Year 4 · Selective School and Opportunity Class
Year 4 Mathematical reasoning practice for selective school tests
Selective and Opportunity Class questions are not harder arithmetic — they are ordinary arithmetic wrapped in a puzzle. The work is in seeing the structure: which quantity depends on which, and what would happen if one of them changed.
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.
Question 1
How much rain fell altogether across the three days?
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.
Question 2
What is the chance that he rolls a 5?
Question 3
How many coins will he use to pay the exact amount?
Question 4
Which pair of grid squares shows the same symbol?
Question 5
When these numbers are written in digits, which one is palindromic?
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?
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?
Question 8
Which of these statements is/are true?
Keep going with the full papers
Fifteen Year 4 papers of mathematical reasoning, 522 questions.
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