Equations

Solve the equation $4x = 10$.

Feb/March 2017

Choose a marble at random from the bag, then replace it. Write down the probability that the marble is black.

Feb/March 2017

Factorise $3x^2 + 11x - 4$ into brackets.

Feb/March 2017

Neelum rents a machine to clean carpets. The hire charge is $25$ for the first day and $9$ for every additional day after that first day. Altogether, Neelum pays $88$ to hire the machine.

Feb/March 2018

Solve the simultaneous equations. Show every stage of your working. $2x+\frac{1}{2}y=13$ and $3x+2y=17$.

Feb/March 2018

Solve the equation $2x^{2}+7x-3=0$. Show all your working, and write each answer correct to 2 decimal places.

Feb/March 2018

A stationery shop sells pens and notebooks. A pen costs $p$ cents, and a notebook costs $n$ cents.

Feb/March 2018

Complete the statement about the value of $w$.

Feb/March 2019

Solve the simultaneous equations below. Show every step of your working. $6x - 3y = 12$, $2x + 3y = 16$.

Feb/March 2019

Find the numerical value of $w$.

Feb/March 2019

You must include all of your working.

Feb/March 2020

Solve the simultaneous equations. You must include all your working. $5x + 6y = 14$, $2x + 8y = 7$.

Feb/March 2021

Solve the simultaneous equations. Show every stage of your working. $x - y = 7$, $x^{2} + y = 149$.

Feb/March 2021

Solve the equation $\frac{25-2u}{3}=2$.

Feb/March 2023

You need to show all your working.

Feb/March 2023

Find the values of $x$ for which $6x + y = 10$ and $y = x^2 - 3x + 10$ both hold.

Feb/March 2023

Find the solution.

Feb/March 2023

Solve the simultaneous equations. You must present all of your working. $3x - 2y = 19$ $x + y = 3$

Feb/March 2023

For $P = 3a + 5$, determine the value of $P$ at $a = 2$.

Feb/March 2024

Solve these simultaneous equations: $4t - 3w = 11$ and $6t + 2w = -3$.

Feb/March 2025

Raj is thinking of a negative number $n$. He adds 10 to $n$ and then multiplies the result by 5. This gives 30. Find the value of $n$.

Feb/March 2025

Solve the equation $5(3y - 2) = 35$.

May/June 2015

Solve $3(x + 4) = 2(4x - 1)$.

May/June 2015

Solve the simultaneous equations below. You must show all your working. $5x + 2y = -2$ $3x - 5y = 17.4$

May/June 2015

Solve for $w$ in $5(w + 4 \times 10^3) = 6 \times 10^4$.

May/June 2015

Solve the equation $2x^2 + x - 2 = 0$. Show all your working and give the answers correct to 2 decimal places.

May/June 2015

Solve the equation given by $3(x + 4) = 2(4x - 1)$.

May/June 2015

Sonia is employed in a toy shop.

May/June 2015

Find the value of $A$ for $r = 5.6$. Round your answer to 1 decimal place.

May/June 2015

Set up an equation and solve it to determine the value of $x$.

May/June 2015

At the start of the trip, Alan covered $x$ km and his car consumed $6$ litres of fuel. Its fuel consumption rate was $\frac{600}{x}$ litres per $100$ km.

May/June 2015

Solve the pair of simultaneous equations. You must show every step of your working.

May/June 2016

Solve the simultaneous equations. Show every step in your working. $3x + 4y = 14$ $5x + 2y = 21$

May/June 2016

Solve the simultaneous equations below. You must show all of your working. $3x+7y=-21$, $6x+4y=3$.

May/June 2016

Solve the equation $6(y+1)=9$ for $y$.

May/June 2016

Solve the simultaneous equations. Provide all the working. $3x + 4y = 14$, $5x + 2y = 21$.

May/June 2016

Solve $6(y+1)=9$ for $y$.

May/June 2016

Solve for $x$ in the equation $x + 7 = 15$.

May/June 2016

Show that the equation $x^2-40x+A=0$ is obtained.

May/June 2016

Alfonso covers 10 km at an average speed of $x$ km/h. On the following day, he covers 12 km at an average speed of $(x - 1)$ km/h. The 10 km journey takes 30 minutes less than the 12 km journey.

May/June 2016

Solve the simultaneous equations. Show all your working. $5x - 2y = 24$ and $7x + 4y = -14$.

May/June 2017

Solve the equation $2 - x = 5x + 1$.

May/June 2017

Finish the statement about the value of $m$.

May/June 2017

Solve for $x$ in $2 - x = 5x + 1$.

May/June 2017

Solve the equation $5x^{2} + 10x + 2 = 0$. You should show every step of your working and present your answers correct to 2 decimal places.

May/June 2017

Camilla signs up for a soccer club. The overall joining cost consists of membership, kit and travel.

May/June 2017

For this question, all lengths are measured in centimetres.

May/June 2017

Solve the simultaneous equations.

May/June 2018

Solve $8x - 5 = 7$.

May/June 2018

If $w = [BLANK],\; 10w = 70$.

May/June 2018

Find the values of $a$ and $b$.

May/June 2018

Solve for $p$: $\dfrac{1 - p}{3} = 4$.

May/June 2018

Complete the sentence relating to the value of $m$.

May/June 2018

Calculate $x$.

May/June 2018

Solve the simultaneous equations. All your working must be shown. $3x - 2y = 23$ $2x + 5y = 9$

May/June 2018

Finish these statements.

May/June 2018

Work out $\frac{1-p}{3}=4$.

May/June 2018

Solve $3(2x - 4) = 4(x + 7)$.

May/June 2018

Solve the equation $7x - 5 = 16$.

May/June 2019

Solve the simultaneous equations $5x - 2y = 26$ and $7x + 6y = 10$. All working must be shown.

May/June 2019

Solve the simultaneous equations, and make sure that all of your working is shown. $5x + 8y = 4$ $\frac{1}{2}x + 3y = 7$

May/June 2019

Solve the equation. Show all your working and give your answers accurate to 2 decimal places.

May/June 2019

Solve the equation $9f + 11 = 3f + 23$.

May/June 2019

The equation $ax^2 + a = 150$ has $x = 7$ as one root.

May/June 2019

The formula is $s = ut + \frac{1}{2}at^2$.

May/June 2019

Solve the simultaneous equations $2x+y=3$ and $x-5y=40$. Show all your working.

May/June 2021

Solve the simultaneous equations below. Show all your working. $2x+y=3$ $x-5y=40$

May/June 2021

Solve $\frac{1}{x + 1} + \frac{9}{x + 9} = 1$.

May/June 2021

Joe chooses a number, $n$, multiplies it by 3, and then takes away 5. The answer is 22.

May/June 2022

Solve the simultaneous equations. Make sure that you show all your working.

May/June 2022

The graphs of $y = x + 1$ and $y = x^2 - 3x - 11$ meet at the points $A$ and $B$.

May/June 2022

Write an expression, in terms of $w$ and $d$, for the team’s total points.

May/June 2022

Find how many apples Geeta buys.

May/June 2022

Find the value of $k$. Show your working in full.

May/June 2022

For $y$ hours of bicycle hire, the cost, $C$, is determined by the formula $C = 12 + 3.5y$. Maria pays $36.50 in order to hire this bicycle.

May/June 2023

In a cinema, the price of an adult ticket is $a$, while the price of a child ticket is $c$.

May/June 2023

All measurements in this question are in centimetres. The diagram shows two line segments, $AB$ and $CD$. $AB$ has length $10x - 12$. $CD$ has length $2x + 3$. $AB$ is 3 times the length of $CD$. The diagram is not drawn to scale.

May/June 2023

Calculate the value of $r$.

May/June 2023

For the equation $ax^2 + b = 181$, one root is $x = 8$. Both $a$ and $b$ are positive integers greater than 1.

May/June 2023

Solve for $x$ in $\frac{30}{x} = 6$.

May/June 2023

Find the solutions to $x^2 + 5x - 7 = 0$. Show every step of your working and give your answers correct to 2 decimal places.

May/June 2023

Calculate how many tins he had at the start of the day.

May/June 2023

Set up and solve an equation to determine the cost of one shirt.

May/June 2023

You are required to show all of your working.

May/June 2024

Determine the value of $x$.

May/June 2024

Solve these simultaneous equations.

May/June 2024

Solve the simultaneous equations. Show every step of your working. $\frac{3x}{2} + 5y = 5$ and $4x - 3y = 46$.

May/June 2024

Solve the simultaneous equations below. You must show every step of your working. $4y + 3x = 13$ $y = x^2 - 18$

May/June 2024

Determine the value of $r$.

May/June 2024

Find the values of $t$ and $w$ that satisfy the simultaneous equations $5t - 2w = 19$ and $3t + 2w = 5$.

May/June 2024

Calculate the total points for this team.

May/June 2024

Solve the equation $5x + 8 = 3x - 2$.

May/June 2025

Solve for $x$ and $y$ using the simultaneous equations $2x + 5y = 5$ and $3x + 4y = 11$.

May/June 2025

Two numbers have a total of $-2$ and a product of $-15$.

May/June 2025

Beth considers a positive number $n$. She squares $n$ and then subtracts 55. The result is 9.

May/June 2025

Solve the simultaneous equations $5x + 2y = 3$ and $3x + 4y = 27$.

May/June 2025

Solve these simultaneous equations: $8x + 5y = 4$ and $2x - y = 10$.

May/June 2025

The line $y = 7x + 3$ meets the curve $y = x^2 + 5x - 12$ at points $A$ and $B$.

May/June 2025

Solve for $x$ in $8x + 7 = 39$.

May/June 2025

Solve the simultaneous equations $4x - 5y = 13$ and $3x - 2y = 8$.

May/June 2025