2023 Grade 11 June Mathematics Paper 1 (past paper)

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GRADE 11


MATHEMATICS P1
MID-YEAR EXAMINATION 2023
MEMORANDUM
MARKS: 100 EDUCATOR:
TIME: 2 hours MODERATOR:
DATE:
Read the following instructions carefully before answering the questions.

1. This question paper consists of 4 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 3 pages and an information sheet.

, Mathematics/P1 Grade 11 June 2023
QUESTION 1

1.1 Solve for x
1.1.1 (𝑥 − 2)(2𝑥 + 6) = 0 (2)
1.1.2 (𝑥 − 2)(𝑥 + 1) − 4 =0 (4)
1.1.3 2(𝑥 + 1)2 + (𝑦 − 2)2 = 17 when 𝑦 = 5 (5)

1.1.4 √3𝑥 + 7 + 2𝑥 = 0 (5)
1.1.5 4 𝑥+1 + 6.2𝑥 − 4 = 0 (7)
1.2 Solve for x 𝑥 2 (𝑥 − 1) ≤ 0 (4)
2 1
1.3 Solve for x ≥ 𝑥−3 (6)
𝑥+2

1.4 Solve for x and y simultaneously 2𝑥 − 𝑦 − 1 = 0 and 𝑥 2 + 𝑦 2 − 𝑥𝑦 − 7 = 0 (6)

1.5 If it is given that 𝑥 = 3 ± √2𝑘; 𝑘 ∈ {−3; −2; −1; 0; 1; 2; 3}

Determine value(s) of k for which the value of x will be:
1.5.1 Irrational and unequal (1)
1.5.2 Rational (1)
1.5.3 Equal (1)
1.5.4 Non-real (1)
1.6 Given that 2𝑥 2 + (𝑘 − 3)𝑥 + 8 = 0
For which value(s) of k will the equation have equal roots? (5)
1.7 The area of a square increases by 33 𝑐𝑚2 if each side is increased by 3 cm. What is the perimeter of
square after being enlarged? (5)
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