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WYNBERG BOYS’ HIGH SCHOOL
GRADE 10 MATHEMATICS TEST
TRIGONOMETRY AND LINEAR FUNCTIONS
29 April 2016
55 marks
60 minutes
INSTRUCTIONS:
1.
2.
3.
4.
Answer ALL questions.
Round off to two decimal places where necessary.
A calculator may be used unless otherwise specified.
Please answer Question 7.1 on the diagram sheet attached and staple to the back
of your script.
QUESTION 1:
If A = 15 and B = 67, determine using a calculator, the value of:
1.1
cos 2A
1.2
cosec (A + B)
1.3
tan2A
[5]
QUESTION 2: Use your calculator to determine  in the following where  is an acute
angle.
2.1
sin   0,34
(1)
2.2
2,4 cot  - 5,6 = 3,1
(3)
[4]
QUESTION 3:
Use the triangle alongside and write down the
following trigonometric ratios in terms of its
sides:
3.1
sin C
3.2 sec D
3.3
tan C
[3]
[3]
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QUESTION 4:
4.1
A CALCULATOR MAY NOT BE USED IN THIS QUESTION
A is the point (8; 15). Without finding the angle  , use the sketch
to determine:
4.1.1 OA
(2)
4.1.2 sin 
(1)
4.1.3 34 cos  . tan 
(3)
4.2
If 2 tanB = -1 and B is an obtuse angle, determine the following by using a
diagram. Leave answers in surd form.
4.2.1 cosB
(4)
4.2.2
sin2B
(2)
4.2.3
sin B  cosecB
5
(3)
[15]
QUESTION 5:
5.1
Using the sketch alongside, determine the
size of Q̂
(3)
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5.2
Two hawks P and Q are flying vertically above one another. Hawk Q is 250m
above hawk P. They both spot a snake at R.
Q
Using the information given, find:
5.2.1
the height of Hawk P above the ground.
(3)
5.2.2
the distance between Hawk P and
the snake at R.
(2)
5.2.3
.
the size of QRP .
(3)

(4)
(4)
T
(9)
[12]
QUESTION 6: A CALCULATOR MAY NOT BE USED IN THIS QUESTION
Using the appropriate sketches, evaluate the following:
6.1
tan 2 30  cos 60
(3)
6.2
cosec 45.sin 30 .cos 60
tan 45 . cos 45
(6)
[9]
QUESTION 7:
7.1 Sketch the graphs of the following on the same set of axes on the diagram sheet
attached:
y  2x  4
and
2x  3y  6
(4)
7.2 By solving simultaneously, find the point of intersection algebraically.
(3)
[7]
THE END
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GRADE 10 MATHEMATICS TEST – 29 APRIL 2016
DIAGRAM SHEET
NAME: _______________________________________
Teacher Code: _____
QUESTION 7.1
6
y
5
4
3
2
1
x
−4
−3
−2
−1
1
2
3
4
5
6
7
−1
−2
−3
−4
P.T.O
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