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Mathamaniacs

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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).

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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).
Factorizing Trinomials with a=1 Lesson
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Factorizing Trinomials with a=1 Lesson

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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.
Factoring By Grouping Worksheet (with solutions)
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Factoring By Grouping Worksheet (with solutions)

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A worksheet on factorising algebraic expressions using the method of grouping. The first exercise is on factoring algebraic expressions by taking the highest common factor of their terms and the remaining exercises are on factoring by grouping. Detailed solutions are included.
Using Division and the Factor Theorem to Factor Polynomials  Worksheets (with solutions)
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Using Division and the Factor Theorem to Factor Polynomials Worksheets (with solutions)

3 Resources
A collection of three worksheets on the following topics: Dividing polynomials using long division Using division to factor polynomials Factorising a polynomial using the factor theorem In the first worksheet, students are required to perform long division for some given pairs of polynomials. In the second worksheet, students must use polynomial division to find the remaining linear factors of a polynomial, given one of its factors. In other exercises, students must find a polynomial using multiplication given all its factors, find the highest common factor of given algebraic expressions and find missing terms in factorized expressions. In the third worksheet, students are required to check whether a given polynomial is a factor of another polynomial by using the factor theorem and then in some other exercises they are required to factor cubic polynomials by first finding one of its linear factors (by checking given polynomials or inspecting using the factor theorem) and then using long division to find the remaining linear factors. Detailed solutions are included.
Using Division to Factor Polynomials Worksheet (with solutions)
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Using Division to Factor Polynomials Worksheet (with solutions)

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A worksheet on using polynomial long division to factor polynomials. In some of the exercises, students must use polynomial division to find the remaining linear factors of a polynomial, given one of its factors. In other exercises, students must find a polynomial using multiplication, given all its factors, find the highest common factor of given algebraic expressions and find missing terms in factorized expressions. Detailed solutions are included.
Powers and Order of Operations Notes and Worksheets (with solutions)
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Powers and Order of Operations Notes and Worksheets (with solutions)

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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.
Ratios, Proportions and Percents Notes and Worksheets
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Ratios, Proportions and Percents Notes and Worksheets

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A Ratios, Proportions, and Percents Unit Bundle that includes introductory notes and three worksheets 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.
Divisibility Rules Worksheets (with solutions)
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Divisibility Rules Worksheets (with solutions)

3 Resources
A collection of three worksheets on the divisibility rules for numbers 2, 3, 4, 5, 9, 10 and 25. Introductory notes (rules and examples) are included. In the exercises, the students are required to decide whether a given number is divisible by 2, 3, 4, 5, 9, 10 and 25, find missing digits in given numbers so that they are divisible or not divisible by one or more of these numbers, answer word problems on this topic and state whether some given statements are true or false. Detailed solutions are included.
Divisibility Rules Worksheet no 3 (with solutions)
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Divisibility Rules Worksheet no 3 (with solutions)

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You will download introductory notes (rules and examples) and a long worksheet on the divisibility rules for numbers 2, 3, 4, 5, 9, 10 and 25. There are 2 pages with the divisibility rules and examples and a 6 page worksheet. In the exercises, the students are required to decide whether a given number is divisible by 2, 3, 4, 5, 9, 10 and 25, find missing digits in given numbers so that they are divisible or not divisible by one or more of these numbers, answer word problems on this topic and state whether some given statements are true or false. Detailed solutions are included.
Divisibility Rules Worksheet no 2 (with solutions)
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Divisibility Rules Worksheet no 2 (with solutions)

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You will download introductory notes (rules and examples) and a long worksheet on the divisibility rules for numbers 2, 3, 4, 5, 9, 10 and 25. There are 2 pages with the divisibility rules and examples and a 6 page worksheet. In the exercises, the students are required to decide whether a given number is divisible by 2, 3, 4, 5, 9, 10 and 25, find missing digits in given numbers so that they are divisible or not divisible by one or more of these numbers, answer word problems on this topic and state whether some given statements are true or false. Detailed solutions are included.
Angle Relationships (Complementary, Supplementary and Vertical) Worksheets
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Angle Relationships (Complementary, Supplementary and Vertical) Worksheets

3 Resources
Three worksheets on complementary angles, supplementary angles, and vertical angles. They includes introductory notes with the definitions of these types of angles. The exercises require to identify complementary, supplementary and vertical angles, find the complementary and supplementary angles of a given angle and write and solve equations to find missing complementary and supplementary angles, as well as angles on a line and angles in a circle. It includes harder exercises on this topic. Detailed solutions are included.
Angle Relationships (Complementary, Supplementary and Vertical) Harder Worksheet
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Angle Relationships (Complementary, Supplementary and Vertical) Harder Worksheet

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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.
Angle Relationships (Complementary, Supplementary and Vertical) Worksheet
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Angle Relationships (Complementary, Supplementary and Vertical) Worksheet

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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. Detailed solutions are included.
Angle Relationships (Complementary, Supplementary and Vertical) Introductory Worksheet
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Angle Relationships (Complementary, Supplementary and Vertical) Introductory Worksheet

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A worksheet on complementary angles, supplementary angles, and vertical angles. It includes introductory notes with the definitions of these types of angles. The exercises require to identify complementary, supplementary and vertical angles, find the complementary and supplementary angles of a given angle and write and solve equations to find missing complementary and supplementary angles. Detailed solutions are included. Good to be used as an introductory worksheet for this topic.
Triangles, Angles and Parallel Lines Bundle
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Triangles, Angles and Parallel Lines Bundle

5 Resources
A collection of seven worksheets on the following topics: Classifying Triangles. There is a worksheet on classifying triangles by their sides, a worksheet on classifying triangles by their angles and a worksheet on classifying triangles by their sides and angles. The students are given some triangles to classify and in some cases they are required to find missing angles of the triangles (using the triangle angle sum theorem). In addition they are given some other exercises (true/false, blanks to complete) in order to test their knowledge on the different types of triangles. Triangle Angle Sum Theorem. There is a worksheet on the triangle angle sum theorem. The exercises require to find missing angles by using the triangle angle sum theorem and the properties of special types of triangles (isosceles and equilateral). Exterior Angle Theorem. There is a worksheet on the triangle exterior angle theorem. The exercises require to find missing angles by using the triangle exterior angle theorem. Triangle Angle Sum Theorem and Exterior Angle Theorem. There is a worksheet on the triangle angle theorem and triangle exterior angle theorem. The exercises require to find missing angles by using the two theorems. Parallel Lines Cut by A Transversal. There is a worksheet to help students strengthen their skills in the concept of parallel lines cut by a transversal. The following angle relationships occur in the exercises: complementary angles, supplementary angles, vertical angles, alternate interior angles, alternate exterior angles, consecutive interior angles and corresponding angles. In the first two exercises, students are given a diagram with two parallel lines cut by a transversal and are required to identify the relationships between some given pairs of angles. In the next exercises, students are given some diagrams with missing angles which are required to find by using their knowledge on the topic. Elementary and harder exercises are included. Detailed solutions are included.
Classifying Triangles Worksheets (with solutions)
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Classifying Triangles Worksheets (with solutions)

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A collection of three worksheets on classifying triangles. One worksheet on classifying triangles by their sides, one worksheet on classifying triangles by their angles and one worksheet on classifying triangles by their sides and angles. The students are given some triangles to classify and in some cases they are required to find missing angles of the triangles (using the triangle angle sum theorem). In addition they are given some other exercises (true/false, blanks to complete) in order to test their knowledge on the different types of triangles. Detailed solutions are included.
Parallel Lines Cut by A Transversal Worksheet (with detailed solutions)
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Parallel Lines Cut by A Transversal Worksheet (with detailed solutions)

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This is a worksheet to help students strengthen their skills in the concept of parallel lines cut by a transversal. The following angle relationships occur in the exercises: complementary angles, supplementary angles, vertical angles, alternate interior angles, alternate exterior angles, consecutive interior angles and corresponding angles. In the first two exercises, students are given a diagram with two parallel lines cut by a transversal and are required to identify the relationships between some given pairs of angles. In the next exercises, students are given some diagrams with missing angles which are required to find by using their knowledge on the topic. Elementary and harder exercises are included. Detailed solutions (with reasoning) are provided.