Linear Equations (Cambridge (CIE) IGCSE International Maths: Core): Exam Questions

Solve these equations.

i) $\frac{x}{3}=18$

$x=$............................[1]

ii) $5x+18=8$

$x=$...............................[2]

iii) $12x-3=4x+21$

$x=$............................[2]

Solve the equation.

$6-2x=3x$

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

Solve.

$5\left(2x+4\right)=85$

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

Solve these equations.

i) $5x=-30$

$x=.................................................\left[1\right]$

ii) $4x-2=28$

$x=.................................................\left[2\right]$

iii) $3\left(2x+7\right)=12$

$x=.................................................\left[3\right]$

Solve.

i) $10x=5$

$x$ = ................................................... [1]

ii) $7x-3=2x+11$

$x$= ................................................... [2]

iii) $3\left(2x-1\right)=27$

$x$ = ................................................... [3]

Solve these equations.

i) $\frac{x}{4}=20$

$x$ = .............................................. [1]

ii) $3x-5=16$

$x$ = .............................................. [2]

iii) $5(2x+1)=27$

$x$= .............................................. [3]

Solve.

$\frac{3-x}{2}=-2$

Solve.

$\frac{3x}{4}+7=12$

Give your answer in an exact and simplified form.

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

Find the value of $x$.

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

In this part, all measurements are in centimetres.

The diagram shows a kite with sides $\left(2x+5\right)$ and $\left(3x-1\right)$. The perimeter of the kite is 33 cm.

Work out the length of a shorter side.

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

Rovers, United and City are football teams.

Rovers scored$x$goals.
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 $x$.

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

In this part, all angles are in degrees.

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

[1]

ii) Solve this equation to find the value of $x.$

$x$= ................................................. [3]

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

[2]

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

Work out the value of $w$.

$w$ = ................................................. [3]

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

Complete this statement about the value of $p$.

.................. $⩽p<$ ................... [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 $15x+625.$

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

Write an expression for the total cost, in dollars, for $x$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 $x$.

$x$= .............................................. [3]

Cara has $n$ 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 $n$.

$n$ = ................................................... 

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.

The diagram below shows a triangle.

Find the size of the smallest angle in the triangle in degrees.