Maths Test. Relations and Transformations T05 Cubic and Quartic Functions

Unit 1 Mathematical Methods - 2011 T04 Functions, Relations and Transformations T05 Cubic and Quartic Functions
40 minutes Name: .......................................................................................... Total /32

Note: Use of a CAS calculator or A4 summary notes is NOT permitted. Section A - Multiple Choice Circle the correct answer ( 9 × 1 = 9 marks )

1) 1. If ax 3 + 2 x 2 + 5 is exactly divisible by x + 1 , the value of a is
A. 1 B. 7 C. -1 D. 3 E. -7

2) The maximal range of f ( x) = x 2 + 5x − 14 is:

 −14  B. 0, C. [ −2,7]   5  3) Which of the following is a one-to-one function?
A. [ −7,2] A. x 2 − y = 10
3

D. ℝ

1 E. [−20 , ∞) 4

B. y = −35

C. y = ( x + 5)2 + y 2

D. 2 x − 3 y = 10

E. y = 16 − x 2 + 7

4) If f ( x) = − 5 x + 3x + 5 , then f (2) = A. -29 B. 51 C. 15 D. 55 E. 50

3 2 5) The polynomial P( x) = x + 2x − 10x + d is divided by x − 1 .The remainder is 6, the value of d is:

A. 2

B. 10

C. 13

D. 14

E. −14

6) The range of the relation A. R

{( x, y ) : y = x

2

− 4 x − 6, x ∈ (1, 4]} is:

B. ( −9,13]

C. [ −10,4]

D. [−10, −6]

E. R \ ( 7,13)

cla 11

1

2 2 2 7) The x axis intercepts of the graph with equation y = ( x + a) ( x − b )

A. −a, b, −b B. a, − a, b, −b C. a, −a, b
2 D. b , a E. −a, a, −b

8) The equation of the graph shown on the right is:
3 A. y = ( x − 1) + 2

y

4

B. y = 3( x − 1) + 2
3 3 C. y = 4( x + 1) + 2 4 D. y = −2( x − 1) + 2

3

2 P.O.I (1,2) 1

1 E. y = ( x + 1)3 + 2 2
-1

1

2

3

4 x

-1 (0,-1)

3 9) The expression 27 x − 8 can be expressed as: 2 A. (3x + 2)(9x + 6x + 4) 2 B. (3x + 2)(9x − 12x + 4) 2 C. (3x − 2)(9x + 6x + 4) 2 D. (3x − 2)(9x − 12x + 4) 2 E. (3x + 2)(9x + 24x + 4)
-2

Section B - Short Answer Appropriate working must be shown to gain full marks.

( 23 marks )

10) A cubic function has the rule P( x) = x3 + ax 2 + bx + 3 where P(−1) = 1 and P(1) = 11 . Find the values of a and b....