Forming & Solving Equations (CIE IGCSE Maths: Extended)

The diagram shows a trapezium.

Work out the value of .

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A cone with height 14.8 cm has volume 275 cm³.
 
Calculate the radius of the cone.
[The volume, , of a cone with radius  and height  is .]
 

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

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.

Here is a right-angled triangle.

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

Show that the area of the square is 

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.

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.

 is a rectangle.
is a trapezium.

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

Work out the area of the rectangle.

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 trapezium.

All the measurements are in centimetres.

The area of the trapezium is 351 cm².

Show that 

Work out the value of x.

The diagram shows the plan of a floor.

The area of the floor is 138 m².

Work out the value of .

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

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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 % per year.
At the end of 5 years, Paddy’s investment is worth the same as Anna’s investment.
 
Calculate the value of .
 

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is inversely proportional to the square of .
When 

Find when .

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is a square with a side length of 
is the midpoint of .
is the point on  where 

 is a right-angled triangle.

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

Here are two right-angled triangles.

Given that

find the value of .

You must show all your working.

The lengths of the sides are in centimetres.

The area of triangle  is equal to the area of triangle .
Work out the value of , giving your answer in the form  where  and  are integers.

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

A counter is taken at random from the bag.

The probability that the counter is green is 

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 
Find the number of red counters and the number of green counters that were in the bag originally.

The diagram shows a rectangle, , and two congruent triangles, and .

area of rectangle  = area of triangle  + area of triangle 

Work out the length of .

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

Here is a right-angled triangle.

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.