Elective Mathematics

Question 1

1The gradient of the normal at a point is

Easy

A. zero B. the tangent gradient squared C. the negative reciprocal of the gradient of the tangent D. equal to the tangent gradient

Question 2

2Find the minimum value of y = x² − 2x + 11.

Medium

A. −1 B. 11 C. 1 D. 10

Question 3

3At a minimum point

Easy

A. y < 0 B. dy/dx > 0 C. d²y/dx² > 0 D. d²y/dx² < 0

Question 4

4The radius of a circle increases at 2 cm/s. Find the rate of increase of the area when r = 3 cm in terms of π.

Hard

A. 12π cm²/s B. 36π cm²/s C. 6π cm²/s D. 18π cm²/s

Question 5

5The radius of a circle increases at 2 cm/s. Find the rate of increase of the area when r = 4 cm in terms of π.

Hard

A. 16π cm²/s B. 64π cm²/s C. 32π cm²/s D. 8π cm²/s

Question 6

6A point of inflexion occurs where

Medium

A. dy/dx changes sign B. dy/dx = 1 C. d²y/dx² changes sign D. y = 0

Question 7

7A rectangle has perimeter 16 cm. Find the dimensions that give the maximum area.

Hard

A. 2 cm by 6 cm B. 3 cm by 5 cm C. 8 cm by 4 cm D. 4 cm by 4 cm

Question 8

8The gradient of y = 1x² at x = 1 is ___

Easy

Your answer (fill in the blank)

Question 9

9The tangent at a stationary point is horizontal.

Easy

A. True B. False

Question 10

10If dy/dx = 0 the point is always a maximum.

Easy

A. True B. False