A graph shows both the speed and acceleration of a car. Identify which line corresponds to which measurement, and calculate the acceleration during a portion of time.

This exercise will help you solve equations of type ax-b = c.

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

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

Displacement-time graphs are given and the student should select the correct velocity-time graphs from a list. Includes linear, piecewise linear and quadratic displacement-time functions.

This exercise will help you solve equations of type ax-b = c.

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

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

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

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

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

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

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

Solve a system of linear equations using Gaussian elimination.

Three questions on linear combinations and products of matrices.

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

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

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

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Apply the factor theorem to check which of a list of linear polynomials are factors of another polynomial.

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

Finding x and y values for straight line graphs

Looking at gradients and values for x and y for straight-line graphs

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

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

Identifying the gradient from a straight-line graph equation y=mx+c

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.

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 $\phi$.