Test 2023
G12 ~ Mathematics
TASK 1: Term test 1
MATHEMATICS
GRADE 12
TASK 1: TERM TEST 1
EXAMINER: B. Pretorius TIME: 1 hour
MODERATOR: P. de Swardt TOTAL: 50
INSTRUCTIONS
1. This paper consists of FOUR questions, ONE diagram sheet and ONE formula page.
2. Answer all the questions.
3. Read through the entire paper before you start.
4. Number your answers as indicated.
5. Write neatly and legibly.
6. Rule off after each question.
7. Start each question on a new page.
8. Only use a blue ballpoint pen to write. Draw sketches in pencil, with the labels in blue ink.
9. Draw a clear line through work that should not be marked.
10. Only an approved calculator may be used.
11. All calculations must be shown to receive marks.
12. Round all answers to two decimal places, unless otherwise stated.
13. Give answers with positive exponents.
14. Clearly show all calculations, diagrams, graphs, etc.
15. Answers only will not necessarily be awarded full marks.
16. Diagrams are not necessarily drawn to scale.
Page 1 of 5 © Impaq
, Test 2023
G12 ~ Mathematics
QUESTION 1
𝑥
Given: 𝑓(𝑥) = log 5 𝑥 and 𝑔(𝑥) = 2 + 3.
1.1 Draw the graph of 𝑓(𝑥) on the diagram sheet. Show all intercepts on the axes. (3)
1.2 Determine 𝑓 −1 (𝑥) and write it in the format 𝑦 = ⋯ (2)
1.3 Draw the graph of 𝑓 −1 (𝑥) on same set of axes as question 1.1 on the diagram
sheet. Show all intercepts on the axes. (3)
1.4 Give the range of 𝑓 −1 . (2)
1.5 Determine 𝑔−1 (𝑥) and write it in the format 𝑦 = ⋯ (2)
1.6 Describe the translation that takes place from 𝑓(𝑥) to 𝑓 −1 (𝑥). (2)
[14]
QUESTION 2
1
2.1 If cos2 𝛽 − sin2 𝛽 = , determine, without the use of a calculator, the value
3
of sin 2𝛽. (4)
2.2 Simplify completely:
cos(90° − 𝜃) × sin(180° + 𝜃) + tan 𝜃 × sin(−𝜃) × sin(270° − 𝜃) (6)
2.3 Given: sin 𝛽 . cos 𝛽 = 0,4698 and cos 2 𝛽 − sin2 𝛽 = 0,3420. Determine the
value of each of the following:
2.3.1 sin 2 𝛽 (2)
2.3.2 cos 2𝛽 (1)
2.3.3 tan 2𝛽 (2)
2.4 Give the period of 𝑦 = −3cos(2𝑥 − 30). (1)
[16]
Page 2 of 5 © Impaq
G12 ~ Mathematics
TASK 1: Term test 1
MATHEMATICS
GRADE 12
TASK 1: TERM TEST 1
EXAMINER: B. Pretorius TIME: 1 hour
MODERATOR: P. de Swardt TOTAL: 50
INSTRUCTIONS
1. This paper consists of FOUR questions, ONE diagram sheet and ONE formula page.
2. Answer all the questions.
3. Read through the entire paper before you start.
4. Number your answers as indicated.
5. Write neatly and legibly.
6. Rule off after each question.
7. Start each question on a new page.
8. Only use a blue ballpoint pen to write. Draw sketches in pencil, with the labels in blue ink.
9. Draw a clear line through work that should not be marked.
10. Only an approved calculator may be used.
11. All calculations must be shown to receive marks.
12. Round all answers to two decimal places, unless otherwise stated.
13. Give answers with positive exponents.
14. Clearly show all calculations, diagrams, graphs, etc.
15. Answers only will not necessarily be awarded full marks.
16. Diagrams are not necessarily drawn to scale.
Page 1 of 5 © Impaq
, Test 2023
G12 ~ Mathematics
QUESTION 1
𝑥
Given: 𝑓(𝑥) = log 5 𝑥 and 𝑔(𝑥) = 2 + 3.
1.1 Draw the graph of 𝑓(𝑥) on the diagram sheet. Show all intercepts on the axes. (3)
1.2 Determine 𝑓 −1 (𝑥) and write it in the format 𝑦 = ⋯ (2)
1.3 Draw the graph of 𝑓 −1 (𝑥) on same set of axes as question 1.1 on the diagram
sheet. Show all intercepts on the axes. (3)
1.4 Give the range of 𝑓 −1 . (2)
1.5 Determine 𝑔−1 (𝑥) and write it in the format 𝑦 = ⋯ (2)
1.6 Describe the translation that takes place from 𝑓(𝑥) to 𝑓 −1 (𝑥). (2)
[14]
QUESTION 2
1
2.1 If cos2 𝛽 − sin2 𝛽 = , determine, without the use of a calculator, the value
3
of sin 2𝛽. (4)
2.2 Simplify completely:
cos(90° − 𝜃) × sin(180° + 𝜃) + tan 𝜃 × sin(−𝜃) × sin(270° − 𝜃) (6)
2.3 Given: sin 𝛽 . cos 𝛽 = 0,4698 and cos 2 𝛽 − sin2 𝛽 = 0,3420. Determine the
value of each of the following:
2.3.1 sin 2 𝛽 (2)
2.3.2 cos 2𝛽 (1)
2.3.3 tan 2𝛽 (2)
2.4 Give the period of 𝑦 = −3cos(2𝑥 − 30). (1)
[16]
Page 2 of 5 © Impaq
