{ "paper": { "school": "Methodist Girls' School (Primary)", "year": 2023, "level": "P4", "label": "End of Year Exam", "source_prefix": "Methodist Girls 2023 P4 End of Year Exam", "has_answer_key": true, "notes": "Answer key (PDF pp.29-31) is printed on a Catholic High School cover sheet but the answers match this MGS paper exactly (Q19=15036, Q23 order, Q31 rope=0.68 m, etc.); used as the key for this paper." }, "questions": [ { "n": 1, "type_id": 1, "question": "43 thousands and 8 tens is the same as [?].", "answer0": "438", "answer1": "4380", "answer2": "43 008", "answer3": "43 080", "correct_answer": 3, "skill_id": 105, "difficulty_id": 1, "explanation": "43 thousands = 43 000. 8 tens = 80. 43 000 + 80 = 43 080.", "hints": [ "1 thousand = 1000, 1 ten = 10.", "Add 43 000 and 80." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 4 (43 080)." }, { "n": 2, "type_id": 1, "question": "Which of the following numbers when rounded to the nearest ten becomes 72 500?", "answer0": "72 444", "answer1": "72 496", "answer2": "72 506", "answer3": "72 554", "correct_answer": 1, "skill_id": 109, "difficulty_id": 2, "explanation": "Rounding to the nearest ten, numbers from 72 495 to 72 504 round to 72 500. 72 496 rounds to 72 500. (72 444->72 440; 72 506->72 510; 72 554->72 550.)", "hints": [ "Look at the ones digit to decide rounding.", "Which value lies between 72 495 and 72 504?" ], "source": "Methodist Girls 2023 P4 End of Year Exam Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 (72 496)." }, { "n": 3, "type_id": 1, "question": "What is the missing number in the box?
$$6\\frac{5}{9}$$ = $$\\frac{[?]}{9}$$", "answer0": "30", "answer1": "49", "answer2": "54", "answer3": "59", "correct_answer": 3, "skill_id": 119, "difficulty_id": 2, "explanation": "Convert the mixed number to an improper fraction: $$6\\frac{5}{9} = \\frac{6\\times 9 + 5}{9} = \\frac{54+5}{9} = \\frac{59}{9}$$. The missing numerator is 59.", "hints": [ "6 whole = how many ninths?", "6 x 9 = 54, then add the 5." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 4 (59)." }, { "n": 4, "type_id": 1, "question": "What fraction of the shapes in the box are triangles?", "answer0": "$$\\frac{5}{12}$$", "answer1": "$$\\frac{5}{7}$$", "answer2": "$$\\frac{7}{12}$$", "answer3": "$$\\frac{7}{5}$$", "correct_answer": 0, "skill_id": 120, "difficulty_id": 2, "explanation": "There are 12 shapes in total. 5 are triangles. So the fraction that are triangles is $$\\frac{5}{12}$$.", "hints": [ "Count the triangles, then count all the shapes.", "Fraction = triangles / total shapes." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q4", "image_needed": true, "image_options": false, "image_file": "q4.png", "image_page": 4, "image_bbox": [ 0.28, 0.14, 0.7, 0.27 ], "image_loc": "boxed grid of 12 shapes (stars and triangles) below the question, top of page", "notes": "Key: option 1 (5/12). 5 triangles out of 12 shapes." }, { "n": 5, "type_id": 1, "question": "The figure is made up of a square S of side 4 cm and a rectangle R with breadth 7 cm. What is the length of the rectangle?", "answer0": "5 cm", "answer1": "9 cm", "answer2": "11 cm", "answer3": "12 cm", "correct_answer": 1, "skill_id": 138, "difficulty_id": 2, "explanation": "The total height marked '?' equals the height of rectangle R. The square S has side 4 cm, and the part of R above the square is 5 cm. So the length (height) of R = 5 + 4 = 9 cm.", "hints": [ "The square's side is 4 cm.", "Add the 5 cm portion to the 4 cm square side." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q5", "image_needed": true, "image_options": false, "image_file": "q5.png", "image_page": 4, "image_bbox": [ 0.28, 0.5, 0.58, 0.74 ], "image_loc": "L-shaped figure of rectangle R and square, with 7 cm, 4 cm, 5 cm and ? labels, middle of page", "notes": "Key: option 2 (9 cm)." }, { "n": 6, "type_id": 1, "question": "Which number is 1.5 less than 4.87?", "answer0": "3.37", "answer1": "4.72", "answer2": "5.02", "answer3": "6.37", "correct_answer": 0, "skill_id": 129, "difficulty_id": 1, "explanation": "4.87 - 1.5 = 3.37.", "hints": [ "Subtract 1.5 from 4.87.", "Line up the decimal points." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 1 (3.37)." }, { "n": 7, "type_id": 1, "question": "The volume of water in a tank is 19 000 $$\\ell$$ when rounded to the nearest thousand litres. Which one of the following is the greatest possible volume of water in the tank?", "answer0": "18 999 $$\\ell$$", "answer1": "19 099 $$\\ell$$", "answer2": "19 499 $$\\ell$$", "answer3": "19 999 $$\\ell$$", "correct_answer": 2, "skill_id": 109, "difficulty_id": 3, "explanation": "Rounded to the nearest thousand, values from 18 500 to 19 499 give 19 000. The greatest possible value is 19 499 (19 500 would round up to 20 000).", "hints": [ "What range rounds to 19 000 to the nearest thousand?", "The largest value just below 19 500." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3 (19 499 l)." }, { "n": 8, "type_id": 1, "question": "Which one of the following pairs of numbers have 3 and 9 as their common factors?", "answer0": "9 and 12", "answer1": "18 and 21", "answer2": "21 and 27", "answer3": "27 and 36", "correct_answer": 3, "skill_id": 113, "difficulty_id": 2, "explanation": "Both numbers must be divisible by 3 and by 9. 27 = 9x3 and 36 = 9x4, so both share factors 3 and 9. (12, 18, 21 are not multiples of 9.)", "hints": [ "A common factor must divide both numbers.", "Which pair are both multiples of 9?" ], "source": "Methodist Girls 2023 P4 End of Year Exam Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 4 (27 and 36)." }, { "n": 9, "type_id": 1, "question": "How many of the letters in the grid have at least one line of symmetry?", "answer0": "1", "answer1": "2", "answer2": "3", "answer3": "4", "correct_answer": 2, "skill_id": 144, "difficulty_id": 2, "explanation": "The grid shows the letters M, I, N, O. M has a vertical line of symmetry, I has lines of symmetry, and O has lines of symmetry. N has no line of symmetry. So 3 letters have at least one line of symmetry.", "hints": [ "A line of symmetry folds the figure onto itself.", "Check M, I, N and O one at a time." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q9", "image_needed": true, "image_options": false, "image_file": "q9.png", "image_page": 5, "image_bbox": [ 0.2, 0.13, 0.8, 0.25 ], "image_loc": "grid showing the letters M, I, N, O drawn on squares, below the question", "notes": "Key: option 3 (3). Symmetric letters: M, I, O; N is not." }, { "n": 10, "type_id": 1, "question": "Mr Lim bought $$\\frac{4}{5}$$ kg of cherries. He and his sons ate $$\\frac{3}{10}$$ kg of the cherries. What was the mass of cherries left?", "answer0": "$$\\frac{1}{5}$$ kg", "answer1": "$$\\frac{1}{2}$$ kg", "answer2": "$$\\frac{7}{15}$$ kg", "answer3": "$$1\\frac{1}{10}$$ kg", "correct_answer": 1, "skill_id": 122, "difficulty_id": 2, "explanation": "$$\\frac{4}{5} = \\frac{8}{10}$$. Cherries left = $$\\frac{8}{10} - \\frac{3}{10} = \\frac{5}{10} = \\frac{1}{2}$$ kg.", "hints": [ "Make the denominators the same.", "4/5 = 8/10, then subtract 3/10." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 (1/2 kg)." }, { "n": 11, "type_id": 1, "question": "James bought 1.27 kg of sweets. His sister bought 0.18 kg more than him. What was the total mass of sweets they bought altogether?", "answer0": "1.09 kg", "answer1": "1.45 kg", "answer2": "2.36 kg", "answer3": "2.72 kg", "correct_answer": 3, "skill_id": 131, "difficulty_id": 2, "explanation": "Sister = 1.27 + 0.18 = 1.45 kg. Total = 1.27 + 1.45 = 2.72 kg.", "hints": [ "Find the sister's mass first.", "Then add both masses together." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 4 (2.72 kg)." }, { "n": 12, "type_id": 1, "question": "Janet's age is a multiple of 7 this year. Next year, her age will be a multiple of 6. Which one of the following is Janet's age this year?", "answer0": "14", "answer1": "35", "answer2": "42", "answer3": "49", "correct_answer": 3, "skill_id": 114, "difficulty_id": 2, "explanation": "Age this year is a multiple of 7; next year (age + 1) is a multiple of 6. 49 is a multiple of 7 and 49 + 1 = 50 is not a multiple of 6... check: 14+1=15 no; 35+1=36 yes (36=6x6, 35=7x5). So 35 works. Re-check key: key gives option 4 = 49? 49+1=50 not multiple of 6. The valid answer is 35.", "hints": [ "List the multiples of 7 among the options.", "Add 1 and check if it is a multiple of 6." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer-key prints option 4 (49) but 49+1=50 is NOT a multiple of 6. Mathematically the correct answer is 35 (35=7x5, 36=6x6); set correct_answer=1 (35). Possible key typo; flagged for human review." }, { "n": 13, "type_id": 1, "question": "The table shows the favourite colour of some children. Black: 30, Blue: 19, Purple: 12, Red: ?. The number of children who like red is three times the number of children who like purple. How many children are there altogether?", "answer0": "36", "answer1": "61", "answer2": "65", "answer3": "97", "correct_answer": 3, "skill_id": 147, "difficulty_id": 2, "explanation": "Red = 3 x 12 = 36. Total = 30 + 19 + 12 + 36 = 97 children.", "hints": [ "Red is three times purple (12).", "Add all four colour counts." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q13", "image_needed": true, "image_options": false, "image_file": "q13.png", "image_page": 7, "image_bbox": [ 0.15, 0.34, 0.82, 0.4 ], "image_loc": "table of colours (Black, Blue, Purple, Red) and number of children, below the question", "notes": "Key: option 4 (97). Table values restated in stem for accessibility." }, { "n": 14, "type_id": 1, "question": "When it is 09 00 in Singapore, it is 10 30 in Australia. Mr Kim makes a call at 14 50 from Singapore to his wife who is in Australia. What is the time in Australia when Mr Kim calls his wife?", "answer0": "04 20", "answer1": "13 20", "answer2": "15 50", "answer3": "16 20", "correct_answer": 3, "skill_id": 135, "difficulty_id": 2, "explanation": "Australia is 1 h 30 min ahead of Singapore (10 30 vs 09 00). At 14 50 in Singapore, Australia time = 14 50 + 1 h 30 min = 16 20.", "hints": [ "Find the time difference between the two places.", "Add 1 h 30 min to 14 50." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 4 (16 20)." }, { "n": 15, "type_id": 1, "question": "A bus departed from Singapore and arrived in Kuala Lumpur at 13 40. The bus ride took 5 hours and 30 minutes. At what time did the bus depart from Singapore?", "answer0": "07 10", "answer1": "07 40", "answer2": "08 10", "answer3": "08 40", "correct_answer": 2, "skill_id": 135, "difficulty_id": 2, "explanation": "Departure = arrival - duration = 13 40 - 5 h 30 min. 13 40 - 5 h = 08 40; 08 40 - 30 min = 08 10.", "hints": [ "Subtract the duration from the arrival time.", "Take away 5 hours, then 30 minutes." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3 (08 10)." }, { "n": 16, "type_id": 1, "question": "The diagram shows the different locations near Siti's school. Siti is at the school and faces the MRT station. Which of the following shows how she could turn to face the shopping mall?", "answer0": "90° clockwise", "answer1": "135° anti-clockwise", "answer2": "180° clockwise", "answer3": "225° anti-clockwise", "correct_answer": 3, "skill_id": 142, "difficulty_id": 3, "explanation": "The 8 locations sit around the school at 45° intervals. Facing MRT Station (bottom-right) and turning to face Shopping Mall (directly left/west) requires a 225° anti-clockwise turn.", "hints": [ "Each neighbouring location is 45° apart from the school.", "Count the 45° steps from MRT Station to Shopping Mall in the turn direction." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q16", "image_needed": true, "image_options": false, "image_file": "q16.png", "image_page": 8, "image_bbox": [ 0.28, 0.38, 0.78, 0.66 ], "image_loc": "diagram of 8 boxed locations connected to a central School box, middle of page", "notes": "Key: option 4 (225° anti-clockwise)." }, { "n": 17, "type_id": 1, "question": "The figure is made up of 5 identical squares. The length of one side of the square is 6 cm. What is the perimeter of the figure?", "answer0": "54 cm", "answer1": "60 cm", "answer2": "72 cm", "answer3": "90 cm", "correct_answer": 1, "skill_id": 138, "difficulty_id": 2, "explanation": "The figure (3 squares in a top row, 2 squares below) has an outline of 10 unit sides of 6 cm each. Perimeter = 10 x 6 = 60 cm.", "hints": [ "Each square side is 6 cm.", "Count the unit sides around the outside of the whole figure." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q17", "image_needed": true, "image_options": false, "image_file": "q17.png", "image_page": 9, "image_bbox": [ 0.38, 0.13, 0.62, 0.27 ], "image_loc": "figure of 5 identical squares with 6 cm side labelled, top of page", "notes": "Key: option 2 (60 cm). Outline has 10 sides of 6 cm." }, { "n": 18, "type_id": 1, "question": "The bar graph shows the number of movies watched by a group of children during the holidays. What fraction of the children watched at least 2 movies?", "answer0": "$$\\frac{3}{18}$$", "answer1": "$$\\frac{7}{18}$$", "answer2": "$$\\frac{11}{18}$$", "answer3": "$$\\frac{14}{18}$$", "correct_answer": 3, "skill_id": 104, "difficulty_id": 2, "explanation": "Children per number of movies: 1->4, 2->3, 3->4, 4->5, 5->2. Total = 4+3+4+5+2 = 18. At least 2 movies = 3+4+5+2 = 14. Fraction = $$\\frac{14}{18}$$.", "hints": [ "Read each bar height and add for the total.", "At least 2 means 2 or more movies." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q18", "image_needed": true, "image_options": false, "image_file": "q18.png", "image_page": 9, "image_bbox": [ 0.18, 0.42, 0.74, 0.68 ], "image_loc": "bar graph of number of children vs number of movies (1 to 5), middle of page", "notes": "Key: option 4 (14/18). Bars: 4,3,4,5,2; total 18, at least 2 = 14." }, { "n": 19, "type_id": 2, "question": "Write fifteen thousand and thirty-six in figures.
[?]", "answer0": "15036", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 106, "difficulty_id": 1, "explanation": "Fifteen thousand = 15 000; thirty-six = 36. So 15 000 + 36 = 15 036.", "hints": [ "Fifteen thousand is 15 000.", "Add 36 to it." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 15036." }, { "n": 20, "type_id": 2, "question": "Write the missing number in the number pattern.
14 000, 13 400, 12 800, 12 200, [?], 11 000", "answer0": "11600", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 108, "difficulty_id": 2, "explanation": "The pattern decreases by 600 each time (14 000, 13 400, 12 800, 12 200, ...). 12 200 - 600 = 11 600 (and 11 600 - 600 = 11 000).", "hints": [ "Find the difference between consecutive terms.", "Each term is 600 less than the one before." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q20", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 11600." }, { "n": 21, "type_id": 2, "question": "Some factors of 32 are 1, 2, 4 and 32. What are the other two factors of 32?
[?] and [?]", "answer0": "8", "answer1": "16", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 111, "difficulty_id": 2, "explanation": "The factors of 32 are 1, 2, 4, 8, 16, 32. The two not listed are 8 and 16.", "hints": [ "List all numbers that divide 32 exactly.", "32 = 8 x 4 = 16 x 2." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q21", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 16 and 8 (order interchangeable)." }, { "n": 22, "type_id": 2, "question": "What is the missing number in the box?
$$\\frac{4}{7}$$ = $$\\frac{[?]}{49}$$", "answer0": "28", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 119, "difficulty_id": 2, "explanation": "49 = 7 x 7, so multiply numerator and denominator of $$\\frac{4}{7}$$ by 7: $$\\frac{4\\times 7}{7\\times 7} = \\frac{28}{49}$$. The missing numerator is 28.", "hints": [ "How many times bigger is 49 than 7?", "Multiply the numerator by the same amount." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q22", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 28." }, { "n": 23, "type_id": 2, "question": "Arrange the following fractions from the greatest to the smallest.
$$\\frac{1}{2}$$, $$\\frac{2}{3}$$, $$\\frac{7}{12}$$
[?], [?], [?]", "answer0": "2/3", "answer1": "7/12", "answer2": "1/2", "answer3": null, "correct_answer": null, "skill_id": 121, "difficulty_id": 2, "explanation": "Use denominator 12: $$\\frac{1}{2}=\\frac{6}{12}$$, $$\\frac{2}{3}=\\frac{8}{12}$$, $$\\frac{7}{12}=\\frac{7}{12}$$. Greatest to smallest: $$\\frac{8}{12}, \\frac{7}{12}, \\frac{6}{12}$$, i.e. $$\\frac{2}{3}, \\frac{7}{12}, \\frac{1}{2}$$.", "hints": [ "Convert all to twelfths.", "Compare the numerators: 8 > 7 > 6." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q23", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 2/3, 7/12, 1/2 (greatest to smallest). FIB answers kept plain a/b." }, { "n": 24, "type_id": 2, "question": "Express 0.6 as a fraction.
[?]", "answer0": "3/5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 126, "difficulty_id": 1, "explanation": "0.6 = $$\\frac{6}{10}$$. Simplify by dividing by 2: $$\\frac{6}{10} = \\frac{3}{5}$$.", "hints": [ "0.6 = 6 tenths.", "Simplify 6/10 to its simplest form." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q24", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 3/5. FIB answer kept plain a/b." }, { "n": 25, "type_id": 2, "question": "Write the decimal represented by A.
[?]", "answer0": "18.17", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 123, "difficulty_id": 2, "explanation": "Between 18.1 and 18.2 the number line is divided into 10 equal parts of 0.01 each. A is at the 7th mark from 18.1, so A = 18.1 + 0.07 = 18.17.", "hints": [ "Each small interval between 18.1 and 18.2 is 0.01.", "Count the marks from 18.1 to A." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q25", "image_needed": true, "image_options": false, "image_file": "q25.png", "image_page": 13, "image_bbox": [ 0.18, 0.13, 0.72, 0.23 ], "image_loc": "number line marked 18.1 and 18.2 with arrow A, below the question", "notes": "Key: 18.17." }, { "n": 26, "type_id": 2, "question": "What is the value of $$\\frac{5}{8} + \\frac{3}{4}$$? Express your answer as a mixed number.
[?]", "answer0": "1 3/8", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 121, "difficulty_id": 2, "explanation": "$$\\frac{3}{4} = \\frac{6}{8}$$. $$\\frac{5}{8} + \\frac{6}{8} = \\frac{11}{8} = 1\\frac{3}{8}$$.", "hints": [ "Make the denominators the same (eighths).", "11/8 is more than 1 whole." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q26", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 1 3/8. FIB mixed-number answer kept plain." }, { "n": 27, "type_id": 2, "question": "ABCD is a square. Find $$\\angle x$$.
[?]", "answer0": "25", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 140, "difficulty_id": 2, "explanation": "Each corner of a square is 90°. At corner D, the 65° angle and $$\\angle x$$ together make the 90° angle. So $$\\angle x = 90° - 65° = 25°$$.", "hints": [ "A square's corner is a right angle (90°).", "65° + x = 90°." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q27", "image_needed": true, "image_options": false, "image_file": "q27.png", "image_page": 13, "image_bbox": [ 0.55, 0.6, 0.78, 0.8 ], "image_loc": "square ABCD with a diagonal line from D, 65° and x angles marked at D, right of question", "notes": "Key: 25 (degrees). Answer unit is degrees." }, { "n": 28, "type_id": 2, "question": "Find the value of 20.7 ÷ 7. Round your answer to the nearest hundredths.
[?]", "answer0": "2.96", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 130, "difficulty_id": 2, "explanation": "20.7 ÷ 7 = 2.957... Rounding to the nearest hundredth (2 decimal places) gives 2.96.", "hints": [ "Divide 20.7 by 7.", "Look at the third decimal place to round to 2 d.p." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q28", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 2.96." }, { "n": 29, "type_id": 2, "question": "A movie started at 11 35 and ended at 14 10. How long was the movie?
[?] h [?] min", "answer0": "2", "answer1": "35", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 135, "difficulty_id": 2, "explanation": "From 11 35 to 14 10. 11 35 to 14 35 is 3 h, but we only need to 14 10, which is 25 min before 14 35... easier: 11 35 to 12 00 = 25 min; 12 00 to 14 00 = 2 h; 14 00 to 14 10 = 10 min. Total = 2 h 35 min.", "hints": [ "Count from 11 35 to the next hour first.", "Then add full hours and the remaining minutes." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q29", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 2 h 35 min. Two blanks: hours and minutes." }, { "n": 30, "type_id": 0, "question": "The square grid shows two lines, WX and WZ. WX and WZ are also the sides of a square WXYZ. Draw square WXYZ and label point Y.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 143, "difficulty_id": 2, "explanation": "WX and WZ are two adjacent sides of the square meeting at W. Complete the square by drawing XY parallel and equal to WZ, and ZY parallel and equal to WX; Y is the fourth vertex opposite W (the answer-key diagram shows the completed square).", "hints": [ "W is the corner where the two given sides meet.", "Y is the vertex opposite W." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q30", "image_needed": true, "image_options": false, "image_file": "q30.png", "image_page": 14, "image_bbox": [ 0.28, 0.62, 0.62, 0.86 ], "image_loc": "square grid with lines WX and WZ drawn, points W, X, Z marked, lower part of question", "notes": "type_id 0: draw-on-grid construction task (no value answer). SKIPPED on insert. Answer = complete square WXYZ, Y opposite W." }, { "n": 31, "type_id": 2, "question": "Mr Lee cuts a 5-m rope into three pieces, A, B and C. Rope A measures 2.88 m and it is twice as long as rope B. What is the length of rope C?
[?] m", "answer0": "0.68", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 131, "difficulty_id": 2, "explanation": "Rope A = 2.88 m. Rope B = 2.88 ÷ 2 = 1.44 m. A + B = 2.88 + 1.44 = 4.32 m. Rope C = 5 - 4.32 = 0.68 m.", "hints": [ "Rope B is half of rope A.", "Subtract A and B from the 5 m total." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q31", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 0.68 m." }, { "n": 32, "type_id": 2, "question": "A rectangle has a perimeter of 32 cm. The length is 3 times as long as its breadth. Find the area of the rectangle.
[?] cm²", "answer0": "48", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 136, "difficulty_id": 2, "explanation": "Length + breadth = half the perimeter = 16 cm. With length = 3 x breadth, that is 4 units = 16 cm, so 1 unit (breadth) = 4 cm and length = 12 cm. Area = 12 x 4 = 48 cm².", "hints": [ "Length + breadth = perimeter ÷ 2.", "Split the 16 cm into 4 equal units (1 breadth + 3 breadths)." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q32", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 48 cm²." }, { "n": 33, "type_id": 2, "question": "The line graph shows the temperature from 08 00 to 18 00 last Friday.
(a) What is the difference between the highest and lowest temperatures recorded?
[?] °C
(b) In which two-hour period was the change in temperature the greatest?
[?] to [?]", "answer0": "6", "answer1": "10 00", "answer2": "12 00", "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 2, "explanation": "(a) Highest temperature = 33°C, lowest = 27°C. Difference = 33 - 27 = 6°C. (b) Changes: 08 00->10 00 = +2, 10 00->12 00 = +3, 12 00->14 00 = +1, 14 00->16 00 = 0, 16 00->18 00 = -2. Greatest change is 3°C from 10 00 to 12 00.", "hints": [ "Read the highest and lowest points on the graph.", "Compare the rise/fall over each 2-hour gap." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q33", "image_needed": true, "image_options": false, "image_file": "q33.png", "image_page": 16, "image_bbox": [ 0.15, 0.18, 0.74, 0.46 ], "image_loc": "line graph of temperature (25-34°C) vs time (08 00 to 18 00), below the question", "notes": "Key: (a) 6°C, (b) 10 00 to 12 00. Three blanks: difference, start time, end time." }, { "n": 34, "type_id": 2, "question": "At a fruit stall, there were 150 more apples than pears. After 46 pears were sold, there were 5 times as many apples as pears. How many pears were there at first?
[?]", "answer0": "95", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "After selling 46 pears, apples are unchanged and apples = 5 x (remaining pears). Apples are 150 more than the original pears, i.e. 150 + 46 = 196 more than the remaining pears. So 4 units (apples - remaining pears) = 196, 1 unit (remaining pears) = 49. Pears at first = 49 + 46 = 95.", "hints": [ "Apples stay the same; only pears decrease by 46.", "Apples are now 5 times the remaining pears, a difference of 4 units = 196." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q34", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 95 (95 pears at first)." }, { "n": 35, "type_id": 2, "question": "Oranges are sold in bags of 5 at $6 for each bag or $1.50 for each orange. Mrs Rahim buys 28 oranges. What is the least amount of money that she has to pay?
$[?]", "answer0": "34.50", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 131, "difficulty_id": 3, "explanation": "Bags are cheaper per orange ($6 ÷ 5 = $1.20 vs $1.50). 28 ÷ 5 = 5 bags remainder 3. Buy 5 bags (25 oranges) at $6 = $30, and 3 single oranges at $1.50 = $4.50. Least amount = $30 + $4.50 = $34.50.", "hints": [ "Buying by the bag is cheaper per orange.", "28 = 5 bags + 3 single oranges." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q35", "image_needed": true, "image_options": false, "image_file": "q35.png", "image_page": 17, "image_bbox": [ 0.28, 0.48, 0.66, 0.64 ], "image_loc": "pictures of a bag of 5 oranges ($6) and a single orange ($1.50), middle of question", "notes": "Key: $34.50. Pictures are decorative price labels; values restated in stem." }, { "n": 36, "type_id": 2, "question": "A pattern is formed by drawing 3 squares between every 2 triangles. Tom used the pattern and drew a total of 81 shapes on a strip of paper from end to end. Part of it was torn off by accident. How many squares were on the part that was torn off?
[?]", "answer0": "53", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 108, "difficulty_id": 3, "explanation": "The strip starts and ends with a triangle, with 3 squares between every 2 triangles. With 81 shapes total: removing the leading triangle, 81 - 1 = 80... using the key method: triangles + squares = 81. Number of triangles t and squares s with pattern T(SSS T)... Total triangles = 21, squares = 60 overall? Key working: 81 - 10 = 71 remaining shapes after the visible end pieces; 71 ÷ 4 = 17 R 3 groups; torn-off squares = 17 x 3 + 2 = 53.", "hints": [ "Each repeating group is 1 triangle + 3 squares = 4 shapes.", "Subtract the shapes that are still visible, then count squares in the torn part." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q36", "image_needed": true, "image_options": false, "image_file": "q36.png", "image_page": 18, "image_bbox": [ 0.16, 0.27, 0.78, 0.33 ], "image_loc": "torn strip showing triangle/square pattern with visible ends and a torn-off middle, below the question", "notes": "Key: 53 squares torn off (working: 81-10=71; 71÷4=17R3; 17x3+2=53)." }, { "n": 37, "type_id": 2, "question": "Weijian had three times as much money as Xavier. After Weijian bought 8 erasers at $1.30 each he had $3.85 left.
(a) How much money did Weijian have at first?
$[?]
(b) How much money did Xavier have?
$[?]", "answer0": "14.25", "answer1": "4.75", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 131, "difficulty_id": 3, "explanation": "(a) Cost of erasers = 8 x $1.30 = $10.40. Weijian at first = $10.40 + $3.85 = $14.25. (b) Weijian had 3 times Xavier, so Xavier = $14.25 ÷ 3 = $4.75.", "hints": [ "Find what Weijian spent, then add what was left.", "Xavier had one third of Weijian's starting amount." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q37", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: (a) $14.25, (b) $4.75. Two blanks." }, { "n": 38, "type_id": 2, "question": "A water container had 1 $$\\ell$$ of water. Mr Muthu used $$\\frac{2}{5}$$ $$\\ell$$ of it to make a drink and $$\\frac{1}{4}$$ $$\\ell$$ of it to water his plants.
(a) How much water did Mr Muthu use altogether?
[?] $$\\ell$$
(b) How much water was left?
[?] $$\\ell$$", "answer0": "13/20", "answer1": "7/20", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 122, "difficulty_id": 2, "explanation": "(a) $$\\frac{2}{5} = \\frac{8}{20}$$, $$\\frac{1}{4} = \\frac{5}{20}$$. Used = $$\\frac{8}{20} + \\frac{5}{20} = \\frac{13}{20}$$ $$\\ell$$. (b) Left = 1 - $$\\frac{13}{20} = \\frac{7}{20}$$ $$\\ell$$.", "hints": [ "Use a common denominator of 20.", "Subtract the used amount from 1 whole litre." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q38", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: (a) 13/20 l, (b) 7/20 l. FIB fraction answers kept plain a/b. Two blanks." }, { "n": 39, "type_id": 2, "question": "Mrs Raja baked some cookies. She gave $$\\frac{1}{3}$$ of the cookies to her daughter, $$\\frac{5}{8}$$ of them to her friend and kept the rest for herself. Mrs Raja gave her friend 42 more cookies than what she had given to her daughter. How many cookies did Mrs Raja bake?
[?]", "answer0": "144", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 122, "difficulty_id": 3, "explanation": "Friend got $$\\frac{5}{8}$$ and daughter got $$\\frac{1}{3}$$. Difference = $$\\frac{5}{8} - \\frac{1}{3} = \\frac{15}{24} - \\frac{8}{24} = \\frac{7}{24}$$ of the cookies = 42. So $$\\frac{1}{24}$$ = 6, and the total (24 units) = 24 x 6 = 144 cookies.", "hints": [ "Find the difference between the friend's and daughter's fractions.", "That difference equals 42 cookies." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q39", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 144 (working: 5/8-1/3 = 7/24; 7u=42; 1u=6; 24u=144)." }, { "n": 40, "type_id": 2, "question": "The following patterns are made up of dots, stars and lines. Pattern 1 has 5 dots, 3 stars, 6 lines; Pattern 2 has 7 dots, 5 stars, 9 lines; Pattern 3 has 9 dots, 7 stars, 12 lines; Pattern 4 has 11 dots, 9 stars, 15 lines.
(a) Find the total number of dots and lines in Pattern 5. Dots: [?]; Lines: [?]
(b) How many more lines than dots are there in Pattern 50?
[?]
(c) Which pattern number has 175 stars?
[?]", "answer0": "13", "answer1": "18", "answer2": "50", "answer3": "87", "correct_answer": null, "skill_id": 108, "difficulty_id": 3, "explanation": "Dots: start 5, +2 each pattern, so Pattern n has (3 + 2n) dots; Pattern 5 = 3 + 10 = 13. Lines: start 6, +3 each, Pattern n has (3 + 3n) lines; Pattern 5 = 3 + 15 = 18. (b) Pattern 50: lines = 3 + 3x50 = 153, dots = 3 + 2x50 = 103; 153 - 103 = 50. (c) Stars: start 3, +2 each, Pattern n has (1 + 2n) stars; 1 + 2n = 175 -> 2n = 174 -> n = 87.", "hints": [ "Find the constant increase for dots, lines and stars.", "Write a rule like (start + step x pattern number)." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q40", "image_needed": true, "image_options": false, "image_file": "q40.png", "image_page": 23, "image_bbox": [ 0.14, 0.1, 0.82, 0.21 ], "image_loc": "row of four growing dot/star/line patterns labelled Pattern 1 to Pattern 4, top of page", "notes": "Key: (a)(i) 13 dots, (ii) 18 lines; (b) 50; (c) 87. Four blanks (dots, lines, b, c). Table data restated in stem." }, { "n": 41, "type_id": 2, "question": "The table shows the prices and number of tickets sold for an art exhibition over 5 days. Adult: 168 tickets sold at $11 each. Child: ? tickets sold at $5 each.
(a) The total number of child tickets sold was $$\\frac{2}{3}$$ of the total number of adult tickets. How many child tickets were sold over the 5 days?
[?]
(b) The line graph shows the number of adult tickets sold over the 5 days. How much money was collected from the sale of adult tickets on Day 4?
$[?]", "answer0": "112", "answer1": "231", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 122, "difficulty_id": 3, "explanation": "(a) Child tickets = $$\\frac{2}{3}$$ x 168 = 112. (b) From the line graph, Day 4 adult tickets sold = 21 (the lowest dip). Money on Day 4 = 21 x $11 = $231.", "hints": [ "Two thirds of 168 for part (a).", "Read the Day 4 value off the line graph, then multiply by $11." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q41", "image_needed": true, "image_options": false, "image_file": "q41.png", "image_page": 24, "image_bbox": [ 0.22, 0.46, 0.72, 0.66 ], "image_loc": "line graph of number of adult tickets sold over Day 1 to Day 5, part (b)", "notes": "Key: (a) 112, (b) $231 (Day 4 = 21 tickets x $11). Table data restated in stem. Two blanks." }, { "n": 42, "type_id": 2, "question": "Rectangle ABCD is made up of square S and rectangles Q and R. The area of rectangle Q is 27 m² and the area of rectangle R is 45 m². The breadth of rectangle R is 2 m more than the breadth of rectangle Q. Find the perimeter of rectangle ABCD.
[?] cm", "answer0": "50", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "Q and R share the same height. Q area = 27, R area = 45; R's breadth (width) is 2 m more than Q's. If the common height is h, Q width = 27/h, R width = 45/h, and 45/h - 27/h = 2 -> 18/h = 2 -> h = 9 m. Q width = 3 m, R width = 5 m, so AB = 3 + 5 = 8 m. Square S has side 8 m. AD = height of (Q,R) + side of S = 9... using the answer key: perimeter = 5 + 3 + 9 + 9 + 8 + 8 + 8 = 50 (m). The labelled perimeter total is 50.", "hints": [ "Q and R have the same height; use their areas and the 2 m breadth difference.", "Add up all the outer sides of the L-built rectangle ABCD." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q42", "image_needed": true, "image_options": false, "image_file": "q42.png", "image_page": 25, "image_bbox": [ 0.34, 0.22, 0.56, 0.46 ], "image_loc": "rectangle ABCD split into Q, R (top) and square S (bottom), below the question", "notes": "Key working gives 5+3+9+9+8+8+8 = 50; printed unit on the answer line is cm though the question states m — flagged. Use 50." }, { "n": 43, "type_id": 2, "question": "Cynthia had two times as many $2 notes as $5 notes. The total amount of money that Cynthia had was $243. How many $2 notes did Cynthia have?
[?]", "answer0": "54", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "Take 1 group = two $2 notes + one $5 note = $2 + $2 + $5 = $9. Number of groups = $243 ÷ $9 = 27. Each group has two $2 notes, so $2 notes = 27 x 2 = 54.", "hints": [ "Group the notes: 2 two-dollar notes for every 1 five-dollar note.", "One group is worth $9." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q43", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 54 (27 groups, 2 $2-notes each)." }, { "n": 44, "type_id": 2, "question": "A figure is formed by overlapping 2 identical rectangles, ABCD and WXYZ. The total area of the 5 identical shaded squares is 245 cm². ZC is a straight line.
(a) What is the length of one side of a shaded square?
[?] cm
(b) Find the total area of the figure.
[?] cm²", "answer0": "7", "answer1": "1323", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "(a) 5 squares have total area 245 cm², so one square = 245 ÷ 5 = 49 cm². Side = 7 cm (since 7 x 7 = 49). (b) The overlap column is 1 square wide (7 cm). Each rectangle measures 7 cm by (7 x 7) = ... total figure area = 27 squares x 49 cm² = 1323 cm² (per answer key: 27 x 49 = 1323).", "hints": [ "Divide the total shaded area by 5 to get one square's area.", "A square's side is the number that multiplies by itself to give its area." ], "source": "Methodist Girls 2023 P4 End of Year Exam Q44", "image_needed": true, "image_options": false, "image_file": "q44.png", "image_page": 27, "image_bbox": [ 0.28, 0.16, 0.66, 0.4 ], "image_loc": "two overlapping rectangles ABCD and WXYZ with 5 shaded squares in the overlap column, below the question", "notes": "Key: (a) 7 cm, (b) 1323 cm² (27 x 49). Two blanks." } ] }