Year 9 Mathematics Examination SEMESTER 2 2018

Year 9 Mathematics Examination

SEMESTER 2 2018

QUESTION AND ANSWER BOOKLET

STUDENT NAME:

TEACHER:

DATE:

TIME ALLOWED FOR THIS PAPER: Reading time before commencing work: 10 minutes Working time for this paper: 105 minutes MATERIAL TO BE PROVIDED BY THE SUPERVISOR:

This Question/Answer Booklet MATERIAL TO BE PROVIDED BY THE CANDIDATE:

Pen/pencil for answering questions.

Erasing stationery.

Up to two scientific calculators.

Written notes on one unfolded A4 sized paper; can be double-sided.

TOTAL QUESTIONS: 37 TOTAL MARKS: 120 Section 1: Non calculator

45 minutes, 51 marks

Section 2: Calculator allowed

55 minutes, 69 marks

AT THE END OF THE EXAMINATION Attach any extra sheets used to this Question/Answer booklet.

Kinross College Year 9 Mathematics Exam, Semester 2 2018 1


IMPORTANT NOTE TO CANDIDATES No other items may be taken into the examination room. It is your responsibility to ensure that you do not have any unauthorised notes or other items of a non-personal nature in the examination room. If you have any unauthorised material with you, hand it to the supervisor BEFORE reading any further.

...Do not turn the page until asked to do so...



Section 1: Non calculator (Multiple choice- 10 marks)

1.

Helen invests $10 000 in a simple interest bank account that pays 4% annually. How much will be in her bank account after 5 years?

(A) $1200 (B) $12000 (C) $2000 (D) $10200

2.

Which statement is not correct?

(A) 𝐴𝐵2 = 𝐵𝐶2 + 𝐴𝐶2 (C) 𝐵𝐶2 = 𝐴𝐵2 − 𝐴𝐶2

(B) 𝐴𝐵2 = 𝐵𝐶2 − 𝐴𝐶2 (D) 𝐴𝐶2 = 𝐴𝐵2 − 𝐵𝐶2

3.

Circle the correct answer for the following statement. (2𝑥)4 in expanded form is:

(A) 2 × 𝑥 × 𝑥 × 𝑥 × 𝑥 (C) 2𝑥4 × 2𝑥4 × 2𝑥4 × 2𝑥4

(B) (2𝑥)4 × ( 2𝑥)4 × (2𝑥)4 × (2𝑥)4 (D) 2 × 2 × 2 × 2 × 𝑥 × 𝑥 × 𝑥 × 𝑥


4.

The expression ℎ8×ℎ

ℎ2 simplifies to:

(A) ℎ7 (B) 1

ℎ7 (C) 1

ℎ6 (D) 1

ℎ4

5.

Which ratio represents sin for angle (∠Y)

(A) 5

6.2 (B)

3.62

6.2 (C)

3.62

5 (D)

5

3.62

6.

What is the solution to the equation 3𝑚 + 1 = 4 − 𝑚?

(A) 𝑚 = 3

4 (A) 𝑚 =

5

4

(B) 𝑚 = 3

2 (D) 𝑚 =

5

2


7.

For the right-angled triangle shown, the value of 𝑥 is given by:

(A) (B)

(C) (D)

0.520.4

2

8.

2 380 000 000 when written in scientific notation is:

(A) 238 × 107

(B) 23.8 × 108

(C) 2.38 × 109

(D) 0.238 × 1010

9.

The gradient of the following line is:

(A) -4

3 (B)

4

3 (C)

3

4 (D) -

3

4

0.520.4

2

0.420.5

2

0.420.5

2


10.

A linear relation gives the following table of values:

The 𝑥 − and 𝑦 − intercepts of the graph of this linear relation are:

(A) (4,0) and (0, −2)

(B) (0, 2) and (−4, 0)

(C) (−4,0) and (0,2)

(D) (−2,0) and (0,4)

(E) (0, −2) and (4,0)

x −3 −2 −1 0 1 2 3

y −2 0 2 4 6 8 10


Section 1: Non calculator (Short answer - 41 marks)

1. [3 marks]

Mike put $1 000 into a simple interest account for a year. He did not take any money out or add any money to the account. At the end of the year he had $1 050 on the account. What was the annual percentage rate?

2. [3 marks]

Find the equation of the line that has a gradient of 2 and passes through the point (3, 5).

3. [3 marks]

Find the midpoint 𝑀 (𝑥, 𝑦) of the segment joining 𝐶(4, 2) and 𝐷(−3, 7).

4. [3 marks]

The midpoint of the line segment joining the points (−1, 8) and (5, 4) is:


5. [4 marks]

Write the following numbers in scientific notation:

a) 350 000

b) 0.097

6. [6 marks]

Examine the Cartesian plane below, together with the two functions

Complete the table:

Function 1

Function 2

𝑦 −intercept (𝑐) gradient (𝑚) rule (𝑦 = 𝑚𝑥 + 𝑐)

Function 1

Function 2


7. [2 marks]

Calculate the length of the side x in the figure below. (Please leave your answer in exact value or round to the nearest cm)

8. [8 marks]

Express each of the following in simplest form.

a) 𝑒 × 𝑒 × 𝑒

b) 4𝑚 × 5

c) 7𝑠𝑡 × 5𝑡𝑢

d) 3𝑑 × 5𝑑

e) 3𝑝𝑞 × (−2𝑝)

f) (−2𝑎) × (−3) × (−4𝑏)

g) 30𝑚 ÷ 5𝑚

h) 15 ÷ 5𝑎


9. [3 marks]

Place the angle q in these triangles to match the labels:

a) b) c)

10. [3,1,1,1 = 6 marks]

Two ice creams are randomly selected without replacement from a box containing one vanilla (V), two strawberry (S) and one chocolate (C) flavoured ice creams.

a) Draw a tree diagram to show each of the possible outcomes. b) Pr(chocolate and strawberry) c) Pr(no vanilla) d) Pr(two strawberry)


Section 2: Calculator allowed (Multiple choice- 5 marks)

1. [1 mark]

How long does Kim need to invest $5 000 at 4% p.a. simple interest in order to produce $100 interest?

(A) 2 months (B) 1 year (C) 3 months (D) 6 months

2. [1 mark]

What is the simple interest earned after six years when $450 is invested into an account that pays 3% per annum?

(A) $81.00 (C) $87.32

(B) $531.00 (D) $537.32

3. [1 mark]

The number 15-2 is equivalent to:

(A) 30-1 (C) -152

(B) 1

30 (D)

1

225


4. [1 mark]

Use your calculator to evaluate √11−1

√3 correct to 2 decimal places.

(A) 1.33 (C) 1.34

(B) 2.73 (D) 2.74

5. [1 mark]

The value of tan 29°, correct to four decimal places, is:

(A) 0.4848 (B) 0.8746 (C) 0.1307 (D) 0.5543 (E) 0.2591


Section 2: Calculator allowed (Short answer- 64 marks)

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

Janelle invests $8500 at 5.2% per annum for 3 years into a savings account offering a flat rate of simple

interest.

a) How much simple interest will she earn?

b) How much will the account be worth at the end of the 3 years?

c) How much extra interest would she earn if she keeps this new balance in the bank for a further 5

months?

2. [2,2,2 = 6 marks]

Callum is saving for a new mountain bike. He has $450 already and increases this amount by 25% with

the money he makes at a garage sale.

a) How much money does Callum have saved now?

b) If the mountain bike he is saving for costs $700, what percentage of the cost has he already saved?

Round your answer to the nearest percent.

c) Callum sees the same bike advertised for $623 at a different store. If the original cost is $700, what

is the percentage discount being offered here?


3. [1,1,2,3 = 7 marks]

Simplify the following:

a) 5b4 ´3b3 b) x 7

x

c) 4x5y3( )3

d) 8a3 ´ 6b8 ´ 5c4

2a2 ´10b4 ´ c2

4. [4 marks]

Use Pythagoras theorem to find the unknown lengths on the triangles below. Round your answers to 1 decimal place.

a) x

b)

8 cm

10 cm

𝑥

11 m 12.9 m

𝑥


5. [3 marks]

Holly is saving to buy her first car.

She created a table to keep track of her savings.

Number of months (𝒙) 2 5 8 10

Amount in Holly’s savings account (𝒚) 310 430 550 630

Complete the rule for the linear relationship between the amount of money in Holly’s savings account and the number of months of saving.

𝑦 = 𝑥 + 230

6. [2 marks]

The mobile phone call rate, in $C, is given by the equation: C = 0.42 + 0.88t, where t is the time of the

call in minutes. Find the length of a call for which the cost was $4.16.


7. [3,3,3 = 9 marks]

For the equation y = 3x – 6

a. Complete the table for the x values given.

b. Graph the equation of the line y = 3x – 6. Plot the information on the axes below.

c. What is the exact x value when y = 33? (use algebra!)


8. [3,1,1,2 = 7 marks]

A bag contains 4 red (R) and 2 white (W) marbles, and two marbles are selected without replacement.

a) Draw a tree diagram showing all outcomes and probabilities.

b) Find the probability of selecting:

i) a red marble and then a white marble (R, W)

ii) 2 red marbles

iii) exactly 1 red marble

9. [8 marks]

For each of the following, find the value of 𝑥 correct to two decimal places.

a) b)

c) d)


10. [4 marks]

Find the value of to the nearest degree. a) b)

11. [3 marks]

Mona can walk from home to school following the roads, or she can cut across Kinross IGA as shown in the diagram below.

Along the roads she walks 600 metres east and 800 metres south.

How many metres less does she walk by cutting across the Kinross IGA?


12. [3,2 = 5 marks]

A pilot flying a plane at an altitude of 11790 m sees a mountain peak 2900 m away from him in the horizontal direction. The direct distance between the plane and the peak is 3000 m.

a) Find the height of the mountain, correct to the nearest metre.

b) Find the pilot’s angle of elevation to the mountain peak to the nearest degree.

…End of Exam…

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Year 9 Mathematics Examination SEMESTER 2 2018