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 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 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 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 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 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 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 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 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 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.
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 using differentiation in order to determine the gradient (and the equation) of the tangent of a function at a given point. Detailed solutions are provided. Good for GCSE/IGCSE students.
A collection of three worksheets on differentiating using the basic rules for functions that are constant, powers of a variable or sums of powers of a variable, products of a constant and another function, products or quotients of two functions. The two worksheets are on functions that are powers of a variable or sums of powers of a variable and the third is on all the above rules. Detailed solutions are provided.
A worksheet on differentiating using the basic rules for functions that are constant, powers of a variable or sums of powers of a variable, products of a constant and another function, products or quotients of two functions. Detailed solutions are provided. Good for GCSE/IGCSE students.
An introductory worksheet on differentiating functions from first principles using the definition of the derivative as the limit of the quotient f(x+h)-f(x)/h as h tends to zero. Detailed solutions are included.
An introductory worksheet on differentiating simple functions from first principles using the definition of the derivative at x0 as the limit of the quotient f(x)-f(x0)/x-x0 at this point. Detailed solutions are included.
