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 worksheet on examining whether a function is one-to-one, given its equation, mapping diagram, set of ordered pairs or graph. Detailed solutions are included.
A worksheet on prime factorisation. The exercises require to find the prime factorisation of a number using repeated division. Detailed solutions are included.
A worksheet on prime numbers and prime factorisation. The exercises require to decide whether some given numbers are prime or not and reach some conclusions about prime numbers, find the factors of a number given its prime factorisation, find the common factors of two numbers given their prime factorisations and find the prime factorisation of a number using repeated division. Detailed solutions are included.
A collection of three worksheets on functions.
The first worksheet aims to introduce the concept of functions. The exercises require to state whether a given mapping diagram represents a function or not, to determine the domain and range of functions given the corresponding mapping diagrams, to evaluate functions at specific values and to use functions to model real life problems.
The second worksheet aims to teach students various ways of representing a function: mapping diagrams, sets of ordered pairs, graphs and equations. The exercises require to find the sets of ordered pairs associated with functions given in the form of mapping diagrams, examine whether some given sets, graphs or equations represent functions and find the domain and range of some functions given their graphs.
The third worksheet is on finding the domain or the range of a given function (including the cases of polynomial functions, rational functions and functions with square roots).
Detailed solutions are included.
A worksheet on examining whether two given functions are equal by examining their domain and their value at each element of their domain. Detailed solutions are included.
A worksheet on adding, subtracting, multiplying and dividing functions and determining the domain of the functions produced. Detailed solutions are included.
A worksheet on determining whether a number belongs in the sets of natural numbers, integers, rational numbers and real numbers. It consists of a table to be completed. Solutions are included.
A worksheet on HCF and LCM. The exercises require to find the prime factorisation of a set of 2 or 3 numbers using repeated division and use it to evaluate their HCF and their LCF, decide whether a given pair of numbers are relatively prime (coprime), simplify fractions as much as possible by dividing their numerator and denominator by their HCF and add or subtract pairs of fractions after changing their denominator and using the LCM of the original denominators. Detailed solutions are included.
A collection of three worksheets on the following:
Prime numbers and prime factorisation. The exercises require to decide whether some given numbers are prime or not and reach some conclusions about prime numbers, find the factors of a number given its prime factorisation, find the common factors of two numbers given their prime factorisations and find the prime factorisation of a number using repeated division.
Prime factorisation. The exercises require to find the prime factorisation of a number using repeated division.
Highest common factor and lowest common multiple. The exercises require to find the prime factorisation of some numbers and then use it to find their HCF and their LCM.
Detailed solutions are included.
A worksheet introducing the students to subtraction of positive and negative numbers (integers, fractions and decimals). The exercises require to perform calculations with two or more terms, find missing terms in given calculations, and compare numerical expressions. Solutions are included.
A worksheet introducing the students to multiplication of positive and negative numbers (integers, fractions and decimals). The exercises require to perform calculations with two or more terms, find missing terms in given calculations, and compare numerical expressions. Solutions are included.
A worksheet introducing the students to addition of positive and negative numbers (integers, fractions and decimals). The exercises require to perform calculations with two or more terms, find missing terms in given calculations, and decide whether some statements are true or false. Solutions are included.
Four worksheets introducing the students to addition, subtraction, multiplication and division of positive and negative numbers (integers, fractions and decimals). The exercises require to perform calculations with two or more terms, find missing terms in given calculations, and compare numerical expressions. Solutions are included.
A worksheet introducing the students to division of positive and negative numbers (integers, fractions and decimals). The exercises require to perform calculations with two or more terms, find missing terms in given calculations, and compare numerical expressions. Solutions are included.
A worksheet on changing recurring decimals into fractions. Including recurring decimals with repeating digits and recurring decimals with repeating and nonrepeating digits. Detailed solutions are provided.
