Year 4 Mathematical reasoning practice for selective school tests

What the section covers

Number puzzles

Working backwards from a result, filling in missing digits, problems with more than one unknown.

Patterns and sequences

Finding the rule, extending it a long way, describing it in words.

Measurement and space

Area and perimeter in unfamiliar shapes, nets and folding, reading diagrams closely.

Logic in numbers

Deciding what must be true, what could be true, and what cannot be true at all.

Sample questions

8 real questions from our Year 4 papers, covering the different ways this section asks things. Answer the ones you can click; the rest show how they work. Nothing to sign up for.

1. Question 1

   It rained on three days in a row last week. Bruce measured the rain each day: Wednesday: 12 mm, Thursday: 11 mm, Friday: 19 mm.

   How much rain fell altogether across the three days?

   32 mm34 mm42 mm43 mm44 mm

2. Question 2

   What is the chance that he rolls a 5?

   
   1 out of 61 out of 51 out of 31 out of 25 out of 6

3. Question 3

   How many coins will he use to pay the exact amount?

   
   34567

4. Question 4

   Which pair of grid squares shows the same symbol?

   
   A5 and D2D3 and E2A4 and D2E2 and B3B5 and C1

5. Question 5

   When these numbers are written in digits, which one is palindromic?

   
   A onlyA and B onlyA and C onlyB and C onlyA, B and C

6. Question 6

   On Saturday, Nina went shopping with her friends. She was at the shops from 9:30 a.m. to 1:00 p.m. How long did she spend shopping?

   

7. Question 7

   Noah is thinking about a hexagonal prism. He wrote down the number of faces and the number of edges. What is the difference between these two numbers?

   468910

8. Question 8

   Which of these statements is/are true?

   

   Choose 1.

   More students liked pineapples than oranges.More students liked mangoes than apples.Fewer students liked bananas than grapes.