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 using the trigonometric identities that convert as sum of two sines or two cosines to a product of sines or cosines. The exercises include using these identities to evaluate expressions and proving other identities. Detailed solutions are included.
A collection of 5 worksheets on Calculus based on the GCSE 9-1 specification.
In these worksheets students are taught to understand the concept of a variable rate of change, differentiate integer powers of x, determine gradients, rates of change, stationary points, turning points (maxima and minima) by differentiation and relate these to graphs, distinguish between maxima and minima by considering the general shape of the graph and apply calculus to linear kinematics and to other simple practical problems).
Detailed solutions are included.
A worksheet on using the trigonometric identities that convert a product of a sine and a cosine or a product of two sines or a product of to cosines to a sum of sines or cosines. The exercises include using these identities to evaluate expressions and proving other identities. Detailed solutions are included.
A collection of 4 worksheets on arithmetic sequences based on the GCSE 9-1 specification.
In these worksheets students are taught to understand and use common difference (d) and first term (a) in an arithmetic sequence, know and use nth term =a+(n-1)d and find the sum of the first n terms of an
arithmetic series.
Detailed solutions are included.
A collection of 6 worksheets on angles, lines and triangles based on the GCSE 9-1 specification.
The following worksheets are included:
Types of angles
Complementary, supplementary and opposite angles
Angles in parallel lines
Sum of angles in a triangle
Exterior Angles of a Triangle
Isosceles, Equilateral and Right-Angled Triangles
Detailed solutions are included.
A collection of 3 worksheets on expressions and formulae based on the GCSE 9-1 specification.
The following worksheets are included:
Solving simultaneous equations using elimination
Solving simultaneous equations using substitution
Graphical Solution of Simultaneous Equations
Detailed solutions are included.
A collection of 4 worksheets on expressions and formulae based on the GCSE 9-1 specification.
The following worksheets are included:
Changing the subject of a formula
Changing the subject of a formula (harder questions)
Equations with variables on both sides
Linear equations with brackets and the variable in both sides
Detailed solutions are included.
A collection of 6 worksheets on algebraic manipulation based on the GCSE 9-1 specification.
The following worksheet are included:
Multiplying out two brackets
Multiplying three brackets
Factorising quadratics
Simplifying algebraic fractions
Operations with algebraic fractions
Completing the square
Detailed solutions are included.
A collection of three worksheets on the following topics:
Domain and Range of a Function:The exercises include polynomial functions, rational functions and functions with square roots.
Injective Functions: The exercises require to decide whether a function is injective or not given its equation or its graph.
Inverse Functions: The exercises require to decide whether a given function is invertible, find the inverse function and the domain of the inverse function.
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.
A collection of 7 worksheets on percentages based on the GCSE 9-1 specification.
The following are included:
Expressing one quantity as a percentage of another (non-calculator)
Expressing one quantity as a percentage of another (calculator)
Percentages, fractions and decimals: conversions between the three of them and word problems
Percentage of a quantity (non-calculator): finding the percentage of a quantity without the use of a calculator
Increasing or decreasing an amount by a percentage (non-calculator): increasing or decreasing an amount by a given percentage without using a calculator
Reverse percentage
Compound interest
Detailed solutions are included.
A collection of three worksheets on multiplying and dividing fractions by fractions, fractions by mixed numbers, fractions by whole numbers, mixed numbers by mixed numbers and mixed numbers by whole numbers. One worksheet on multiplication, one on division and one on both operations. Detailed solutions are included.
A worksheet on multiplying and dividing fractions by fractions, fractions by mixed numbers, fractions by whole numbers, mixed numbers by mixed numbers and mixed numbers by whole numbers. Detailed solutions are included.
A worksheet on dividing fractions by fractions, fractions by mixed numbers, fractions by whole numbers, mixed numbers by mixed numbers and mixed numbers by whole numbers. Detailed solutions are included.
A worksheet on multiplying fractions by fractions, fractions by mixed numbers, fractions by whole numbers, mixed numbers by mixed numbers and mixed numbers by whole numbers. Detailed solutions are included.
A collection of 4 worksheets on set language and notation based on the GCSE 9-1 specification.
The following are included:
An introductory worksheet on sets. The exercises require to list the elements of a described set, to describe a set given its elements and to use the symbols for belongs to and does not belong to.
A worksheet on set notation: belongs to, does not belong to, union, intersection, empty set, complement of a set, number of elements of a set etc.
A worksheet on the union and intersection of two or more sets and the complement of a set.
A worksheet on Venn diagrams and set notation ( the symbols for belongs/ does not belong to, union and intersection, empty set, complement of a set, number of elements of a set).
Detailed solutions are included.
A collection of 12 worksheets on fractions based on the GCSE 9-1 specification. The following topics are included:
Equivalent fractions
Simplifying fractions
Mixed numbers to improper fractions
Improper fractions to mixed numbers
Ordering fractions
Fraction of an amount
Adding and subtracting fractions and mixed numbers
Equivalences between fractions, decimals and percentages
Multiplying fractions
Dividing fractions
Multiplying and dividing mixed numbers
Multiplying and dividing fractions and mixed numbers
Detailed solutions are included.