Free OC-style mathematical reasoning practice paper

35 questions in 40 minutes, for Years 3 and 4. Free, with no sign-up.

Thirty-five maths questions in forty minutes, the count and time of the real OC test section, from the Years 3 and 4 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 OC 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

Geometry 4 questions

Measurement 4 questions
What it leaves out: The OC test also has reading and thinking skills. Learnest has an OC-style thinking skills paper, and no OC-style reading 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 bead string repeats red, blue, blue, green, yellow. What colour is bead 47?
- A: blue
- B: green
- C: yellow
- D: red
Question 2 of 35
How many different ways can 3 children sit in a row of 3 chairs?
- A: 6
- B: 3
- C: 4
- D: 9
Question 3 of 35
Mei collected 456 cans and Jack collected 459. How many did they collect altogether?
- A: 815
- B: 915
- C: 805
- D: 905
Question 4 of 35
How many whole numbers from 1 to 60 contain the digit 5 exactly once?
- A: 14
- B: 15
- C: 16
- D: 6
Question 5 of 35
Leila buys 7 packets with 29 lollies in each packet. How many lollies in total?
- A: 36
- B: 140
- C: 143
- D: 203
Question 6 of 35
A library holds 8114 books. Nadia counted 3477 of them on the shelves. How many are not on the shelves?
- A: 4637
- B: 5363
- C: 5637
- D: 4737
Question 7 of 35
A spinner has 10 equal parts, 4 of them green. In 40 spins, about how many times would you expect green?
- A: 4
- B: 16
- C: 24
- D: 10
Question 8 of 35
Which way does a pointer face after three quarter turns clockwise, if it starts facing south?
- A: east
- B: west
- C: south
- D: north
Question 9 of 35
Count the edges and the vertices of a triangular pyramid. How many more edges are there?
- A: 6
- B: 10
- C: 4
- D: 2
Question 10 of 35
Priya gave half her stickers away, then got 6 more, and now has 20. How many did she start with?
- A: 14
- B: 52
- C: 34
- D: 28
Question 11 of 35
Training starts at 5:50 pm and runs for 35 minutes. When does it end?
- A: 5:35 pm
- B: 6:25 pm
- C: 5:25 pm
- D: 5:85 pm
Question 12 of 35

A 3 cm wide rectangle covers 15 square centimetres. How long is it in centimetres?
- A: 5
- B: 12
- C: 3
- D: 45
Question 13 of 35
Begin at 5 and add 3 each time. What is the 8th number?
- A: 29
- B: 23
- C: 26
- D: 24
Question 14 of 35
What is 4.65 + 0.39?
- A: 4.104
- B: 5.04
- C: 4.04
- D: 5.4
Question 15 of 35
Chairs are set out in 6 rows of 8. How many chairs are on the outside edge?
- A: 28
- B: 14
- C: 48
- D: 24
Question 16 of 35

Zara leaves A2 and goes 4 squares east, 1 north and 1 west. Rows count from the top. Which square?
- A: E1
- B: D3
- C: D1
- D: F1
Question 17 of 35
9 tickets are sold. Child tickets cost $4 and adult tickets $7. The total is $51. How many adult tickets?
- A: 15
- B: 5
- C: 4
- D: 17
Question 18 of 35

Which fraction is the same as ³⁄₅?
- A: ³⁄₁₀
- B: ⁵⁄₇
- C: ⁶⁄₁₀
- D: ⁶⁄₅
Question 19 of 35
Which number has 7 thousands, 7 hundreds and 3 ones?
- A: 7073
- B: 773
- C: 7730
- D: 7703
Question 20 of 35
43 apples are packed into bags of 8. Each full bag sells for $2. How much money is that?
- A: 86
- B: 5
- C: 10
- D: 12
Question 21 of 35
151 + ? = 363 - 88. What number goes in the box?
- A: 275
- B: 212
- C: 124
- D: 300
Question 22 of 35
What is 3929 + 3873 + 1132?
- A: 7934
- B: 5005
- C: 7802
- D: 8934
Question 23 of 35
Five hats pair with 5 scarves, yet the 5 pairs that match in colour are not allowed. How many pairs remain?
- A: 24
- B: 25
- C: 10
- D: 20
Question 24 of 35

How many sides do 4 pentagons and 4 quadrilaterals have altogether?
- A: 36
- B: 9
- C: 20
- D: 24
Question 25 of 35
Six lamingtons and one 12 dollar fruit platter came to 30 dollars at the stall. How much does a lamington cost?
- A: 15
- B: 18
- C: 3
- D: 5
Question 26 of 35

The four columns are 3, 5, 6, 8 squares tall. One square means 2 votes. How many votes altogether?
- A: 22
- B: 44
- C: 16
- D: 46
Question 27 of 35
Seven classes each received 15 books and 9 books remained on the library trolley. How many books were on it at the start?
- A: 96
- B: 31
- C: 105
- D: 114
Question 28 of 35
A ribbon is 2 metres long. 5 bows each use 29 cm. How many centimetres of ribbon are left?
- A: 55
- B: 84
- C: 171
- D: 145
Question 29 of 35
What is 126 divided by 6, then divided by 3?
- A: 7
- B: 8
- C: 18
- D: 21
Question 30 of 35
10 cartons of milk each hold 750 mL. How many whole litres of milk is that?
- A: 8
- B: 7500
- C: 7
- D: 10
Question 31 of 35
Priya counts 120 students. ⁵⁄₈ of them go to sport. How many do not go?
- A: 15
- B: 45
- C: 75
- D: 105
Question 32 of 35
Up to 60, how many multiples of 5 cannot be split into two equal whole numbers?
- A: 7
- B: 6
- C: 12
- D: 5
Question 33 of 35
Beads thread on in a repeat of 8, with 3 of them wooden. A necklace uses 56 beads. How many are wooden?
- A: 24
- B: 7
- C: 21
- D: 35
Question 34 of 35
Round 9590 to the nearest thousand.
- A: 9600
- B: 10000
- C: 9000
- D: 9590
Question 35 of 35
Bunting is pinned to a 36 m wire every 3 m, and a pin holds each end too. Work out the number of pins.
- A: 11
- B: 14
- C: 13
- D: 12

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.

1	2	3	4	5	6	7	8	9	10
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