Equations which can be written in the form

\[\dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(y),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x)f(y)\]

can all be solved by integration.

In each case it is possible to separate the $x$'s to one side of the equation and the $y$'s to the other

Solving such equations is therefore known as solution by separation of variables

This is a test of the Numbas math question examiner

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

Two questions on solving systems of simultaneous equations.

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

Solve a pair of linear equations by writing an equivalent matrix equation.

Questions about percentage and ratio, applied to finance.

Based on section 3.2 of the Maths-Aid workbook on numerical reasoning.

Solve a pair of linear equations by writing an equivalent matrix equation.

5 questions on indefinite integration. Includes integration by parts and integration by substitution.

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

$g: \mathbb{R} \rightarrow \mathbb{R}, g(x)=\frac{ax}{x^2+b^2}$. Find stationary points and local maxima, minima. Using limits, has $g$ a global max, min? 

Demo of Mathematical expression and Number input questions

Questions on vector arithmetic and vector operations, including dot and cross product, as well as the vector equations of planes and lines.

Solve a pair of linear equations by writing an equivalent matrix equation.

Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

Questions on linear programming techniques, with interactive graphics.

Statistics and probability. 2 questions. Both simple regression. First with 8 data points, second with 10. Find $a$ and $b$ such that $Y=a+bX$. Then find the residual value for one of the data points.

Three questions on linear combinations and products of matrices.

Find the inverses of three $2 \times 2$ invertible matrices.

5 questions on finding local and global maxima and minima on compact intervals and on the real line for differentiable functions.

4 questions. Qualitative, quantitative random variables, types of sampling, frequencies, stem and leaf plot, descriptive statistics.

Find the modulus and argument of complex numbers.

Questions about percentage and ratio, applied to finance.

Based on section 3.2 of the Maths-Aid workbook on numerical reasoning.

6 questions on numerical reasoning using percentages and ratios.

Three questions on parametric hypothesis testing and confidence intervals, aimed at psychology students.

3 questions on probability density functions - find the probability density function of a distribution, and apply it.

6 questions on standard statistical distributions.

Binomial, Poisson, Normal, Uniform, Exponential.

Use a probability mass function; determine if a given function is a probability mass function; find the probability mass function of a discrete distribution and use it.

Rearrange equations to make $x$ the subject.

3 questions. One question on limits of standard sequences. Other two on finding least $N$ such that $|a_n-L |\lt 10^{-r},\;\;n \geq N$ where $L$ is limit of $(a_n)$.