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YEAR 9 EXAM

MATHEMATICS

CALCULATOR ASSUMED SECTION

INSTRUCTIONS:

There are 9 questions in this section of the test. Answer ALL questions.

Show all working. Solutions with insufficient work may not obtain full marks.

Where necessary, leave answers correct to two (2) decimal places.

NAME: _____________________________________________

SCORE: / 45

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Question 1 [2, 2, 2 = 6 marks]

Taxable income Tax on this income

$0 - $6000 Nil

$6001 - $37 000 15c for each $1 over $6000

$37 001 - $80 000 $4650 plus 30c for each $1 over $37 000

$80 001 - $180 000 $17 550 plus 37c for each $1 over $80 000

$180 001 and over $54 550 plus 45c for each $1 over $180 000

Jeslyn has two permanent part-time jobs. In her first job, she works 15 hours a week at an hourly

rate of $38.43 per hour. In her second job, she works 10 hours a week at an hourly rate of $42.79 an

hour. For her first job, Jeslyn bought some protective gear that costs $168. Her union fees cost her

$102 a year. Assume there are no holidays and she works 52 weeks a year.

a) Calculate Jeslyns annual gross income.

b) Calculate Jeslyns annual taxable income.

c) Calculate the tax payable on Jeslyns taxable income.

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Question 2 [2, 2, 2 = 6 marks]

Alicia borrows $25 500 to purchase a car. She will pay 8.2% simple interest over a period of 5

years.

a) How much interest is payable?

b) How much will Alicia pay back altogether?

c) If Alicia makes fortnightly repayments, how much will these repayments need to be, to ensure

she pays off both the principal and the interest in 5 years. (Assume 52 weeks in a year)

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Question 3 [3, 2, 2 = 7 marks]

The figure shows is an isosceles triangle with sides 12 cm, 12 cm and 7 cm.

a) Find the height of the triangle, h

b) Hence, find the area of the area

c) Hence, or otherwise, find the total surface area of the solid below

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Question 4 [2, 2 = 4 marks]

Given that the formula forv is

v = u + at

a) Find v ifu = 13, a = 11 and t = 9

b) Rearrange the formula to make tthe subject of formula

Question 5 [3 marks]

A cube has volume of 1728 cm3. Find its surface area.

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Question 6 [3 marks]

A cylindrical tank has a capacity of 3000 L. If it has a height of 1.2 m find its base radius.

Question 7 [3 marks]

A line segment has midpoint (6, 10). Given that an endpoint of the line segment has coordinate

(-3, 5) find the coordinate of the other endpoint.

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Question 8 [3, 3 = 6 marks]

The figure on the right shows a sector formed by two concentric circles.

The angle at the centre is 40.

a) Find the perimeter of the figure

b) Find the area of the shaded region

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Question 9 [4, 3 = 7 marks]

a) William is 4 times as old as Ben. 12 years ago, William was 7 times as old as Ben. How old is

Ben now?

b) A pen costsp dollars. An eraser costs $1.20 less than a pen. If Alex pays for 5 pens and two

erasers with a $20 note, he will receive $4.20 in change. Find the cost of a pen.

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YEAR 9 EXAM

MATHEMATICS

NON-CALCULATOR SECTION

INSTRUCTIONS:

There are 11 questions in this section of the test. Answer ALL questions.

Show all working. Solutions with insufficient work may not obtain full marks.

Where necessary, leave answers in surd or fractional form.

NAME: _____________________________________________

SCORE: / 55

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Question 1 [2, 3, 2, 3 = 10 marks]

a) Find 30% of $250

b) Increase $720 by 25%

c) The price of fuel today is 125 cents per litrelitre. If Bart receives a discount of 5 cents per litre,

calculate his saving as a percentage of the original price.

d) A restaurant has a policy of selling their menu items with a mark up on the cost price of 150%.

Calculate the price they would charge for a dish that has a cost price of $12.

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Question 2 [2, 2 = 4 marks]

Find the perimeter of these shapes:

a)

b)

(leave your answer in terms of)

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Question 3 [3, 2 = 5 marks]

a) Find the area of the following shape

b) Hence, find the volume of the solid below

4

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Question 4 [3, 3 = 6 marks]

The diagram below shows a line segment joining the points A (-3, 2) and B (9, 7) on the Cartesian

plane.

a) Calculate, and label on the diagram, the midpoint of AB

b) Find the length of the line segment AB

5

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Question 5 [1, 1, 1 = 3 marks]

Simplify each of the following:

a) a4 a

5

b) (m3n

4)3

c)

p5q

pq4

Question 6 [1, 1 = 2 marks]

Round the following numbers to 3 significant figures:

a) 3 705 000

b) 0.0212121

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Question 7 [2, 2, 3 = 7 marks]

Expand and simplify:

a) 3(x1) 2 5 x( )

b) x+ 5( ) x+ 8( )

c) (3c d)2

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Question 8 [ 2, 3 = 5 marks]

Solve the following linear equations:

a) 2x+1= 5

b)

3x+ 2

4=4 5x

3

Question 9 [1, 2 = 3 marks]

Factorise completely:

a) 12pq 18pq2

b) 20ac 6bd+ 24ad 5bc

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Question 10 [3, 3 = 6 marks]

Find, leaving your answer in exact (surd) form if necessary, the lengths of the missing sides.

a)

b)

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Question 11 [3, 1 = 4 marks]

a) State, with reason, weather the triangle ABC with the following lengths is a right-angled

triangle.

AB = 1.5 cm

BC = 2 cm

AC = 2.5 cm

b) Using the fact that (5.6, 9, 10.6) is a Pythagorean triple, write down another set of numbers

which will also form a Pythagorean triple.

10