# Mathematics Past Paper

Practice Paper #2September 2, 2010

1. If h(x) = 1 + 3x and k(x) = x +2( CXC 1999 # 5 ) evaluate:

a) hk (x)

b) hk(4)

c) (hk)-1 (x)5 marks

2. Given that :

f : x 3 – x and

g: x x + 2

x – 5

a) Calculate g(2)

b) State the value of x for which g(x) is NOT defined

c) Derive an expression for gf(x)

d) Calculate the value of f-1 (4)

e) Derive an expression for g-1 (x) 12 marks ( CXC 2000 #5 )

3. Given that f(x) = x2 and g(x) = 5x + 3

Calculate :

a) f(-2)

b) gf(-2)

c) g-1(x) 7 marks (CXC 1998 # 6)

4. Given that f(x) = 2x2 + 2x -1 , copy and complete the table below

|x |-3 |-2 |-1 |0 |1 |2 |3 | |f(x) | |3 | |-1 | |11 |23 |

b)Using 1 cm to represent 1 unit on the x-axis and 1 cm to represent 5 units on the y-axis, draw the graph of f(x) = 2x2 + 2x -1 for the values of x in the domain -3 ≤ x ≤ 2 .

c)On the graph of f(x) = 2x2 + 2x -1 , draw in the axis of symmetry for f(x) , and state the value of x where this occurs.

d)From your graph, obtain estimates for:

- The values of x for which f(x) = 0

- The set of values of x for which f(x) < x

- The least value f(x) can take.15 marks ( CXC 1998 #9)

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