Powers, Roots & Standard Form (Edexcel GCSE Maths: Higher)

One sheet of paper is  cm thick.

Mark wants to put sheets of paper into the paper tray of his printer.
The paper tray is cm deep.

Is the paper tray deep enough for sheets of paper?
You must explain your answer.

Write the following numbers in order of size.
Start with the smallest number.

Write down the value of .

Write down the value of .

Write these numbers in order of size. Start with the smallest number.

Write down the value of  .

Find the value of .

Write down the value of .

Write down the value of .

Work out the value of .

The table shows some information about eight planets.

Write down the name of the planet with the greatest mass.

Find the difference between the mass of Venus and the mass of Mercury.

Nishat says that Neptune is over a hundred times further away from Earth than Venus is.

Is Nishat right?
You must show how you get your answer.

Work out 
Give your answer as an ordinary number.

Write down the value of 10⁰.

Write 6.7 x 10^-5 as an ordinary number.

Work out the value of (3 x 10⁷) x (9 x 10⁶).
Give your answer in standard form.

Calculate .
Give your answer in standard form.

Work out the value of .
Give your answer in standard form.

Work out the value of 25^-3.

Work out the value of 350³.
Give your answer in standard form.

Patrick has to work out the exact value of 
Patrick says,

      " of  is  so "

Explain what is wrong with what Patrick says.

The table shows information about the surface area of each of the world’s oceans.

Work out the difference, in square kilometres, between the surface area of the Atlantic Ocean and the surface area of the Indian Ocean.
Give your answer in standard form.

.......................square kilometres

The surface area of the Pacific Ocean is  times the surface area of the Arctic Ocean.

Work out the value of .
Give your answer correct to the nearest whole number.

...........................

Write  as a power of 2.

You are given that 

Find the value of

Work out.

Give your answer in standard form.

Carol says that 

Explain her error and give the correct value of in the form .

A company makes sweets.
The sweets are put into packets.

Here are some facts.

Calculate the mean number of sweets in one packet.

Sweets are made on 288 days each year.

Calculate the number of sweets made each year.
Give your answer in standard form.

The company has 152 machines making the sweets.
Each machine operates for 15 hours each day.

i) Calculate the number of sweets made by one machine each hour.
Give your answer as an ordinary number correct to the nearest 10.

[3]

ii) State one assumption you have made in part (c)(i).

[1]

Find the value of .

can be written in the form .

Find the value of .

Find the value of .

Find the value of .

Write down the value of .

Find the value of .

Find the value of .

Find the value of     .

Solve     .

Write in standard form.

Work out 
Give your answer in standard form.

Write  as a number in standard form.

Write as an ordinary number.

The mass of the Sun is kg.
The mass of the largest known star is times the mass of the Sun.

Work out the mass of this star.
Give your answer in kg in standard form.

Write  as an ordinary number.

Work out the value of 
Give your answer in standard form.

Find the value of .
Give your answer in standard form correct to significant figures.

Work out the value of .
Give your answer in standard form correct to significant figures.

is increased by 
is increased by 

Lottie says,          
"The value of will increase because both and are increased."

Lottie is wrong.
Explain why.

Write 8.2 x 10⁵ as an ordinary number.

Write 0.000 376 in standard form.

Work out the value of (2.3 x 10¹²) ÷ (4.6 x 10³)
Give your answer in standard form.

Work out the value of (3.5 x  10⁶) ÷ (5 x 10^-3).
Give your answer in standard form.

Simplify  .

Give your answer in the form where is an integer.

Show each stage of your working clearly.

where is an integer.

Find an expression, in terms of  , for 

Give your answer in standard form.

There are two errors in Sam’s method for finding the value of shown below.

Find the cube root of and then multiply by .
The cube root of is and then .
The negative power makes the answer negative so answer equals .

Describe these errors and then give the correct value of .

Correct value ..........................................................

Show that   can be written as .