Find the solution of a first order separable differential equation of the form $a\sin(x)y'=by\cos(x)$.

Calculate and work with measures of central tendency such as mean, median and mode, and measures of spread such as range and standard deviation.

Calculate and work with measures of central tendency such as mean, median and mode, and measures of spread such as range and standard deviation.

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

Compute a 95% confidence interval for the population mean given a small sample, and compare it with a confidence interval for a different population.

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.

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.

Students seem to struggle with Sigma notation, this is about the easiest question possible for sigma notation.

Students seem to struggle with Sigma notation, this is about the easiest question possible for sigma notation.

Students seem to struggle with Sigma notation, this is a simple question to ensure they understand the index can change without affecting the sum.

Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by substitution 3 with parts' by Joshua Boddy.

Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by elimination 1 with parts' by Joshua Boddy.

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).

Some practice collecting like terms of algebraic expressions, with detailed advice.

Adapted from 'Collecting like terms' by Ben Brawn.

Transposing formulae

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Scientific Notation

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Compute a 95% confidence interval for the population mean given a small sample, and compare it with a confidence interval for a different population.

Compute a 95% confidence interval for the population mean given a small sample, and compare it with a confidence interval for a different population.

Given the cost of hiring a room for a given number of hours, compare with competing prices given per hour and per minute.

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

Practice with adding, subtracting and dividing basic algebraic fractions

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each .

Example of a universal statement over the integers and its negation

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

Testing addition, multiplication and division involving negative numbers.

Addition, multiplication and division of fractions.

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