Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

Just showing how to use the stdev function from the stats extension to calculate the standard deviation of a list of numbers.

Students explore the relationship between length and area of a rectangle.

The perimeter of the rectangle is randomised. Students are given 11 different lengths, and asked to compute rectangle width and area for each. They are then asked to graph the function, identify it as a parabola, and estimate the maximum value.

Students are given an exponential equation and asked to identify the y-intercept from a list of choices.

The constants in the exponential equation have been randomised.

The student is shown an exponential graph and asked to evaluate the function at some given value.

They are also asked whether or not the model is valid for all real inputs, but they only give a yes/no response. The reasoning is explained in the advice but is not required from students.

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

Derive the expressions for the shear and bending moment as functions of $x$ for a cantilever beam with a uniformly varying (triangular) load.

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 $y=y_0$.

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.

Calculating the derivative of a function of the form $\sin(ax^m+bx^n)$ using the chain rule.

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.

Solve a trigonometric equation

This test will assess a students ability to work with piecewise and composite functions.

Definite integation of basic functions.

Differentiate $\displaystyle (ax^m+b)^{n}$.

Finding the transformation of a function with a modulus, from $f(x)=nx-m|x|$ to $af(x)$.

Finding the transformation of an exponential function $f(x)=e^{nx}$ to $af(x)$.

Finding the transformation of a function $f(x)=\frac{nx^2}{x+c}$ to $af(x)$.

Finding the transformation of a quadratic function $f(x)=ax^2+bx+c$ to $nf(x)$.

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

Finding the transformation of a function with a modulus, from $f(x)=nx-m|x|$ to $f(x)+a$.

Finding the transformation of an exponential function $f(x)=e^{nx}$ to $f(x)+a$.

Finding the transformation of a function $f(x)=\frac{nx^2}{x+c}$ to $f(x)+a$.

Finding the transformation of a quadratic function $f(x)=ax^2+bx+c$ to $f(x)+n$.

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

Finding the transformation of a function with a modulus, from $f(x)=nx-m|x|$ to $f(ax)$.

Finding the transformation of an exponential function $f(x)=e^{nx}$ to $f(ax)$.

Finding the transformation of a function $f(x)=\frac{nx^2}{x+c}$ to $f(ax)$.

Finding the transformation of a quadratic function $f(x)=ax^2+bx+c$ to $f(nx)$.

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