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Mathematical Reasoning Entrance Examination. MATHEMATICS. PRACTICE TEST . PRACTICE QUESTIONS. Here are some practice examples to show you ...

MATHEMATICS PRACTICE TEST PRACTICE QUESTIONS Here are some practice examples to show you what the questions on the real test are like.

Practice Example 1

5+2= A: 5

B: 6

C: 7

D: 8

E: None of these

C: 406

D: 4060

E: None of these

Practice Example 2 Which is the largest number?

A: 403

B: 4600

Practice Example 3

4879 What value does the circled number in the number above represent?

A: 4879

B: 700

C: 70

D: 7

E: None of these

You will have 30 minutes to do as many questions as you can.

NO CALCULATORS PERMITTED FOR THIS TEST.

PLEASE DO NOT TURN THIS PAGE UNTIL YOU ARE ASKED TO DO SO. Mathematics Practice Test

Page 1

Question 1 − 10 + −3 − −4 + 5

A: 2

B: – 12

C: – 4

D: 16

E: None of these

B: 12

C: – 12

D: – 2

E: None of these

Question 2 − 96 ÷ −6 ÷ 8 =

A: 2 Question 3

Jo bought a used car for $6000 and paid 15% deposit. How much did he still have to pay? A: $900

C: $4500

D: $5100

E: None of these

B: – 8

C: – 16

D: – 6

E: None of these

B: $480

C: $48

D: $58

E: None of these

C: 75000mm

D: 15.5m

E: 0.1km

B: $5000

Question 4 5 × −2 − (8 − 12) + 16 ÷ −8 =

A: 6 Question 5 What is 8% of $600?

A: $580 Question 6

Which is the longest distance?

A: 3500cm

B: 65.5m

Mathematics Practice Test

Page 2

Question 7 The perimeter of the shape is

12cm

10cm

25cm

A: 47cm

B: 72cm

C: 69cm

D: 94cm

E: Not enough information to find perimeter

Question 8 If the length of the shorter arc AB is 22cm and C is the centre of the circle then the circumference of the circle is:

A: 990cm

B: 67cm

C: 176cm

D: 88cm

E: None of these

Question 9 If 2 fligs make a flog and 3 flogs make a flug, how many fligs in 12 flugs?

A: 72

B: 17

C: 36

D: 34

Mathematics Practice Test

E: None of these

Page 3

Question 10 If 2 1/3 : 4 1/3 then

A: 12

7:

=

C: 8 2/3

B: 13

D: 6 1/3

E: None of these

Question 11 Concrete is made by mixing screenings cement and sand in the ratio 3:1:15. How much sand would be needed to make 125 tonnes of concrete?

A: 27 tonnes

B: 33.75 tonnes

C: 45 tonnes

D: 75 tonnes

E: None of these

Question 12 a°

127°

a° =

87°

A: 53

B: 40

C: 93

D: 146

E: None of these

Question 13 x° = x°

56°

A: 124

B: 304

C: 54

D: 66

Mathematics Practice Test

E: None of these

Page 4

Use the following graph to answer questions 14 and 15

10

The graph shows the number of hours a year 8 group spent doing homework for one week.

9

Frequency

8 7 6 5 4 3 2 1 0 3

4

5

6

7

8

9

10

11

12

Hours of Study

Question 14 How many students studied for more than 8 hours in the week?

A: 22

B: 29

C: 42

D: 50

E: None of these

D: 12

E: None of these

Question 15 How many students studied for 6 hours or less per week?

A: 9

B: 18

C: 15

Question 16 Two six sided dice are thrown together. What is the probability that a total of 10 is thrown?

A: 1/6

B: 1/12

C: 1/2

D: 5/6

B: 2 3

C: − 2 3

D: −

E: None of these

Question 17 The gradient of the line is

A: 3 2

Mathematics Practice Test

3 2

E: None of these Page 5

Question 18

y

The y intercept of the graph could only be:

x

A: (4,0)

C: (− 4,0)

B: (0,−3)

D: (− 3,0)

E: (0,3)

Question 19 Which inequation shows the following statement?

x is 6 or less and more than – 5 A: – 5 < x ≤ 6

B: – 5 > x ≤ 6

C: – 5 ≤ x ≤ 6

D: – 5 < x < 6

E: – 5 ≤ x < 6

D: 7 + 12 x

E: None of these

Question 20 Expand and simplify

– 6 (2x – 3) – 11 A: − 12 x − 29

B: 7 − 12 x

C: 12 x − 7

Mathematics Practice Test

Page 6

Question 21 Which option would make this solid?

A:

B:

C:

D:

E: None of the nets would make the solid

Question 22 The diagram shows a small rectangular field. If Linda runs from A to B to D to C to A, how far does she run?

40m

C

B

30m

D

A: 120m

A

B: 160m

C: 140m

D: 150m

Mathematics Practice Test

E: None of these Page 7

Question 23 Simplify the surd 3 56 completely A: 12 14

B: 5 14

C: 6 14

D: 6 28

E: None of these

Question 24 The length of x equals

A: 6cm

5cm

B:

6cm

C: 5 2cm 4cm

x

D: 2 5cm E: None of these 3cm

Question 25 The rectangle box has dimensions as shown. What is the length AG ? B

C

A: 2 26

F

B: 4 6 G

C: 2 3

D

A

6cm

D: 16 2cm E

8cm

E: None of these

H

Question 26 Sam bought a car valued at $7700. One year later the car’s value had decreased by 2/7. What is the new value of the car?

A: $2200

B: $5500

C: $9900

D: $4400

Mathematics Practice Test

E: None of these

Page 8

Question 27 If Density = Mass ÷ Volume, what is the Mass of the solid in the diagram if its Density is 1.2gm / cm3?

A: 50gm 6cm

B: 60gm C: 72gm D: 38.4gm

5cm 2cm

E: None of these

Question 28 What is the speed in m/s of a car that travels 30km in 20 minutes?

A: 1500 m/s

B: 150 m/s

C: 90 m/s

D: 540 m/s

E: None of these

Question 29 If R =

A:

(S + T ) P then T equals 3

3R − S P

B:

PR −S 3

C:

3R +S P

D:

3R + S P

E:

3R −S P

Question 30 Solve the inequation for x 5(9 − x) + 1 < 11 3 A: x < 3

B: x > 3

D: x > 14/5

C: x > – 3

E: None of these

Question 31 Solve for x 4x − 3 2 x − 3 − = −2 5 2

A: x = 1 11 18

B: x = 5 1

2

C: x = −5 1

2

D: x = 14 1

Mathematics Practice Test

2

E: x = −14 1

2

Page 9

Question 32 Which equation could only be the equation of the graph?

A: y = 3 x + 2

y

B: y = −3 x − 2

x

C: y = 3 x − 2 D: y = −3 + 2 E: y = − x − 2

Question 33 Which set of coordinates lie outside the shaded area?

A: (0,0) B: (− 1,−6 ) C: (1,−50 ) D: (1,1) E: (4,1) Question 34 The equation of this graph is:

A: y = − B: y =

6x +4 5

5x +4 6

C: y = 5 x + 4 D: y = −

E: y =

5x +4 6

− 5x −4 6

Mathematics Practice Test

Page 10

Question 35 The coordinates of the point of intersection for the two graphs could only be: y

A: (− 1,2) B: (− 1,−2)

x

C: (1,2) D: (1,−2) E: (2,−1)

Question 36 3 − (− 3) = A: - 9

B: 27

C: 9

D: -27

E: None of these

2y B: x

2 xy 5 C: xy

D: 4 xy 2

E: None of these

B: 36xy3

C: 2y2

D: 6xy2

E: None of these

Question 37 10 x 2 8 y 3 × = 4y 5x 2

A: 4 x y Question 38 (3° y )2 × 2(xy )° A: 18y2 Question 39

3 x −2 y 2 = 6 y −1 x 3 A:

y3 2x 5

B:

y 2x

C:

y 3x

C:

( 32 )

3y x5

D:

2 y3 x

E

Question 40 Which is not the same as 323 / 5 ?

(

A: 321 / 5

)

3

( )

B: 323

1/ 5

5

3

(

D: 321 / 3

Mathematics Practice Test

)

5

E:

5

32 3

Page 11

Use the Venn diagram to answer questions 41, 42 and 43

S

F

7

5

The diagram shows a class of music students and instruments they learn. 10

S = Saxophone F = Flute 6

Question 41 What is the total number of students in the class?

A: 33

B: 22

C: 17

D: 23

E: 28

D: 10

E: None of these

D: 15

E: None of these

Question 42 How many students learnt neither saxophone nor flute?

A: 5

B: 6

C: 7

Question 43 How many students learnt just the saxophone or the flute?

A: 12

B: 22

C: 17

Question 44

Frequency

Which is the best cumulative frequency graph for the histogram?

Score

Question 45 Jack’s Dad invested some money and for every $12 he invested he got a total of $15 back. If Jack’s Dad invested $300, how much in total did he get back?

A: $225

B: $525

C: $480

D: $375

Mathematics Practice Test

E: None of these Page 12

Question 46 Expand the brackets and simplify

(2

5− 2

)

2

A: 4 5 + 2 2

B: 12 − 4 10

C: 8 − 4 10

D: 2 10 − 2

E: None of these

Question 47 Rationalise and simplify

A:

4 5 3

B: 3 6

2

C:

D:

6

6 3

E: None of these

3 4

E: None of these

Question 48 If x = 1

y=2

2

3

and

z=3

4

evaluate

x÷ y+ z

A: 1

1 2

B:

3 7

C: 1

1 12

D:

Question 49 Expand and simplify

(3a − 5b )(3a + 5b) A: 9a − 25b

B: 9a + 25b

C: 9a 2 + 25b 2

D: 9a 2 − 25b 2

E: None of these

B: 3(a − 3)(a + 2)

C: 3(a − 3)(a − 2)

D: 3(a + 3)(a − 2)

E: None of these

Question 50 Factorise and simplify 3a 2 + 3a − 18

A: (a + 3)(a − 2) Question 51 x2 − 9 x + 3 Simplify ÷ 4 x − 12 2

A:

x+3 4

B:

1 2

C:

x+3 2( x − 3)

D:

Mathematics Practice Test

2 1

E: None of these

Page 13

Question 52 The correct ratio to find x is:

15 72°

x 6

A: 6 Cos 72°

B: 6 Tan 72°

C: 15 Sin 18°

D: 15 Sin 72°

E: 15 Cos 18°

Question 53 The turning point of the graph could only be:

A: (− 3,3)

B: (4,−2)

C: (3,4)

D: (− 2,3)

E: (− 3,−2)

Question 54 A number x is subtracted from two times its square and the result is 45. An equation to find the value of x would be:

A: x 2 − 2 x = 45

B: 2 x − x 2 = 45

C: 2 x 2 − x = 45

D: 2 x 2 − 2 x = 45

E: x − 2 x 2 = 45

Question 55 Find the points of intersection of the graphs of y = x2 and y = 3x – 2.

A: (1,1)(1,4)

B: (2,4 )(1,1)

C: (1,−1)(2,4)

D: (− 2,4)(1,1)

Mathematics Practice Test

E: None of these

Page 14

Use the graph to answer questions 56, 57 & 58 The graph shows the price paid and weight for bags of sugar bought at different shops.

Question 56 Which shop gave the worst value for money?

A: Shop z

B: Shop y

C: Shop x

D: Shop w

E: Shop v

D: Shops v & w

E: Shops x & y

Question 57 Which two shops charged the same price per kilogram?

A: Shops z & x

B: Shops z & v

C: Shops y & z

Question 58 At which shop would you get three times the amount of sugar for the same price as shop z?

A: Shop v

B: Shop x

C: Shop w

D: Shop y

Mathematics Practice Test

E: None of these

Page 15

Question 59

x= x+5 x+3

x +1

B: 5

A: 4

C: 6

D: 3

E: None of these

Question 60 Factorise ab + b 2 − ac − bc

A: (b − c )(a − c )

B: (b + a )(b + c )

C: (b − c )(a + b )

D: (b + c )(a − b )

E: (b − c )(a + c )

WELL DONE. THIS IS THE END OF THE TEST. IF YOU STILL HAVE TIME LEFT, PLEASE CHECK OVER YOUR ANSWERS.

Mathematics Practice Test

Page 16

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