Laws of Indices & Surds (Edexcel AS Maths: Pure): Exam Questions

Show how to write

in the form

without using a calculator, where , and are integers to be found.

Give your answer in simplest form.

Given that

write

in the form where and are constants to be found.

Given that

write

in the form where and are constants to be found.

Given that

write

in the form where and are constants to be found.

A student believes that 

for all values of and .

By substituting in two different square numbers for and , show that the student is not correct.

Show how to write 

in the form

without using a calculator, where and are integers to be found.

Solve the equation 

giving your answer in the form

where and are non-zero integers to be found and your answer is in simplest form.

You must show the steps in your working clearly.

A rectangle has an area of 14 m² and a length of m. 

Without using a calculator, find the exact width of the rectangle, showing the steps in your working clearly.

Expand and simplify

giving each term in simplest form.

Use a non-calculator method to solve the equation

to find the exact value of .

Show the steps in your working clearly.

Write 

in the form

where , and are constants to be found.

Solve the equation

showing clearly the steps in your working.

Write

in the form

where and are constants to be found.

Write

in the form

where and are constants to be found.

Write

in the form

where and are constants to be found.

Given that

write

in the form where and are constants to be found.

Given that

write

in the form where and are constants to be found.

Given that

write

in the form where and are constants to be found.

A teacher claims that

for some values of and .

Is the teacher correct? Show your reasoning clearly.

Show how to write

in the form

without using a calculator, where and are rational numbers to be found.

Show how to write 

as an integer, without using a calculator.

Use your answer to part (a) to find the value of 

without using a calculator.

Given that

find the possible values of .

Write

in the form

where is an integer to be found.

In this question you should show all stages of your working.

Solutions relying on calculator technology are not acceptable.

Given

express in terms of , writing your answer in simplest form.

Solve the equation

giving your answer in the form

where and are integers to be found and your answer is in simplest form.

You must show the steps in your working clearly.

A trapezium has the following properties:

• The two parallel sides have lengths  cm and  cm

• The area is  cm²

Without using a calculator, find the perpendicular distance between the two parallel sides of the trapezium, showing the steps in your working clearly.

Give your answer in the form  where and are integers to be found and your answer is in simplest form.

Use a non-calculator method to solve the equation

to find the value of .

Show the steps in your working clearly.

Expand and simplify

giving each term in simplest form.

Show that

can be written in the form

where is a function of which you should state.

Given that

write

in the form where and are constants to be found.

Given that

write

in the form where and are constants to be found.

Given that

write

in the form where and are constants to be found.

Given

express as a function of .

Write

in the form

where and are integers to be found.

Write

in the form

where and are constants to be found.

Show that

can be written in the form

where is a constant to be found.

A square has an area of  m² and a side length of   m, where and are rational numbers with and .

Use algebra to find and .