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 negative rational numbers. The exercises require to order a given set of numbers, compare pairs of given numbers, find missing numbers in a given sequence.
A review worksheet on the equation of a straight line and simultaneous equations. The exercises require to find the midpoint of a line segment and the distance between two points, to find the relative position of two given lines, find the equation of a line passing through a given point and parallel to a given line, use graphs of lines to find the solution of simultaneous equations, solve simultaneous equations algebraically and solve word problems using simultaneous equations. Detailed solutions are included.
An introductory worksheet on the trigonometric ratios sine, cosine and tangent. The exercises require to evaluate these ratios for an angle in a given triangle, to identify the trigonometric ratio that corresponds to a given ratio for a given triangle, to use a calculator to evaluate the trigonometric ratio of a given angle or the angle given one of its trigonometric ratios, to associate the sine or cosine of an angle to the cosine or sine of its complementary angle and and to solve word problems using trigonometric ratios. Detailed solutions are included.
An introductory worksheet on logarithms. The exercises require converting expressions from exponential to logarithmic form, evaluating given logarithms and solving equations involving logarithms or exponential equations.
Detailed solutions are included.
Three worksheets on the following basic properties of logarithms:
log_a 1=0
log_a a=1
log_a a^x=x
a^{log_a x}=x
product rule
division rule
power rule/exponential rule
change of base rule
Detailed solutions are included.
A worksheet with exercises that require to determine whether a given quadrilateral is a rectangle or not. It aims to help students understand the properties that can be used to prove that a quadrilateral is a rectangle. 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 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 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 adding, subtracting, multiplying and dividing functions and determining the domain of the functions produced. Detailed solutions are included.
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 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 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 , add or subtract pairs of fractions after changing their denominator and using the LCM of the original denominators and solving word problems using the highest common factor and the lowest common multiple. 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 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 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 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.