Students are shown a graph of the value of a machine over time. The line equation is randomised.

They are asked to evaluate value at a given time, and the time at which a given value is reached. They are asked when the machine has no value, and the range of times over which the model is valid. They are also asked to explain the physical meaning of the gradient.

Students are given the equations of two lines in the form y=mx+b and asked if they are parallel.

The line equations are randomised.

The answer is yes or no. There is a 1 in 6 chance of the lines being parallel.

Students are given equations for a line, a parabola, a hyperbola and an exponential, and their respective graphs and are asked to match them.

Students are shown an exponential curve and asked to identify it as either linear, parabolic, hyperbolic or exponential.

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. 

A question to practise the following skills in the context of Earth Sciences:

• using a data set to deduce a linear relationship
• using the graph to make predictions

Calculating the area enclosed between a linear function and a quadratic function by integration. The limits (points of intersection) are not given in the question and must be calculated.

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Questions shown in my presentation for the Teaching And Learning Mathematics Online session, 16th November 2022.

A line with random $x$- and $y$- intercepts is plotted, and you have to drag two dots over the points where the line crosses the $x$ and $y$ axes.

Denominators with linear factors, repeated factors and non-factorisable quadratics.

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Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

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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A graph shows both the speed and acceleration of a car. Identify which line corresponds to which measurement, and calculate the acceleration during a portion of time.

Finding the transformation of a linear function $f(x)=mx+c$ to $af(x)$.

Finding the transformation of a linear function $f(x)=mx+c$ to $f(x)+a$.

Finding the transformation of a linear function $f(x)=mx+c$ to $f(ax)$.

Finding the transformation of a linear function $f(x)=mx+c$ to $f(x+a)$.

Finding the transformation of a linear function $f(x)=mx+c$ to $f(ax)+b$.

Finding the transformation of a linear function $f(x)=mx+c$ to $af(bx)$.

Finding the transformation of a linear function $f(x)=mx+c$ to $af(x+b)$.

Finding the transformation of a linear function $f(x)=mx+c$ to $f(ax+b)$.

Finding the inverse of a linear function $f(x)=mx+c$.

Evaluating a linear function for a given value of $x$.

Evaluating composite functions involving a linear function and a modulus function of the form $f(x)=|x|+c$, for a given value of $x$.

Finding composite functions of a linear function and a modulus function.

Finding composite functions of a linear function and an exponential function.