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

Simplifying expressions such as $b^{\log_b(x)}$ and $b^{\log_b(x)}$.

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

Transposition of formulae. Changing the subject of an equation. 

rebel rebelmaths

Instructions on inputting ratios of algebraic expressions.

rebelmaths

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Cofactors Determinant and inverse of a 3x3 matrix.

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Find the determinant of a $3 \times 3$ matrix.

Multiplication of $2 \times 2$ matrices.

Linear combinations of $2 \times 2$ matrices. Three examples.

Elementary Exercises in multiplying matrices. 

Cofactors Determinant and inverse of a 3x3 matrix.

Solving quadratic equations using a formula

Solving quadratic equations using a formula,

Solving quadratic equations using a formula,

Solve a logarithmic equation

Basic question on limit laws and the squeeze theorem for sequences.

Solve an exponential equation

Manipulation of an exponential function

Manipulación de expresiones algebraicas

Este test contiene ecuaciones de fracciones algebraicas, ecuaciones logarítmicas, ecuaciones exponenciales y ecuaciones cuadráticas.

Often students need practice re-indexing series, these are three questions that give them that opportunity.

Test whether a student knows the divergence test of a series, and how to use it. Series include those that the diverence test is inconclusive for. This question could be better in that it could go through the working of determining the limit but I hope to make a separate question which deals with that.

This question tests to see if students can recognise a $p$-series and based on its $p$-value determine if it is convergent or divergent.

This question tests to see if students can recognise a geometric series and based on its common ratio determine if it is convergent or divergent.