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Mathematics Pre exam Grade 11
1
NSC
Capricorn South Paper 1 Term2 2024
CAPRICORN SOUTH DISTRICT
GRADE 11
MATHEMATICS
PRE – FORMAL
MID – YEAR EXAMINATION
P1
17/05/2024
MARKS
: 100
DURATION
: 2 HOURS
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Mathematics Pre exam Grade 11
2
NSC
Capricorn South Paper 1 Term2 2024
INSTRUCTIONS AND INFORMATION
Read the following instructions carefully before answering the questions.
1.
This Pre exam consists of 7 questions.
2.
Answer ALL the questions.
3.
Clearly show ALL calculations, diagrams, and etcetera that you have used in
determining your answers.
4.
ANSWER ONLY will not necessarily be awarded full marks.
5.
You may use an approved scientific calculator (non-programmable and nongraphic), unless stated otherwise.
6.
Round off to TWO decimal places unless stated otherwise.
7.
Number the answers correctly according to the numbering system in this question
paper.
8.
Write legibly and present your work neatly.
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Mathematics Pre exam Grade 11
3
NSC
Capricorn South Paper 1 Term2 2024
QUESTION 1
1.1
Simplify fully, WITHOUT using a calculator:
1.1.1
3𝑚+4 − 6. 3𝑚+1
7. 3𝑚+2
(4)
1.1.2
2𝑥−3 − 3. 2𝑥−1
2𝑥−2
(4)
1.1.3
√𝑎2 − 𝑏 2 × (𝑎 + 𝑏)2
5
1
(𝑎 − 𝑏)2
1.1.4
1.2
(4)
if 𝑎 ≠ 𝑏
√108𝑥12 + √243𝑥12
Rewrite the following expression as a power of y:
(3)
𝑦√𝑦 √𝑦 √𝑦
(4)
8
√𝑦 7
[19]
QUESTION 2
2.1
2.2
Solve for x:
2.1.1
𝑥(2𝑥 − 1) = 0
(2)
2.1.2
5𝑥 2 − 2𝑥 − 6 = 0 correct to two decimal places
(3)
2.1.3
√𝑥 − 1 + 3 = 𝑥
(5)
2.1.4
√(𝑥 − 2)−3 = 64
(4)
2.1.5
𝑥 2 > 3(𝑥 + 6)
(4)
Solve for x and y simultaneously:
2𝑦 = 1 − 𝑥 and 𝑥 2 + 𝑦 2 + 3𝑥𝑦 + 𝑦 = 0
(6)
[24]
QUESTION 3
3.2
For which values of b are the roots of 𝑥(2𝑥 + 𝑏) = −3 non – real?
4𝑥 − 3
For which values of k will the roots of be real?
=𝑘
(𝑥 − 1)2
3.3
Show that the roots of 𝑥 2 − 2(𝑝 − 1)𝑥 − 4𝑝 = 0
3.1
rational values of p.
(3)
(3)
are rational for all
(3)
[9]
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Mathematics Pre exam Grade 11
4
NSC
Capricorn South Paper 1 Term2 2024
QUESTION 4
PRAM is a rectangle with an area of (𝑥 2 − 3𝑥 − 10)cm2 . Q is a point
4.1
on PR and L is a point on MA such that PQLM is a square with sides of
length (𝑥 + 2)cm each.
P
Q
R
M
L
A
(𝑥 + 2)
Calculate the length of LA.
(6)
[6]
QUESTION 5
5.1
−2
Given: 𝑓(𝑥) = 𝑥+1 + 1 and 𝑔(𝑥) = 2−𝑥 − 3
5.1.1
Determine 𝑓(−2)
(1)
5.1.2
Determine x if 𝑔(𝑥) = 3
(2)
5.1.3
Write down the asymptotes of f .
(2)
5.1.4
Write down the range of g.
(1)
5.1.5
Determine the coordinates of the x and y intercepts of f .
(5)
5.1.6
Determine the equation of the axis of symmetry of f which has a
negative gradient. Leave your answer in the form 𝑦 = 𝑚𝑥 + 𝑐
5.1.7
(2)
Sketch the graphs of f and g on the same system of axes. Clearly
show ALL intercepts with the axes and any asymptotes.
5.1.8
(6)
If it is given that 𝑓(−1) = 𝑔(−1), determine the values of 𝑥 for
which 𝑔(𝑥) ≥ 𝑓(𝑥)
(2)
[21]
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Mathematics Pre exam Grade 11
5
NSC
Capricorn South Paper 1 Term2 2024
QUESTION 6
6.1
Find the equation of the parabola that cuts the x – axis at −2 and 3,
and the y - axis at the point (0; 12).
(4)
6.2
Write your answer in 6.1 above in the form: 𝑦 = 𝑎(𝑥 − 𝑝)2 + 𝑞
(3)
6.3
In the diagram below, 𝑓(𝑥) = −𝑥 2 + 𝑥 + 12 and 𝑔(𝑥) = 𝑚𝑥 + 𝑐
6.3.1
Determine the coordinates of C and D.
6.3.2
Determine the values of m and c and hence determine the
equation of 𝑔(𝑥)
1
(3)
(2)
6.3.3
If OB = 2 , find the length of AE.
(3)
6.3.4
For which values of x is 𝑓(𝑥) decreasing?
(1)
6.3.5
Write down the range of 𝑓(𝑥)
(1)
[17]
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Mathematics Pre exam Grade 11
6
NSC
Capricorn South Paper 1 Term2 2024
QUESTION 7
7.1
Give the equation of the quadratic function if it is given that:
▪
The range of 𝑓 is: 𝑦 ≥ −4
▪
Domain: 𝑥 ∈ ℝ
▪
Zero points are (3; 0), (−1; 0) and (0; −3)
(4)
[4]
[100]
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