𝟏𝟓𝟎
Trinity House Glenvista
Grade 10 Mathematics revision Assignment
Date: 6 August 2021
Examiner: Dr. N A Bhebhe
Moderators: Ms. M Rabothata
Mr. Deepchund
Name…………………………………
Teacher………………………. Class…………
PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY
1. This assignment consists of 20 pages and additional graph paper. Please check that your
question paper is complete.
2. Read the questions carefully.
3. Answer all the questions.
4. You may use an approved non-programmable and non-graphical calculator unless
otherwise stated.
5. Clearly show ALL calculations, diagrams, graphs, etc. that you have used in determining
your answers.
6. Answers only will NOT necessarily be awarded full marks.
7. Diagrams are not necessarily drawn to scale.
8. If necessary, round off answers to ONE decimal place, unless otherwise stated.
9. It is in your own interest to write legibly and to present your work neatly.
10. Blank pages are included at the end of the paper. If you run out of space for a question,
use these pages. Clearly indicate the question number of your answer should you use this
extra space.
FOR OFFICE USE ONLY: MARKER TO ENTER MARKS
Q1
Q2
Q3
Q4
Q5
Q6
Q7
TOTAL
19
14
24
26
23
16
28
150
1
SECTION A
QUESTION 1
Find the product and simplify the following:
(a)
(𝑥 + 2)(𝑥 2 − 𝑥 + 3)
(b)
5
3
−
𝑥+3 2−𝑥
(2)
(3)
(c)
2𝑥+1 + 2𝑥
Recall that: 7𝑚+𝑛 = 7𝑚 . 7𝑛
(2)
2
(d)
3𝑡 −3𝑡−2
(3)
2.3𝑡 −3𝑡
(e)
(2)
102𝑥+3 .41−𝑥
(4)
252+𝑥
(c)
3
(3)
2
21
+ 𝑎+3 − 𝑎2 −𝑎−12
𝑎−4
(5)
(2)
[8]
[19]
3
QUESTION 2
Factorise the following expressions fully:
(a)
5𝑥 2 − 125
(b)
−7𝑥 3 − 42𝑥 2 − 63𝑥
7𝑥
(2)
(3)
(c)
3𝑥 2 + 3𝑝𝑥 − 2𝑚𝑥 − 2𝑚𝑝
(3)
4
(d)
3𝑥 2 + 9𝑥
𝑥 4 − 81
(−6𝑥 4 − 54𝑥 2 )
× 2
÷
𝑥−3
𝑥 + 6𝑥 + 9
2
(6)
[14]
QUESTION 3
Solve for x in the following:
(a)
1
5𝑥 =
125
(b)
(2)
𝑝𝑥 + 𝑞𝑥 = 𝑎
(2)
5
(c)
15𝑥 2 − 8 = 14𝑥
(3)
(d)
3𝑥 + 2 1
+ = −5
3
𝑥
(5)
(f)
𝑥
2
−(𝑥 + 2)
+
=
𝑥 2 − 1 1 − 𝑥 (𝑥 − 1)(𝑥 + 1)
6
(6)
(g)
Solve the inequality, then draw a number line and write your answer
in interval notation.
𝑥 2 − 2𝑥 − 3 ≤ 0.
(4)
(h)
Solve the simultaneous equation:
4𝑥 2 − 𝑦 2 = 171 𝑎𝑛𝑑 2𝑥 − 𝑦 = 9
(4)
(6)
[26]
QUESTION 4
Given the following Linear pattern: 8; 3; -2;…
(a)
Write down the next two terms (T4 and T5)
(2)
(b)
Determine the nth term (general formula)
(2)
7
(c)
Calculate T32, the thirty second term of the pattern
(2)
(d)
Is -490 a term in the pattern?
(3)
Given the Quadratic Sequence (Pattern), 0; 5; 12;… , has a
general formula (term): 𝑇𝑛 = 𝑛2 + 2𝑛 + 𝑐
(e)
Show that 𝑐 = −3
(2)
(f)
Calculate the 10th term (T10)
(2)
[13]
8
SECTION B
QUESTION 5
ΔQPR and ΔSQR are Right-angled triangles, as shown in the diagram
below:
𝑃𝑅 = 26, 𝑃𝑄 = 24, 𝑄𝑆 = 8, 𝑆𝑅 = 6, 𝑄𝑅 = 10 𝑎𝑛𝑑 𝑃𝑅̂𝑄 = 𝜃
Refer to the diagram and, answer without using a calculator; write
down the value of:
(a)
tan 𝑃̂
(1)
(b)
sin(𝑆𝑄̂𝑅)
(1)
9
(c)
cos 𝜃
(1)
(d)
sec 𝑆𝑅̂𝑄
(1)
(e) Determine the value of
cot 𝜃
csc 𝑄𝑅̂ 𝑆
(3)
Given 17 cos 𝛽 + 15 = 0 , 0˚ < 𝛽 < 270˚
(f) Draw a sketch of the equation
(2)
10
(g) What are your values for the opposite, adjacent and
hypotenuse?
(3)
Without the use of a calculator and using the previous
questions (f) and (g) determine:
(h)
sec 𝛽
(i)
(cos 30)2 . tan 𝛽
(1)
(2)
Without the use of a calculator, simplify the following:
(j)
(k)
sin(30)
(4)
cos(45).cot2 (60)
tan2 60 + 4 cos 60
(4)
11
[23]
QUESTION 6
The graph of 𝑓(𝑥) = 𝑎 sin 𝜃, for 𝑥 ∈ [0˚, 360˚] and the graph
𝑔(𝑥) = cos 𝑥 + 1, 𝑖𝑠 𝑔𝑖𝑣𝑒𝑛 below:
(a)
(b)
Sketch the graph of g(x) on the same axis as f(x).
What is the value of a in f(x)?
(2)
(1)
(c)
The period of f(x)
(1)
(d)
The range of g(x)
(1)
12
(e)
For which values of x for 𝑥 ∈ [0˚, 360˚], will
𝑓(𝑥). 𝑔(𝑥) > 0
(2)
(f)
Find p(x), if 𝑝(𝑥) = −𝑔(𝑥) + 2
(2)
(g)
Draw the function h(𝑥)= tan 𝑥 for 𝑥 ∈ [ 0°, 360°] and 𝑦 ∈ ℝ.
Clearly show all intercepts with the axes and the coordinates of
any turning points
(3)
What are the asymptotes of h(x)?
13
(2)
(h)
Write down the equation of s(x), if 𝑠(𝑥) = 2ℎ(𝑥)
(2)
[16]
QUESTION 7
(a)
𝑘
The sketch below shows the graphs of𝑓(𝑥) = − 1 and
𝑥
𝑔(𝑥) = −𝑥 − 1
The graphs of f and g intersect at P and Q.
(1)
What are the asymptotes of f ? and indicate them on the graph.
(3)
(2)
The point (-4;0) lies on f. Calculate the value of k.
(2)
14
(3)
Calculate the coordinates of P and Q.
(4)
(b) The function 𝑡(𝑥) = 𝑘 𝑥 + 𝑞 is described by the following properties:
• 0<𝑘<1
• X-intercept at (-2,0)
• The horizontal asymptote is 𝑦 = −4
(1)What is the range of t?
(1)
(1)
Determine the equation of t
(3)
(c) Sketch the graph t(x) on the axis below, with 𝑧(𝑥) = 𝑎𝑥 2 + 𝑞
15
Show all asymptotes and intercepts with the x-axis clearly.
(3)
(1)
Calculate the coordinates of A
(2)
(2)
Calculate the values of a and q in z(x)
(4)
(3)
The intercepts of t(x) and z(x)
(4)
16
(4)
For which values of 𝑥 𝑖𝑠 𝑓(𝑥) > 0 ?
(1)
(5)
For which values of 𝑥, 𝑖𝑠 𝑓 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑖𝑛𝑔 ?
(1)
[28]
17
EXTRA WORKING SPACE
18
19
20