Given a description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression, and finally evaluate it at a given point.

The word problem is about the costs of sweets in a sweet shop.

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

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.

Find the solution of a first order separable differential equation of the form $axyy'=b+y^2$.

Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.

Find the equation of a straight line which has a given slope or gradient $m$ and passes through the given point $(a,b)$.

There is a video in Show steps which goes through a similar example.

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

No description given

No description given

Polar form of a complex number.

Using trig identities to find solutions to equations

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

rebelmaths

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

rebelmaths

Implicit differentiation question with customised feedback to catch some common errors.

Implicit differentiation question with customised feedback to catch some common errors.

Given data on probabilities of three levels of success of three options and projections of the profits that the options will accrue depending on the level of success, find the expected monetary value (EMV) for each option and choose the one with the greatest EMV.

This question assesses the students ability to find the expected number of times an event occurs given the probability of the event occurring for a single trial and the total number of trials.

Footballer expects to score in a/b matches.

Basic data structures and maths/stats functionality given.

You can configure the rest.

rebelmaths

rebelmaths

A student selects a card from a deck of 52 and rolls a dice once.

rebelmaths

Using the reduction formulas for products of powers or sin and cosine

Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$  with coefficients in the real numbers. Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by: \[\phi(p(x))=p(a)+p(bx+c).\]Using the standard basis for range and domain find the matrix given by $\phi$.

Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$  with coefficients in the real numbers.

Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by:

$\phi(p(x))=ap(x) + (bx + c)p'(x) + (x ^ 2 + dx + f)p''(x)$

Using the standard basis for range and domain find the matrix given by $\phi$.

Given a matrix in row reduced form use this to find bases for the null, column and row spaces of the matrix.

Reduce a 5x6 matrix to row reduced form and using this find rank and nullity.

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

Multiplication of $2 \times 2$ matrices.