Fully comprehensive math worksheets with detailed solutions and other math resources for students of all abilities and levels (KS2, KS3, SATs, 11+, GCSEs, iGCSEs, A-Levels, Scottish Highers and Advanced Highers, International Baccalaureate, BTECs or even university or college degree level).
Fully comprehensive math worksheets with detailed solutions and other math resources for students of all abilities and levels (KS2, KS3, SATs, 11+, GCSEs, iGCSEs, A-Levels, Scottish Highers and Advanced Highers, International Baccalaureate, BTECs or even university or college degree level).
A collection of three worksheets on the following topics:
Dividing polynomials using long division
Using division to factor polynomials
Factorising a polynomial using the factor theorem
In the first worksheet, students are required to perform long division for some given pairs of polynomials.
In the second worksheet, students must use polynomial division to find the remaining linear factors of a polynomial, given one of its factors. In other exercises, students must find a polynomial using multiplication given all its factors, find the highest common factor of given algebraic expressions and find missing terms in factorized expressions.
In the third worksheet, students are required to check whether a given polynomial is a factor of another polynomial by using the factor theorem and then in some other exercises they are required to factor cubic polynomials by first finding one of its linear factors (by checking given polynomials or inspecting using the factor theorem) and then using long division to find the remaining linear factors.
Detailed solutions are included.
A worksheet on the following: finding the gradient of a line given its equation, finding the equation of a line given its gradient and one point on it or two points on it and finding the equation of a line parallel to another line passing through a given point. Detailed solutions are included.
A collection of ten worksheets on the following algebra topics: Changing the subject of a formula, equation of a straight line ( finding the gradient of a line given its equation, finding the equation of a line given its gradient and one point on it or two points on it and finding the equation of a line parallel to another line passing through a given point), expanding expressions by multiplying brackets by a single number or variable and collecting like terms when appropriate, factorising polynomials (extracting a common factor, difference of two squares, perfect square, quadratic factorisation), indices, inverse and composite functions, linear equations. Detailed solutions are included.
A collection of 5 worksheets on ratio and proportion based on the GCSE 9-1 specification.
The following worksheet are included:
Introduction to ratios: converting ratios to fractions, writing and simplifying ratios
Simplifying ratios
Ratios: simplifying ratios and dividing an amount in a given ratio
Dividing amounts in a given ratio
Direct proportion: calculating the constant of proportionality using the given information and then use the resulting equation to calculate the value of the one of the two variables given the value of the other
Detailed solutions are included.
A worksheet introducing students to the concept of ratios. The exercises include converting ratios to fractions, writing and simplifying ratios. Solutions are included.
A worksheet on factorising algebraic expressions using the method of grouping.
The first exercise is on factoring algebraic expressions by taking the highest common factor of their terms and the remaining exercises are on factoring by grouping.
Detailed solutions are included.
A worksheet on factoring quadratics and simplifying algebraic fractions. Including quadratic expressions that can be factored by taking out the highest common factor of their terms, trinomials with leading coefficient one or greater and the special cases of perfect squares and difference of two squares. Detailed solutions are provided.
Three worksheet on factorising quadratics including the special cases of perfect squares and difference of two squares. Detailed solutions are provided.
A collection of six worksheets with GCSE/IGCSE style questions on algebra and number topics such as simplifying algebraic expressions, factorisation, algebraic fractions, operations between fractions, hcf and lcm and surds, Detailed solutions are included.
A collection of 6 worksheets on algebraic manipulation based on the GCSE 9-1 specification.
The following worksheet are included:
Multiplying out two brackets
Multiplying three brackets
Factorising quadratics
Simplifying algebraic fractions
Operations with algebraic fractions
Completing the square
Detailed solutions are included.
A worksheet on factoring quadratics. Including quadratic expressions that can be factored by taking out the highest common factor of their terms, trinomials with leading coefficient one or greater and the special cases of perfect squares and difference of two squares. Good for GCSE/IGCSE students. Detailed solutions are provided.
Four worksheets on factorising polynomials covering different cases: extracting a common factor, difference of two squares, perfect squares, quadratic factorisation. Detailed solutions are provided.
Three worksheets on expanding and factorising quadratics (binomials, trinomials ,differences of two squares and perfect squares) and simplifying algebraic fractions. Detailed solutions are provided.
Five worksheets on ratios including exercises on writing and simplifying ratios, expressing ratios as fractions and dividing and amount in a given ratio. Detailed solutions are provided.
