Algebraic Reasoning (Edexcel GCSE Maths: Foundation)

Exam Questions

34 mins15 questions
1
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1 mark

In the table below, put a tick (✓) in the box next to the formula.

7 x minus 2 x equals 5 x  
C equals 2 pi space r  
2 y plus 8 greater than 3  
3 t plus 4 equals 19  
6 k plus 5  

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2
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3 marks

Here is a rectangle.

Rectangle with length 2x + 1 and width x

All measurements are in centimetres.

Show that when x equals 4, the perimeter of the rectangle is 26 cm.

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3
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1 mark

Write down an example to show that the following statement is not correct.

The sum of an even number and an odd number will be even.

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4
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1 mark

An unknown integer can be expressed as n.

Write down an algebraic expression for the next integer value.

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5
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1 mark

An integer value can be expressed as n.

Write down an algebraic expression for an even number.

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1a
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1 mark

Write down an example to show that each of the following two statements is not correct.

The multiples of an odd number are always odd.

1b
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1 mark

 All the digits in even numbers are even.

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2
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1 mark

The nth even number is 2 n.

Write down an expression for the next even number.

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3
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2 marks

a and b are two consecutive odd numbers.

Give an example to show that the value of 3 open parentheses a plus b close parentheses is a multiple of 12

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4
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4 marks

p is a positive number.

n is a negative number.

For each statement, tick the correct box.

  Always true Sometimes true Never true
p plus n is positive square square square
p minus n is positive square square square
p squared plus n squared is positive square square square
p cubed divided by n cubed is positive square square square

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5
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1 mark

Which of these is a correct identity?

Circle your answer.

x space plus space 4 x space identical to space 5 x 6 x space identical to space 18 2 x space plus space 1 space identical to space 7 7 x space plus space 9 space identical to space x

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1
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4 marks

The diagram shows a cube with edges of length 4 cm and cone of radius x cm and height 8 cm.

E3gfnt_K_picture-1

The volume of the cube is equal to the volume of the cone.

Show that x equals square root of k over pi end root, where k is an integer.

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2a
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1 mark

The nth odd number is 2 n plus 1.

The next odd number after is 2 n plus 3.

Explain why.

2b
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1 mark

Write down an expression, in terms of n, for the next odd number.

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3
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3 marks

Here is a right-angled triangle.

A right-angled triangle with base 2x and height x

Four of these triangles are joined to enclose the square A B C D as shown below.

Four right-angled triangles enclosing square ABCD

Show that the area of square A B C D is 5 x squared.

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4a
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2 marks

a and b are two even numbers.

Give an example to show that the value of 3 open parentheses a plus b close parentheses is a multiple of 6

4b
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2 marks

Show that when a and b are both even numbers, the value of 3 open parentheses a plus b close parentheses will always be a multiple of 6

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5a
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2 marks

Here is a rectangular wooden block.

Wooden rectangular block

The measurements of the diagram are in centimetres.

Three of these wooden box are put together to construct a shelf.

 

Shelf made from three rectangular wooden blocks

 

The perimeter of the shelf is P cm.

Show that P equals 2 x plus 6 y

5b
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2 marks

Consider the statement,

'When x and y are whole numbers, P is always a multiple of 2."

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

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