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• #### Expansion of brackets

This question is made up of 10 exercises to practice the multiplication of brackets by a single term.

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Key Stage 4 / GCSE, A-Level, Transition to university, Stage 1

• #### Expand brackets and collect like terms

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

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• #### Create an algebraic expression from a word problem, simplify, and evaluate

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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Key Stage 4 / GCSE, A-Level, Transition to university, Stage 1

• #### Find and use the formula for a geometric sequence

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.

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• #### Identifying different types of sequences

Differentiate between linear and quadratic sequences and arithmetic and geometric sequences through a series of multiple choice questions. Spot different patterns in sequences like the triangle sequence, square sequence and cubic sequence and then use this pattern to find the next three terms in each of the sequences.

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• #### Extract common factors of polynomials

Factorise polynomials by identifying common factors. The first expression has a constant common factor; the rest have common factors involving variables.

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• Pure mathematics
• Algebra

Key Stage 4 / GCSE, Transition to university, Stage 1

• #### Complete a frequency table and find the measures of central tendency

Given a table of data, calculate the mean, mode and median, and complete a frequency table.

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• Statistics
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Key Stage 4 / GCSE, Transition to university

• #### Using Laws for Addition and Subtraction of Logarithms

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

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• #### Find the equation of a line through two points - negative 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 negative gradient.

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Key Stage 4 / GCSE, A-Level, Transition to university, Stage 1

• #### Find the equation of a line through two points - 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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