MATHSCIECAT TUTORIALS ACADEMY (MTA)
GRADE 11
2025 MATHEMATICS TEST 01
Functions
TIME: 1 Hours (60 Minutes) MARKS: 50
MODERATOR: Mookamedi wa Maths Dr Geek EXAMINER: Mr Ramodisha T
NAMEs: Student Number:
CAMPUS: POLOKWANE JOHNNESBURG Other: ___________________CENTRES
INSTRUCTIONS AND INFORMATION
Read the following instructions carefully before answering the questions.
1. This question paper consists of 8 questions.
2. Answer ALL the questions.
3. Number the answers correctly according to the numbering system used in this question
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. You may use an approved scientific calculator (non-programmable and non-
graphical), unless stated otherwise.
7. If necessary, round off answers to TWO decimal places, unless stated otherwise.
8. Diagrams are NOT necessarily drawn to scale.
9. Write neatly and legibly.
Mathematics p1 MTA Grade 11 Test 2025
QUESTION 1
The accompanying diagram shows the graph of 𝑓(𝑥) = 𝑎 𝑥
A
B(4 ; 1 ) x
16
1.1 Write down the coordinate of A; explain. (2)
1.2 How can we tell that: 0 < 𝑎 < 1? (1)
1
1.3 Determine 𝑎 if B is the point (4; ). (3)
16
1.4 Determine the equation of the graph obtained if the graph above is reflected
about the y-axis . (2)
1.5 Write down the coordinates of the point of intersection of the two graphs. (2)
[10]
QUESTION 2
The sketch below; which is not drawn to scale, represents the graphs of
1
𝑓(𝑥) = −1 𝑎𝑛𝑑 𝑔(𝑥) = 𝑚𝑥 + 𝑐
𝑥−2
The graphs intersect at points 𝑅 𝑎𝑛𝑑 𝑇
y
x=2
S(a ; 0) T x
y = -1
R
2.1 Write down the equations of the asymptotes of 𝑓. (2)
2.2 Write down the value of 𝑎. (1)
MATHSCIECAT & MTA GROUP SERVICE Page 2 of 3
Mathematics p1 MTA Grade 11 Test 2025
2.3.1 Calculate the value of 𝑚 , the gradient of the straight line 𝑔 (to the nearest integer) if 𝑔 makes
an angle of 63,43° with the 𝑥 − 𝑎𝑥𝑖𝑠 . (1)
2.3.2 Hence, determine the value of 𝑐. (1)
2.4 Determine the coordinate of 𝑅 𝑎𝑛𝑑 𝑇. (5)
2.5 For what value of 𝑥 𝑖𝑠 𝑔(𝑥) ≥ 𝑓(𝑥). (4)
2.6 Determine an equation for the axis of symmetry of 𝑓 which has a positive slope. (3)
[17]
QUESTION 3
−4
Given: 𝑓(𝑥) = 3(𝑥 − 1)2 − 12 𝑎𝑛𝑑 𝑔(𝑥) = 𝑥+2 + 1
3.1 Calculate the coordinates of the 𝑥 – intercept and the 𝑦 – intercept of 𝑔. (3)
3.2 Calculate the coordinates of the 𝑥 – intercept and the 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 of 𝑓. (3)
3.3 What is the minimum value of 𝑓(𝑥) ? (1)
3.4 On the same set of axes, sketch the graphs of 𝑓 𝑎𝑛𝑑 𝑔 . Indicate all intercepts with the axes and
the coordinates of the turning point of 𝑓. (5)
3.5 For which values of 𝑥 will both 𝑓(𝑥) 𝑎𝑛𝑑 𝑔(𝑥) increase as 𝑥 increases? (2)
[14]
QUESTION 4
4 x 10
Given: f ( x)
x2
4.1 Determine the x and y intercepts of f . (2)
4.2 a
Write f (x) in the form: f ( x) q.
x2 (2)
4.3 Draw the graph of f , clearly show the intercepts with
the axes and the asymptotes. (4)
4.4 Give the equations of the asymptotes of f ( x) 3 . (2)
[10]
TOTAL MARKS: [50]
MATHSCIECAT & MTA GROUP SERVICE Page 3 of 3
