Revision Test 6
This Revision Test covers the material contained in Chapters 18 and 19.The marks for each question are shown in
brackets at the end of each question.
- Sketch the following graphs, showing the relevant
points:
(a) y=(x− 2 )^2 (c) x^2 +y^2 − 2 x+ 4 y− 4 = 0
(b) y= 3 −cos2x(d) 9x^2 − 4 y^2 = 36
(e) f(x)=
⎧
⎪⎪
⎪⎪
⎪⎨
⎪⎪
⎪⎪
⎪⎩
− 1 −π≤x≤−
π
2
x −
π
2
≤x≤
π
2
1
π
2
≤x≤π
(15)
- Determine the inverse off(x)= 3 x+1(3)
- Evaluate, correct to 3 decimal places:
2tan−^11. 64 +sec−^12. 43 −3cosec−^13 .85 (3)
- Determine the asymptotes for the following
function and hence sketch the curve:
y=
(x− 1 )(x+ 4 )
(x− 2 )(x− 5 )
(8)
- Plot a graph ofy= 3 x^2 +5 fromx=1tox=4.
Estimate, correct to 2 decimal places, using 6 inter-
vals, the area enclosed by the curve, the ordinates
x=1andx=4,andthex-axis by (a) thetrapezoidal
rule, (b) the mid-ordinate rule, and (c) Simpson’s
rule. (11)
- A circular cooling tower is 20m high. The inside
diameter of the tower at different heights is given
in the following table:
Height (m) 0 5.0 10.0 15.0 20. 0
Diameter (m) 16.0 13.3 10.7 8.6 8.0
Determine the area corresponding toeach diameter
and henceestimatethecapacity of thetower in cubic
metres. (5)
- A vehicle starts from rest and its velocity is
measured every second for 6 seconds, with the
following results:
Timet(s) 0 1 2 3 4 5 6
Velocity 0 1.2 2.4 3.7 5.2 6.0 9.2
v(m/s)
Using Simpson’s rule, calculate (a) the distance
travelled in 6s (i.e. the area under thev/tgraph)
and (b) the average speed over this period. (5)