Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

A graph is drawn. A student is to identify the derivative of this graph from four other graphs.

A graph is drawn. A student is to identify the derivative of this graph from four other graphs. There are four version of this question: I: cubic, II: linear, III: quadratic, IV: sinusoisal.

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Students are given a line equation in the form y=mx+b and asked to graph it.

m and b are randomised.

The question is not auto-marked, students need to "reveal answers" to see a sample graph that they can compare to their own.

Students are given a word problem and are asked to construct a line equation, evaluate it at a given point, and graph the line.

The line parameters and the given point are randomised.

Students are given a line equation (where the coefficient of y is 1) and asked to rearrange it into gradient-intercept form.

Students are given a word problem with the distance travelled and the time taken by a cyclist. They need to choose the correct form for the linear equation, compute the gradient, and plot the line.

The distance travelled and time taken are randomised.

Speed, distance and time are all integer values.

Students are shown to intersecting lines in the context of comparing the costs of services from two companies. They are asked to identify the y-intercept, the gradients, the point of intersection and are asked to interpret the graphs in the context of the word problem.

A bill (for a random amount) is divided equally between a number of people.

Students evaluate the per-person cost for a random number of people.

They then complete a table showing the cost per person for various numbers of people.

Finally they are asked to identify the shape of the graph that represents this function. They are given 2 exponentials, a hyperbola and a line to choose from.

Students are given 2 equations of the form y=mx+b and asked to solve them using either the substitution or the elimination method. The lines are randomised but the solution coordinates are always integers.

Describe a given linear transformation as a vector in Cartesian coordinates.

Students are shown to intersecting lines in the context of a gym visiting program. They are asked to identify the y-intercept, the gradients, the point of intersection and are asked to interpret the graphs in the context of the word problem.

Studnents are asked to write down equations for cost and income for a business.

They are then asked to graph the two lines.

Students are shown a graph that simultaneously plots cost and revenue lines. They are asked to identify the break-even point.

They are asked to give the x- and y- coordinate values.

The graph is randomised, but it is set up so that the point of intersection lies on gridlines.

This demonstrates how to construct a JSXGraph diagram in JME code.

The construction shows a triangle and its orthocentre, circumcentre and centroid. They are always collinear. You can move the vertices of the triangle.

Students are given the equation of a parabola and asked to identify its graph. They are given the parabolic curve, an exponential, a hyperbola and a line to choose from.

Questions used in a university course titled "Group theory".

The questions deal with permutations written in cycle or two-line notation.

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Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

Solve for $x$ each of the following equations: $n^{ax+b}=m^{cx}$ and $p^{rx^2}=q^{sx}$.

Solve for $x$: $c(a^2)^x + d(a)^{x+1}=b$ (there is only one solution for this example).

Express a sum of linear terms in $x$ and $y$ as a single linear term in $x$ and $y$.

Expand $ax(cx+d)$ and expand $(rx+s)(px)$

Expand $(ax+b)(cx+d)$.

Expand $(pw+q)(aw^2+bw+c)$.

Expand $(az^2+bz+c)(pz+q)$.

Rotate the graph of  $y=a\ln(bx)$  by $2\pi$ radians about the $y$-axis between $y=c$ and $y=d$. Find the volume of revolution.

Inverse and division of complex numbers.  Four parts.