1 Write the equation of the line through (3.2) and (1,10), preferably in the ax+by=c form.

2 Write the equation of the line perpendicular to 2x + 3y = 16 that passes through (-1,2).

3 Write the equation of the circle with centre (2,3) and radius 5.

4 Show that x2 + 8x + y2 – 6y = 24 is a circle by finding its centre and radius.

5 Identify and classify the stationary values of y = 2x5 + 5x4 – 10x3 .

6 The curve y = (x - 3) (x + 1) has a tangent at x = 2. Find the equation of this line and state its intercepts.

7 Sketch the line in Question 5, showing intercepts and stationary values.

8 Attempt a sketch of the line y = (x + 3) .

(x + 2)(x - 1)

Differentiation Practice

1 d (x3 + 5x2)

dx

2 d (x-2 + 2x-1)

dx

3 d (5 √t – 1/t)

dt

4 d (y3)

dt

5 d (x2 + 5)4

dx

6 d (3x4 + 6)2

dx

7 d (x y)

dt

8 d (3x2 + 1)( x3 - 3)

dx

9 d (1 + x + x2/2 + x3/6 + x4 /24)

dx

10Where is the maximum of

y = 2x3 – 6x2 + 7 ?

This exercise is graduated through the chain rule and the product rule. Revise as necessary.