NATIONAL SENIOR CERTIFICATE EXAMINATION MATHEMATICS …

NATIONAL SENIOR CERTIFICATE EXAMINATION

MATHEMATICS JUNE EXAMINATION

2015 GRADE 10

PAPER

This paper consists of 7 pages.

MARKS : 100 TIME: 2 HOURS

Mathematics INSTRUCTIONS:

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MDoE/June Exam 2015

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Read the following instructions carefully before answering the questions.

1. This question paper consists of 8 questions. Answer ALL the questions.

2. Clearly show ALL calculations, diagrams, graphs, etcetera that you have used in determining the answers.

3. Answers only will not necessarily be awarded full marks.

4. An approved scientific calculator (non-programmable and non-graphical) may be used, unless stated otherwise.

5. If necessary, answers should be rounded off to TWO decimal places, unless stated otherwise.

6. Diagrams are NOT necessarily drawn to scale.

7. Number the answers correctly according to the numbering system used in this question paper.

8. It is in your own interest to write legibly and to present the work neatly.

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Mathematics

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QUESTION 1

1.1 Show that 3.56 is a rational number

MDoE/June Exam 2015

(3)

1.2 Determine between which two integers 5 7 lies.

(3)

1.3 Find the product of (2x ? 3y)(2x2 ? 3xy + 7y2) and simplify your answer

(3)

1.4 Simplify:

1.4.1

2x

2x 2

1 3x

1

1

x

x

(4)

1.4.2

4x 1 2x 1

(3)

1.4.3 22n1.4n1.2

(3)

16n

1.5 Show that 2x 12 x 32 can be simplified to x 23x 4.

(3)

[22]

QUESTION 2

2.1 Solve for x:

2.1.1 2x(x + 5) ? 3(x +2) = 9

(4)

2.1.2 3.5x-1 = 15

(2)

2.2 Solve for x and represent your answer on a number line:

5 d 3 ? 2x < 9

(4)

2.3 The formula for the total surface area of a cylinder is given by:

SA = 2SrH + Sr2

Make H the subject of the formula:

(2)

2.4 Three rulers and five pencils cost R26. One ruler and two pencils cost R10. Let the cost of a ruler be x rand and the cost of a pencil be y rand.

2.4.1 Write down a system of equations, in terms of x and y that reflect the

above mentioned situation.

(2)

2.4.2 Solve the system of equations in QUESTION 2.4.1 simultaneously and

state the cost of a ruler and the cost of a pencil.

(4)

[18]

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Mathematics

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QUESTION 3 3.1 As a start Linda earns R1400 per month as a sales assistant. Each month thereafter she

receives a R40 increase.

3.1.1 Write down what Linda will earn each month for the first three month

(3)

3.1.2 Write down a formula for the amount she earns after n months.

(2)

3.1.3 How much will Linda earn after one year?

(2)

3.2 A pattern of rectangular and triangular shapes is constructed as follows:

Figure1

Figure2

Figure3

3.2.1 Calculate the total number of arrows in the first four figures

3.2.2 Determine the number of arrows in the nth figure in the form Tn ....... 3.2.3 Which figure will have exactly 143 arrows?

QUESTION 4

4.1 In the triangle given below, find the value of cosT and the size of angleT . 29

T

2

5

(2) (2) (3) [14]

(2)

4.2 If sin T = 5 , ( 0 ................
................

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