Selective Practice Mock 1 — Mathematical Reasoning (Year 5, early preparation)
A free NSW Selective High School placement test practice paper for Year 5 in the format of the real test: 35 questions in 40 minutes, covering Section A — Number and patterns; Section B — Measurement and geometry; Section C — 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 fraction is equivalent to 3/4?
Q2. What is 3/4 + 5/8?
Q3. Mia had $45. She spent 3/5 of it on a book. How much money did she have left?
Q4. Which list shows 0.305, 0.35, 0.053, 0.5 and 0.3 in order from smallest to largest?
Q5. A jacket normally costs $80. In a sale it is 25% off. What is the sale price?
Q6. How many prime numbers are there between 20 and 40?
Q7. At a bus station, Route 1 buses leave every 6 minutes and Route 2 buses leave every 8 minutes. Both leave together at 7:00 am. When is the next time both routes leave together?
Q8. What is the value of 20 − 12 ÷ 4 + 3 × 2?
Q9. Matchsticks are used to make a row of squares. 1 square uses 4 matchsticks, 2 squares use 7 and 3 squares use 10. How many matchsticks are needed for a row of 12 squares?
Q10. Jai thinks of a number. He multiplies it by 3, subtracts 6, then halves the result. His answer is 15. What number did he start with?
Q11. Pens cost $1.35 each and notebooks cost $2.80 each. Sam buys 4 pens and 3 notebooks and pays with a $20 note. How much change should he get?
Q12. In a class, the ratio of boys to girls is 3 : 4. There are 28 students in the class. How many girls are there?
Q13. In a survey of 200 students, 50% chose soccer as their favourite sport. 25% of the remaining students chose tennis. The rest chose swimming. How many students chose swimming?
Q14. Part of a bus timetable is shown. Ava arrives at the Park Road stop at 1:20 pm and catches the next bus. At what time does she arrive at Beach Parade?
Q15. A jug holds 2.4 litres of juice. Tom pours out 3 glasses of 350 mL each. How much juice is left in the jug?
Q16. The shape is made from rectangles and all corners are right angles. What is its area?
Q17. Six identical squares are joined to make this shape. The area of the whole shape is 54 cm². What is the perimeter of the shape?
Q18. Liam builds a rectangular prism from 1 cm cubes. The bottom layer has 4 rows of 6 cubes, and the prism is 5 layers high. He then removes the whole top layer. How many cubes are left?
Q19. Three angles meet at a point, as shown. What is the size of angle x?
Q20. In triangle ABC, angle A is 48° and angle B is twice the size of angle A. What is the size of angle C?
Q21. Which statement is always true?
Q22. Points A, B and C are three corners of a rectangle ABCD. What are the coordinates of corner D?
Q23. Triangle PQR is reflected in the dashed mirror line. What are the coordinates of the image of point P?
Q24. The arrow points North-East. It turns 135° clockwise. In which direction does it point now?
Q25. This net is folded to make a cube. Which face is opposite face A?
Q26. The graph shows how many cans a class collected each day for recycling. Their goal was 200 cans for the week. How many more cans did they need to reach their goal?
Q27. The picture graph shows the favourite fruit of a group of students. How many more students chose mango than banana?
Q28. The mean (average) of Priya's five test scores is 16. Four of her scores are 12, 18, 15 and 20. What is her fifth score?
Q29. Every Year 5 student chose one favourite pet. The results are in the table. What fraction of the girls chose a cat?
Q30. A bag holds 4 red, 5 blue and 3 green marbles. One marble is taken out without looking. What is the chance that it is not blue?
Q31. The spinner has 8 equal parts. What is the chance of the spinner landing on a prime number?
Q32. A school buys 7 boxes of pencils with 24 pencils in each box. It gives 15 pencils to each of its 9 classes. How many pencils are left over?
Q33. I am a two-digit number. I am a multiple of 7. The sum of my digits is 10. I am an odd number. What number am I?
Q34. Adult tickets to a show cost $12 and child tickets cost $7. A group of 9 people paid $83 altogether. How many adults were in the group?
Q35. Asha, Ben and Cleo have 60 stickers altogether. Asha has twice as many as Ben. Cleo has 12 more than Ben. How many stickers does Asha have?
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