Download Simultaneous equations : two equations, two variables (e

Stephenson College
Adv. Dip. Engineering
Practice test – Differentiation & Integration 1
1. Differentiate:
(i)
y = 5x4 – 3x3 + 4x2 – x + 7
(ii)
y = 1/x2 - x
(iii)
y = (t4 – 3t2 + 2 )/ t3
(Pass mark 36/60)
(6 marks)
2. Differentiate with respect to x:
(i)
4 e 2x
(ii)
e(x+1)
(iii)
e3x
(iv)
5  ex
(v)
6  e2x - 1
(vi)
1/ e3-x
(2 questions, 4 marks)
3. Differentiate with respect to x:
(i)
( 3 + 2x )5
(ii)
( 2 – 3x )1/2
(iii)
( 2x + 5 )5/2
(1 question, 8 marks)
4.
Differentiate with respect to x:
y = 2x3 cos 4x
(8 marks)
5.
Differentiate:
y = e5x/(x4 – 1)
(8 marks)
HM Lorimer
1
565313622
Stephenson College
6.
Adv. Dip. Engineering
An object travels a distance s = 2t3 – 7t2 + 10t + 5 metres in t seconds. Find both
velocity and acceleration of the object at time 4 seconds.
(6 marks)
7.
The equation of a curve is y = x3 - 2x2 - 7x + 8 . Find by calculation the value of
the maximum and minimum turning points on the curve.
(8 marks)
8.
9.
Evaluate:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(6 marks)
 (4x5 – 2x3 + x – 2 ) dx
 ( cos 6) d
 (sin 2) d
 (sec2) d
 e6x dx
 (1/x) dx
Evaluate  (4x2 + 3x – 1) dx between the limits +2 and –1.
HM Lorimer
2
(6 marks)
565313622