Students are given the equation of a hyperbola and asked to identify the hyperbolic graph out of a set of 4 graphs.

Students are given an exponential equation and asked to evaluate it at two points.

The constants in the exponential are randomised.

Students are shown an exponential function formula and asked to identify the correct graph, given an exponential, a hyperbola, a parabola and a line.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Using the given information to complete the equation $y= A \cos{ \left( \frac{2 \pi}{P} x  \right) }+V $ that describes an electromagnetic wave and calculating the smallest angle, $x$, for which $y=y_0$.

Solving a separable differential equation that describes the population growth over time with a known initial condition to calculate the population after $n$ years. 

Integrating a polynomial functions which describe the rate of change of a population over time to find and use an equation that describes the total population according to time.

Solving a quadratic equation of the form $ax^2+bx+c=0$.

Solve a trigonometric equation

Solve a trigonometric equation involving a conversion to tangent by division by cosine.

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Topics: Trigonometeric equations and complex numbers
Students must complete the exam within 90 mins (standard time).
Questions have variables to produce randomised questions.

Trigonometric equations with degrees

Simple trig equations with radians

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.