Perth Academy

Perth Academy

Higher Homework Differentiation

Multiple Choice

1. The rate of change of the function 32xy = when x = 2 is

A. 16

B. 24

C. 24

D. 16

2. The rate of change of the function 22

1

xy = when x = 2 is

A. 8

1

B. 2

1

C. 32

D. 1

3. The derivative of )23(2 2 xx is

A. x8

B. )1(12 xx

C. 432 xx

D. x

4. The gradient of the tangent to the curve 2316 xy = at the point (4, 0) is

A. 0

B. 16

C. 32

D. 24

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5. 34

3)( xxf = . The value of )8(' f is

A. 48

B. 48

C. 8

D. 8

6. The angle which the tangent to the curve 33 += xxy at the point (0, 3) makes with the

positive direction of the x-axis is

A. 135o

B. 45o

C. 1

D. undefined

7. Which one of these statements about the curve 13 += xy is true?

A. it is always increasing

B. it is always decreasing

C. it has 1 stationary point

D. it has more than 1 stationary point

8. The gradient of the tangent to the curve 32 xxy = is 10 . The value(s) of x is/are

A. 2

B. 2

C. 2 and 2

D. 0

9. The stationary point on the curve xxy 243 2 = is

A. (4, 0)

B. (8, 0)

C. )48,4(

D. (0, 0)

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10. A function is defined as .324 xxy += The nature of the turning point on this curve is

A. maximum

B. minimum

C. rising point of inflexion

D. falling point of inflexion

11. The rate of change of the function f defined by 238)( xxxf = when x = 2 is

A. 4

B. 4

C. 8

D. 075

12. The derivative of xx 3 with respect to x is

A. 22

3

3

223

xx

B. xx

32

1

C. 32

1 x

D. 32

1 x

13. The derivative of 24

1

x with respect to x is

A. 32

1

x

B. x8

1

C. 38

1

x

D. x4

1

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14. Function f is defined by 25)( xxxf = . )1(' f equals

A. 4

B. 7

C. 6

D. 3

15. The gradient of the curve )2( = xxy at the point (4, 2) is

A. 2

B. 6

C. 8

D. 0

16. The range of values of x for which the function 54)( 2 += xxxf is decreasing is

A. 2x

C. 2x

17. 323)( zzzf = . The value of )2('f

A. 2

B. 10

C. 21

D. 61

18. Given that )5)(2()(' += xxxf , the x-coordinate(s) of the turning point(s) is/are

A. 2 and 5

B. 2 and 5

C. 2 only

D. 5 only

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19. The gradient of the tangent to the curve 635 2 += axxy at the point (2, 3) is 8.

The value of a is

A. 2

B. 4

C. 3

17

D. 3

14

20. The gradient of the tangent to the curve 365 4 += xxy at the point (1, 2) is

A. 154

B. 2

C. 71

D. 14

21. A function is defined as 14)( 23 += xxxf . The value of )2('f is

A. 0

B. 20

C. 4

D. 7

22. A curve has equation 3833 23 += xxxy . Here are three statements about its graph.

I It has 2 turning points

II It has a minimum turning point at x = 3

2

III It has a maximum turning point at x = 3

4

Which of the above is/are true?

A. I only

B. I and II

C. I and III

D. some other combination

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23. A function g is defined as xxxg 62)( 3 = . The range of values for which the function g is

increasing is

A. 1x

B. 11

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28. A function is defined as 334)( xxf = . Here are 3 statements about this curve.

I it is never increasing

II it is always decreasing

III it has a stationary point at x = 0

Which of these statements is/are true?

A. I only

B. I and II

C. I and III

D. II only

29. Given that )23(3 xxy = , dx

dy equals

A. 269 xx

B. 32 254 xx

C. 329 x

D. x129

30. The tangent to 223 ++= axxy at the point (1, 3) has gradient 5. The value of a is

A. 1

B. 1

C. 55

D. 55

31. 2)3(2)( xxf = , )(' xf equals

A. x62

B. x

62

C. x6

12

D. 26 x

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32. The range of values for which the function 23)(' 2 = xxxf is decreasing is

A. 13

2

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D. 25

5

2x

37. The gradient of the tangent to the curve 543 2 += xxy is 2 at the point where x = a.

The value of a is

A. 3

1

B. 8

C. 1

D. 3

2

38. The graph shows )(xfy = .

The graph of )('xfy = could be

A. B.

C. D.

39. The coordinates and nature of the turning point on 234 xy = are

A. (0, 4) and maximum

B. (0, 4) and minimum

C. (4, 0) and maximum

D. (4, 0) and minimum

x

y (3,2)

x

y

0 3 x

y

0 2

x

y (3,2)

x

y

0 3

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40. The graph shows )(xfy = .

The graph of )('xfy = could be

A. B.

C. D.

-4

-2

x

y

2

-4

-2

x

y

2 -2

x

y

2

4

-2

x

y

2 -2

x

y

2