1. Maximize your use of the
Graphic Display Calculator

2. Solve the equation:
2a
2
6a 8

3. Given
f x
2x
2
8x 10
Write down f(x) in the forms:
a)
b)
f x
2 x h
f x
2 x
2
k
p x q
c) Write down the equation of the axis of
symmetry of the graph.

5. Consider the curve f x x 3 2 x 2 x
Find the transformations of this curve
where:
g x
hx
f x 1
2f x
1

7. Solve the simultaneous equations
a)
b)
2x y 3 0
x y 2
2e
x
e
3e
x
y
e
y
15
10

9. Find the sum of the first 30 terms of the
sequence 3, 5, 7, 9, …

10. Find the following sums
15
a)
23 5n
n 1
20
b)
320 3.2
n 5
c)
0.2
n 1
n
n

12. Find the numbers in the
Pascal’s triangle:
th
6
row of

13. Evaluate the following:
5
0
5
1
5
2
5
3
5
4
5
5

14. Find the coefficient of x5 in the
7
expansion of
(2 x 3)

15. Solve the equations:
a)
x
3
b) ln(1
3x
2
x)
e
x 5
3
xe
2x 2

17. Consider the functionf x x 3 5 x 2 7 x 50
Draw the tangent to the curve at x=0 and
give its equation.
Find the other point of intersection of this
tangent with the curve.

18. 8) Find the equation of the tangent
and normal at x =3 of the following
function:
f x
0.5 x
3
0.5 x
2
10x

19. Find the area between the curve
y
x( x 6) and the x-axis .

20. Represent on the same pair of axes f(x),
its inverse function and the line y=x.
f x
e
x
3

21. Consider the function
f x
2x 6
x 3
(a) Write down the equations of the asymptotes to the
graph of
f x
(b) Find the set of values of for which
f x
0
(c) Find the gradient at -5
(d) Explain why
f
x
0 for any value of x.

23. Given f x
3
xe
2x 2
and g x
ln 1 x
a. Write down the domain of g.
b. Sketch the graph of f for f(x) >0
c. Write down the coordinates of the maximum point on the
graph of f.
d. Find
lim f x
x
e. Find the x-coordinate of the points at which the graphs of
f and g have the same gradient in the interval 0<x<1.5

25. On the same pair of coordinate
axes draw the graphs of the function
f(x) and its inverse function if.
f x
ln
x 10
State the domain of f(x) and its inverse.

26. Solve the equations
a)
b)
x
1
1
x 1 x 2
1
x
c) e
x
ln x
e
5 2x