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GRADE 11
MATHEMATICS P2
MID-YEAR EXAMINATION 2023
MARKS: 100 MEMORANDUM EDUCATOR:
TIME: 2 hours MODERATOR:
DATE:
Read the following instructions carefully before answering the questions.
1. This question paper consists of 6 questions.
2. Answer ALL the questions.
3. Clearly show ALL calculations, diagrams, graphs, et cetera which you have used in
determining the 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. If necessary, round off answers to TWO decimal places, unless stated otherwise.
7. Diagrams are NOT necessarily drawn to scale.
8. Write neatly and legibly.
This question paper consists of 5 pages, an information sheet and an answer sheet.
, Mathematics/P2 Grade 11 June 2023
QUESTION 1
The points 𝐴(−5; 3), 𝐵(−3; −3)𝑎𝑛𝑑 𝐶(5; 3) are the vertices of the triangle below.
Determine:
1.1 The length of BC (leave your answer in SURD form). (2)
1.2 The coordinates of point D, the midpoint of BC. (2)
1.3 The equation of line AD. (3)
1.4 The coordinates of point 𝐸(𝑥; 𝑦), such that ABEC is a parallelogram. (3)
1.5 The magnitude of angle 𝐷𝐴̂𝐵 if the gradient of 𝐴𝐵 is −3. (4)
[14]
QUESTION 2
2.1 Simplify, without use of calculator:
2.1.1 sin2 𝑥 . sin(90° − 𝑥) (2)
2.1.2 sin 52,5° . sin 7,5° − cos 52,5° . cos 7,5° (3)
1
2.2 Prove that cos 15° = 4 (√6 + √2), without use of calculator (5)
2.3 Prove, without use of a calculator: (5)
sin 36° cos 36°
− =2
sin 12° cos 12°
[15]
2 Please Turn Over
GRADE 11
MATHEMATICS P2
MID-YEAR EXAMINATION 2023
MARKS: 100 MEMORANDUM EDUCATOR:
TIME: 2 hours MODERATOR:
DATE:
Read the following instructions carefully before answering the questions.
1. This question paper consists of 6 questions.
2. Answer ALL the questions.
3. Clearly show ALL calculations, diagrams, graphs, et cetera which you have used in
determining the 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. If necessary, round off answers to TWO decimal places, unless stated otherwise.
7. Diagrams are NOT necessarily drawn to scale.
8. Write neatly and legibly.
This question paper consists of 5 pages, an information sheet and an answer sheet.
, Mathematics/P2 Grade 11 June 2023
QUESTION 1
The points 𝐴(−5; 3), 𝐵(−3; −3)𝑎𝑛𝑑 𝐶(5; 3) are the vertices of the triangle below.
Determine:
1.1 The length of BC (leave your answer in SURD form). (2)
1.2 The coordinates of point D, the midpoint of BC. (2)
1.3 The equation of line AD. (3)
1.4 The coordinates of point 𝐸(𝑥; 𝑦), such that ABEC is a parallelogram. (3)
1.5 The magnitude of angle 𝐷𝐴̂𝐵 if the gradient of 𝐴𝐵 is −3. (4)
[14]
QUESTION 2
2.1 Simplify, without use of calculator:
2.1.1 sin2 𝑥 . sin(90° − 𝑥) (2)
2.1.2 sin 52,5° . sin 7,5° − cos 52,5° . cos 7,5° (3)
1
2.2 Prove that cos 15° = 4 (√6 + √2), without use of calculator (5)
2.3 Prove, without use of a calculator: (5)
sin 36° cos 36°
− =2
sin 12° cos 12°
[15]
2 Please Turn Over
