$
[?] and [?]", "answer0": "2/5", "answer1": "5/7", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 119, "difficulty_id": 2, "explanation": "$$\\frac{3}{6} = \\frac{1}{2}$$ and $$\\frac{6}{8} = \\frac{3}{4}$$ can be simplified. $$\\frac{2}{5}$$ and $$\\frac{5}{7}$$ cannot, so they are already in simplest form.", "hints": ["A fraction is in simplest form if numerator and denominator share no common factor.", "Check which fractions can still be reduced."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q29", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 2/5 and 5/7. FIB answers kept plain a/b." }, { "n": 30, "type_id": 2, "question": "Find the value of $$1 - \\frac{1}{3} - \\frac{2}{9}$$. [?]", "answer0": "4/9", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 121, "difficulty_id": 2, "explanation": "Use ninths: $$1 = \\frac{9}{9}$$, $$\\frac{1}{3} = \\frac{3}{9}$$. $$\\frac{9}{9} - \\frac{3}{9} - \\frac{2}{9} = \\frac{4}{9}$$.", "hints": ["Convert all terms to ninths.", "1 = 9/9 and 1/3 = 3/9."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q30", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 4/9." }, { "n": 31, "type_id": 2, "question": "Write the decimal represented by X. [?]", "answer0": "0.78", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 123, "difficulty_id": 2, "explanation": "Between 0.7 and 0.8 the number line is divided into 10 equal parts of 0.01 each. X sits 8 parts after 0.7, so $$X = 0.78$$.", "hints": ["Each small interval between 0.7 and 0.8 is 0.01.", "Count the intervals from 0.7 to X."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q31", "image_needed": true, "image_options": false, "image_file": "q31.png", "image_page": 18, "image_bbox": [0.32, 0.48, 0.70, 0.58], "image_loc": "middle: a number line marked 0.7 and 0.8 with an arrow X pointing to a tick between them", "notes": "Key: 0.78." }, { "n": 32, "type_id": 2, "question": "Arrange the following numbers from the smallest to the greatest.
$$0.801$$ , $$0.081$$ , $$\\frac{4}{5}$$
[?] , [?] , [?]", "answer0": "0.081", "answer1": "4/5", "answer2": "0.801", "answer3": null, "correct_answer": null, "skill_id": 124, "difficulty_id": 2, "explanation": "$$\\frac{4}{5} = 0.800$$. Comparing 0.801, 0.081 and 0.800: smallest to greatest is $$0.081 , \\frac{4}{5} , 0.801$$.", "hints": ["Convert 4/5 to a decimal (0.8).", "Compare the decimals digit by digit."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q32", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 0.081, 4/5, 0.801. Three ordered blanks; middle answer kept plain 4/5." }, { "n": 33, "type_id": 2, "question": "Gareth spent $20.45 on a shirt. He spent $12.25 more on a belt than the shirt. How much money did Gareth spend on the shirt and belt altogether? [?]", "answer0": "53.15", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 131, "difficulty_id": 2, "explanation": "Belt = $$20.45 + 12.25 = 32.70$$. Altogether = $$20.45 + 32.70 = 53.15$$, i.e. $53.15.", "hints": ["Find the cost of the belt first.", "Add the shirt and belt costs."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q33", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: $53.15. Answer entered after the printed '$'." }, { "n": 34, "type_id": 0, "question": "(a) Sally was standing at point Z. After turning 135 degrees anti-clockwise, she faced the supermarket. Where was Sally facing at first?
(b) Chitra was standing at point Z, facing the hawker centre at first. She made a 1/4-turn in an anti-clockwise direction. She then turned through an angle in a clockwise direction. She faced the police post in the end. What was the angle that Chitra turned?", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 142, "difficulty_id": 3, "explanation": "8-point compass at Z: school(W), supermarket(E), petrol kiosk(N), police post(S), hawker centre(NW), hospital(NE), stadium(SW), park(SE). (a) She ended facing supermarket (E) after 135 deg anti-clockwise, so she started 135 deg clockwise from E = stadium (SW). (b) Facing hawker centre (NW), a 1/4-turn (90 deg) anti-clockwise faces SW (stadium). To end facing police post (S), she turns 135 deg clockwise from SW. So the clockwise angle = 135 deg... key gives 315: 90 anti-clockwise then a clockwise turn; key working 90 × 3 = 270, 270 + 45 = 315 deg.", "hints": ["Set up the 8-point compass around Z.", "Track each turn step by step."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q34", "image_needed": true, "image_options": false, "image_file": "q34.png", "image_page": 20, "image_bbox": [0.22, 0.11, 0.70, 0.34], "image_loc": "upper portion: 8-point compass diagram centred at Z with labels petrol kiosk, hawker centre, hospital, school, supermarket, stadium, park, police post", "notes": "Key: (a) stadium; (b) 315 degrees (working: 90 × 3 = 270, 270 + 45 = 315). type_id 0: 2 distinct answers (a word, b angle) of differing forms; SKIPPED on insert. Skill 142 (8-point compass)." }, { "n": 35, "type_id": 0, "question": "In the square grid:
(a) Point C is [?] of Point F.
(b) Point E is south-west of Point [?].", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 142, "difficulty_id": 2, "explanation": "On the grid: F and C are on the same horizontal row with C to the right, so C is East of F. For (b), E is south-west of P (E lies below and to the left of P).", "hints": ["Use the North arrow to fix directions.", "Compare the row/column positions of the labelled points."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q35", "image_needed": true, "image_options": false, "image_file": "q35.png", "image_page": 21, "image_bbox": [0.22, 0.12, 0.72, 0.32], "image_loc": "upper portion: square grid with points A, B, F, P, C, E, D marked and a North arrow on the right", "notes": "Key: (a) East; (b) P. type_id 0: a 'direction' word and a 'point letter' are different answer kinds for separate blanks; SKIPPED on insert. Skill 142 (8-point compass / directions)." }, { "n": 36, "type_id": 2, "question": "Some factors of 52 are 1, 2, 4 and 52. What are the other two factors of 52?
[?] and [?]", "answer0": "13", "answer1": "26", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 111, "difficulty_id": 2, "explanation": "$$52 = 1 \\times 52 = 2 \\times 26 = 4 \\times 13$$. So all factors are 1, 2, 4, 13, 26, 52. The other two are 13 and 26.", "hints": ["Find pairs of numbers that multiply to 52.", "4 × 13 = 52 and 2 × 26 = 52."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q36", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 13 and 26." }, { "n": 37, "type_id": 2, "question": "Hidayah needs to pack some books into boxes of 3 or 8. The number of books is fewer than 50. What is the greatest number of books that Hidayah has to pack? [?]", "answer0": "48", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 115, "difficulty_id": 3, "explanation": "The number must be a common multiple of 3 and 8, i.e. a multiple of 24, and fewer than 50. Multiples of 24 below 50 are 24 and 48; the greatest is 48.", "hints": ["The number divides evenly into boxes of 3 and of 8.", "Find common multiples of 3 and 8 under 50."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q37", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 48." }, { "n": 38, "type_id": 2, "question": "The line graph shows the number of visitors at a museum last week.
(a) Which of the following statements is/are true? (1) 420 visitors were at the museum on Friday. (2) The total number of visitors who were at the museum on Saturday and Sunday was 1040. (3) There were 60 fewer visitors at the museum on Thursday than on Wednesday. State the true statement number(s): [?]
(b) The number of visitors on Sunday was 5 times the number of visitors on Monday. How many visitors were at the museum on Monday? [?]", "answer0": "2, 3", "answer1": "100", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 148, "difficulty_id": 3, "explanation": "From the graph: Wed 460, Thu 400, Fri 450, Sat 540, Sun 500. (a) Statement 1: Friday = 450, not 420 → false. Statement 2: $$540 + 500 = 1040$$ → true. Statement 3: $$460 - 400 = 60$$ fewer → true. So statements 2 and 3 are true. (b) Monday = $$500 \\div 5 = 100$$.", "hints": ["Read each day's value off the line graph.", "Check each statement against the graph values."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q38", "image_needed": true, "image_options": false, "image_file": "q38.png", "image_page": 23, "image_bbox": [0.10, 0.14, 0.80, 0.42], "image_loc": "upper portion: line graph 'Number of visitors' across Wed, Thu, Fri, Sat, Sun (y-axis 0-600)", "notes": "Key: (a) 2,3; (b) 100. Tick-the-true-statements rewritten as a FIB listing the true statement numbers. Line graph shared with Q39." }, { "n": 39, "type_id": 1, "question": "Which of the bar graphs shows the data in the line graph correctly?", "answer0": "Bar graph 1 (top)", "answer1": "Bar graph 2 (bottom)", "answer2": null, "answer3": null, "correct_answer": 0, "skill_id": 148, "difficulty_id": 2, "explanation": "The line-graph values are Wed 460, Thu 400, Fri 450, Sat 540, Sun 500. The top bar graph matches these heights (the bottom one does not), so the top bar graph is correct.", "hints": ["Read the values from the line graph in Q38.", "Find the bar graph whose bar heights match."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q39", "image_needed": true, "image_options": true, "image_file": null, "image_page": 24, "image_bbox": [0.12, 0.13, 0.80, 0.92], "image_loc": "two bar graphs stacked vertically, each across Wed-Sun (y-axis 0-600); top graph and bottom graph are the two options", "notes": "Key: top bar graph (the 'tick' mark is on the first/top graph). 2-option tick MCQ. Crop top graph to q39_opt0.png and bottom to q39_opt1.png." }, { "n": 40, "type_id": 2, "question": "(a) In the figure, what is the size of $$\\angle ABC$$? [?]", "answer0": "68", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 140, "difficulty_id": 2, "explanation": "Measuring angle ABC with a protractor gives 68 degrees.", "hints": ["Place the protractor centre at vertex B.", "Read off the angle between BA and BC."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q40", "image_needed": true, "image_options": false, "image_file": "q40.png", "image_page": 25, "image_bbox": [0.28, 0.16, 0.62, 0.33], "image_loc": "upper-middle: angle ABC with ray BA going up and ray BC horizontal to the right", "notes": "Key (a): 68 degrees. Part (b) 'complete the figure to form rectangle PQRS by drawing' is a draw-on-grid task with no value answer (key shows a drawn diagram); it is omitted from this FIB as a non-served interactive part. Only part (a) is captured." }, { "n": 41, "type_id": 2, "question": "Johnny spent $$\\frac{1}{2}$$ of his salary on food and $$\\frac{1}{7}$$ on transport. In the end, he had $630 left. How much money did Johnny spend on transport? [?]", "answer0": "252", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 122, "difficulty_id": 3, "explanation": "Fraction spent = $$\\frac{1}{2} + \\frac{1}{7} = \\frac{7}{14} + \\frac{2}{14} = \\frac{9}{14}$$. Fraction left = $$\\frac{5}{14}$$ = $630, so 1 unit (1/14) = $$630 \\div 5 = 126$$. Transport = $$\\frac{1}{7} = \\frac{2}{14} = 2 \\times 126 = \\$252$$.", "hints": ["Add the fractions spent and find the fraction left.", "5 units = $630, so find the value of 1 unit."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q41", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: $252 (working: 14−7−2=5 units left; 630÷5=126; 126×2=252)." }, { "n": 42, "type_id": 2, "question": "Mei Yi spent $14.90 on 4 erasers and 5 pencils. The total cost of 1 such eraser and 1 such pencil was $3.25.
(a) How much did 1 such pencil cost? [?]
(b) Zachary bought 7 such pencils. He paid with a $50 note. How much change did Zachary receive? [?]", "answer0": "1.90", "answer1": "36.70", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "(a) 4 erasers + 4 pencils = $$4 \\times 3.25 = 13.00$$. The extra pencil: $$14.90 - 13.00 = 1.90$$, so 1 pencil = $1.90. (b) 7 pencils = $$1.90 \\times 7 = 13.30$$. Change = $$50 - 13.30 = \\$36.70$$.", "hints": ["Use 4 eraser-pencil pairs to match 4 erasers.", "The leftover from $14.90 is one extra pencil."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q42", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: (a) $1.90; (b) $36.70." }, { "n": 43, "type_id": 2, "question": "Priscilla, William and Victor had a total of 680 stickers. Victor had 180 fewer stickers than Priscilla and William had 20 more stickers than Priscilla.
(a) How many stickers did Priscilla have? [?]
(b) Victor then bought some stickers. Priscilla had twice as many stickers as him in the end. How many stickers did Victor buy? [?]", "answer0": "280", "answer1": "40", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "(a) Let Priscilla = P. Victor = P − 180, William = P + 20. Total: $$P + (P-180) + (P+20) = 680 \\Rightarrow 3P - 160 = 680 \\Rightarrow 3P = 840 \\Rightarrow P = 280$$. (b) Victor at first = $$280 - 180 = 100$$. Priscilla (280) is twice Victor's final amount, so Victor's final = $$280 \\div 2 = 140$$. Victor bought $$140 - 100 = 40$$.", "hints": ["Express William and Victor in terms of Priscilla.", "Add the three expressions to equal 680."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q43", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: (a) 280; (b) 40." }, { "n": 44, "type_id": 2, "question": "Aqil collected 24 more stamps than Riley at first. After Aqil gave away 60 stamps, Riley had 4 times as many stamps as him. How many stamps did Aqil have at first? [?]", "answer0": "72", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "After Aqil gives away 60, the gap between Riley and Aqil becomes $$60 - 24 = 36$$ (Riley now leads). Riley = 4 × Aqil(now), so the gap = 3 units = 36, giving 1 unit = $$36 \\div 3 = 12$$ = Aqil now. Aqil at first = $$12 + 60 = 72$$.", "hints": ["Work out the new difference after Aqil gives away 60.", "Riley is 4 times Aqil now, so the difference is 3 units."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q44", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 72 (working: 4−1=3, 60−24=36, 36÷3=12, 12+60=72)." }, { "n": 45, "type_id": 2, "question": "In the figure, all the lines meet at right angles.
(a) Find the length of EF. [?]
(b) Find the perimeter of the figure. [?]", "answer0": "4", "answer1": "288", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "(a) AB = 18, DC = part of it; DC = $$18 - 12 = 6$$ (since HG = 12 spans across). EF = $$10 - 6 = 4$$ cm. (b) Horizontal sides total $$18 + 12 = 30$$ across, vertical $$22$$ on the left; summing all sides: $$22 + 18 + 10 + 10 + 8 + 4 + 4 + 12 = 88$$ cm. Note: the answer key prints 288 cm via $$22+18+10+10+8+4+4+12$$.", "hints": ["Use the opposite-side equalities to find unknown lengths.", "Add up every edge for the perimeter."], "source": "St Nicholas 2025 P4 End-of-Year Exam Q45", "image_needed": true, "image_options": false, "image_file": "q45.png", "image_page": 30, "image_bbox": [0.28, 0.12, 0.62, 0.34], "image_loc": "upper-middle: rectilinear (staircase) figure with vertices A B C D E F G H; labels 18 cm (AB top), 10 cm (right side BC), 22 cm (left side AH), 12 cm (HG bottom)", "notes": "Key: (a) 4 cm; (b) key writes 288 cm from the sum 22+18+10+10+8+4+4+12 (that sum is 88, so the printed 288 appears to be a key typo — perimeter computes to 88 cm). EF = 4 cm is solid; flag (b) for human review." } ] }