Syllabus Edition

First teaching 2021

Last exams 2024

|

Forming & Solving Equations (CIE IGCSE Maths: Extended)

Exam Questions

5 hours61 questions
1
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3 marks

Rangan buys 3.6kg of potatoes and 2.8kg of leeks.
The total cost is $13.72.
Leeks cost $2.65 per kilogram.

Find the cost of 1 kg of potatoes.

$ ................................................ 

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2a
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2 marks

Esme buys x magazines at $2.45 each and y cards at $3.15 each.

Write down an expression, in terms of x and y, for the total cost, in dollars, of the magazines and the cards.

$ ................................................... 

2b
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2 marks

Esme spends $60.55 in total.
She buys 8 magazines.

How many cards does she buy?

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3
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3 marks

5 n is the mean of the three numbers 391, n and n minus 1.

Find the value of n.


n
= ................................................... 

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4
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5 marks

Julie and Liam write down the same number.

Julie multiplies the number by 5 and then adds 4 to the result.
She writes down her answer.

Liam subtracts the number from IO
He writes down his answer.

Julie's answer is two thirds of Liam's answer.

Work out the number that Julie and Liam started with.
You must show your working.

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5
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4 marks

A pattern is made using identical rectangular tiles.

q2-meduim-2-13-forming-and-solving-equations-edexcel-gcse-maths

Find the total area of the pattern.

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6
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4 marks

The diagram shows a trapezium.

xyopd_Z~_q3-meduim-2-13-forming-and-solving-equations-edexcel-gcse-maths

A D = x cm.
B C spaceis the same length as A D.
A B is twice the length of A D.
D C is 4 cm longer than A B.

The perimeter of the trapezium is 38 cm.
Work out the length of A D.

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7
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4 marks

Gemma has the same number of sweets as Betty.

Gemma gives 24 of her sweets to Betty.
Betty now has 5 times as many sweets as Gemma.

Work out the total number of sweets that Gemma and Betty have.

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8
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3 marks

The diagram shows a right-angled triangle.

q9-meduim-2-13-forming-and-solving-equations-edexcel-gcse-maths

All the angles are in degrees.
Work out the size of the smallest angle of the triangle.

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9
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5 marks

A B C spaceis a triangle.

q10-meduim-2-13-forming-and-solving-equations-edexcel-gcse-maths

Angle A B C space=  angle B C A.

The length of side space A B spaceis left parenthesis 3 x space long dash space 5 right parenthesis cm.
The length of side space A C spaceis left parenthesis 19 space long dash x right parenthesis cm.
The length of side space B C spaceis 2 x cm.

Work out the perimeter of the triangle.
Give your answer as a number of centimetres.

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10
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4 marks

Here is a rectangle.

q12-meduim-2-13-forming-and-solving-equations-edexcel-gcse-maths

All measurements are in centimetres.
The area of the rectangle is 48 cm2.
Show that  y space equals space 3

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11
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3 marks

q7-meduim-2-13-forming-and-solving-equations-edexcel-gcse-maths

The diagram shows a parallelogram.
The sizes of the angles, in degrees, are

2 x
3 x space minus 15
2 x
2 x space plus space 24

Work out the value of x.

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1
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3 marks

The diagram shows a trapezium.

cie-igcse-2020-may-june-p2-tz1-q6

Work out the value of x.


x equals .................................................. 

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2
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3 marks

A cone with height 14.8 cm has volume 275 cm3.
 
Calculate the radius of the cone.
[The volume, V, of a cone with radius r and height h is V equals 1 third straight pi r squared h.]
 

............................................... cm

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3
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4 marks

The diagram shows a triangle.

q1-hard-2-13-forming-and-solving-equations-edexcel-gcse-maths

In the diagram, all the measurements are in metres.

The perimeter of the triangle is 56 m.
The area of the triangle is A m2.

Work out the value of A.

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4
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3 marks

Here is a right-angled triangle.

q2-1-hard-2-13-forming-and-solving-equations-edexcel-gcse-maths

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

q2-2-hard-2-13-forming-and-solving-equations-edexcel-gcse-mathsShow that the area of the square space A B C D spaceis x squared space plus space y squared

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5
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3 marks

Becky has some marbles.
Chris has two times as many marbles as Becky.
Dan has seven more marbles than Chris.

They have a total of 57 marbles.

Dan says,
"If I give some marbles to Becky, each of us will have the same number of marbles."

Is Dan correct?
You must show how you get your answer.

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6
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5 marks

Here is a rectangle.

q3-1-hard-2-13-forming-and-solving-equations-edexcel-gcse-maths

The length of the rectangle is 7 cm longer than the width of the rectangle.

4 of these rectangles are used to make this 8-sided shape.

q3-2-hard-2-13-forming-and-solving-equations-edexcel-gcse-maths

The perimeter of the 8-sided shape is 70 cm.
Work out the area of the 8-sided shape.

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7
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5 marks

A B C D is a rectangle.
E F G H spaceis a trapezium.

q4-hard-2-13-forming-and-solving-equations-edexcel-gcse-maths

All measurements are in centimetres.
The perimeters of these two shapes are the same.

Work out the area of the rectangle.

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8
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4 marks

A cinema sells adult tickets and child tickets.

   The total cost of 3 adult tickets and 1 child ticket is £30
   The total cost of 1 adult ticket and  3 child tickets is £22

   Work out the cost of an adult ticket and the cost of a child ticket.

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9a
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2 marks

The diagram shows a trapezium.

q9a-hard-2-13-forming-and-solving-equations-edexcel-gcse-maths

All the measurements are in centimetres.

The area of the trapezium is 351 cm2.

a)
Show that  2 x squared space plus space x space long dash space 351 equals space 0
9b
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3 marks

Work out the value of x.

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10
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4 marks

The diagram shows the plan of a floor.

q10-hard-2-13-forming-and-solving-equations-edexcel-gcse-maths

The area of the floor is 138 m2.

Work out the value of x.

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11
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4 marks

3 teas and 2 coffees have a total cost of £7.80
5 teas and 4 coffees have a total cost of £14.20

Work out the cost of one tea and the cost of one coffee.

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1
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3 marks

The total perimeter of a semicircle is 19.02 cm.
 
Calculate the radius of the semicircle.
 

................................................ cm

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2
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5 marks

Paddy and Anna each invest $2000 for 5 years.
Paddy earns simple interest at a rate of 1.25% per year.
Anna earns compound interest at a rate of r% per year.
At the end of 5 years, Paddy’s investment is worth the same as Anna’s investment.
 
Calculate the value of r.
 

r equals................................................ 

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3
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3 marks

m is inversely proportional to the square of open parentheses p minus 1 close parentheses.
When p equals 4 comma space m equals 5.

Find m when p equals 6.


m equals ..................................................

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4
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4 marks

q1-veryhard-2-13-forming-and-solving-equations-edexcel-gcse-maths

A B C D is a square with a side length of 4 x
M is the midpoint of D C.
N is the point on A D where N D space equals space x

B M N is a right-angled triangle.

Find an expression, in terms of x, for the area of triangle B M N.
Give your expression in its simplest form.

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5
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5 marks

Here are two right-angled triangles.

q2-veryhard-2-13-forming-and-solving-equations-edexcel-gcse-maths

Given that

      tan space e space equals space tan space f

find the value of x.

You must show all your working.

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6
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5 marks

q3-veryhard-2-13-forming-and-solving-equations-edexcel-gcse-maths

The lengths of the sides are in centimetres.

The area of triangle bold T subscript bold 1 is equal to the area of triangle bold T subscript bold 2.
Work out the value of x, giving your answer in the form a space plus space square root of b where a and b are integers.

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7
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5 marks

There are only r red counters and g green counters in a bag.

A counter is taken at random from the bag.

The probability that the counter is green is 3 over 7

The counter is put back in the bag.

2 more red counters and 3 more green counters are put in the bag.
A counter is taken at random from the bag.

The probability that the counter is green is 6 over 13
Find the number of red counters and the number of green counters that were in the bag originally.

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8
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4 marks

The diagram shows a rectangle, A B D E , and two congruent triangles, space A F E spaceand B C D.

q5-veryhard-2-13-forming-and-solving-equations-edexcel-gcse-maths

area of rectangle A B D E = area of triangle A F E + area of triangle B C D

A B space colon thin space A E space equals space 1 space colon space 3

Work out the length of A E.

.....................................cm

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9
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6 marks

Here is a right-angled triangle.

q6-veryhard-2-13-forming-and-solving-equations-edexcel-gcse-maths

All measurements are in centimetres.
The area of the triangle is 2.5 cm2 .

Find the perimeter of the triangle.
Give your answer correct to 3 significant figures.
You must show all of your working.

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