Fractions, Decimals & Percentages (Edexcel IGCSE Maths A (Modular): Higher Unit 1): Exam Questions

Railtickets and Cheaptrains are two websites selling train tickets.

Each of the websites adds a credit card charge and a booking fee to the ticket price.

Nadia wants to buy a train ticket.
The ticket price is £60 on each website.
Nadia will pay by credit card.

Will it be cheaper for Nadia to buy the train ticket from Railtickets or from Cheaptrains?

A company sells boxes to factories.
Fred buys boxes.
The boxes are sold in packs of 1000.
Each pack costs £193.86

Fred orders 3 packs of boxes.
He gets a discount on his total order.

The table shows the discount he will get.

Work out the total cost of the order after the discount. You must show your working.

Greg sells car insurance and home insurance.

The table shows the cost of these insurances.

Each month Greg earns

£530 basic pay

5% of the cost of all the car insurance he sells

and   10% of the cost of all the home insurance he sells

In May Greg sold

6 car insurances

and   4 home insurances

Work out the total amount of money Greg earned in May. 

The table gives some information about student attendance at a school on Friday.

The school has a target of 94% of students being present each day.

Did the school meet its target on Friday?

Bill buys and sells laptops.

Last month Bill bought 50 laptops.
He paid £400 for each laptop.

He sold

40 of these laptops at a profit of 30% on each laptop
10 of these laptops at a profit of 15% on each laptop

Bill's target last month was to sell all 50 laptops for a total of at least £25 000
Did Bill reach this target?

Renee buys 5 kg of sweets to sell.
She pays £10 for the sweets.

Renee puts all the sweets into bags.
She puts 250 g of sweets into each bag.
She sells each bag of sweets for 65p.

Renee sells all the bags of sweets.

Work out her percentage profit.

Mr Brown and his 2 children are going to London by train.

An adult ticket costs £24
A child ticket costs £12

Mr Brown has a Family Railcard.

Work out the total cost of the tickets when Mr Brown uses his Family Railcard.

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

Prove that the recurring decimal 

Show that the recurring decimal  

Use algebra to show that the recurring decimal 

The people working for a company work in Team or in Team .

number of people in Team : number of people in Team = 3 : 4

 of Team work full time.
24% of Team work full time.

Work out what fraction of the people working for the company work full time.
Give your fraction in its simplest form.

Use algebra to show that the recurring decimal  =  

Josh buys and sells books for a living.

He buys 120 books for £4 each.

He sells   of the books for £5 each.

He sells 40% of the books for £7 each.
He sells the rest of the books for £8 each.

Calculate Josh’s percentage profit.

James is taking three examination papers in Spanish. Here are his first two results.

Paper 1:            Paper 2:   

Paper 3 is out of 95.
The marks in each of the three papers are added together.

Find the lowest mark that James needs in Paper 3 to achieve 60% of the total marks.

Without using a calculator, show that  o can be written as .

Explain how  can be used to find  as a decimal and write down its value.

= ...............

The diagram shows three identical rectangles.

of rectangle A is shaded.

80% of rectangle C is shaded.

What fraction of rectangle B is shaded?

Show that      

Rosie says,

“160% of 40 = 140% of 60 because of = of ”

Is she correct?
Tick a box.

Yes             No

Give a reason for your answer.

Amrit’s income is 32% more than Bethan’s income.
Amrit and Bethan’s combined income is £54868.

Calculate Amrit’s income.

£ ........................................................

Express the recurring decimal  as a fraction in its simplest form.

Prove algebraically that  can be written as 

Using algebra, prove that   is equal in value to

Prove algebraically that can be written as 

Prove algebraically that the recurring decimal  can be written as 

Show that the recurring decimal 

Use algebra to show that the recurring decimal 

 is a recurring decimal.

is a whole number such that

Find, in terms of , the recurring decimal  as a fraction.
Give your fraction in its simplest form.
Show clear algebraic working.

Use algebra to show that 

At a country park there is a house, a museum and a garden.

The table shows the prices per person to visit the park.

One day, 480 people visit the park.

67 visit the garden only.
40% visit the house and the museum.
 visit the house only.
The rest visit the museum only.

In total, how much do the 480 people pay to visit the park?
You may use the Venn diagram to help you.

Prove algebraically that  converts to the fraction 

Write as a fraction in its simplest form.
You must show full working in support of your answer.

Use algebra to show that

Use algebra to show that