Year 8 · Selective School and Opportunity Class
Year 8 Mathematical reasoning practice for selective school tests
By Year 8 the reasoning questions assume fluency and test judgement: which method is worth starting, and when an estimate is enough to eliminate three of the four options.
What the section covers
- Algebraic thinking
- Expressing a situation as a relationship and reasoning about it without solving.
- Proportional reasoning
- Ratio, percentage change, scale and rates in unfamiliar contexts.
- Geometry and measurement
- Angles, area and volume, and problems where the diagram is described in words.
- Data and chance
- Interpreting statistics honestly and recognising when they mislead.
Sample questions
8 real questions from our Year 8 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
A group of students took a math test, and the results showed that 60% of the students passed the test. Of those who passed, 80% received an ‘A’ grade. If there were 200 students in total, how many students received an ‘A’ grade?
Question 2
A rectangular garden should be enlarged so that its new length is twice its original length and its new width is 50% more than its original width. If the original garden has an area of 300 square metres, what is the area of the enlarged garden?
Question 3
The length of a rectangle increases by 20% and breadth decreases by 10%. What is the percentage increase or decrease in the area of the rectangle?
Question 4
Find the equation of the given line segment AB.
Question 5
Two copper wire of same length bent in a rectangular and in a circular shape. If the length and breadth of the rectangle are 42cm and 35 cm respectively find the diameter of the circle.
Question 6
A dartboard has a radius of 1 unit. Suppose a dart is thrown randomly, and the probability of hitting the dartboard is 1. What is the probability of the dart landing within the dartboard's inner half (radius = 0.5 units)?
Question 7
In the given figure AB = AC and ∠ACD = 115°. Write the measurement of ∠BAC.
Question 8
A company buys 100 units of a product at 10 dollars each. Due to storage issues, 20% of the units get damaged and cannot be sold. The company sells the remaining units at a 25% profit. If the selling price per unit is 15, dollars what is the overall profit or loss %?
Keep going with the full papers
Eight Year 8 papers, 271 questions.
Aussie Edu Hub is an independent educational practice platform and is not affiliated with ACARA or any state education authority. NAPLAN is a registered trademark of ACARA.