CORE 1 QUICK FIRE REVIEWS 1

Mark

1. Simplify the following:

a)

b)

c)

2. Factorise the following:

a)

b)

c)

1. Simplify these surds: 2. 3.

a)

b)

c)

4. Rationalise the denominators:

a)

b)

c)

5. a) Sketch the following graphs on the

same axes

b) Solve the equation:

c) Use your answers to a) and b) to solve

the inequality

6. Find the value of the gradient of the curve

at the point

CORE 1 QUICK FIRE REVIEWS 2

Mark

1. Express the equation

a) i) In completed square form

ii) As a product of linear factors

b) Using your answers to a) sketch the graph

clearly labelling the key features

2. Without using a calculator and showing all of the working, find a value for the following

a)

b)

3. Express in the form

4.

4. Differentiate the following functions with respect to x

a)

b)

c)

5. For the function

a) Find , and ,

hence find a factor of

b) Use your answer to a) to fully factorise the

function

c) Solve the equation

6. Find the equation of the line that is parallel to

and passes through the point (2,-1)

CORE 1 QUICK FIRE REVIEWS 3

MARK

1. Expand and simplify

2. Express in the form

3. Sketch the following graphs

and the same axes labelling all

important features

Hence solve the inequality

4. a) Use the factor theorem to show

that is a factor of

b) Find such that

c) Solve fully the equation

giving your answers in exact form.

5. The equation has two

distinct real roots.

a) Write down the dicriminant

.

b) Hence or otherwise find all of the

values of c for which this is true

6. a) Find the gradient of the equation

curve at

b) Hence find the equation of line parallel

to the tangent through the point (-1, 1 )

CORE 1 QUICK FIRE REVIEWS 4

MARK

1. What are the gradients and intercepts

of the following straight lines:

a)

b)

2. A quadratic function has vertex at

express the function in the form

3. Sketch

labelling the important features

4. Simplify and hence solve the equation

5. Two numbers differ by 1 and have a

product of 10. If is the smallest number.

a) Explain why

b) Find the exact values of the two

numbers

6. is a factor of the

equation

a) Use the factor theorem to find

b) Fully factorise and solve the equation