MATHEMATICS/P1/JUNE 2025 GRADE 12
PAGE 2 OF 9
INSTRUCTIONS AND INFORMATION
Read the following instructions carefully before answering the questions.
1. This paper consists of 10 questions.
2. Answer ALL questions.
3. Number the answers correctly according to the numbering system used in
this question paper.
4. Clearly show ALL calculations, diagrams, graphs, etc. that you have used in
determining your answers.
5. Answers only will NOT necessarily be awarded full marks.
6. You may use an approved scientific calculator (non – programmable and non
– graphical), unless stated otherwise.
7. If necessary, round off answers correct to TWO decimal places, unless stated
otherwise.
8. Diagrams are NOT necessarily drawn to scale.
9. An information sheet with formulae is included at the end of the question
paper.
10. Write neatly and legibly.
PAGE 3 OF 9
QUESTION 1
1.1. Solve for x:
1.1.1. (𝑥 + 2)(5 − 𝑥) = 0 (2)
MATHEMATICS
, MATHEMATICS/P1/JUNE 2025 GRADE 12
1.1.2. 3𝑥 − 2𝑥 = 4
2
(correct to TWO decimal places)
(4)
1.1.3.
(4)
1.1.4. 𝑥 + 12 ≤ 𝑥2
(4)
1.1.5. 7. 3𝑥 − 3𝑥+1 = 0
(4)
1.2. Solve for x and y simultaneously:
𝑥 − 2𝑦 = 3
𝑥2 + 6𝑦 = 5𝑥𝑦
(6)
1.3. Simplify, without the use of a calculator,
5𝑥.5𝑥+1
52𝑥
(3)
1.4. Determine the values of 𝑝 for which the following equation will have real roots:
4 − 𝑝 = 3𝑥
(3)
[30]
QUESTION 2
Given the quadratic sequence: −8; −2; 8; 22 …
2.1. Write down the next term.
(1)
2.2. Determine the formula for the general term, 𝑇𝑛, of the sequence.
(4) 2.3. Determine the general term, 𝑇𝑛, of the sequence formed by the first
differences of the
quadratic sequence.
(3)
PLEASE TURN OVER
PAGE 2 OF 9
INSTRUCTIONS AND INFORMATION
Read the following instructions carefully before answering the questions.
1. This paper consists of 10 questions.
2. Answer ALL questions.
3. Number the answers correctly according to the numbering system used in
this question paper.
4. Clearly show ALL calculations, diagrams, graphs, etc. that you have used in
determining your answers.
5. Answers only will NOT necessarily be awarded full marks.
6. You may use an approved scientific calculator (non – programmable and non
– graphical), unless stated otherwise.
7. If necessary, round off answers correct to TWO decimal places, unless stated
otherwise.
8. Diagrams are NOT necessarily drawn to scale.
9. An information sheet with formulae is included at the end of the question
paper.
10. Write neatly and legibly.
PAGE 3 OF 9
QUESTION 1
1.1. Solve for x:
1.1.1. (𝑥 + 2)(5 − 𝑥) = 0 (2)
MATHEMATICS
, MATHEMATICS/P1/JUNE 2025 GRADE 12
1.1.2. 3𝑥 − 2𝑥 = 4
2
(correct to TWO decimal places)
(4)
1.1.3.
(4)
1.1.4. 𝑥 + 12 ≤ 𝑥2
(4)
1.1.5. 7. 3𝑥 − 3𝑥+1 = 0
(4)
1.2. Solve for x and y simultaneously:
𝑥 − 2𝑦 = 3
𝑥2 + 6𝑦 = 5𝑥𝑦
(6)
1.3. Simplify, without the use of a calculator,
5𝑥.5𝑥+1
52𝑥
(3)
1.4. Determine the values of 𝑝 for which the following equation will have real roots:
4 − 𝑝 = 3𝑥
(3)
[30]
QUESTION 2
Given the quadratic sequence: −8; −2; 8; 22 …
2.1. Write down the next term.
(1)
2.2. Determine the formula for the general term, 𝑇𝑛, of the sequence.
(4) 2.3. Determine the general term, 𝑇𝑛, of the sequence formed by the first
differences of the
quadratic sequence.
(3)
PLEASE TURN OVER
