Simon Vaughan

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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.

A set of Numbas exercises for students transitioning from school to University. Designed to help students gain familiarity with using Numbas to enter mathematics, and as revision for algebra, geometry and calculus. 

Find $\displaystyle I=\int \frac{2 a x + b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.

Find $\displaystyle \int x\sin(cx+d)\;dx,\;\;\int x\cos(cx+d)\;dx $ and hence $\displaystyle \int ax\sin(cx+d)+bx\cos(cx+d)\;dx$

Students must find $\int \frac{1}{x-a} \, dx$.

Differentiate $x^m\cos(ax+b)$

Differentiate $ (a+bx) ^ {m} \sin(nx)$

The derivative of $\displaystyle x ^ {m}(ax^2+b)^{n}$ is of the form $\displaystyle x^{m-1}(ax^2+b)^{n-1}g(x)$. Find $g(x)$.

Substitute values into formulae for the area or volume of various geometric objects.

Curl and divergence of a vector field.  Determine whether the vector field is irrotational or solenoidal.

Summation Notation

rebelmaths

Multiplying two 2 x 2 matrices.

Elementary Exercises in multiplying matrices. 

aij  notation and definition of the order of a matrix.

$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Multiplication of $2 \times 2$ matrices.