OC Mock Test 1 — Mathematical Reasoning (Year 4)
A free NSW Opportunity Class (OC) placement test practice paper for Year 4 in the format of the real test: 35 questions in 40 minutes, covering Section A — Number and patterns; Section B — Measurement, space and geometry; Section C — Fractions, data, chance and problem solving. No calculator. Choose the best answer. Answer every question — there is no penalty for a wrong answer. Attempt it online — every question is marked instantly and the correct answers are shown at the end.
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Q1. Which number is made from 3 ten-thousands, 14 hundreds, 5 tens and 12 ones?
Q2. Which of these has the same value as 48 × 25?
Q3. What is the value of 36 − 12 ÷ 4 × 2 + 5?
Q4. Which number is a multiple of both 6 and 8, but is not a multiple of 16?
Q5. What is the 8th number in this pattern?
3, 7, 15, 31, 63, …
Q6. Sam thinks of a number. He multiplies it by 4, subtracts 6, and then halves the result. His answer is 25. What number did Sam think of?
Q7. Pencils cost 65c each, or $3.20 for a pack of 6. Lucy needs exactly 20 pencils. What is the least she can pay?
Q8. A school hall has 28 rows of 35 chairs. Then 175 chairs are taken away. How many chairs are left?
Q9. A number rounded to the nearest hundred is 3700. Which of these could not be the number?
Q10. Each bus has 48 seats, and on every bus 3 seats must be kept for teachers. 330 students are going on an excursion. What is the smallest number of buses needed?
Q11. In this subtraction, each box stands for a missing digit.
5 □ 2 − 2 7 □ = 2 6 8
What is the sum of the two missing digits?
Q12. Matches are used to make a row of squares, as shown. How many matches are needed to make a row of 15 squares?
Q13. The clock shows the time Jack started his homework in the afternoon. He finished 1 hour 35 minutes later. What time did he finish?
Q14. Ava arrives at the Library stop at 8:05 am and catches the next bus. How long after she arrives at the Library stop does she reach the Beach?
Q15. Which length is the longest?
Q16. All the corners of this shape are right angles. What is its perimeter?
Q17. The shaded shape is drawn on a grid of 1 cm squares. What is its area?
Q18. This stack is made of identical cubes. Every cube sits on the table or on another cube. What is the smallest number of extra cubes needed to turn the stack into a solid cuboid 3 cubes long, 2 cubes wide and 3 cubes high?
Q19. Zara is facing north. She turns 135° clockwise, and then turns 270° anticlockwise. Which direction is she facing now?
Q20. This net is folded to make a cube. Which face is opposite face 1?
Q21. A prism has 18 edges. How many faces does it have?
Q22. Some squares on this grid are shaded. What is the smallest number of extra squares that must be shaded so that both dashed lines are lines of symmetry?
Q23. Kai starts at the Library. He walks 3 squares east, then 4 squares north, then 1 square west. Where is he now?
Q24. A box holds 12 identical cans. The full box has a mass of 3 kg 600 g. The empty box has a mass of 240 g. What is the mass of one can?
Q25. What fraction of this square is shaded?
Q26. Maya had $60. She spent 1/3 of it on a book, and then 1/4 of the money that was left on lunch. How much money does she have now?
Q27. Which number is exactly halfway between 2.4 and 3.1?
Q28. The graph shows how many books five students read in a term. How many more books did Cal read than Ben and Dee together?
Q29. The picture graph shows how many ice creams a shop sold each day. How many ice creams did the shop sell altogether from Monday to Friday?
Q30. 50 students each chose one sport. Some numbers are missing from the table. How many girls chose Netball?
Q31. A bag holds 6 red, 4 blue and 2 green marbles. One marble is picked without looking. Which statement is true?
Q32. Ella is 4 years older than Finn. In 3 years' time, their ages will add up to 30. How old is Ella now?
Q33. I am a two-digit number greater than 50. I am a multiple of 7. My two digits add up to 10. What number am I?
Q34. A rectangular garden is 3 times as long as it is wide. Its perimeter is 48 m. What is the area of the garden?
Q35. Each shape stands for a number.
▲ + ▲ + ■ = 20
■ + ■ + ▲ = 22
What is ▲ + ■?
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