Free selective-style mathematical reasoning practice paper

35 questions in 40 minutes, for Years 5 and 6. Free, with no sign-up.

Thirty-five maths questions in forty minutes, the count and time of the real selective test section, from the Years 5 and 6 syllabus and problem solving. Your child picks an answer for each, with no calculator. Then you see the marks, what the paper found and the skills to look at first.

The real section: In the selective test, the mathematical reasoning section has 35 questions in 40 minutes, as the parent guide sets out from the NSW Department of Education's pages. This paper has the same number of questions and the same time. Its questions are Learnest's own, in the style of the test.
What it covers: Problem solving 12 questions

Number and algebra 13 questions

Data and chance 2 questions

Measurement 5 questions

Geometry 3 questions
What it leaves out: The selective test also has reading, thinking skills and writing. Learnest has a selective-style thinking skills paper, and no reading or writing paper.
How to sit it: A quiet table, a pencil and spare paper for working, and no calculator. Press Start the clock below, or set a timer for 40 minutes. Your child picks one answer for each question.
Sitting it again: The questions are the same every time, so your child can sit this paper again. Leave a few weeks first, so the second try shows what they can do rather than what they remember.

Learnest marks the answers and keeps none of them. There is nothing to sign up for and no email to give.

Prefer paper? Print the paper, with the answers on the last page.

Question 1 of 35
A light show flashes red, orange, yellow, green, blue, purple, then starts again at red. What colour is the 100th flash?
- A: blue
- B: yellow
- C: purple
- D: green
Question 2 of 35
What number is 1000 less than 3,000,400?
- A: 2,000,400
- B: 3,999,400
- C: 3,001,400
- D: 2,999,400
Question 3 of 35
Inputs 2, 3, 4 and 5 give outputs 9, 13, 17 and 21. What output goes with an input of 20?
- A: 81
- B: 80
- C: 24
- D: 27
Question 4 of 35
A fair number cube numbered 1 to 6 is rolled 60 times in a board game and a 2 comes up 15 times. How many more 2s than expected is that?
- A: 45
- B: 15
- C: 5
- D: 10
Question 5 of 35
Two jugs held equal amounts. 300 mL was poured from one and 900 mL from the other. Then the first held 3 times as much as the second. How much did each hold at first?
- A: 900 mL
- B: 1200 mL
- C: 300 mL
- D: 600 mL
Question 6 of 35

A skip bin is 3 m long, 2 m wide and 2 m high. What is its volume in cubic metres?
- A: 12
- B: 7
- C: 16
- D: 6
Question 7 of 35
A money box holds 20 coins, all 20c or 50c, worth $7.30. How many 50c coins are in the money box?
- A: 10
- B: 11
- C: 9
- D: 12
Question 8 of 35

Point R at (-2, -5) is reflected in the x-axis. Where is its image?
- A: (2, -5)
- B: (2, 5)
- C: (-5, -2)
- D: (-2, 5)
Question 9 of 35
Amara must be at the airport by 2:15 pm. The drive takes 1 hour 20 minutes, and packing the car takes 25 minutes before that. When should she start packing?
- A: 12:55 pm
- B: 12:30 pm
- C: 1:50 pm
- D: 4:00 pm
Question 10 of 35
Three angles meet at a point. Two are 40 and 95 degrees. How many degrees is the third?
- A: 135
- B: 265
- C: 225
- D: 45
Question 11 of 35
Which of these is the same as 0.09?
- A: ¹⁄₉
- B: 90%
- C: 9%
- D: 0.09%
Question 12 of 35
What is 0.408 × 100?
- A: 4.08
- B: 40.8
- C: 0.40800
- D: 408
Question 13 of 35
Which fraction is ⁶⁄₁₀ in its simplest form?
- A: ³⁄₅
- B: ²⁄₆
- C: ⁶⁄₅
- D: ³⁄₁₀
Question 14 of 35

A rectangle has a perimeter of 26 cm and a length of 8 cm. How wide is it, in centimetres?
- A: 5
- B: 18
- C: 10
- D: 13
Question 15 of 35
Work out 100 - (6 + 4) × 8.
- A: 90
- B: 126
- C: 20
- D: 720
Question 16 of 35
A 3 by 3 board is divided into 9 small squares. How many squares of all sizes can be found on the board?
- A: 14
- B: 11
- C: 9
- D: 10
Question 17 of 35
Which number is composite?
- A: 57
- B: 2
- C: 59
- D: 1
Question 18 of 35
Twenty-one cones are set out in a straight line, 3 m apart. How far is it from the first cone to the last?
- A: 66 m
- B: 60 m
- C: 57 m
- D: 63 m
Question 19 of 35
Four swimmers finish in 12.405 s, 12.4 s, 12.54 s and 12.045 s. Which is the fastest time?
- A: 12.405
- B: 12.54
- C: 12.045
- D: 12.4
Question 20 of 35
Bella has six letter tiles that spell SEESAW. Laying all six in a row, how many different orders of letters can she make, SEESAW included?
- A: 60
- B: 180
- C: 360
- D: 720
Question 21 of 35
A column graph shows fruit stall sales of 82 and 88. Its scale is marked 80, 82, 84, 86, 88 and 90. What makes the graph misleading?
- A: The scale does not start at zero
- B: The columns are different colours
- C: The scale stops at 90
- D: The scale goes up in steps of 2
Question 22 of 35
A truck is loaded with 40 bags of cement of 25 kg each. How many tonnes is that?
- A: 1000
- B: 1
- C: 65
- D: 1000000
Question 23 of 35
Leo eats ¹⁄₆ of a pizza. Zara eats ¹⁄₄ of the same pizza. Who eats more?
- A: Leo
- B: You cannot tell
- C: They eat the same
- D: Zara
Question 24 of 35
A diver is at -18 m. The diver rises 6 m, then sinks 11 m. At what level is the diver now?
- A: 23
- B: -35
- C: -23
- D: -1
Question 25 of 35
A class of 30 plans an excursion, but ¹⁄₁₀ of the students are away sick. How many students go on the excursion?
- A: 27
- B: 20
- C: 300
- D: 3
Question 26 of 35
Ruby builds a skeleton of a prism whose two ends have 12 sides each, with a straw for each edge. How many straws does Ruby use?
- A: 14
- B: 24
- C: 36
- D: 12
Question 27 of 35
Mei's flight leaves Sydney at 22:50 and takes 2 hours 25 minutes. At what time does it land?
- A: 25:15
- B: 1:15 am
- C: 1:15 pm
- D: 12:15 am
Question 28 of 35
Five lockers side by side carry whole numbers that follow on from each other, and the five numbers total 135. What number is on the highest-numbered locker?
- A: 29
- B: 25
- C: 27
- D: 32
Question 29 of 35
A class has 3 girls for every 2 boys. When 4 more boys join, there are equal numbers of girls and boys. How many children are in the class now?
- A: 28
- B: 20
- C: 12
- D: 24
Question 30 of 35
A clock chimes 4 times at 4 o'clock, taking 6 seconds from the first chime to the last. How many seconds does it take to chime 12 times at noon?
- A: 24 seconds
- B: 18 seconds
- C: 22 seconds
- D: 26 seconds
Question 31 of 35
In a three-digit number the digits add to 16. The hundreds digit is 4 more than the ones digit, and the tens digit is double the ones digit. What is the number?
- A: 736
- B: 763
- C: 367
- D: 673
Question 32 of 35
A dam held 1,000,000 litres. Then 463,218 litres were used. How many litres are left?
- A: 647,892
- B: 463,218
- C: 1,463,218
- D: 536,782
Question 33 of 35

An L-shaped garden is 11 m along the bottom and 8 m up the left. Its top edge is 4 m and the edge below drops 3 m. What is its area in square metres?
- A: 88
- B: 53
- C: 38
- D: 67
Question 34 of 35
Each of 27 classes raises $164. How many dollars is that altogether?
- A: 1476
- B: 3228
- C: 1148
- D: 4428
Question 35 of 35
Trains leave at 6:48 am and then every 22 minutes. The trip takes 38 minutes, and Dev walks 9 minutes to work. To start by 9:00 am, which is the latest train Dev can catch?
- A: 7:32 am
- B: 8:16 am
- C: 7:54 am
- D: 8:13 am

Leave a question blank if your child does not know. It shows as not answered.

Learnest is not affiliated with ACARA, NESA, the NSW Department of Education or the Australian Maths Trust. Every question in this paper is Learnest's own, written for practice. None comes from a past paper.

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2	4	6	8	10	12	14	16	18	20
3	6	9	12	15	18	21	24	27	30
4	8	12	16	20	24	28	32	36	40
5	10	15	20	25	30	35	40	45	50
6	12	18	24	30	36	42	48	54	60
7	14	21	28	35	42	49	56	63	70
8	16	24	32	40	48	56	64	72	80
9	18	27	36	45	54	63	72	81	90
10	20	30	40	50	60	70	80	90	100