Matric · South Africa · Predicted papers

Matric Mathematics

2 papers300 marks6 h

What we predict comes up

From the syllabus weighting and how the papers are usually set. The papers below follow it.

Euclidean geometry and measurement17%About 50 of 150 marks on Paper 2: circle theorems, a proof of a theorem, proportionality and similarity.
Analytical geometry13%About 40 of 150 marks on Paper 2: gradients, inclination and the circle with its tangent.
Trigonometry13%About 40 of 150 marks on Paper 2: reduction, identities, the general solution, graphs and a 3D problem.
Functions and graphs12%About 35 of 150 marks on Paper 1: the hyperbola, parabola and exponential graphs, with inverses and logarithms.

Paper 1

3 h · 150 marks · Calculator allowed

180:00

This question paper consists of 11 questions. Answer ALL the questions.
Clearly show ALL calculations, diagrams, graphs and so on that you have used in determining your answers.
Answers only will NOT necessarily be awarded full marks.
You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise.
If necessary, round off answers to TWO decimal places, unless stated otherwise.
Diagrams are NOT necessarily drawn to scale.
Number the answers correctly according to the numbering system used in this question paper.

Answer or mark a question and your score adds up here.

Answer all the questions150 marks

125 marks

(1.1.1)Solve for

x

x (x - 3) = 10

[3]

(1.1.2)Solve for

x

3 x^{2} - 5 x - 4 = 0

(correct to TWO decimal places)[3]

(1.1.3)Solve for

x

2 x^{2} + x \geq 6

[4]

(1.1.4)Solve for

x

x - x + 10 = 2

[4]

(1.2)Solve for

x

and

y

simultaneously:

y - 2 x = 1

and

x^{2} + x y - y^{2} = - 11

[6]

(1.3)Without using a calculator, determine the value of

\frac{2 ^{2024} + 2 ^{2022}}{5 \cdot 2 ^{2021}}

[2]

(1.4)Determine the values of

p

for which the equation

2 x^{2} + p x + 8 = 0

has non-real roots.[3]

212 marks

The following quadratic number pattern is given:

4; 9; 18; 31; \dots

(2.1)Write down the next term of the pattern.[1]

(2.2)Determine the general term

T_{n}

of the pattern.[4]

(2.3)Calculate

T_{40}

.[2]

(2.4)Which term of the pattern is equal to

4374

?[3]

(2.5)Between which two consecutive terms of the pattern is the first difference equal to

401

?[2]

313 marks

(3.1.1)Given the arithmetic series

7 + 11 + 15 + \dots

. Calculate the sum of the first 30 terms.[2]

(3.1.2)How many terms of the series

7 + 11 + 15 + \dots

must be added to give a sum of

3400

?[4]

(3.2.1)In a convergent geometric series, the third term is

18

and the sixth term is

\frac{2}{3}

. Determine the common ratio.[2]

(3.2.2)Calculate the sum to infinity of the series in 3.2.1.[2]

(3.3)Determine the value of

p

k = 1 \sum p 3 (2)^{k - 1} = 3069

.[3]

8 more questions

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