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).
An introductory worksheet on 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. Detailed solutions are provided.
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 that 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. Detailed solutions are provided.
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 adding, subtracting, multiplying and dividing functions and determining the domain of the functions produced. Detailed solutions are included.
A worksheet on prime numbers and prime factorization. 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 factorization, find the common factors of two numbers given their prime factorizations and find the prime factorization of a number using repeated division. Detailed solutions are included.
A worksheet on prime factorization. The exercises require to find the prime factorization of a number using repeated division. Detailed 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 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 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 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.
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 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 complementary angles, supplementary angles, and vertical angles. The exercises require to identify complementary, supplementary and vertical angles and write and solve equations to find missing complementary, supplementary and vertical angles, as well as angles on a line and angles in a circle. Detailed solutions are included.
A worksheet on complementary angles, supplementary angles, and vertical angles. It includes introductory notes with the definitions of these types of angles. The exercises require to identify complementary, supplementary and vertical angles, find the complementary and supplementary angles of a given angle and write and solve equations to find missing complementary and supplementary angles. Detailed solutions are included. Good to be used as an introductory worksheet for this topic.
Three worksheets on complementary angles, supplementary angles, and vertical angles. They includes introductory notes with the definitions of these types of angles. The exercises require to identify complementary, supplementary and vertical angles, find the complementary and supplementary angles of a given angle and write and solve equations to find missing complementary and supplementary angles, as well as angles on a line and angles in a circle. It includes harder exercises on this topic. Detailed solutions are included.
This is a worksheet to help students strengthen their skills in the concept of parallel lines cut by a transversal. The following angle relationships occur in the exercises: complementary angles, supplementary angles, vertical angles, alternate interior angles, alternate exterior angles, consecutive interior angles and corresponding angles.
In the first two exercises, students are given a diagram with two parallel lines cut by a transversal and are required to identify the relationships between some given pairs of angles. In the next exercises, students are given some diagrams with missing angles which are required to find by using their knowledge on the topic. Elementary and harder exercises are included.
Detailed solutions (with reasoning) are provided.
A collection of seven worksheets on the following topics:
Classifying Triangles. There is a worksheet on classifying triangles by their sides, a worksheet on classifying triangles by their angles and a worksheet on classifying triangles by their sides and angles. The students are given some triangles to classify and in some cases they are required to find missing angles of the triangles (using the triangle angle sum theorem). In addition they are given some other exercises (true/false, blanks to complete) in order to test their knowledge on the different types of triangles.
Triangle Angle Sum Theorem. There is a worksheet on the triangle angle sum theorem. The exercises require to find missing angles by using the triangle angle sum theorem and the properties of special types of triangles (isosceles and equilateral).
Exterior Angle Theorem. There is a worksheet on the triangle exterior angle theorem. The exercises require to find missing angles by using the triangle exterior angle theorem.
Triangle Angle Sum Theorem and Exterior Angle Theorem. There is a worksheet on the triangle angle theorem and triangle exterior angle theorem. The exercises require to find missing angles by using the two theorems.
Parallel Lines Cut by A Transversal. There is a worksheet to help students strengthen their skills in the concept of parallel lines cut by a transversal. The following angle relationships occur in the exercises: complementary angles, supplementary angles, vertical angles, alternate interior angles, alternate exterior angles, consecutive interior angles and corresponding angles. In the first two exercises, students are given a diagram with two parallel lines cut by a transversal and are required to identify the relationships between some given pairs of angles. In the next exercises, students are given some diagrams with missing angles which are required to find by using their knowledge on the topic. Elementary and harder exercises are included.
Detailed solutions are included.
