Forming & Solving Equations (Edexcel IGCSE Maths): Exam Questions

The diagram shows a triangle.

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.

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 10 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.

The diagram shows a rectangle.

All measurements are given in centimetres.

The perimeter of the rectangle is 45 cm.

Work out the value of $x.$

Here is a right-angled triangle.

Four of these triangles are joined to enclose the square $ABCD$ as shown below.

Show that the area of the square $ABCD$is $x^{2}+y^{2}$

A pattern is made using identical rectangular tiles.

Find the total area of the pattern.

Kalinda buys $x$ packs of currant buns and $y$ boxes of iced buns.

There are 6 currant buns in a pack of currant buns. There are 8 iced buns in a box of iced buns.

Kalinda buys a total of $T$ buns. Write down a formula for $T$ in terms of $x$ and $y$.

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.

The diagram shows a trapezium.

$AD$ = $x$ cm.

$BC$is the same length as $AD$.

$AB$ is twice the length of $AD$.

$DC$ is 4 cm longer than $AB$.

The perimeter of the trapezium is 38 cm.

Work out the length of $AD$.

A shop sells packets of envelopes.

There are 5 envelopes in a small packet. There are 20 envelopes in a large packet.

There is a total of $T$ envelopes in $x$ small packets and $y$ large packets.

Write down a formula for $T$ in terms of $x$ and $y$.

Here is a rectangle.

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.

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

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.

In the diagram, all angles are in degrees.

Angle $AOB$is a right angle. Angle $AOC$= Angle $BOC$.

Work out the value of $x$.

$ABCD$ is a rectangle.

$EFGH$is a trapezium.

All measurements are in centimetres.

The perimeters of these two shapes are the same.

Work out the area of the rectangle.

Here is a cuboid.

All measurements are in centimetres.

$x$ is an integer.

The total volume of the cuboid is less than 900 cm³

Show that $x$less-than or slanted equal to 5

The area of square $ABCD$ is $10\mathrm{cm}^{2}$.

Show that $x^{2}+6x=1$

Here is a rectangle and a right-angled triangle.

All measurements are in centimetres.

The area of the rectangle is greater than the area of triangle.

Find the set of possible values of $x$.

3 kg of potatoes and 4 kg of carrots have a total cost of 440p. 4 kg of potatoes and 3 kg of carrots have a total cost of 470p.

Work out the total cost of 1 kg of potatoes and 1 kg of carrots.

The diagram shows a triangle.

Work out the value of $x$.

$x$ = ..................

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.

The diagram shows a parallelogram.

The sizes of the angles, in degrees, are

$2x\,3x-15\,2x\,2x+24$

Work out the value of $x$.

Three tins, $A$, $B$and $C$ , each contain buttons.

Tin $A$ contains $x$buttons. Tin $B$ contains 4 times the number of buttons that tin $A$ contains. Tin $C$ contains 7 fewer buttons than tin $A$.

The total number of buttons in the three tins is 137

Work out the number of buttons in tin $C$.

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.

The diagram shows a garden in the shape of a rectangle.

All measurements are in metres. The perimeter of the garden is 32 metres.

Work out the value of $x$.

$b$ is 3 more than the square root of $a$.

Circle the correct equation.

The diagram shows a trapezium.

All the measurements are in centimetres.

The area of the trapezium is 351 cm².

Show that $2x^{2}+x---351=0$

Work out the value of $x$.

The diagram shows a right-angled triangle.

All the angles are in degrees.

Work out the size of the smallest angle of the triangle.

The length of a rectangle is five times the width. The area of the rectangle is 1620 cm²

Work out the width of the rectangle.

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

There are 56 metal bars in a box. Each metal bar is gold or silver or zinc.

• $y$ metal bars are gold.
• $(3y+7)$ metal bars are silver.
• $( 2 y - 5 )$ metal bars are zinc.

Work out the number of metal bars that are zinc. Show clear algebraic working

The diagram shows the plan of a floor.

The area of the floor is 138 m².

Work out the value of $x$.

$ABC$is a triangle.

Angle $ABC$= angle $BCA$.

The length of side $AB$is $(3x---5)$ cm. The length of side $AC$is $(19---x)$ cm. The length of side $BC$is $2x$ cm.

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

$ABCD$ is a trapezium.

$STUV$ is a rectangle.

All measurements are in centimetres.

The two shapes have the same perimeter.

Work out the length of $ST$.

Redlands School sent $x$ students to a revision day.

St Samuel's School sent twice as many students as Redlands School.
Francis Long School sent 7 fewer students than Redlands School.

Each student paid £ 15 for the revision day. The students paid a total of £1155

Work out how many students were sent by each school to the revision day.
You must show all your working.

Given that

$x^{2} : ( 3 x + 5 ) = 1 : 2$

find the possible values of $x$.

Here is a rectangle.

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

In a chess club, there are $x$ boys and $y$ girls.

If 5 more boys and 8 more girls join, there would be half as many boys as girls.

Show that $y=2x+2$

If instead,

10 more boys and 1 more girl join, there would be the same number of boys and girls.

Work out $x$ and $y$.

$x$ = ...................

$y$ = ...................

Ali is $y$ years old.

Bhavara is twice as old as Ali.

Ceris is 3 years younger than Ali.

The total of their ages is 125 years.

Work out the age of each person.

Three identical isosceles triangles are joined to make this trapezium.

Each triangle has base $b$ cm and perpendicular height $h$ cm

Work out an expression, in terms of $b$ and $h$, for the area of the trapezium.

Give your answer in its simplest form.

......................................cm²

This diagram shows the same trapezium.

$b:s=2:3$

Work out an expression, in terms of $b$, for the perimeter of the trapezium.

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

Kate has the following question for homework.

Show that Kate can form the equation $x^{2}+5x--1400=0$

Kate correctly factorises the equation to get $(x+40)(x--35)=0$

Her answer to the homework question is $x=--40\mathrm{or}x=35$

Is her answer correct?

Tick a box.

square Yes $\text{square}$ No

Give a reason for your answer.

Theo starts with savings of £18

James starts with no savings.

Each week from now,

Theo will save £4.50 and James will save £4

In how many weeks will Theo and James have savings in the ratio 15 : 8 ?

$A,B$ and $C$ are three points on a circle.

The radii from $A,B$ and $C$ are shown.

Is $AC$ a diameter of the circle? You must show your working.

$ABCD$ is a trapezium.

$BC$ is parallel to $AD$

Find the size of the largest angle inside the trapezium.

Rana sells 192 cakes in the ratio small : medium : large = 7 : 6 : 11

The profit for one medium cake is twice the profit for one small cake. The profit for one large cake is three times the profit for one small cake.

Her total profit is £532.48

Work out the profit for one small cake.

£.....................

Sundip and Emma have some money. The ratio of Sundip’s money to Emma’s money is 3 : 5. Emma spends £450 of her money. The ratio of Sundip’s money to Emma’s money is now 2 : 3.

Find how much money Sundip has.

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

The diagram shows a hexagon $ABCDEF$

$AB=25\mathrm{cm}BC=(x+2)\mathrm{cm}CD=8\mathrm{cm}EF=7\mathrm{cm}AF=(x+6)\mathrm{cm}$

The area of hexagon $ABCDEF$ is 258 cm²

Work out the value of $x$