Trigonometric Graphs (Grade 10) — Worksheet & Memo

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Grade 10 · Functions & Graphs

Trigonometric Graphs (Grade 10)

EXAM-STYLE CLASS TEST

Marks

Duration

50 minutes

Questions

Name:

Class:

Date:

Mark

/ 31

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
The AMPLITUDE of y = 3 sin x is …
(1)
A)3
B)1
C)6
D)0
1.2
The RANGE of y = sin x is …
(1)
A)−1 ≤ y ≤ 1
B)0 ≤ y ≤ 1
C)−360° ≤ y ≤ 360°
D)y ∈ R
1.3
The RANGE of y = 2 cos x + 1 is …
(1)
A)−1 ≤ y ≤ 3
B)−2 ≤ y ≤ 2
C)0 ≤ y ≤ 3
D)1 ≤ y ≤ 3
1.4
On [0° ; 360°], y = tan x has asymptotes at …
(1)
A)x = 90° and x = 270°
B)x = 0° and x = 180°
C)x = 180° and x = 360°
D)it has no asymptotes
1.5
The PERIOD of y = sin x is …
(1)
A)360°
B)180°
C)90°
D)1
1.6
The graph of y = cos x cuts the y-axis at …
(1)
A)(0 ; 1)
B)(0 ; 0)
C)(1 ; 0)
D)(0 ; −1)
1.7
On [0° ; 360°], y = sin x equals ZERO at …
(1)
A)0°, 180° and 360°
B)90° and 270°
C)0° and 360° only
D)180° only
1.8
The graph of y = sin x + 2 …
(1)
A)never cuts the x-axis
B)cuts the x-axis twice
C)cuts the x-axis once
D)has amplitude 2
1.9
Compared with y = sin x, the graph of y = −sin x is …
(1)
A)reflected in the x-axis
B)shifted down 1 unit
C)reflected in the y-axis
D)shifted 90° to the right
1.10
The MAXIMUM value of y = 4 sin x − 1 is …
(1)
A)3
B)4
C)5
D)−1

Answer grid — circle your answers for Question 1

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[11 MARKS]

Consider f(x) = 2 sin x and g(x) = cos x − 1 for x ∈ [0° ; 360°].

2.1
Write down the amplitude and the period of f.
(2)
2.2
Write down the range of f and the range of g.
(3)
2.3
Write down the coordinates of the maximum turning point of f and the minimum turning point of g.
(3)
2.4
Determine the values of x for which f(x) = 0 on this interval.
(3)

Question 3

[10 MARKS]

Answer the questions below.

3.1
Describe the transformation from y = cos x to y = cos x + 3, and write down the new range.
(3)
3.2
Write down the equations of the asymptotes of y = tan x for x ∈ [0° ; 360°], and explain why they occur there.
(4)
3.3
Explain the difference between the effect of a and the effect of q in y = a sin x + q.
(3)

TOTAL: 31 marks

This question paper consists of 3 questions.