oc mathematical reasoning paper 2 v2

OC Placement Test

Practice Paper 2

OC Mathematical Reasoning Paper 2

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.

Emily has a basket of 4 counters numbered from 1 to 4.

Without looking, she takes one counter out of the bag at random.

Which of the following statements below is/are correct?

1 Emily’s chances of taking out an even or odd numbered counter is equal. 2Emily’s chances of taking out a counter greater than 2 are equal to her chances oftaking out a counter less than 3.3 Emily would have to reach into the bag a minimum of 2 times or a maximumof 4 times to guarantee that she got all even counters.

A statement 2 only

B statement 3 only

C statements 1 and 2 only

D statements 1 and 3 only

E statements 1, 2 and 3

2.

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

Juliet has a regular diamond.

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

these can she make with one cut?

X Two trianglesY Two quadrilateralsZ A triangle and a pentagon

A Y only

B Z only

C X and Z only

D Y and Z only

E X, Y and Z

3.

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 $4 each, but the price of apizza has been smudged off.

If I had $4 left afterwards, how much did each pizza cost?

a) $18b) $17c) $16d) $15e) $14


4.

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 5cm more than the perimeter of his

starting rectangle. Which of the positions are possible?

a) P and Sb) Q and Rc) S and Qd) Se) None of the above

5.


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

Jimmy then makes TWO folds in the paper, without moving the paper in any other way.Which of the following shapes could not be the result?

6.

▲ represents a number.

18 + ▲ = 36 + 12What number is ▲ ?A 48B 10C 30D 12


E 6

7.

What number is three hundreds more than 64978?

A 64 278

B 64 578

C 65 278

D 70 978

E 65 478

8.

Dr Torres got on a ferry at ten past 6 in the morning

She got off the ferry at 9:20 am the same day.

How long was she on the train?

A 3 hours 10 minutes

B 27 hours 10 minutes

C 3 hours 50 minutes

D 2 hours 45 minutes

E 20 hours 50 minutes


9.

The shape below is made up of 9 small rectangles, all the same size.

How many more small rectangles need to be shaded so thatthree-quarters of the shape is shaded?A 2B 3C 4D 5E 6

10.

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

a. 31b. 89c. 53d. 110


11.

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

She follows these instructions, in order:1. Walk 10 metres south.2. Walk 5 metres west.3. Walk 10 metres north.4. Walk 20 metres east.After this, how far is Jenny from her starting position?

a. 10 metresb. 15 metresc. 20 metresd. 50 metrese. 100 metres

12.


A wire of length 50 cm is made into a rectangle.

Two sides of the rectangle are 10 cm long.

All of the wire is used.

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

A 5 cm

B 10 cm

C 15 cm

D 20 cm

E 25 cm

13.

Two containers of water are shown below.

Container X Container Y

Water is poured from X into Y until Y contains 40 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

14.

Daisy makes a necklace by putting objects on a string.She makes the necklace by repeating this step:

● Add 3 pearls and then 3 diamonds onto the string.If the finished necklace has 8 diamonds, how many pearls does it have?

a. 3b. 4c. 8d. 9e. 10

15.

In the five circles below, Esther is going to write the numbers 2, 3, 4, 5, 6 once each.The numbers in each line must add to 12. What number must she write in the middlecircle?


a. 2b. 3c. 4d. 5e. 6

16.

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 12


D 9

E 8

17.

Woof dog food is sold in two different sizes. A box

containing 500g costs $2

A box containing 2.5 kg costs $9


Joe needs to buy exactly 5kg of dog food.

What is the lowest total price he can pay? A $9

B $10

C $12

D $18

E $22

18.

In this diagram, 4 × 2 = 8

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


What is the value of Y × Z ?a. 23b. 23c. 23d. 52e. 78

19.

Andrew glued 6 identical cubes together to make the following

staircase figure:


Andrew 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), Andrew placed glue on just 1 face.

When Andrew made the staircase figure, how many faces of all the cubes used didAdam not put glue on?

a. 22b. 10c. 13d. 14e. 20

20.

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’s stand in the two weeks after opening:


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

achieve this?

A 63

B 47

C 11

D 9

E 71


21.

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

A X onlyB Y onlyC Z onlyD X and YE Y and Z

22.

Here are four shapes, X, Y and Z.


Which of these shapes has/have ½ shaded?

A Shape X only

B Shape X and Y only

C All of themD Shape Z only

E Shapes Y and Z only

23.

Arnold keeps track of the family budget using graphs. He has $1000each month to spend on the weekly shopping. Here is his grocery graphso far for the month of February.

What is the maximum that his family can spend on groceriesduring the last week of February so that they do not go over thebudget?


A 220

B 265

C 280

D 210

E 250

24.

Joan has four cards. Each card has a different number on it.

She uses all four cards to make different four-digit numbers.

What is the difference between the largest four-digit number Joan can make, and

the smallest four-digit number Joan can make?

A 6993

B 6663

C 6363

D 9663

E 9363


25.

Sarah thinks of a two digit number.

She increases it by 7 then divides it by 5.

Her answer has one digit.

She then doubles it to get 10.

What was her original number?

A 4B 10

C 13

D 16

E 18

26.

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

The sections shaded black are then cut out and thrown away.


The paper is then unfolded completely.

What is the area of the paper that is left?A. 15cmᒾB. 7.5cmᒾC. 34cmᒾD. 45cmᒾE. 25cmᒾ

27.

A pen costs $1.40 and a pencil costs 80 cents.

Jane buys a pen and a pencil and pays with a $5 note.The shop assistant has no $1 or $2 coins.Jane’s change contains exactly four 50 cent coins.

What is the greatest number of 20 cent coins that Jane could have inher change?

A. 2B. 3C. 4D. 7E. 8


28.

15th February 2010 was a Monday. Which day of the week was March 9th 2010?(note: 2010 was not a leap year)

A. TuesdayB. WednesdayC. ThursdayD. FridayE. Saturday

29.

A group of students were asked to record how many books they readover a week. The graph shows the results:


Mabel reads the graph and makes 3 claims:● More than 20 students read at least 2 books over the week● The number of students who read 1 book in the week was exactly 3

times as many as the students who read 0 books● There were 10 less students who read 3 books than students who read 2 books

Using the graph, which of Mabel’s claims is/are correct?A. Claim 1 onlyB. Claim 2 onlyC. Claim 3 onlyD. Claim 1 and 2E. Claim 2 and 3

30.

The sum of Vincent and his daughter’s age is 60. Vincent is 5 times as old as hisdaughter. How old is Vincent?

a) 40b) 50c) 35d) 55e) 25

31.

To run 10km, it takes Sarah 60 minutes.To walk 5km, it takes her 60 minutes.

This morning, Sarah walked 5km and ran 5km. How long did it take her intotal? A. 120 minutesB. 90 minutes


C. 100 minutesD. 75 minutesE. 95 minutes

32.

This diagram shows the location of clues in a treasure hunt.On this diagram, north is to the right as shown.

Sarah stands at F1. Her friend Suzie said that the prize is hidden under the cluenorth-west to where Sarah is standing. The clue is more than 10m away from


where Sarah is standing.

What is the grid reference for the clue with the prize hidden under it?A. C1B. E4C. G2D. H3E. G8

33.

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

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

What are the grid references of the three squares Carly needs toshade? A. G5, B2, A5


B. G5, D1, D2C. C3, E5, B4D. E5, B4, G3E. E2, G3, G5

34.Ekaterina builds an object from connecting cubes. She counts 30 faces of thesmall cubes.

It falls onto the floor and splits into two identical pieces. Ekaterinapicks up each piece and looks at it from every side.

How many faces can she see now?A 20B 30C 40D 50E 60

35.


Juliet has a plate of 7 pieces of toast numbered from 1 to 7.

Without looking, she eats one piece from the plate at random.Which of the following statements below is/are correct?

1 Juliet is equally likely to eat an odd or even numbered piece of toast.

2 Juliet is more likely to eat a piece of toast that's odd numbered than a pieceof toast that's even.3 Juliet is equally likely to eat a piece of toast number 6 and piece of toastnumber 7.

A statement 2 only

B statement 3 only

C statements 1, 2 and 3

D statements 2 and 3 only

E statements 1 and 3 only


AnswersOC Mathematical Reasoning - Practice Paper 2

Question#

CorrectAnswer

Question#

CorrectAnswer

1 E 20 --

2 C 21 B

3 D 22 C

4 E 23 D

5 A 24 A

6 E 25 E

7 C 26 C

8 A 27 C

9 A 28 A

10 D 29 E

11 A 30 B

12 C 31 B

13 A 32 D

14 D 33 D

15 C 34 C

16 A 35 D

17 D

18 E

19 A

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oc mathematical reasoning paper 2 v2

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