TRIGONOMETRIC FUNCTIONS
BY MASALA LOVEWELL MULAUDZI
Grade 12 Functions Question Paper
Instructions:
1. Read all questions carefully.
2. Answer all questions.
3. Show all workings and calculations.
4. The use of a non-programmable calculator is allowed.
5. Write neatly and legibly.
Total Marks: 50
Duration: 90 minutes
QUESTION 1: 10 Marks
Given: 𝑓(𝑥) = −𝑥 3 + 6𝑥 2 − 9𝑥 + 4 𝑎𝑛𝑑 𝑓(4) = 0
8.1 Determine the coordinates of the turning points 𝑜𝑓 𝑓. (2)
8.2 Draw a sketch graph of f. Clearly label all the intercepts with the axes and any turning
points. (4)
8.3 Use the graph to determine the value(s) of k for which −𝑥 3 + 6𝑥 2 − 9𝑥 + 4 = 𝑘 will have
three real and unequal roots. (2)
8.4 The line g(x) = ax + b is the tangent to f at the point of inflection of 𝑓. Determine the
equation of 𝑔. (2)
BY MASALA LOVEWELL MULAUDZI
Grade 12 Functions Question Paper
Instructions:
1. Read all questions carefully.
2. Answer all questions.
3. Show all workings and calculations.
4. The use of a non-programmable calculator is allowed.
5. Write neatly and legibly.
Total Marks: 50
Duration: 90 minutes
QUESTION 1: 10 Marks
Given: 𝑓(𝑥) = −𝑥 3 + 6𝑥 2 − 9𝑥 + 4 𝑎𝑛𝑑 𝑓(4) = 0
8.1 Determine the coordinates of the turning points 𝑜𝑓 𝑓. (2)
8.2 Draw a sketch graph of f. Clearly label all the intercepts with the axes and any turning
points. (4)
8.3 Use the graph to determine the value(s) of k for which −𝑥 3 + 6𝑥 2 − 9𝑥 + 4 = 𝑘 will have
three real and unequal roots. (2)
8.4 The line g(x) = ax + b is the tangent to f at the point of inflection of 𝑓. Determine the
equation of 𝑔. (2)
