oc mathematical reasoning paper 4

OC Placement Test

Practice Paper

OC Mathematical Reasoning Paper 4

Instructions:

There are 35 questions in this test. For each question there are 5 possible answers, A, B, C, Dor E. Choose one correct answer for each question.

You have 40 minutes to complete this test.

You will not lose marks for incorrect answers, so you should attempt all 35 questions.

Calculators and dictionaries are not allowed in the test.

This paper has been designed to replicate the questions that are asked in the real selective school test.

The purpose of taking a practice test is to familiarise yourself with the types of questions you will be asked. Themore comfortable you can be with the questions, the faster and more accurate you will be in the test!

Every question is unique - even if it looks similar to one you have already attempted there will be something uniqueabout it that requires you to think differently. If you start recognising question types this is a good thing! It will giveyou a huge advantage in the test.

This practice test remains the intellectual property of Alchemy Tuition and should only be used in conjunction withan accredited Alchemy Tutor.

For more details about the test, Alchemy Tuition or our OC preparation program please visit our website atwww.alchemytuition.com.au..

1.The diagram shows the location of sand castles on the beach.On this diagram, north is to the right as shown.

Mandy is standing at H5. There is a colourful flag on a sandcastle to the east of where sheis standing. The sandcastle is more than 10m away from where Mandy is standing.

What is the grid reference of the sandcastle with the colourful flag?A. H4B. H6C. H8D. H2E. F5

Alchemy Tuition Level 39, 1 Farrer Pl, Sydney NSW 2000 // [email protected] // 1300 914 329 // alchemytuition.com.au

2.To feed her 12 grandchildren for afternoon tea, Oma needs to make a total of 36cupcakes. To feed her 6 children, Oma needs to make a total of 36 cupcakes.

How many cupcakes does she need to make for 6 grandchildren and 12children? A. 88B. 50C. 72D. 90E. 96

3.A square piece of centimetre squared paper is folded as shown:

The unshaded sections (White) are then cut out and thrown away.


The paper is then unfolded completely.

What is the area of the paper that is left?A. 6cmᒾB. 12cmᒾC. 18cmᒾD. 21cmᒾE. 24cmᒾ

4.

A whiteboard marker costs $2.30 and a whiteboard eraser costs $3.40.

Mitchell buys two whiteboard markers and a whiteboard eraser and payswith a $20 note. The shop assistant has no $1 coins and no notes.Mitchell’s change contains exactly thirteen 50 cent coins.

What is the greatest number of $2 coins that Mitchell could have in his change?

A. 0B. 1C. 2D. 3E. 4

5.

27th January 1909 was a Wednesday. What day of the week was 1st January 1909?

A. WednesdayB. ThursdayC. FridayD. Saturday


E. Sunday

6.

A group of children were asked about their favourite sports. The graphshows the results:

Jordan reads the graph and makes 3 claims:● Soccer was chosen by more students than both tennis andnetball combined ● Tennis was chosen by half the number ofchildren that chose netball● 20 more children chose football compared to swimming

Using the information on the graph, which of Jordan’sclaims is/are correct? A. Claim 1 onlyB. Claim 2 onlyC. Claim 3 onlyD. Both claim 1 and 2E. None of the claims


7.Noor builds a 3D object from small connecting cubes. She rotates the

object and counts 34 small cube faces.

Noor carefully splits the object into two matching pieces.

She rotates each piece and counts all of the small cube faces on them.How many faces does she count?

A 34B 38C 40D 44E 48


8.The sum of Vincent and his daughter’s age is 60. Vincent is twice as old as hisdaughter. How old is Vincent’s daughter?

a) 10b) 20c) 30d) 25e) 5

9.

Ellis opens a lemonade stand. It is open Monday to Friday.

Below are two column graphs showing the sales of glasses of lemonade at Ellis’sstand in the two weeks after opening:


Ellis wants to sell more cups of lemonade in week 2 than in week 1. What is thesmallest number of cups of lemonade he needs to sell on Friday of week 2 to

achieve this?

A 63

B 47

C 11

D 9

E 71

10.Here are three squares, X, Y and Z. Which of the squares has/have 3/12 shaded?

A X onlyB Y only


C Z onlyD X and YE Y and Z

11.

Here are three rectangles, X, Y and Z.

Which of these rectangles has/have ½ shaded?

A Rectangles X and Y only

B Rectangle Z only.

C All of them


D Rectangles Y and Z only

E Rectangle X only

12.

Houda runs a market stall that sells seasonal fruit. To track her sales, Houda uses agraphing program. Below are her sales graphs for April and May.

How many bananas does Houda need to sell in May so that her total sales in Mayare better than her total April sales?


A 40

B 35

C 20

D 25

E 30

13.

Rob has three cards. Each card has a different number on it.

He uses all three cards to make different three-digit numbers.

What is the difference between the largest three-digit number Rob can make, and

the smallest three-digit number Rob can make?

A 494

B 512

C 594

D 495

E 479


14.

Mark thinks of a two digit number.

He decreases it by 4 and then multiplies it by 3.

His answer has two digits.

He adds the two digits to get 6.

What was his original number?

A 20

B 23

C 18

D 12

E 15

15.

Adam glued 12 identical cubes together to make the following

staircase figure:


Adam wanted to save glue, so when he had to stick 2 cubes together, he randomlypicked one face, of the two, to put the glue on. For example, to make a simple figure(on the right), Adam placed glue on just 1 face.

When Adam made the staircase figure, how many faces of all the cubes did Adam notput glue on?

a. 18b. 36c. 48d. 54e. 72

16.

In this diagram, 10 − 3 = 7

Here is a new diagram that works in the same way:


What is the value of Z −Y ?a. 13b. 26c. 36d. 56e. 69

17.

Woof dog food is sold in two different

A box containing 500g costs $1


A box containing 2.5 kg costs $4

Joe needs to buy exactly 5kg of dog food.

What is the lowest total price he can pay?

A $6B $7

C $8

D $9

E $10

18.

Here are three cards showing digits made of horizontal and vertical lines:


If you choose two different cards, what is the largest possible number of rightangles you can count in your digits?

A 11

B 10

C 13

D 14

E 15

19.

Stephanie has a box of 8 buttons numbered from 1 to 8.Without looking, she takes one counter out of the bag at random.

Which of the following statements below is/are correct?

1 Stephanie is more likely to take out an odd button than an even button. 2Stephanie is more likely to take out a button greater than 6 than a button lessthan 6.3 Stephanie is equally likely to take out button 2 or button 11.

A statements 1, 2 and 3 are false

B statement 1 only

C statements 2 only

D statements 1 and 3 only

E statements 1, 2 and 3


20.

I went grocery shopping with $50.After shopping, I checked my receipt, and it showed that I had bought 2 pizzas and4 chocolate bars. The price of the chocolate bars is $10 each, but the price of apizza has been smudged off.

If I had $2 left afterwards, how much did each pizza cost?

a) $6b) $5c) $4d) $3e) $2

21.

Jonny draws a rectangle of 4cm long and 3cm wide.NOTE: Each square below has side length 1cm.

He has a paper rectangle which is 2cm long and 1cm wide. He wants to place it in oneof the four positions shown, P, Q, R or S, to make a new shape.


Jonny wants the perimeter of the new shape to be 2cm more than the perimeter of his

starting rectangle. Which of the positions are possible?

a) P and Sb) Q and Rc) Pd) Se) S and R

22.

James starts with a piece of paper in the shape of a square, as shown.

James then makes four folds in the paper, without moving the paper in any other way.Which of the following shapes could be the result?


23.

Rosie has a regular dodecagon.

She makes one straight-line cut to divide the dodecagon into two shapes. Which of

these can she make with one cut?

X A quadrilateral and a decagonY A quadrilateral and an octagonZ 2 octagons

A X and Y only

B X and Z only

C X, Y and Z

D Y only

E Z only

24.

▲ represents a number.


42 + ▲ = 72 - 19What number is ▲ ?A 11B 6C 9D 30E 53

25.What number is seven tens more than 64978?

A 65 948B 64 878C 65 048D 69 048E 65 078

26.

April got on a bus at half past seven in the morning.

She got off the bus at 1:45 pm the same day.

How long was she on the train?

A 2 hours 15 minutes

B 3 hours 45 minutes

C 6 hours 15 minutes


D 2 hours 45 minutes

E 7 hours 15 minutes

27.

The shape below is made up of 8 small rectangles, all the same size.

How many more small rectangles need to be shaded so that half of the shape isshaded?A 2B 3C 4D 5E 6

28.

After rounding each number to the nearest 10, which number will have changed the

least? a. 63

b. 85c. 15d. 94e. 26


29.

Mohammed is standing at the X in the centre of the grid.

He follows these instructions, in order:1. Walk 3 metres east.2. Walk 1 metre west.3. Walk 2 metres south.4. Walk 2 metres west.

After this, how far is Mohammed from his starting position?

a. 1 metreb. 2 metresc. 3 metresd. 5 metrese. 20 metres


30.

In the five circles below, Lauren is going to write the numbers 0, 1, 2, 3, 4 once each.The numbers in each line must add to 7. What number must she write in the middle

circle?a. 0b. 1c. 2d. 3e. 4

31.

Simran makes a necklace by putting beads on a string.She makes the necklace by repeating this step:

● Add 3 sparkly beads and then 2 plain beads onto the string. If the finishednecklace has 5 plain beads, how many sparkly beads does it have?

a. 3b. 6c. 7d. 9e. 10


32.

Two containers of water are shown below.

Container X Container Y

Water is poured from X into Y until Y contains 60 mL altogether.

How much water is left in container X?

A 10 mL

B 15 mL

C 20 mL

D 25 mL

E 30 mL

33.

A wire of length 30 cm is made into a rectangle.

Two sides of the rectangle are 6 cm long.

All of the wire is used.

What is the length of one of the longer sides of the rectangle?

A 6 cm


B 9 cm

C 12 cm

D 15 cm

E 18 cm

34.

Dinesh is going to shade in three more squares in the diagram above.

He wants the dotted line to be a line of symmetry. When he has finished shading, thepatterns of squares on the left and right will be reflections of each other.

What are the grid references of the three squares Dinesh needs toshade? A. B2, C2, G2B. B5, D3, G4C. G4, F3, C2D. F3, B2, C2E. D1, G2, G4


35.This diagram shows the location of fish in a tropical reef.On this diagram, north is to the right as shown.

A marine biologist stands at D4. There is a fish with an injured fin south-east ofwhere they are standing. The fish is more than 20m away from where the marinebiologist is standing.

What is the grid reference of the fish with the injured fin?A. F7B. H9C. F3D. B2E. A1


AnswersOC Mathematical Reasoning - Practice Paper 4

Question#

CorrectAnswer

Question#

CorrectAnswer

1 D 20 C

2 D 21 A

3 E 22 B

4 C 23 C

5 C 24 A

6 A 25 C

7 D 26 C

8 B 27 B

9 -- 28 A

10 B 29 B

11 C 30 E

12 A/B 31 D

13 C 32 E

14 D 33 B

15 D 34 C

16 C 35 E

17 C

18 B

19 A

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