Calculating gradient and finding intercept from a geogebra graph.

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Find the equation of a line given a point and a parallel or perpendicular line.

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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 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.

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

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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. 

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.

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

Finding composite functions of a linear function and a function of the form $x^n+a$.