A worksheet on complementary angles, supplementary angles, and vertical angles. The exercises require to identify complementary, supplementary and vertical angles and write and solve equations to find missing complementary, supplementary and vertical angles, as well as angles on a line and angles in a circle. It includes harder exercises on this topic. Detailed solutions are included.

A lesson on factorizing trinomials with leading coefficient 1. The students are first asked to multiply out pairs of brackets containing linear polynomials. Then they are asked to make some observations. They are expected to observe that in the trinomial obtained after multiplying out the brackets the coefficient of x is the sum of the numbers in the brackets and the constant term is their product. Then they are asked to generalize that for any pair of linear polynomials. Once this result has been established, they are given some trinomials with leading coefficient equal to one and are asked to factorize them. In this exercises they must work in the converse way, they must try to find pairs of numbers whose product and sum equal the coefficients of the given polynomial. Finally, there is an exercise on signs, including the four possible combinations of signs for the product and sum of the trinomial. Detailed solutions are provided.

A Ratios, Proportions, and Percents Unit Bundle that includes introductory notes and three worksheet on ratios and proportions, properties of proportions and ratios. The following topics are covered: Ratios Proportions Scale Ratios Ratio Word Problems Properties of Proportions Solving Equations by Cross Multiplication Dividing Amounts in Given Ratio Proportion Word Problems Percentages Percentage of an Amount Percentage Word Problems Percentage Change Reverse Percentage Detailed solutions are included.

A worksheet on the following algebraic identities: Square of a Binomial Difference of Squares Cube of a Binomial The exercises require to expand and simplify algebraic expressions involving these identities and prove other identities using these identities. Very detailed solutions are included.

You get introductory notes and two worksheets on powers and order of operations (PEMDAS). The notion of a power is introduced and the relevant terminology is explained (base, exponent) through examples. The first worksheet is on powers and the exercises require to examine whether some given expressions can be written as powers, recognize the base and the exponent of powers, evaluate and compare powers and find missing numbers in given calculations. Then the order of operations is explained and illustrated through an example. The second worksheet is on order of operations and the exercises require to perform calculations using the correct order. Detailed solutions are provided.

A worksheet on multiplying whole numbers with up to 3 digits by 10 or 100. The exercises include direct calculations and filling missing numbers in given calculations. Answers are included.

A worksheet on parallel, perpendicular and intersecting lines. The exercises included require to determine whether two lines are parallel, intersect or coincide and examine if they are perpendicular, find the equation that passes through a given point and is parallel, perpendicular or intersects a given line, find the relative position of lines given their graphs and find the equations of lines given their graphs and the equation of another line parallel to them. Detailed solutions are included.

A worksheet on expanding and simplifying expressions using the identities for the square of a sum or a difference of two terms, the cube of a sum or a difference of two terms and the difference of two squares. It starts with easy exercises requiring application of the identities and continues with more demanding exercises that require to prove new identities or evaluate the value of given expressions using the identities. Solutions are included.

A worksheet on evaluating powers with rational exponents (positive and negative fractions). Solutions are included.

A worksheet on writing fractions in their simplest form. Answers are included.

A worksheet on deciding whether a given triangle is an isosceles triangle using the properties of isosceles triangles( two equal sides, two equal angles, any two of the median, bisector and height corresponding to the same side coincide). Detailed solutions are included.

A worksheet on deciding whether a given pair of triangles are congruent. Detailed solutions are included.

A worksheet on deciding whether a given pair of right-angled triangles are congruent. Detailed solutions are included.

A worksheet on finding terms of a sequence by spotting the pattern given the first few terms or given the general term. Detailed solutions are included.

A worksheet on performing the four operations between fractions. Solutions are included.

An e-book on solving quadratic equations using: Factorisation The method of completing the square Square roots The quadratic formula It consists of four worksheets (one on each method) with detailed solutions.

A worksheet on adding, subtracting, multiplying and dividing integers (up to 200). Solutions are included.