Apply and combine logarithm laws in a given equation to find the value of $x$.

Multiple choice question. Given a randomised polynomial select the possibe ways of writing the domain of the function.

Multiple choice questions. Given randomised trig functions select the possible ways of writing the domain of the function.

Multiple choice questions. Given randomised trig functions select the possible ways of writing the domain of the function.

A graph of an (invertible) cubic is given. The question is to determine values of $f$ from graph.

Given an equation or a worded formula determine if it is a function or not

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.

Given a graph of some line or curve - the student is asked about the nature of the map and whether it constitutes a function.

Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.

Given three vectors with integer components, find the corresponding magnitude and direction.

Given three vectors with integer components, find the corresponding magnitude and direction.

Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.

Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.

Choose which of 5 matrices are in a) row echelon form but not reduced b) reduced row echelon form c) neither.

Find the first few terms of the Maclaurin and Taylor series of given functions.

Use a given factor of a polynomial to find the full factorisation of the polynomial through long division.

Given a factor of a cubic polynomial, factorise it fully by first dividing by the given factor, then factorising the remaining quadratic.

Given a graph of some line or curve - the student is asked about the nature of the map and whether it constitutes a function.

Given the graph of the line determine the equation of the line.

Given one point and the gradient determine the equation of the line.

Find the lowest common multiple and highest common factors of given numbers. Also a question on identifying prime numbers.

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.

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 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.

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.

Basic data structures and maths/stats functionality given.

You can configure the rest.

rebelmaths

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 $\phi$.