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2021 Task 2 with solutions
Maths advanced past paper
Subject
math advanced
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Student Number: _________________________Teacher: Ms Blair Mrs Karagiannis (Circle)
Year 11 Mathematics Advanced
31
st
May 2021
Task 2 - Topic Test
General Instructions
Write using black pen
Working Time 45 minutes
Structure of the Paper
Section I /5 Marks Allow about 5
minutes for this
section
Section II /40 Marks Allow about 40
minutes for this
section
Total / 45 Marks Weighting: 30 %
Special Instructions
NESA approved calculator may be used.
A reference sheet is provided.
Show all relevant mathematical reasoning and/or calculations.
Attempt all questions.
This examination must not be removed from the Examination Room.
2021 Year 11 Mathematics Advanced Task 2
Section I
5 marks
Attempt questions 1 - 5
Allow about 5 minutes for this section
Use the multiple-choice answer sheet for questions 1-
1. 2 x × 5 xis equal to:
(A) 7 x
(B) 72 x
(C) 10 x
(D) 102 x
2. What is the solution to the equation log (2 3 x − 5) = 2
(A) x = 1
(B)
11
2
x =
(C)
13
2
x =
(D) x = 7
3. What is the solution to the equation 2cos𝑥𝑥 = −√3 for 𝑥𝑥, where − 180 ° ≤ x≤ 180 .°
(A) x = −30 ,30 ° °
(B) x = −60 , 60 ° °
(C) x = −120 ,120 ° °
(D) x = −150 ,150 ° °
4. Which of the following is an expression for
1 sin 2
cot
x
x
−
?
(A) cos 2 x
(B) sin x cosx
(C) tan x
(D) tan x −sin x cosx
5.
log 3
y ax
= −is equivalent to:
(A) 3
####### y
x =a
(B) 3
####### y
x a
####### −
=
(C) x =a 3 y
(D) x =a− 3 y
2021 Year 11 Mathematics Advanced Task 2
Question 7 ( 4 marks) Marks
Simplify
(a) 2 𝑛𝑛 × 4 𝑛𝑛+ 1
8 𝑛𝑛
2
(b) 2 𝑚𝑚+ 3 + 2 𝑚𝑚
9
2
Question 8 (3 marks)
Solve for x: 9 3 6
####### x x
= + 3
2021 Year 11 Mathematics Advanced Task 2
Question 9 ( 2 marks)
Simplify
cos (90 )
cos (180 )
θ
θ
° −
° +
.
2
Question 10 (5 marks)
In a triangle ABC, AB = 12 cmand AC = 15 cm area of the triangle is
####### 2
80 cm.
(a) Find the size of ∠A. Give your answer(s) correct to the nearest minute. 3
(b) Given that ∠A is obtuse, find the length BC, correct to 1 decimal place. 2
Question 1 1 (2marks)
Find tan A if cosec
13
12
A = − and sec A > 0. 2
2021 Year 11 Mathematics Advanced Task 2
Question 14 (4 marks)
Prove the identity
cot𝑥𝑥
cosec𝑥𝑥 − 1
−
cos𝑥𝑥
1 + sin𝑥𝑥
= 2tan𝑥𝑥
4
2021 Year 11 Mathematics Advanced Task 2
Question 15 ( 6 marks) Marks
The diagram below shows a vertical cliff ( C) of height h metres.
A ship,A, is due east of the cliff and the captain determines the angle of elevation to the top
of the cliff to be 12 ̊. The captain of the second ship, B, determines that the ship is on a
bearing of 051 ̊T from the base of the cliff and the angle of elevation to the top of the cliff is
11 ̊. ShipsA andB are 100 metres apart.
(a) Show that ∠AOB = 39 .° 1
(b) Find expressions for OA and OB in terms of h. 2
(c) Find the height of the cliff. Give your answer correct to the nearest metre. 3
End of paper
2021 Year 11 Mathematics Advanced Task 2
Section II extra writing space
If you use this space, clearly indicate which question you are answering.
2021 Year 11 Mathematics Advanced Task 2
Section II extra writing space
If you use this space, clearly indicate which question you are answering.
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2021 Task 2 with solutions
Subject: math advanced
513 Documents
Students shared 513 documents in this course
Was this document helpful?
Student Number: _________________________Teacher: Ms Blair Mrs Karagiannis (Circle)
Year 11 Mathematics Advanced
31st May 2021
Task 2 - Topic Test
General Instructions
Write using black pen
Working Time
45 minutes
Structure of the Paper
Section I
/5 Marks
Allow about 5
minutes for this
section
Section II
/40 Marks
Allow about 40
minutes for this
section
Total
/45 Marks
Weighting: 30%
Special Instructions
NESA approved calculator may be used.
A reference sheet is provided.
Show all relevant mathematical reasoning and/or calculations.
Attempt all questions.
This examination must not be removed from the Examination Room.
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