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 5 worksheets on sets: set notation, Venn diagrams, union and intersection, empty set, complement of a set and number of elements of a set. Detailed solutions are included.
A collection of three worksheets on the following methods of proof:
Direct Proof
Proof By Contradiction
Proof By Induction
Detailed solutions are included.
A worksheet on double angle identities for sine, cosine, tangent and cotangent. The exercises require to evaluate the exact values of such trigonometric numbers and prove identities involving them. Detailed solutions are included.
A worksheet on finding the domain and range of a function. The exercises include polynomial functions, rational functions and functions with square roots. 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.
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 and to associate the sine or cosine of an angle to the cosine or sine of its complementary angle. Detailed solutions are included.
A worksheet on factorizing algebraic expressions for cases where there is a common factor or the method of grouping can be used. Detailed solutions are included.
A worksheet on evaluating powers of positive and negative integers. The exponents in these powers are positive integers or zero. Solutions are included.
A worksheet with exercises that require to determine whether a given quadrilateral is a parallelogram or not. It aims to help students understand the five properties that can be used to prove that a quadrilateral is a parallelogram. Detailed solutions are included.
A collection of three worksheets on the order of operations in calculations with integers (positive and negative). One of the worksheets is on positive integers only and the other two on both positive and negative integers. The exercises aim to practice the correct order of operations: Brackets, Indices, Division, Multiplication, Addition, Subtraction (BIDMAS) and include two or more operations. Detailed solutions are provided.
A worksheet on the order of operations. The exercises aim to practice the correct order of operations: Brackets, Indices, Division, Multiplication, Addition, Subtraction (BIDMAS) and include two or more operations. Expressions with two or more operations are given and some terms are missing. Detailed solutions are included.
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 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.
