This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

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Practice solving equations with integer solutions. 

Rearraning the constant acceleration equation $v^2=u^2+2as$ to make $s$ the subject.

Rearraning the constant acceleration equation $v^2=u^2+2as$ to make $a$ the subject.

Rearraning the constant acceleration equation $v^2=u^2+2as$ to make $u$ the subject.

Rearraning the constant acceleration equation $s=ut+\frac{1}{2}at^2$ to make $a$ the subject.

Rearraning the constant acceleration equation $s=ut+\frac{1}{2}at^2$ to make $u$ the subject.

Rearraning the constant acceleration equation $v=u+at$ to make $t$ the subject.

Rearraning the constant acceleration equation $v=u+at$ to make $a$ the subject.

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Solving $\sin(3x)=\sin(x)$ for $x\in \left(0,\frac{\pi}{2}\right)$.

Solving $\sin(2x)-\tan(x)=0$ for $x\in \left(0,\frac{\pi}{2}\right)$.

Solving $\sin(nx)=a$ for $x\in (0,\pi)$, where $n$ is an integer and $a\in(0,1)$.

Given an equation of the form $m=m_0 e^{-kt}$ to model the mass of a radioactive material, calculate the decay constant $k$ and the time taken for the material to reach a certain percentage of its initial mass. 

Given an equation of the form $T=T_0 e^{kt}$ to model temperature, calculate the temperature after a given time, the time taken to reach a certain temperature, and the time taken for the temperature to double.

Solving $\log(y)+\log(x)=\frac{1}{n}\log(ay^n)$ for $x$, where $a$ and $n$ are positive integers.

Solving $a\log(x)+\log(b)=\log(c)$ for $x$, where $a$, $b$ and $c$ are positive integers.

Finding $x$ from a logarithmic equation of the form $\log_a\left(\frac{1}{x}\right) = b$, where $a$ is a positive integer and $b$ is a negative integer.

Finding $x$ from a logarithmic equation of the form $\log_x \left(\frac{1}{\sqrt(a)}\right) = \frac{1}{2}$, for a positive integer $a$.

Finding $x$ from a logarithmic equation of the form $\log_ax = b$, where $a$ is a positive integer and $b$ is a positive fraction.

Finding $x$ from a logarithmic equation of the form $\log_ax = b$, where $a$ and $b$ are positive integers.

Finding $x$ from a logarithmic equation of the form $\log_xa = b$, where $a$ and $b$ are positive integers.

Solving an equation of the form $a^x=b$ using logarithms to find $x$.

Finding the value of a variable

Extra practice on some basic algebra skills, including solving linear equations. You can try as many times as you like and also generate new versions of the questions for extra practice.

Find the equation from the image of graph

Finding the stationary points of a cubic equation and determining their nature.

Solving a differential equation of the form $\frac{dy}{dx}=a \cos(x) e^{-y}$ using separation of variables.

Solving a differential equation of the form $\frac{dy}{dx}=ax^n e^{-y}$ using separation of variables.