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.
1. Sketch the following graphs, showing the relevant
points:
(a) y = (x − 2) 2 (c) x 2 + y 2 − 2x + 4y − 4 = 0
(b) y = 3 −cos 2x (d) 9x 2 − 4y 2 = 36
(e) f (x) =
⎧
⎪ ⎪ ⎪ ⎪ ⎪ ⎨
⎪ ⎪ ⎪ ⎪ ⎪ ⎩
−1 −π ≤ x ≤ −
π
2
x −
π
2
≤ x ≤
π
2
1
π
2
≤ x ≤ π
(15)
2. Determine the inverse of f (x) = 3x + 1
( 3 )
3. Evaluate, correct to 3 decimal places:
2 tan −1 1.64 + sec −1 2.43 − 3 cosec −1 3.85
(3)
4. Determine the asymptotes for the following
function and hence sketch the curve:
y =
(x − 1)(x + 4)
(x − 2)(x − 5)
(8)
5. Plot a graph of y = 3x 2 + 5 from x = 1 to x = 4.
Estimate, correct to 2 decimal places, using 6 intervals, the area enclosed by the curve, the ordinates
x = 1 and x = 4, and the x-axis by (a) the trapezoidal
rule, (b) the mid-ordinate rule, and (c) Simpson’s
rule.
(11)
6. A circular cooling tower is 20 m 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 to each diameter
and hence estimate the capacity of the tower in cubic
metres.
(5)
7. A vehicle starts from rest and its velocity is
measured every second for 6 seconds, with the
following results:
Time t (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 6 s (i.e. the area under the v/t graph)
and (b) the average speed over this period.
(5)