1. The stem and leaf plot below shows the age of people who enter through thegates of a concert in the first 5 seconds.

Key: 1    |    2  = 12 years old

 

a. How many people passed through the gates in the first 5 seconds?

b. What was the age of the youngest person?The youngest person was    years old.

c. What was the age of the oldest person?The oldest person was    years old.

d. What is the age difference between the youngest and oldest person?

2. State whether or not these lines are perpendicular.

L1: y= −x− 2L2: y= x+ 8

3. Expand the following perfect square:  7x+ 9y

4. Simplify the following, writing without negative indices.

3p q × 6p q

5.

YesA

NoB

( ) 2

2 −5 −2 −3

Find the surface area of the composite figure shown, correct to 2 decimal places.

6. Simplify the following: 21

−9x yz 

÷2x−3y 

7. The line −6x+ 2y+ 7= 0 is parallel to dx+ 4y+ 9= 0. 

a. What is the gradient of each line?

Gradient of −6x+ 2y+ 7= 0 :

m =  

Gradient of dx+ 4y+ 9= 0 :

m =  

b. Hence, solve for the value of d.

8. Factorise  49x + 112x+ 64

2 2

2

9.The Cancer Council surveyed some random people, asking them approximatelyhow many hours they spent in the sun during the previous summer. Thefrequency histogram for their responses is given.

a. How many people were surveyed?

b. What proportion of the responders spent 30 hours in the sun? Leave youranswer as a fraction.

c. What proportion of responders spent at least 50 hours in the sun? Leaveyour answer as a fraction.

d. What was the total number of hours spent in the sun by all responders?

e. On average, how many hours did each responder spend in the sun? Leaveyour answer to two decimal places if needed.

10. Simplify the following: 9

−8x 

×5

7y 

11. Simplify: 2 × 11

Hours in the sun

Frequency

0 10 20 30 40 50 60 70 80

5

10

15

√ √

12.

Consider the two given triangles.

Is the information given enough to deduce that the two triangles arecongruent?

13. Simplify the following algebraic surd:

ax

14. Consider the Points A −4, 8 and B −10, 17 .

a. Find the exact length of AB.

b. Given that M is the midpoint of AB, find the exact length of AM.

15. Simplify: 16 10 ÷ 2 5

16. By finding the value of each of its angles, prove that the angle sum of △ABC  is180°.

NoA

YesB

√ 2

( ) ( )

√ √

17.

Find the surface area of the figure shown,correct to 2 decimal places.

18. Express as an entire surd:

9 a

19. Given AC is parallel to DG, prove that x+ y+ z= 90.

20. Find the equation of a line that has a y-intercept of −9 and is perpendicular to the

line that goes through A −4, − 5  and B 1, 20 .

21. Express in scientific notation.

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√

( ) ( )

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