JOHANNESBURG WEST DISTRICT
NATIONAL
SENIOR CERTIFICATE
GRADE 11
TERM 1 CONTROL TEST
09 MARCH 2026
MARKS: 50
DURATION: 1 HOUR
This question paper consists of 4 pages.
Mathematics/ Term 1 Test
2
Grade 11
JW-PLC/ MARCH 2026
INSTRUCTIONS AND INFORMATION
1.
This question paper consists of 3 questions.
2.
Answer ALL the questions in your answer book.
3.
Use the appropriate and correct numbering system as it is used on this paper.
4.
Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in
determining your answers.
5.
Answers only will NOT necessarily be awarded full marks.
6.
An approved scientific calculator (non-programmable and non-graphical) may be used,
unless stated otherwise.
7.
If necessary, answers should be rounded off to TWO decimal places, unless stated
otherwise.
8.
It is in your own interest to write legibly and to present your work neatly.
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Mathematics/ Term 1 Test
3
Grade 11
JW-PLC/ MARCH 2026
QUESTION 1
1.1.
1.2.
1.3.
Solve the following equations.
1.1.1.
𝑥(𝑥 − 6) = −8
(4)
1.1.2.
𝑥 2 − 2𝑥 − 7 = 0 (correct to two decimal places)
(3)
1.1.3.
2 − √𝑥 − 2 = 𝑥
(5)
1.1.4.
(2𝑥 − 7)(𝑥 + 3) ≥ 0
(3)
Solve for 𝑥 𝑎𝑛𝑑 𝑦 simultaneously:
22𝑥−1 = 8𝑥+𝑦 and 𝑥 2 + 𝑦 2 − 2𝑥𝑦 = 1
(6)
Prove that the roots of 𝑥 2 + (1 − 𝑘)𝑥 + 𝑘 − 3 = 0 are real for all values of 𝑘.
(4)
[25]
QUESTION 2
2.1.
Simplify the following expressions without the use of a calculator.
2.1.1.
2.1.2.
2.2.
2𝑛+2 . 4𝑛+1
(3)
8𝑛−1
(2)
2√12−3√48
8√3
Given that 𝑥 =
1−√3
and 𝑦 =
√2
numerical value of (𝑥 − 𝑦)2.
3−√3
√2
, without the use of a calculator, determine the
(3)
[8]
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Mathematics/ Term 1 Test
4
Grade 11
JW-PLC/ MARCH 2026
QUESTION 3
3.1.
In the diagram below, P(2√3; 𝑦) is a point in the Cartesian plane such that 𝑂𝑃 = 4 units.
𝑇 is a point on the negative 𝑥 − 𝑎𝑥𝑖𝑠.
(1)
3.1.1. Calculate the value of 𝑦.
3.1.2. Determine the following without using a calculator.
a) cos 𝛼
(1)
b) tan(−𝛼)
(2)
c)
1
sin(360°−𝛼)
(3)
(simplify your answer)
(2)
3.1.3. Calculate the value of 𝑇𝑂̂𝑃
3.2.
3.3.
Simplify
sin(𝑥−360).sin(90−𝑥).tan (180−𝑥)
cos (90+𝑥)
(6)
to a single trigonometric ratio.
Prove, without using a calculator, that sin 225°. tan 315° =
1
(2)
√2
[17]
TOTAL [50]
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