Everything Maths Grade 10

Complete the following statements:

i.sinC=AB?

(1 mark)

ii.?A=ABBC

(1 mark)

b)Without using a calculator, determine the value ofsin^60 sec°: 45 tan°^30 °

(4 marks)

c)In the diagram,P(5; 12)is a point in the Cartesian plane andROP^ =.

0

y

x

P(5; 12)



Determine the value of:

i.cos

(3 marks)

ii.cosec^2 + 1

(3 marks)

[TOTAL: 12 marks]

5. a)Solve forx, correct to ONE decimal place, in each of the following equations where 0 °x 90 °.
   i. 5 cosx= 3
   (2 marks)
   ii.tan 2 x=1,19
   (3 marks)
   iii. 4 secx3 = 5
   (4 marks)
   b)An aeroplane atJis flying directly over a pointDon the ground at a height of 5 kilometres. It is heading to land at pointK. The angle of
   depression fromJtoKis 8°.Sis a point along the route fromDtoK.

5 km

D S K

J

8 ◦

i.Write down the size ofJKD^.

(1 mark)

ii.Calculate the distanceDK, correct to the nearest metre.

(3 marks)

iii.If the distanceSKis 8 kilometres, calculate the distanceDS.

(1 mark)

iv.Calculate the angle of elevation from pointStoJ, correct to ONE decimal place.

(2 marks)

[TOTAL: 16 marks]

6. a)Consider the functiony= 2tanx.
   i.Make a neat sketch ofy= 2tanxfor 0 °x 360 °on the axes provided on DIAGRAM SHEET 1. Clearly indicate on your sketch
   the intercepts with the axes and the asymptotes.
   (4 marks)
   ii.If the graph ofy= 2tanxis reflected about thex-axis, write down the equation of the new graph obtained by this reflection.
   (1 mark)
   b)The diagram below shows the graph ofg(x) =asinxfor 0 °x 360 °.

Past exam papers 519