Draws a triangle based on 2 angles and a side length.

Uses JSXGraph to generate a plot for a cubic, with given critical points, along with three other incorrect graphs with modified properties. JSXGraph code is commented.

No description given

Differentiate $f(x) = ax^m$.

Differentiate $f(x) = ax^m$.

Differentiate $f(x) = x^m(a x+b)^n$.

Differentiate $f(x) = x^m(a x+b)^n$.

No description given

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

rebelmaths

Calculation of modulus, argument, multiplication by complex conjugate, given two complex numbers.

order of operations

A quadratic function $ax^2+bs+c$ is given. Six parabolas are sketched. Question is to select the correct parabola.  Need to consider the y-intercept, the coefficient of x^2, and the x-coordinate of the minimum/maximum point.

Quadratic factorisation that does not rely upon pattern matching.

Elementary Exercises in multiplying matrices. 

Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector $(x=1)$.

The random variable $X$ has a PDF which involves a parameter $c$. Find the value of $c$. Find the distribution function $F_X(x)$ and $P(a \lt X \lt b)$.

Also find the expectation $\displaystyle \operatorname{E}[X]=\int_{-\infty}^{\infty}xf_X(x)\;dx$.

Finding the coordinates and determining the nature of the stationary points on a polynomial function

Find the dot product and the angle between two vectors

Given vectors $\boldsymbol{a,\;b}$, find $\boldsymbol{a\times b}$

rebelmaths

Find the solution of a constant coefficient second order ordinary differential equation of the form $ay''+by'+cy=0$.

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

Cofactors Determinant and inverse of a 3x3 matrix.

Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

Given a random variable $X$ normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

Question on the exponential distribution involving a time intervals and arrivals application, finding expectation and variance. Also finding the probability that a time interval between arrivals is less than a given period. All parameters and times randomised. 

Normal distribution $X \sim  N(\mu,\sigma^2)$ given. Find $P(a \lt X \lt b)$. Find expectation, variance, $P(c \lt \overline{X} \lt d)$ for sample mean $\overline{X}$.

Provided with information on a sample with sample mean and known population variance, use the z test to either accept or reject a given null hypothesis.

Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.

order of operations