2.9 Forming & Solving Equations

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.

A pattern is made using identical rectangular tiles.

Find the total area of the pattern.

The diagram shows a trapezium.

 = cm.
is the same length as .
 is twice the length of .
 is 4 cm longer than .

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

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.

The diagram shows a right-angled triangle.

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

is a triangle.

Angle =  angle .

The length of side is  cm.
The length of side is  cm.
The length of side is  cm.

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

Here is a rectangle.

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

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

Work out the value of .

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 .
 

................................................ 

is inversely proportional to the square of .
When 

Find when .

..................................................

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.