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 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.
A worksheet on factorising 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 factorising algebraic expressions involving differences of two squares or differences and sums of two cubes. Detailed solutions are included.
A collection of three worksheets on factorising polynomials including the following cases:
Common Factor and Grouping
Difference of two squares - Difference and sum of two cubes
Trinomial-Perfect squares
Detailed solutions are included.
Four worksheet on the following topics:
Simplifying algebraic fractions
Adding and subtracting algebraic fractions
Multiplying and dividing algebraic fractions
Solving equations with algebraic fractions
Detailed solutions are provided.
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 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.
