CAIE IGCSE Mathematics Core C2.5 Equations Question Bank

Practise forming, rearranging and solving equations from algebraic statements, formulae, shape facts and real-life cost contexts.

Exam points

form an equation from a perimeter, percentage or word problem, then solve for the unknown
solve linear equations and substitute into formulae to find a specified variable
write and solve simultaneous equations from paired cost or quantity information

[Maximum number: 3]

(a)

A minibus can be hired from Dhruv's Minibuses.

The cost is $ h per hour plus $ p per passenger.

[ 3 ]

(i)

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

Complete the equation.

3 h+10 p=\ldots \ldots \ldots \ldots \ldots \ldots \ldots .

[ 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 h and p. You must show all your working.

\begin{aligned} & h=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . \\ & p=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . \end{aligned}

[Maximum number: 2]

Solve.

6 x+5=29

4

M1 for 6x=29-5 or $x+\frac{5}{6}=\frac{29}{6}$ oe

[Maximum number: 4]

(a)

Solve these equations.

[ 4 ]

(i)

7 x=-42

x=

[ 1 ]

(ii)

9(8 x-7)=72

x=

[ 3 ]

(b)

Solve the simultaneous equations.
$\begin{aligned}-6x-y&=13\\8x+y&=-51\end{aligned}$ $x=\quad y=$

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