Forming & Solving Equations (Edexcel GCSE Maths: Foundation)

  The area of square is  cm².

Show that 

The size of the largest angle in a triangle is times larger than the smallest angle. 
The other angle is  less than the largest angle.

Work out, in degrees, the size of each angle in the triangle.
You must show your working.

The diagram shows triangle .

Angle  is an obtuse angle.

Find the minimum value of .

You must show all your working

is larger than ..........

In this part, all measurements are in centimetres.

The diagram shows a kite with sides  and . The perimeter of the kite is 33 cm.

Work out the length of a shorter side.

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

In this part, all angles are in degrees.

i) Use the information in the triangle to write down an equation in terms of .

[1]

ii) Solve this equation to find the value of

= ................................................. [3]

iii) Work out the size of the smallest angle in the triangle.

[2]

i) Navja weighs a parcel with mass kg on her scales. She uses the masses shown to balance the scales.

Work out the value of .

= ................................................. [3]

ii) Sometimes Navja uses an electronic weighing machine. The machine gives the mass, kg, of a parcel as 12.4kg, correct to the nearest 100g.

Complete this statement about the value of .

.................. ................... [2]

A club is arranging transport for its members.

Speedy Coaches charge $625 plus $15 per member.

The total cost, in dollars, for x members is given by the expression

i) Sporty Coaches charge $117 plus $19 per member.

Write an expression for the total cost, in dollars, for members.

[2]

ii) The total cost is the same for both Speedy Coaches and Sporty Coaches.

Write down an equation and solve it to find .

= .............................................. [3]

Esme buys 8 magazines at $2.45 each and y cards at $3.15 each.

Esme spends $60.55 in total.

How many cards does she buy?

Neelum hires a machine to clean carpets.
It costs $25 to hire the machine for the first day and $9 for each extra day after the first day.
Neelum pays a total of $88 to hire the machine.

Work out the total number of days she hires the machine for.

A shop sells pens and notebooks.
The cost of a pen is  cents and the cost of a notebook is  cents.

On Monday, the shop sells 5 pens and 4 notebooks for 450 cents.

Complete the equation.

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

On Tuesday, the shop sells 10 pens and 3 notebooks for 525 cents.

Write this information as an equation.

................................................ = .........................

Solve your two equations to find the cost of a pen and the cost of a notebook.

You must show all your working.

Cost of a pen = ...................................... cents  Cost of a notebook = ...................................... cents 

Beindu goes to the market to buy apples and bananas.

She can buy

• 7 apples and 4 bananas for 85 cents

or

• 3 apples and 8 bananas for 93 cents.

Apples cost  cents each and bananas cost  cents each.

i) This information can be used to write down two equations.
One of these is .

Write down the other equation.

....................... = ............... [2]

ii) Solve these two simultaneous equations. You must show all your working.

a = ................................. 
b = .................................  [3]

Sharon has double the number of sweets that Josephine has. Martin has 8 fewer sweets than Sharon.

The total number of sweets between the three of them is .

Find the ratio of Martin to Josephine to Sharon for the number of sweets that each of them has.

Rectangle  is a rectangle.
All measurements are in centimetres.

The rectangle has an area of  cm².

Show that 

The first four terms of a quadratic sequence are

The sum of the first five terms of this sequence is .

Find the value of the sixth term.

The diagram shows a shape made from rectangles.
The shape has a total area of 517m².

Find the value of .

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

Rovers, United and City are football teams.

Rovers scoredgoals.
United scored 8 goals more than Rovers.
City scored 3 goals less than twice the number of goals scored by Rovers.

The three teams scored a total of 117 goals.

Write down and solve an equation to find the value of .

= .................................................

Cara has pencils.
Alice has twice as many pencils as Cara.
Leon has three more pencils than Alice.
The three children have a total of 58 pencils.

Use this information to write down an equation and solve it to find the value of .

= ................................................... 

The Fraser family and the Singh family go to the cinema.
The Fraser family buys 6 adult tickets and 2 child tickets for $124. The Singh family buys 3 adult tickets and 5 child tickets for $100.

Find the price of an adult ticket and the price of a child ticket.

Adult ticket $ .....................................................
Child ticket $ .................................................

A plant costs dollars and a bush costs dollars.
Ana buys 2 plants and 4 bushes for $42.
Paola buys 7 plants and 9 bushes for $107.

Write down a pair of simultaneous equations and solve them to find the value of and the value of . You must show all your working.

Alphonse is years old and Beatrice is  years old. Three times Alphonse’s age is equal to 5 times Beatrice’s age. Twice Beatrice’s age is 4 years more than Alphonse’s age.

i) Use this information to write down two equations in and .

[2]

ii) Find the age of Alphonse and the age of Beatrice.

                                                                                Alphonse .................................. years old 
Beatrice .................................. years old [3]

Des thinks of two numbers.
The sum of his two numbers is -6.
The difference between his two numbers is 62.

Find the two numbers.

..................... and .....................

A cost to hire a minibus depends on the number of hours it is hired for, and the number of passengers. The cost is $h per hour plus $p per passenger.

i)When the minibus is hired for 3 hours with 10 passengers the cost is $61.

Complete the equation.

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

[1]

ii) When the minibus is hired for 5 hours with 8 passengers the cost is $80.

Write this information as an equation.

[2]

 iii) Solve your two simultaneous equations to find and .
You must show all your working.

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

................................................[4]