Number Toolkit (AQA GCSE Maths)

Exam Questions

2 hours38 questions
1a
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1 mark

Given that    1793 space cross times space 185 space equals space 331 space 705

Write down the value of

   1.793 space cross times space 185

1b
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1 mark

331 space 705 space divided by space 1.85

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2
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2 marks

Use the fact that

   5.4 space cross times space 36 space equals space 194.4

to find the value of

   i) 5.4 space cross times space 3.6

[1]

   ii) 54 space cross times space 360

[1]

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3
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3 marks

Using the information that

 space 6.7 space cross times space 52 space equals space 348.4

find the value of

i)  6.7 space cross times space 520

[1]

ii) 67 space cross times space 0.52

[1]

iii)  3484 space divided by space 5.2

[1]

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4
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3 marks

Work out     1.83 space cross times space 47

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5
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3 marks

Work out     54.6 space cross times space 4.3

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6
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3 marks

Work out     6.34 space cross times space 5.2

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7
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2 marks

There are 14 boys and 12 girls in a class.

Work out the total number of ways that 1 boy and 1 girl can be chosen from the class.

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8
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1 mark

Circle the reciprocal of 5 over 6

6 over 5 1 over 6 negative 1 over 6 negative 6 over 5

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9
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1 mark

Circle the list of all the integers that satisfy – 2 space less than space x space less-than or slanted equal to space 4

–2, –1, 0, 1, 2, 3 –1, 0, 1, 2, 3
–2, –1, 0, 1, 2, 3, 4 –1, 0, 1, 2, 3, 4

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10
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1 mark

Give one reason why 0 is an even number.

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11
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2 marks

Marta says

   odd square numbers have exactly three factors.

Give one example where this is correct and another where this is not correct.
In each case, write down the number and its factors.

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1
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4 marks

Here is part of Gary's electricity bill.

NaTF3t_w_q1-1-1-medium-edexcel-gcse-maths

Work out how much Gary has to pay for the units of electricity he used.

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2a
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1 mark

Tracey is going to choose a main course and a dessert in a cafe.
She can choose from 8 main courses and 7 desserts.

Tracey says that to work out the number of different ways of choosing a main course and a dessert you add 8 and 7.

Is Tracey correct?
   You must give a reason for your answer.

2b
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2 marks

12 teams play in a competition.
Each team plays each other team exactly once.

Work out the total number of games played.

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3a
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2 marks

There are 17 men and 26 women in a choir.
The choir is going to sing at a concert.

One of the men and one of the women are going to be chosen to make a pair to sing the first song.

Work out the number of different pairs that can be chosen.

3b
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1 mark

Two of the men are to be chosen to make a pair to sing the second song.

Ben thinks the number of different pairs that can be chosen is 136.
Mark thinks the number of different pairs that can be chosen is 272.

Who is correct, Ben or Mark?
Give a reason for your answer.

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4
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2 marks

There are 16 hockey teams in a league.
Each team played two matches against each of the other teams.

Work out the total number of matches played.

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5a
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2 marks

There are three dials on a combination lock.
Each dial can be set to one of the numbers 1, 2, 3, 4, 5
The three digit number 553 is one way the dials can be set, as shown in the diagram.

q5-1-1-medium-edexcel-gcse-maths
Work out the number of different three digit numbers that can be set for the combination lock.

5b
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2 marks

How many of the possible three digit numbers have three different digits?

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6a
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3 marks

Tom is tiling a wall.

He needs to buy at least 100 tiles.
The tiles are sold in large packs and small packs.

Large pack 40 tiles     £18
Small pack 28 tiles     £14
Special offer

25% reduction when you buy 3 or more large packs

Work out the cheapest cost for Tom to buy the packs of tiles he needs.

£.............................

6b
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1 mark

Tom is also tiling a floor.

The floor is a rectangle with length 600 cm and width 240 cm
Each tile is a square with side 40 cm

Tom uses this method to work out the number of tiles he needs.

Number of tiles that will fit along the length = 600 ÷ 40
                                                                              = 15
Number of tiles that will fit along the width = 240 ÷ 40
                                                                             = 6
Total number of tiles needed = 15 + 6
                                                   = 21


Give a reason why Tom’s method is wrong.

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7a
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2 marks

A building company employs

2 labourers
14 joiners
9 electricians
8 plumbers.

For a job, the company needs one of each type of worker.

In how many ways can the company choose the four workers?

7b
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2 marks

One labourer and two plumbers are on holiday.

In how many ways can the company now choose the four workers?

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8
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3 marks

Lunch

Choose one starter and one main course

There are four starters and ten main courses to choose from.

Two of the starters and three of the main courses are suitable for vegans.


What percentage of the possible lunches have both courses suitable for vegans?

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9
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2 marks

Meal Deal

Choose one sandwich, one drink and one snack

There are
   7 different sandwiches
   5 different drinks
   and
   3 different snacks.

How many different Meal Deal combinations are there?

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10
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2 marks

A code has 4 digits.

Each digit is a number from 0 to 9.

Digits may be repeated.

The 4-digit code is an even number.

The first digit is 3

How many possible codes are there?

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11
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3 marks

Ann picks a 4-digit number.

The first digit is not zero.
The 4-digit number is a multiple of 5

How many different 4-digit numbers could she pick?

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12
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4 marks

The table shows the children nominated to win the subject prize in Mathematics and the subject prize in English.

Mathematics English
Alice Alice
Ben Claire
Emma Gabi
Paddy Simon


The winner of each subject prize is picked at random.
It is possible for Alice to win both prizes.

In what percentage of the combinations of prize winners does Alice win at least one prize?

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13a
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2 marks

A menu has

  • 6 starters
  • 10 main dishes
  • 7 desserts.

A three-course meal consists of a starter, a main dish and a dessert.

How many different three-course meals are possible?

13b
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3 marks

A two-course meal consists either of a starter with a main dish, a starter with a dessert or a main dish with a dessert.

Show that there are 172 possible different two-course meals.

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14
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4 marks

Andrew is thinking of a number.

  • It is between 1 and 150.
  • It is one more than a square number.
  • It is three less than a cube number.
  • It is not a prime number.

What is Andrew’s number?
You must show all your reasoning.

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15
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3 marks

A restaurant menu has 8 starters, 12 mains and 6 desserts.
A customer can choose from the following meals

  • a starter and a main,
  • a main and a dessert,
  • a starter, a main and a dessert.

Show that there are 744 different ways of choosing a meal at this restaurant.

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1a
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3 marks

The diagram shows a patio in the shape of a rectangle.
q1-1-1-hard-edexcel-gcse-mathsThe patio is 3.6m long and 3 m wide.

Matthew is going to cover the patio with paving slabs.
Each paving slab is a square of side 60 cm.

Matthew buys 32 of the paving slabs.

Does Matthew buy enough paving slabs to cover the patio?
You must show all your working.

1b
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3 marks

The paving slabs cost £8.63 each.

Work out the total cost of the 32 paving slabs.

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2
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4 marks

Steve wants to put a hedge along one side of his garden.

He needs to buy 27 plants for the hedge.
Each plant costs £5.54

Steve has £150 to spend on plants for the hedge.

Does Steve have enough money to buy all the plants he needs?

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3
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4 marks

Train tickets

day return £6.45

monthly saver £98.50


Sue goes to work by train.

Sue worked for 18 days last month.
She bought a day return ticket each day she worked.

A monthly saver ticket is cheaper than 18 day return tickets.
How much cheaper?

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4
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2 marks

Jeff is choosing a shrub and a rose tree for his garden.
At the garden centre there are 17 different types of shrubs and some rose trees.

Jeff says,

"There are 215 different ways to choose one shrub and one rose tree."

Could Jeff be correct?
You must show how you get your answer.

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5a
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2 marks

Marie has 25 cards.
Each card has a different symbol on it.

Marie gives one card to Shelley and one card to Pauline.

In how many different ways can Marie do this?

5b
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3 marks

There are 12 boys and IO girls in David's class.
David is going to pick three different students from his class and write their names in a list in order.

The order will be
q5b-1-1-hard-edexcel-gcse-maths
How many different lists can David write?

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6
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5 marks

Tom is going to buy 25 plants to make a hedge.

Here is information about the cost of buying the plants.


q6-1-1-hard-gcse-maths
Tom wants to buy the 25 plants as cheaply as possible.

Should Tom buy the plants from Kirsty's Plants or from Hedge World?
You must show all your working.

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7a
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3 marks

Ali and Mel are making 3-digit codes.
The digit 0 is not used.

Ali only uses odd digits.
Mel only uses even digits.

Ali can make x more codes than Mel.
Assume that digits cannot be repeated.

Work out the value of x.

7b
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1 mark

In fact, digits can be repeated.

What does this tell you about the actual value of x?

Tick one box.

square It is bigger than my answer to part (a)
square It is smaller than my answer to part (a)
square It is the same as my answer to part (a)

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8
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1 mark

a is a prime number.

b is an even number.

N space equals space a squared space plus space a b

Circle the correct statement about N.

could be
even or odd
always even
always prime always odd

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9
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3 marks

Here are two methods to make a 4-digit code.

Codes can have repeated digits.

Method A

  For the first two digits use an odd number between 30 and 100
  For the last two digits use a multiple of 11

Method B

  Use four digits in the order       even       odd          even       odd
  Do not use the digit zero

Which method gives the greater number of possible codes?
You must show your working.

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10a
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3 marks

Diners choose one starter and one main from the options given in the table below.
Vegetarian dishes are indicated with a (v).

Starter Main
Cheese salad (v) Steak and chips
Prawn cocktail Fish and chips
Mozzarella sticks (v) Tomato pizza (v)
  Pork chops
  Nut cutlet (v)

Work out the fraction of all the meal combinations which have at least one vegetarian option.

10b
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2 marks

Diners also choose one of 6 dessert options.

How many different three-course meal combinations are available?

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11
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3 marks

Alfie paints his model lorry.
He has eight colours available.

He decides to paint the cab in one colour and the trailer in a different colour.

He then wants to paint his name on the trailer.
The name must be in a different colour to the trailer.

In how many different ways can Alfie paint his model lorry?

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12a
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1 mark

John has

  • 8 different shirts
  • 6 different hats
  • 4 different scarves.

On Monday, he picks a shirt, a hat and a scarf.

Show that there are 192 different combinations he can pick.

12b
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3 marks

John thinks that if he picks just two of the three items of clothing there will be more than 192 combinations.

Is he correct?
Show your reasoning.

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