Y11+gdc+maximize+your+use+of+the++ev+2

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Solve the equation:

2a

2

6a 8

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.

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

Solve the simultaneous equations

a)

b)

2x y 3 0
x y 2

2e

x

e

3e
x

y

e

y

15
10

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

Find the following sums
15

a)

23 5n
n 1
20

b)

320 3.2
n 5

c)

0.2
n 1

n

n

Find the numbers in the
Pascal’s triangle:

th
6

row of

Evaluate the following:

5
0

5
1

5
2

5
3

5
4

5
5

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

Solve the equations:

a)

x

3

b) ln(1

3x

2

x)

e

x 5

3

xe

2x 2

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.

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

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

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

f x

e

x

3

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.

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

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.

Solve the equations

a)

b)

x

1

1

x 1 x 2
1
x

c) e

x

ln x

e

5 2x

Y11+gdc+maximize+your+use+of+the++ev+2

Y11+gdc+maximize+your+use+of+the++ev+2

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