GANSBAAI ACADEMIA

MATHEMATICS
Grade 10 / /

EXAM

June 2014

Total: 75
Time: 1 h 30 min
EDUCATOR
MODERATOR / L. Havenga
S. Kotze

INSTRUCTIONS

1.This question paper consists of 9 questions. Answer ALL questions.

2.Clearly show ALL calculations, diagrams, graphs, et cetera, which you have used in determining the answers.

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

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

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

6.Diagrams are not necessarily drawn to scale.

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

SECTION A

QUESTION 1

1.1Simplify:

1.1.1(4)

1.1.2(5)

1.2Faktorice:

1.2.1(2)

1.2.2(2)

1.3Simplify:

1.3.1(3)

1.3.2(4)

[20]

QUESTION2

2.1Given the sequence: 10; 6; 2; -2

2.1.1Determine the next 3 terms in the sequence.(3)

2.1.2Determine the general term of the sequence.(2)

2.1.3Using the general term, calculate the 50th term of the sequence.(2)

2.2The general term of a sequence is .

2.2.1Calculate the 10th term of the sequence.(2)

2.2.2Which term of the sequence is equal to -30?(2)

[11]

QUESTION3

3.1Solve for :

3.1.1(4)

3.1.2(6)

3.2Determine the inequality and draw your solution on a number line.(5)

[15]

QUESTION4

Two straight lines, and intersect at the point . Find the coordinates of point C by solving 2 simultaneous equations. (4)

[4]

TOTAL SECTION A: 50

SECTION B

QUESTION5

In each of the following right-angles triangles, write down the value of the required trigonometric ratio (leave your answers as ratios) and calculate the size of the angle marked :

5.1Find the value of and the size of angle .(3)

5.2Find the value of and the size of angle .(3)

5.3Find the value of and the size of angle.(3)

[9]

QUESTION6

6.1If sin = , determine each of the following without the use of a calculator:

(Hint: Use a sketch) (< 90o)

6.1.1(2)

6.1.2(3)

6.1.3(2)

6.1.4(2)

6.2Simplify the following expressions without the use of a calculator and show ALL the workings:

(5)

[14]

QUESTION7

Use a calculator to determine (correct to ONE decimal place) in each of the following:

7.1(3)

7.2(3)

7.3(5)

[11]

QUESTION8

With reference to the figure alongside:

8.1Write down two ratios forcos 34.(4)

8.2If CD = 8,3 cm, calculate the value of BD.(4)

8.3Write down a trigonometric definition for .(2)

[10]

QUESTION9

A shark spotter is standing at lookout point 25m above the water’s edge. He spots a shark in the water at an angle of depression of. If the swimmer that is also in the water is 5m from the foot of the lookout spot, how far is the shark from the swimmer?

[6]

TOTAL SECTIONB: 50

TOTAL MARKS: [100]

1

DIAGRAM SHEET 1

NAME AND SURNAME :......

QUESTION 5.1.4

DIAGRAM SHEET 2

NAME AND SURNAME :......

QUESTION 6.6

1