Matthew James Sykes

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

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

Missing: Application with bacteria, turning points, difficult chain rule

Load data on some items held in the Cooper Hewitt collection, and show a table of 5 randomly picked items.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Practice of conversion between SI units of mass, volume & length.

Questions involving various techniques for rearranging and solving quadratic expressions and equations

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Questions asking you to find the equation of a line between two points, in Cartesian coordinates.

A collection of questions on working with units of measurement, mainly in the SI/metric system.

Several 'real-world' examples.

Questions on manipulating logarithms.

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

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

Power rule

Equating coefficients of a polynomial. Basic ones that don't require simultaneous equations.

Slope of a curve at a point

Convert from degrees to radians

Questions on powers, the laws of indices, and exponential growth.

 Some questions on working with surds.

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product and chain rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$. Non-calculator. Advice is given.

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In parts (a) and (b) rearrange linear inequalities to make $x$ the subject.

In the parts (c) and (d) correctly give the direction of the inequality sign after rearranging an inequality.

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

A few simple functions are provided of the form ax, x+b and cx+d. Values of the functions, inverses and compositions are asked for. Most are numerical but the last few questions are algebraic.

Very good feedback and corresponds to instance of randomisation