Teacher Mr Nicolaou □ Mr Trapnell □

Mr van Geelen □ Mr Shimmen □Mr Rault □

First Name

Surname

2015

Year 10

MathematicsSemester 2

Exam

Reading time: 10 minutes Writing time: 90 minutes Total time: 100 minutes

QUESTION AND ANSWER BOOKStructure of book

SectionNumber ofquestions

Number ofquestions tobe answered

Marks

A 20 20 40B 16 16 108

Total /148

Directions to students

MaterialsStudents are permitted to bring pens, pencils, highlighters, calculators, erasers, sharpeners, rulers and study booklet.

The TaskPlease ensure that you write your name in the space provided on this book and that you have placed a tick next to the name of your teacher.All written responses should be in English.

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Section AMultiple choice questions.Choose the most correct answer for each question by filling in the appropriate box . If you wish to change your answer place a clear cross through the wrong box and fill in your corrected choice. Each question is worth 2 marks.

Question 1If cosine Ѳ = 0.2960 Then Ѳ = (to two decimal places).

A. 17.13˚

B. 72.70˚

C. 16.29˚

D. 72.78˚

E. 58.29˚

Question 2A surveyor is 12 km from the base of a mountain and measures the angle to the top as 15o What is the height (t) of the mountain?

A. 3.22 km

B. 0.02km

C. 11.59km

D. 3.10km

E. 21.21km

Question 33 x+2(4 y−x) is equal to

A. 5 x+8 y

B. 2 x+8 y

C. 4 x+4 y

D. 4 x+8 y

E. x+8 y

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X

Question 48 x+10 y factorised is

A. 8 x (10 y )

B. x (8+10 y )

C. 2 (4 x+5 y )

D. 2 xy ( 4+5 )

E. xy (8+10)

Question 5The gradient of the line joining the points (0,6) and (6,12) is

A. 1

B. 2

C. 3

D. 6

E. 12

Question 6The y-intercept of the equation y=3 x−5 is

A. 0

B. -3

C. 3

D. -5

E. 5

Question 7The gradient of the following straight-line graph is close to

A. 0

B. 0.1

C. 1

D. 1.5

E. 15

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Question 8When −2(3 g+4d ) is expanded you get

A. 14 gd

B. −6 g−8d

C. 6 g+4d

D. 6 g−8d

E. −6 g+8dQuestion 9A linear graph with a y-intercept of -3 and a gradient of -2 has the equation

A. y=3 x−2

B. y=−3x−2

C. y=−2x−3

D. y=2x−3

E. y=−2x+3

Question 10

Find the value of , correct to the nearest degree

A. 35°

B. 44°

C. 46°

D. 55°

E. 61°

Question 11

From the top deck of a lighthouse which is built on a vertical cliff, the angle of depression of a yacht is 35o.

The deck of the lighthouse is 240m above the level of the ocean.

How far is the yacht from the base of the cliff?

A. 138m

B. 168m

C. 196m

D. 343m

E. 840m

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Question 12The gradient of the line shown is :

A. -3

B. -1/3

C. 1

D. 1/3

E. 3

Question 13The points P (-2, -8) and Q (1, 1) lie on the line as shown.

The equation of the line is:

A. y=3 x−2B. y=−3x−2C. y=2x−3D. y=−2x−3E. y=3 x+2

Question 14Which of the following points lies on the line ¿3 x+2 ?

A. (0,0)

B. (3,2)

C. (2,3)

D. (5,1)

E. (1,5)

Question 15What is the gradient of a line which passes through the points (−4, 3) and (−2, 5)?

A. -4

B. -1/3

C. 1/3

D. ¼

E. 1

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Question 16Which of the following relations is represented by the graph shown here?

A. y=−2x+4

B. y=12x−2

C. y=−12x+2

D. y=2x−4

E. y=12x+2

Question 17

If the equation of a straight line is ¿−13x−2 , when x=9 what does y = ?

A. -5

B. -3

C. -1

D. 1

E. 25

Question 18The graph of y=5 x+4 is

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Question 19Expand and simplify (2b−b)(2b+b)

A. 3b

B. 3b2

C. 4 b2+2b2−2b2−b2

D. 4 b+2b−2b−b

E. ¿ is already∈its simplest form

Question 20Expand (2 x+3)(4 x−7)

A. 6 x+3−7 y

B. 6 x2−5 xy+7 x−4 y

C. 55 x2 y

D. 8 x2−14 xy+12 x−21 y

E. −4 x−14 xy−21 y

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Section BShort response questions.Answer each question in the space provided. You should show any working out.Marks for each question are indicated. There are 16 questions.

Question 1Calculate the value of x in these triangles. Write your answers to two decimal places.

a)

b)

6 marks

Question 2The navigation chart in Jessica’s boat shows that the height of the Rottnest Lighthouse is 42m above sea level. Using navigational instruments she measures the angle of elevation to the top of the lighthouse. The angle was 11°.How far was Jessica from the base of the lighthouse?Express your answer to the nearest metre.

3 marks

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Question 3Find the size of the angle x to the nearest degree.

3 marks

Question 4At lunch-time in summer the shadow of a 10m pole was 1.4m. What was the angle of elevation of the sun, correct to the nearest degree?

3 marks

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Question 5When Stephen was about to start High School the Student Council raised money to build a ramp to make it easier for him to get to class in his wheel chair. He can travel up a ramp without help when the angle of the ramp is less than 15˚.

Can Stephen travel up this ramp without help?Show calculations to support your answer.

4 marks

Question 6Simplify the following:

a) 3x – 9x + 4y – 2 =

b) m – 4n + 6m – 3n =

c) 6 + 9a – 4a2 – 3 – 2a2 – a =

d) 8mn + 4m2n +3mn2 – 8mn2 – 3m2n =

8 marks

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Question 7Expand the following:

a) 3( x – 8 ) =

b) 4( 5 – 2y + 3 ) =

c) – 2( 6h + 1 ) =

d) 2x( 4x + 5y ) =

e) 6( 3x + 2 ) – 8x =

f) – 7( 2x + 3 ) – 2( 10x + 11 ) =

g) ( 4x + 3 ) ( 2x – 5 ) =

14 marks

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Question 8Factorise the following:

a) 4x + 16 =

b) 14b – 2=

c) ab + 7b =

d) 2xy – 4x =

e) 4a2b - 2ab2 =

f) -4 - 2k =

g) -2 - 8h =

h) p2qr + pr2q2 - pqr + pqr2 =

16 marks

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Question 9Find the gradient of the line joining the points:

a) ( 3, 4 ) and ( 5, 14 )

b) (– 2, 4 ) and ( – 8, 1 )

4 marks

Question 10Find the gradient and the y-intercept.

a) y = 2x – 7

b) y = 3 – 4x

c) 6x + 2y = 9

9 marks

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Question 11Find the equation of the line that has gradient 4 and passes through the point ( -1, 8 ).

3 marks

Question 12Find the equation of the line that passes through the points ( -1, -10 ) and ( -5, 2 ).

4 marks

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Question 13Fill the table and plot the graph of y=x−2

x -3 -2 -1 0 1 2 3 4y

5 marks

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Question 14Sketch the graph of the following using the y-intercept gradient method:

a) y=2 x−6

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b) y=−3x+2

8 marks

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Question 15Cataglyphis is a tiny ant that lives in the desert on hot sand that often reaches 50° C.This little ant also has the ability to do incredible trigonometry in its head. For example, It can run out from its ant nest due North for 27 metres before turning due West and travelling for another 39 metres. In a second it can calculate how far and in which direction it needs to travel to get home in a straight line after which it runs home as fast as it can over the hot sand.

a) Draw a diagram of this little ant’s journey.

b) Calculate all of the angles to the nearest whole number in the triangle and mark them in your diagram above. Show your workings in the space below.

8 marks

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Question 16Scientists at NASA are testing a new space vehicle that will carry astronauts to Mars and land them on the surface. Experiments have been carried out and show how far the lander will sink into the Martian soil for every kg of extra mass carried. The results of the experiment are shown below.

x = extra mass (kg) 1 4 6Y = depth sunk (mm) 5.5 13 18

a) Draw a graph of the results and connect the points with a straight line.

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b) Use the y-intercept gradient method to find the equation of the line. Show your working out in the space below.

c) If the lander carried 300kg or extra mass, how deep into the soil would the lander sink? Give you answer in centimetres.

10 marks

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