2020 SSC M Ext 1 Trial WME

2020 TRIAL HIGHER SCHOOL CERTIFICATE EXAMINATION.




Mathematics - Extension 1
General • Reading time – 10 minutes
Instructions
• Working time – 2 hours
• Write using black pen
• Approved calculators may be used
• A reference sheet is provided at the back of this paper
• In Questions in Section II, show relevant mathematical reasoning
and/or calculations

Total marks: Section I – 10 marks (pages 2 – 6)
70
• Attempt Questions 1 – 10
• Allow about 15 minutes for this section

Section II – 60 marks (pages 7 – 13)

• Attempt Questions 11 – 14
• Allow about 1 hour and 45 minutes for this section




-1-

,Section I

10 marks
Attempt Questions 1–10
Allow about 15 minutes for this section

Use the multiple-choice answer sheet for Questions 1 – 10.

1. There are eight questions in a multiple-choice test. Each question has four possible answers,
only one of which is correct.
What is the probability of answering exactly five questions correctly by chance alone, correct to
3 significant figures?

A. 0.0000153

B. 0.000412

C. 0.000977

D. 0.0231

4 −1
2. Find the vector projection of 𝑝̰ = ( ) onto 𝑞̰ = ( ).
−3 2

−2
A. ( )
4

2
B. ( )
−4

−2√5
C. ( )
4√5

2√5
D. ( )
−4√5




-2-

,3. Write the expression in the form 𝑅 sin (𝑥 + 𝛼).


A.



B.



C.



D.



4. Which of the following differential equations could be represented by the slope field diagram
below?




A.

B.

C.

D.




-3-

, 5. Given that and , find an expression for .



A.



B.


C.

D.




6. The polynomial has roots -1 and 2, one of which is a triple root.
Find the values of a and b.


A.

B.

C.

D.




7. Find the primitive function of 𝑦 = sin 𝑥 cos 3 𝑥 𝑑𝑥

1
A. 𝑦 = cos 4 𝑥 + 𝐶
4

1
B. 𝑦 = − 4 cos 4 𝑥 + 𝐶

1
C. 𝑦 = 8 sin2 𝑥 cos 4 𝑥 + 𝐶

1
D. 𝑦 = − 8 sin2 𝑥 cos 4 𝑥 + 𝐶




-4-