NATIONAL SENIOR CERTIFICATE
GRADE 10
MATHEMATICS MASTER PRACTICE EXAMINATION
PAPER 1: FUNCTIONS FOCUS
TIME: 2 Hours
MARKS: 100
INSTRUCTIONS AND INFORMATION
Read the following instructions carefully before answering the questions.
1. This question paper consists of FOUR main questions totaling 100 marks.
2. Answer ALL the questions.
3. Clearly show ALL calculations, diagrams, and graphs that you have used in determining
your answers.
4. Answers only will NOT necessarily be awarded full marks.
5. You may use an approved scientific calculator (non-programmable and non-graphical),
unless stated otherwise.
6. Diagrams are NOT necessarily drawn to scale.
7. Write neatly and legibly.
,QUESTION 1 (25 Marks)
𝑎
The diagram below shows the graphs of 𝑓(𝑥) = 𝑚𝑥 + 𝑐 and 𝑔(𝑥) = 𝑥
+𝑞
● The graph of 𝑓 has a 𝑦-intercept at (0; 2) and an 𝑥-intercept at (− 2; 0).
● The hyperbola 𝑔 has a horizontal asymptote at 𝑦 =− 1 and passes through the point
(2; 1).
● The two graphs cross each other at point 𝐴 in the first quadrant and point 𝐵 in the third
quadrant.
1.1 Write down the equation of the vertical asymptote of 𝑔. (1)
1.2 Determine the values of 𝑚 and 𝑐, and hence write down the full equation of 𝑓(𝑥). (3)
4
1.3 Show by calculation that the equation of the hyperbola is given by 𝑔(𝑥) = 𝑥
− 1. (3)
1.4 Calculate the coordinates of the 𝑥-intercept of 𝑔. (2)
1.5 Determine the coordinates of the intersection points 𝐴 and 𝐵 by solving 𝑓(𝑥) = 𝑔(𝑥)
algebraically. (6)
1.6 Use the provided graphs to write down the values of 𝑥 for which:
1.6.1 𝑔(𝑥) > 0 (2)
, 1.6.2 𝑔(𝑥) ≥ 𝑓(𝑥) (2)
1.7 Write down the equations of both axes of symmetry for the hyperbola 𝑔(𝑥). (4)
1.8 Write down the range of the function 𝑔. (2)
[25 MARKS]
QUESTION 2 (30 Marks)
2
The graphs of 𝑓(𝑥) =− 𝑥 + 9 and 𝑔(𝑥) =− 𝑥 + 3 are illustrated on the system of axes below.
● Point 𝐶 is the turning point of the parabola 𝑓.
● Points 𝐴 and 𝐵 are the 𝑥-intercepts of 𝑓.
● The straight line 𝑔 passes through point 𝐵 and cuts the 𝑦-axis at point 𝐷.
● The two graphs intersect each other at point 𝐵 and point 𝐸.
2.1 Write down the coordinates of the turning point 𝐶. (2)
2.2 Calculate the coordinates of the 𝑥-intercepts 𝐴 and 𝐵. (5)
2.3 Write down the coordinates of the 𝑦-intercept 𝐷 of the line 𝑔. (1)
2.4 Draw a neat sketch of 𝑓 and 𝑔 on the same system of axes in your answer book. Clearly
label points 𝐴, 𝐵, 𝐶, and 𝐷 with their coordinates. (6)
2.5 Calculate the coordinates of the second intersection point 𝐸. (7)
GRADE 10
MATHEMATICS MASTER PRACTICE EXAMINATION
PAPER 1: FUNCTIONS FOCUS
TIME: 2 Hours
MARKS: 100
INSTRUCTIONS AND INFORMATION
Read the following instructions carefully before answering the questions.
1. This question paper consists of FOUR main questions totaling 100 marks.
2. Answer ALL the questions.
3. Clearly show ALL calculations, diagrams, and graphs that you have used in determining
your answers.
4. Answers only will NOT necessarily be awarded full marks.
5. You may use an approved scientific calculator (non-programmable and non-graphical),
unless stated otherwise.
6. Diagrams are NOT necessarily drawn to scale.
7. Write neatly and legibly.
,QUESTION 1 (25 Marks)
𝑎
The diagram below shows the graphs of 𝑓(𝑥) = 𝑚𝑥 + 𝑐 and 𝑔(𝑥) = 𝑥
+𝑞
● The graph of 𝑓 has a 𝑦-intercept at (0; 2) and an 𝑥-intercept at (− 2; 0).
● The hyperbola 𝑔 has a horizontal asymptote at 𝑦 =− 1 and passes through the point
(2; 1).
● The two graphs cross each other at point 𝐴 in the first quadrant and point 𝐵 in the third
quadrant.
1.1 Write down the equation of the vertical asymptote of 𝑔. (1)
1.2 Determine the values of 𝑚 and 𝑐, and hence write down the full equation of 𝑓(𝑥). (3)
4
1.3 Show by calculation that the equation of the hyperbola is given by 𝑔(𝑥) = 𝑥
− 1. (3)
1.4 Calculate the coordinates of the 𝑥-intercept of 𝑔. (2)
1.5 Determine the coordinates of the intersection points 𝐴 and 𝐵 by solving 𝑓(𝑥) = 𝑔(𝑥)
algebraically. (6)
1.6 Use the provided graphs to write down the values of 𝑥 for which:
1.6.1 𝑔(𝑥) > 0 (2)
, 1.6.2 𝑔(𝑥) ≥ 𝑓(𝑥) (2)
1.7 Write down the equations of both axes of symmetry for the hyperbola 𝑔(𝑥). (4)
1.8 Write down the range of the function 𝑔. (2)
[25 MARKS]
QUESTION 2 (30 Marks)
2
The graphs of 𝑓(𝑥) =− 𝑥 + 9 and 𝑔(𝑥) =− 𝑥 + 3 are illustrated on the system of axes below.
● Point 𝐶 is the turning point of the parabola 𝑓.
● Points 𝐴 and 𝐵 are the 𝑥-intercepts of 𝑓.
● The straight line 𝑔 passes through point 𝐵 and cuts the 𝑦-axis at point 𝐷.
● The two graphs intersect each other at point 𝐵 and point 𝐸.
2.1 Write down the coordinates of the turning point 𝐶. (2)
2.2 Calculate the coordinates of the 𝑥-intercepts 𝐴 and 𝐵. (5)
2.3 Write down the coordinates of the 𝑦-intercept 𝐷 of the line 𝑔. (1)
2.4 Draw a neat sketch of 𝑓 and 𝑔 on the same system of axes in your answer book. Clearly
label points 𝐴, 𝐵, 𝐶, and 𝐷 with their coordinates. (6)
2.5 Calculate the coordinates of the second intersection point 𝐸. (7)
