Year 10 & 10A Mathematics Semester 2 2017

Am I Exam Ready? Sheet 3

Name: _________________________________ 56 marks

Semester 2 examinations will consist of:

(1) 60 minute non CAS paper and (2) 90 minute CAS allowed paper

Topics to be tested:

• Exponential Relationships

• Geometry and Trigonometry

• Quadratic Relationships

PART I: Short Answer ( 30 marks)

Try and do this section in 30 minutes.

No calculators are to be used to complete this section.

1. Expand, giving your answer in simplest form.

(a)

4 2x x x (b) 2

2 3 1

(2 + 2 = 4 marks)

Simplify the following expressions, giving your answer with positive indices.

2. (i)

6

29

2p

pp (ii)

12

323 )2(

2

tk

kkt

k

(2 + 2 = 4 marks)

3. Evaluate 5−2 + 50 + 161

2 + 115

(2 marks)

4. Karina and Lucy evaluated 32−2

5 , but finished with different answers. Circle the correct answer, and circle where

the other student made her mistake.

Karina

32−25

= (25)−25

= 25×−25

= 2−2

= −22

= −4

Lucy

32−25

= (3215)−2

= 2−2

=1

22

=1

4

(2 marks)

5. Rationalise the denominator and write this expression in simplest form:

2√3 + 1

√6

(2 marks)

6. Solve the following equations:

(a) 2 16k k (b)

24 12 8 0x x

(2 +2 = 4 marks)

7. For the diagram below, find the magnitude of XDC , showing your working or giving reasons.

(2 marks)

A

B

C D

X

35 100

8. (a) Find the turning point, by completing the square, for the parabola with the rule:

2 8 1y x x

(b) Find the co-ordinates of the y-intercept of the parabola with the rule above.

(c) Show that the x-intercepts of the graph for the parabola are 𝑥 = −4 + √17 and 𝑥 = −4 − √17

(d) Sketch the graph on the axes below, showing the axial intercepts and turning point.

( 2 + 1 + 2 + 2 = 7 marks)

9. From the collection of rules and tables of values given below, there is only ONE set which is a match (one rule,

which has a matching table of values). Draw a line connecting the matching set.

x 0 1 2 3 4

y 2 8 32 128 512

x 0 1 2 3 4

y 4 8 16 32 64

x 0 1 2 3 4

y 4 5 4 5 8

x 0 1 2 3 4

y 4 2 0 -2 -4 (1 mark)

10. In the plan below, the entry gate of an adventure park is located at point G. A canoeing activity is located at point

C. The straight path GC is 40 metres long. The bearing of C from G is 060°T.

N

N

40 m

C canoeing

G entry gate

m

a) Write down the size of the angle that is marked m in the plan above.

b) What is the true bearing of the entry gate from the canoeing activity?

(1 + 1 = 2 marks)

End of Part 1

𝑦 = 2 × 4𝑥

𝑦 = (𝑥 − 2)2 + 4

𝑦 = 2 − 4𝑥

𝑦 = 4 × 2𝑥

PART 2 : MULTIPLE CHOICE AND EXTENDED RESPONSE QUESTIONS

(Calculator use permitted)

Try and do this section in 60 minutes.

MULTIPLE CHOICE QUESTIONS

1. When using the quadratic formula to solve the equation 2𝑥2 − 3𝑥 = −1, the values of a, b, c,

respectively are

A. 2, -3, -1 B. -3, 2, -1 C. 2, 3, 1

D. 2, -3, 1 E. 1, 2, 3

2. For the quadratic equation, 2𝑥2 − 4𝑥 + 5 = 0, the discriminant has the value:

A. 0 B. 6 C. −26

D. −56 E. −24

3. Determine the coordinates and the nature of the turning point of the graph with equation

2

3 4 5y x :

A. Maximum at (5,4)

B. Maximum at (-4,5)

C. Minimum at (4,5)

D. Maximum at (4,5)

E. Minimum at (-4,5)

4. In the diagram below AB is a diameter. If 25BAC , then the angle ADC equals:

A. 100

B. 110

C. 120

D. 115

E. 150

5. A true bearing of 195° is the same direction as:

A. N15°W B. N175°W C. N195°S

D. S15°W E. S15°E

6. The number of bacteria in Brian’s bowl of soup is increasing by 12% every hour. Right now, there are 1200

bacteria. The rule describing the number of bacteria, B, after n hours is given by:

A. 𝐵 = 1200 × 12𝑛 B. 𝐵 = 12 × 1200𝑛 C. 𝐵 = 1.12 × 1200−𝑛

D. 𝑛 = 1200 × 1.12𝐵 E. 𝐵 = 1200 × 1.12𝑛

7. Erin and Risha went on a hike, from point A to point B and then on to point C. Their journey is shown on the

scaled diagram below.

N

N

A

B

C

The best description of their journey

is:

A. 7 km on a bearing S40°W then

10 km on a bearing 105°T.

B. 7 km on a bearing S40°W then

10 km on a bearing S15°W.

C. 7 km on a bearing 220°T then

10 km on a bearing 15°T.

D. 7 km on a bearing S50°E then

10 km on a bearing S75°E.

E. 7 km on a bearing S50°E then

10 km on a bearing 105°T.

8. In scientific notation, the number 0.00000207 is written as:

A. 2.7× 106 B. 2.7× 10−6 C. 20.7× 10−7

D. 2.07× 106 E. 2.07× 10−6

A B

C

D

25

O

9. The total surface area of a square-based prism is 168 cm2. If the base length of the prism is 6cm what is the

height of the prism?

A. 3 cm B. 4 cm C 6 cm

D. 7 cm E. 16 cm

10. 12𝑎

𝑏 is not the same as which one of the following expressions?:

A. 121

𝑏 × 12𝑎 B. (12𝑎)1

𝑏 C. (121

𝑏)𝑎

D. (3 × 22)𝑎

𝑏 E. (1

12)−𝑎

𝑏

11. The following diagram should be used to answer this question.

y

x

1

P

Q

R

T

The rules for the relationships shown are:

(i) 𝑦 = 0.1𝑥 (ii) 𝑦 = 1𝑥

(iii) 𝑦 = 𝑥+1 (iv) 𝑦 = 10𝑥

Correctly matching graphs with rules gives:

A. P(i), Q(ii), R(iii), T(iv) B. T(i), P(ii), Q(iii), R(iv)

C. T(i), Q(ii), R(iii), P(iv) D. T(i), R(ii), Q(iii), P(iv)

E. There is no correct matching.

EXTENDED RESPONSE QUESTIONS ( 15 marks)

1. A student’s performance level p (as a percentage of her ability) is related to her anxiety level a by

the formula 27 29

50240 12

p a a , where 0a .

a) What will be student’s performance level if the anxiety level is 0?

b) Sketch the graph of p against a, showing all relevant points to 2 decimal points.

c) What level of anxiety gives the best level of performance?

(1+ 2+ 1 = 4 marks)

2. When the Fukushima Nuclear Power Plant was damaged by the earthquake and tsunami in March 2011, a large

number of radioactive Caesium 137 particles were released into the atmosphere. It is estimated that these nuclear

particles will decay according to the rule:

𝑷 = 𝟑𝟎𝟎 × 𝟎. 𝟗𝟕𝟕𝒏

where P is the Sieverts/hour of particles remaining after n years.

a) How many Sieverts/hour were released initially, at the time that the power plant was damaged?

b) To the nearest whole number, how many Sieverts/hour of nuclear particles will remain after 5 years?

c) After how many years will the nuclear particles reach their half-life? (when half of the particles will have

decayed) Give your answer to the nearest whole number.

(1 + 1 + 2 = 4 marks)

3. A spherical artwork is cleverly suspended from a ceiling hook with a single leather strap holding the ball,

encircling it as shown in the diagram below: The centre of the sphere, shown as a circle in the diagram, is

50 cm below the hook and the sphere has a radius of 14 cm. In the diagram, O marks the centre of the circle.

*Ensure that you draw all diagrams that you use.

a

. O

a) Show that the angle marked with an a measures 16.26°, to 2 decimal places.

b) Hence find (to the nearest centimetre) the full length of the leather strap, shown in bold.

(2 + 5 = 7 marks)