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 four worksheets on logarithms. The following worksheets are included:
Basic properties of logarithms
Addition and power laws of logarithms
Laws of logarithms
Changing the base of logarithms
Solutions are provided.
A collection of three worksheets on the following topics:
Unit Circle-Trigonometric Ratios: on using the unit circle to find the sign and the value of the trigonometric ratios of given angles
Expressing Trigonometric ratios in Terms of Trigonometric Ratios of Acute Angles
Trigonometric identities: on the trigonometric identities tanx=sinx/cosx, cotx=cosx/sinx and sin^2x+cos^2x=1
Detailed solutions are provided.
A worksheet on the trigonometric identities tanx=sinx/cosx, cotx=cosx/sinx and sin^2x+cos^2x=1. The exercises require to use these identities to evaluate expressions and trigonometric ratios and prove other identities. Detailed solutions are included.
A worksheet on determining whether two given circles intersect each other at two points, touch each other externally, touch each other internally, lie outside each other or the one lies inside the other, by considering the distance of their centres. Detailed solutions are included.
A worksheet on the graph of the parabola y=ax^2. The exercises require to match a set of graphs (of parabolas) to their equations and find the equation of a parabola given its graph and a point on it. Solutions are included.
An introductory worksheet on vectors and the notions of magnitude of a vector, parallel vectors, like vectors, unlike vectors, equal vectors and opposite vectors.Detailed solutions are included.
A collection of three worksheets on the following topics:
Circle theorems
Alternate Segment Theorem
Relative Position of Two Circles
Detailed solutions are included.
A worksheet on quadratic functions of the form f(x) = ax² + bx + c and equations of the form ax² + bx + c=0. The exercises require to use the graph of such functions to determine the sign of the discriminant and the solution or solutions if they exist, find the sign of a, the value of c the range of f, the line of symmetry of the graph and the maximum value of f. In addition, functions or equations of this form with parameters in them are given and the students are required to determine the values of the parameters so that the value has specific solutions, a given line of symmetry, a given number of roots or a given point of intersection with the y-axis.
Detailed solutions are included.
A worksheet on sum and product of roots of quadratics. The exercises require to find the sum or product of the roots of a given quadratic equation, evaluate parameters in a given quadratic equation so that its roots have a specific sum or product, find a quadratic equation given its roots, factorise quadratic expressions and simplify algebraic fractions involving quadratic expressions. Detailed solutions are included.
A worksheet on determining the sign of trinomials given the trinomials or their graphs and solving quadratic inequalities using sign tables. Detailed solutions are included.
A collection of four worksheets on the following topics
Graph of the Parabola y=ax^2 : A worksheet on the graph of the parabola y=ax^2. The exercises require to match a set of graphs (of parabolas) to their equations and find the equation of a parabola given its graph and a point on it.
Graph of a Parabola-Transformations: A worksheet on transforming horizontally or vertically a parabola.
Quadratic Function of the Form f(x) = ax² + bx + c: A worksheet on quadratic functions of the form f(x) = ax² + bx + c and equations of the form ax² + bx + c=0. The exercises require to use the graph of such functions to determine the sign of the discriminant and the solution or solutions if they exist, find the sign of a, the value of c the range of f, the line of symmetry of the graph and the maximum value of f. In addition, functions or equations of this form with parameters in them are given and the students are required to determine the values of the parameters so that the value has specific solutions, a given line of symmetry, a given number of roots or a given point of intersection with the y-axis.
Sum and Product of Roots of Quadratics - Viete’s Theorem: A worksheet on sum and product of roots of quadratics. The exercises require to find the sum or product of the roots of a given quadratic equation, evaluate parameters in a given quadratic equation so that its roots have a specific sum or product, find a quadratic equation given its roots, factorise quadratic expressions and simplify algebraic fractions involving quadratic expressions.
Detailed solutions are included.
A worksheet on The Basic Proportionality Theorem also known as Thales’ Theorem which states that if three or more parallel lines intersect two transversals, then they cut off the transversals proportionally. The exercises require to apply the theorem to find missing lengths or prove other statements.
Detailed solutions are included.
Three worksheets on expanding algebraic expressions of the form (a+b)(a-b), (a+b)^2, (a-b)^2, (a+b)^3 and (a-b)^3 using the corresponding identities. Solutions are included.
A worksheet on expanding and simplifying expressions and proving other identities using the identities for the square of a sum or a difference of two terms. Solutions are included.
