{ "paper": { "school": "Catholic High", "year": 2023, "level": "P4", "label": "Weighted Assessment 3", "source_prefix": "Catholic High 2023 P4 Weighted Assessment 3", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "What is the value of the digit 1 in 4.123?", "answer0": "0.1", "answer1": "0.01", "answer2": "0.001", "answer3": "10", "correct_answer": 0, "skill_id": 123, "difficulty_id": 1, "explanation": "In 4.123, the digit 1 is in the tenths place. Its value is 1 tenth = 0.1.", "hints": [ "Identify the place value of each digit after the decimal point.", "The first digit after the decimal point is the tenths place." ], "source": "Catholic High 2023 P4 Weighted Assessment 3 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 1 (0.1)." }, { "n": 2, "type_id": 1, "question": "$$3\\frac{5}{6}$$ = $$\\frac{[?]}{6}$$
What is the missing number in the box?", "answer0": "15", "answer1": "18", "answer2": "21", "answer3": "23", "correct_answer": 3, "skill_id": 119, "difficulty_id": 1, "explanation": "Convert the mixed number to an improper fraction: $$3\\frac{5}{6}$$ = (3 × 6 + 5)/6 = (18 + 5)/6 = $$\\frac{23}{6}$$. The missing number is 23.", "hints": [ "Multiply the whole number by the denominator.", "Add the numerator to that product to get the new numerator." ], "source": "Catholic High 2023 P4 Weighted Assessment 3 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 4 (23). Original prints 3 5/6 = [box]/6." }, { "n": 3, "type_id": 1, "question": "Arrange the following in increasing order.
$$\\frac{4}{5}$$, $$\\frac{4}{7}$$, $$\\frac{9}{4}$$", "answer0": "$$\\frac{4}{5}$$, $$\\frac{4}{7}$$, $$\\frac{9}{4}$$", "answer1": "$$\\frac{4}{7}$$, $$\\frac{4}{5}$$, $$\\frac{9}{4}$$", "answer2": "$$\\frac{9}{4}$$, $$\\frac{4}{5}$$, $$\\frac{4}{7}$$", "answer3": "$$\\frac{9}{4}$$, $$\\frac{4}{7}$$, $$\\frac{4}{5}$$", "correct_answer": 1, "skill_id": 79, "difficulty_id": 2, "explanation": "$$\\frac{9}{4}$$ is greater than 1 (improper), so it is the largest. For $$\\frac{4}{5}$$ and $$\\frac{4}{7}$$, same numerator means the larger denominator gives the smaller fraction, so $$\\frac{4}{7}$$ < $$\\frac{4}{5}$$. Increasing order: $$\\frac{4}{7}$$, $$\\frac{4}{5}$$, $$\\frac{9}{4}$$.", "hints": [ "An improper fraction is larger than any proper fraction.", "With the same numerator, the larger the denominator, the smaller the fraction." ], "source": "Catholic High 2023 P4 Weighted Assessment 3 Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 (4/7, 4/5, 9/4)." }, { "n": 4, "type_id": 1, "question": "Express $$10\\frac{1}{4}$$ as a decimal.", "answer0": "10.1", "answer1": "10.14", "answer2": "10.25", "answer3": "10.025", "correct_answer": 2, "skill_id": 127, "difficulty_id": 1, "explanation": "$$\\frac{1}{4}$$ = 25/100 = 0.25, so $$10\\frac{1}{4}$$ = 10 + 0.25 = 10.25.", "hints": [ "Convert the fraction part to a decimal.", "One quarter equals 0.25." ], "source": "Catholic High 2023 P4 Weighted Assessment 3 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3 (10.25)." }, { "n": 5, "type_id": 2, "question": "What mixed number does the letter A represent on the number line? Give your answer in the simplest form.
[?]", "answer0": "2 3/4", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 119, "difficulty_id": 2, "explanation": "Each interval between whole numbers is divided into 8 equal parts, so each small mark is $$\\frac{1}{8}$$. A is 6 marks past 2, i.e. $$2\\frac{6}{8}$$ = $$2\\frac{3}{4}$$ in simplest form.", "hints": [ "Count how many equal parts each whole number is divided into.", "Simplify $$\\frac{6}{8}$$ by dividing top and bottom by 2." ], "source": "Catholic High 2023 P4 Weighted Assessment 3 Q5", "image_needed": true, "image_options": false, "image_file": "q5.png", "image_page": 3, "image_bbox": [ 0.18, 0.21, 0.74, 0.3 ], "image_loc": "number line near top of page, marked 1, 2, 3 with arrow labelled A between 2 and 3", "notes": "Key answer: 2 3/4 (from 2 6/8). FIB answer kept as plain mixed-number text '2 3/4'." }, { "n": 6, "type_id": 2, "question": "Divide 5 by 8. Correct your answer to 2 decimal places.
[?]", "answer0": "0.63", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 125, "difficulty_id": 2, "explanation": "5 ÷ 8 = 0.625. Rounding to 2 decimal places, the third decimal digit is 5, so round up: 0.63.", "hints": [ "Divide 5.000 by 8 using long division.", "Look at the third decimal place to decide rounding." ], "source": "Catholic High 2023 P4 Weighted Assessment 3 Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 5000 ÷ 8 = 0.625 ≈ 0.63." }, { "n": 7, "type_id": 2, "question": "The mass of a bag of potatoes is 3 $$kg$$ when rounded to the nearest kilogram. What is the greatest possible value of the bag of potatoes in 1 decimal place?
[?]", "answer0": "3.4", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 109, "difficulty_id": 3, "explanation": "Masses from 2.5 kg up to (but not including) 3.5 kg round to 3 kg. The greatest value below 3.5 kg expressed to 1 decimal place is 3.4 kg.", "hints": [ "Find the range of values that round to 3 when rounding to the nearest whole number.", "The largest value just under 3.5 to 1 decimal place is 3.4." ], "source": "Catholic High 2023 P4 Weighted Assessment 3 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 3.4 kg. Answer requires unit kg." }, { "n": 8, "type_id": 2, "question": "Find the product of 15.24 and 3.
[?]", "answer0": "45.72", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 130, "difficulty_id": 1, "explanation": "15.24 × 3 = 45.72.", "hints": [ "Multiply as whole numbers then place the decimal point.", "15.24 has 2 decimal places, so the product has 2 decimal places." ], "source": "Catholic High 2023 P4 Weighted Assessment 3 Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 15.24 x 3 = 45.72." }, { "n": 9, "type_id": 2, "question": "Andy and Ben drank a total of $$\\frac{4}{5}$$ $$l$$ of juice. Andy drank $$\\frac{1}{2}$$ $$l$$ of the juice. How much more juice did Andy drink than Ben?
[?]", "answer0": "1/5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 122, "difficulty_id": 3, "explanation": "Ben drank $$\\frac{4}{5}$$ − $$\\frac{1}{2}$$ = $$\\frac{8}{10}$$ − $$\\frac{5}{10}$$ = $$\\frac{3}{10}$$ l. Andy drank $$\\frac{1}{2}$$ = $$\\frac{5}{10}$$ l. Andy drank $$\\frac{5}{10}$$ − $$\\frac{3}{10}$$ = $$\\frac{2}{10}$$ = $$\\frac{1}{5}$$ l more than Ben.", "hints": [ "First find how much Ben drank by subtracting Andy's amount from the total.", "Use a common denominator of 10 to add and subtract the fifths and halves." ], "source": "Catholic High 2023 P4 Weighted Assessment 3 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key working: Ben = 4/5 - 1/2 = 3/10; Andy - Ben = 5/10 - 3/10 = 2/10 = 1/5 l. Answer unit l." }, { "n": 10, "type_id": 2, "question": "Ray and Sherman shared a box of cards. Ray received $$\\frac{5}{12}$$ of the cards and Sherman received the remaining 105 cards. How many cards were there in the box?
[?]", "answer0": "180", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 120, "difficulty_id": 3, "explanation": "Ray had $$\\frac{5}{12}$$, so Sherman had $$\\frac{7}{12}$$ = 7 units = 105 cards. 1 unit = 105 ÷ 7 = 15 cards. The whole box = 12 units = 12 × 15 = 180 cards.", "hints": [ "Find the fraction of cards Sherman received.", "Sherman's 7 units equal 105 cards; find 1 unit first." ], "source": "Catholic High 2023 P4 Weighted Assessment 3 Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 7u=105, 1u=15, 12u=180." }, { "n": 11, "type_id": 2, "question": "The cost of a packet of sweets is twice the cost of a packet of peanuts. The cost of 2 such packets of sweets and a packet of peanuts is $18.50.
(a) What is the cost of a packet of peanuts?
(b) John bought 2 such packets of peanuts and a packet of sweets. How much did he pay?
(a) [?]
(b) [?]", "answer0": "3.70", "answer1": "14.80", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 131, "difficulty_id": 3, "explanation": "Let 1 packet of peanuts = 1 unit; 1 packet of sweets = 2 units. 2 sweets + 1 peanut = 4 + 1 = 5 units = $18.50, so 1 unit = $18.50 ÷ 5 = $3.70 (a). (b) 2 peanuts + 1 sweet = 2 + 2 = 4 units = $3.70 × 4 = $14.80.", "hints": [ "Express both items in units, with peanuts as 1 unit and sweets as 2 units.", "Add up the units in the given total to find the value of 1 unit." ], "source": "Catholic High 2023 P4 Weighted Assessment 3 Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 5u=$18.50, 1u=$3.70 (a); 4u=$3.70x4=$14.80 (b). Two-part word problem combined into one multi-blank FIB; answers are dollar amounts." } ] }