Perth Academy

Perth Academy Higher Homework

Unit 1

Multiple Choice

1. The line 1232 =+ yx cuts the x-axis at A and the y-axis at B. The midpoint of AB is

A. (3, 2) B. (2, 3) C. (5, 0) D. (0, 5)

2. The value of the derivative of the function f defined as 13)( 2 = xxf at the point where x = 4 is A. 60 B. 23

C. 24 D. 64

3. The gradient of the line perpendicular to the line with equation 532 = yx is

A. 32

B. 32

C. 23

D. 23

4. If )(2 hrrA += pi , where h is a constant, the derivative of A with respect to r is A. )(2 hr +pi B. )2(2 hr +pi C. rpi2 D. rpi6

Perth Academy

5. For the functions defined by 25)( xxf = and 13)( = xxg . ))(( xgf equals A. 53045 2 + xx

B. 115 2 x

C. 545 2 x

D. 545 2 +x

6. The vertices of a triangle are A(3, 8), B )2,1( and C(5, 4). Here are two statements about the triangle ABC:

I it is isosceles

II it is right-angled at B

Which of these statements is/are true? A. Both B. I only

C. II only D. Neither

7. A sequence is defined by the recurrence relation 541 +=+ nn UU , 50 =U .

The value of 2

12 UU equals

A. 80 B. 40

C. 10 D. 75

8. For x

xxf 3)( = , )(' xf equals

A. x

x3

B. x

3

C. x2

3

D. 23

2x

Perth Academy

9. The line PQ is perpendicular to RS where P is (4, 2), Q(6, 4) , R(0, -3) and S(2, k). The value of k is

A. 1 B. 1

C. 5 D. 5

10. The exact limit of the sequence defined by the recurrence relation 6801 =+ nn UU is

A. 57

B. 75

C. 30 D. 30

11. A function is defined is 34 43)( xxxf = . Here are 3 statements about the function I it is always increasing

II it is never decreasing

III it has stationary points where x = 0 and x = 1 Which of these statements is/are true for the above function?

A. I only B. II only

C. III only D. some other combination

12. A function is defined is 34 43)( xxxf = . The range of values of x for which this function is NOT increasing is

A. 1x

B. 1x

Perth Academy

13. When 382 2 + xx is written in the form cbxa ++ 2)( the values of a, b and c are

14. The gradient of the tangent to the curve 23 2 = xy at the point where x = 2 is

A. 10 B. 0

C. 12 D. 8

15. The line 6= mxy is parallel to the line 323 =+ xy . The value of m is

A. 1

B. 32

C. 32

D. 2

16. A curve has equation 32 3 = xy . Which line in the table correctly identifies the coordinates and

nature of its turning point?

a b c

A 2 2 3

B 2 2 7

C 2 2 11

D 2 2 7

Turning point Nature

A )3,0( Point of inflexion B (0, 6) Point of inflexion C (0, 0) Minimum D )3,0( Minimum

Perth Academy

17. A(4, -2), B (-2, 5) and C (6, 3) are the three vertices of a triangle. The gradient of the median AD is

A. 31

B. 51

C. 3

D. 31

18. A(4, -2), B (-2, 5) and C (6, 3) are the three vertices of a triangle. The gradient of the altitude BE is

A. 25

B. 52

C. 52

D. 25

19. The lines with equations 82 =+ yx and 1623 = yx intersect at the point T. The coordinates of

T are

A. (2, 5) B. (6, 1) C. (2, 3) D. )5,2(

20. The gradient of all lines perpendicular to the line AB where A is the point (2, 1) and B is )1,2( is

A. 21

B. 2

C. 21

D. 2

Perth Academy

21. The equation of the line through the point (0, 2) which is parallel to 72 = yx is A. )1(2 = xy B. )1(2 += xy C. )1(2 += xy D. )1(2 = xy

22. The derivative of the function 34

2)( xxf = with respect to x is

A. 37

76

x

B. 31

31

x

C. 31

38

x

D. 31

43

x

23. The function f is defined as .3)( 3 xxxf = The range of values for which this function is increasing is

A. 11

Perth Academy

25. The coordinates and nature of the turning point of the graph of 2)5(6 += xy are

Turning point Nature

A )6,5( Maximum B )6,5( Minimum C )5,6( Maximum D )5,6( Minimum