Sue Pemberton, Julianne Hughes and, Julian Gilbey Solutions for Chapter: Differentiation, Exercise 9: END-OF-CHAPTER REVIEW EXERCISE 4

Author:Sue Pemberton, Julianne Hughes & Julian Gilbey

Sue Pemberton Mathematics Solutions for Exercise - Sue Pemberton, Julianne Hughes and, Julian Gilbey Solutions for Chapter: Differentiation, Exercise 9: END-OF-CHAPTER REVIEW EXERCISE 4

Attempt the free practice questions on Chapter 4: Differentiation, Exercise 9: END-OF-CHAPTER REVIEW EXERCISE 4 with hints and solutions to strengthen your understanding. Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book solutions are prepared by Experienced Embibe Experts.

Questions from Sue Pemberton, Julianne Hughes and, Julian Gilbey Solutions for Chapter: Differentiation, Exercise 9: END-OF-CHAPTER REVIEW EXERCISE 4 with Hints & Solutions

HARD
AS and A Level
IMPORTANT

Question Image

The parametric equations of a curve are x=6sin2t, y=2sin 2t+3cos 2t for 0t<π The curve crosses the x -axis at the points B and D and the stationary points are A and C, as shown in the diagram.

Find the values of t atA  and C, giving each answer correct to 3 decimal places.

HARD
AS and A Level
IMPORTANT

Question Image

The parametric equations of a curve are x=6sin2t, y=2sin 2t+3cos 2t for 0t<π. The curve crosses the x -axis at the points B and D and the stationary points are A and C, as shown in the diagram.

Find the value of the gradient of the curve at B.

HARD
AS and A Level
IMPORTANT

Question Image

The diagram shows the curve y=1-x1+x. Find dydx.

The gradient of the normal to the curve has its maximum value at the point P shown in the diagram. Find, by differentiation, the x-coordinate of P.

MEDIUM
AS and A Level
IMPORTANT

The parametric equations of a curve are x=31+sin2t, y=2cos3t. Find dy dx in terms of t, simplifying your answer as far as possible.

MEDIUM
AS and A Level
IMPORTANT

The equation of a curve is lnxy-y3=1.

Find the coordinates of the point where the tangent to the curve is parallel to the y -axis, giving each coordinate correct to 3 significant figures.

EASY
AS and A Level
IMPORTANT

The curve with equation 6e2x+key+e2y=c, where k and c are constants, passes through the point P with coordinates ln3, ln2.

Show that 58+2k=c.

MEDIUM
AS and A Level
IMPORTANT

The curve with equation 6e2x+key+e2y=c, where k and c are constants, passes through the point P with coordinates ln3, ln2.

Given also that the gradient of the curve at P is -6, find the values of k and c.