How many questions are on the Mathematical Reasoning paper, and how long do I get?

35 multiple-choice questions in 40 minutes — the same shape as the Mathematical Reasoning sample papers published by the NSW Department of Education.

What topics does Mathematical Reasoning cover?

Number and operations, number patterns and algebra, measurement, geometry, and statistics and probability — based on our analysis of the published official samples.

How many answer options does each question have?

Five (A to E) — matching the real NSW Selective Mathematical Reasoning paper.

Is there a free Mathematical Reasoning paper?

Yes — one paper in the series is free. It is sat in the online test mode, with the correct answer and an explanation shown in the review screen after each attempt, with 24-hour access. Claiming the full sample requires an email, a child’s first name and agreement to receive practice tips. The ten-question preview needs no sign-up.

Mathematical Reasoning Practice Tests

Ten questions · No sign-up

Year 6 Mathematical Reasoning, taken from Practice Paper 10. The full paper is 35 questions in 40 minutes — about 70 seconds each. There is no clock here.

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Q1Divisibility multiples
Question 1.
Two warning lights flash at the same moment. One light then flashes every 15 seconds and the other every 9 seconds. After how many seconds will they next flash at the same time?
A24 secondsB135 secondsC15 secondsD3 secondsE45 seconds
Q2Clock arithmetic
Question 2.
A flight departs at 9:10 pm and lasts 3 hours 25 minutes. What is the arrival time in 24-hour format?
A00:10 (next day)B12:35 (next day)C00:35 (next day)D23:35E17:45
Q3Number sequence
Question 3.
In a number sequence, each term after the second term is the sum of the previous two terms. The first two terms are 6, 5. What is the 6th term?
A27B43C70D11E80
Q4Ratio chain
Question 4.
Kira, Vik and Uma share 231 biscuits. Kira's share and Vik's share are in the ratio 5 : 4. Uma has 3 times as many biscuits as Vik. How many biscuits does Uma have?
A55B44C99D77E132
Q5Probability spinner
Question 5.
A spinner is divided into the following unequal sectors: orange (1/2 of the disc), yellow (1/4 of the disc), pink (1/8 of the disc), purple (1/8 of the disc). The spinner is spun once. What is the probability that the spinner does NOT land on yellow?
A1/4B3/4C1/2D1/8E7/8
Q6Balance scale
Question 6.
The balance scale shown is exactly level. The left pan holds 3 circles and 1 pentagon; the right pan holds 4 hexagons. One circle weighs 60 g and one hexagon weighs 50 g. What is the weight of one pentagon?
A46 gB80 gC70 gD10 gE20 g
Q7Column graph
Question 7.
The bar graph shows how many of each kind of animals are in a group. How many legs are there in total?
A12 legsB18 legsC216 legsD52 legsE76 legs
Q8Two variable linear
Question 8.
At the local cafe, a sandwich and a juice together cost $6.25. A slice of cake and a juice together cost $4.50. A sandwich, a slice of cake and a juice all together cost $9.00. How much does a sandwich and a slice of cake (without a juice) cost?
A$7.25B$10.75C$2.75D$4.50E$1.75
Q9Shaded area
Question 9.
A rectangular lawn measuring 24 m by 12 m is surrounded by a path of uniform width 3 m. What is the area of the shaded path?
A540 m²B288 m²C252 m²D828 m²E216 m²
Q10Cube counting
Question 10.
The solid on the left is made from small cubes stacked together. Its Top, Front and Side views are shown on the right. How many small cubes make up the solid?
A18B11C27D24E8