Introduction to Algebra and Algebraic Expressions notes
137 notes by 113 users · Page 1 of 4
This page gathers over 110 community-made notes on Introduction to Algebra and Algebraic Expressions, covering equations, factorising, inequalities and formulae. They are for school students practising algebra and teachers looking for ready-made material, with most notes aimed at secondary level. Choose a note to get started.
Select topic
- Algebra Vocabulary and Variables44
- Simplifying and Evaluating Expressions45
- Indices and Surds46
- Polynomials63
- Expanding and Factorising182
- Algebraic Fractions24
- Solving Linear Equations102
- Simultaneous Equations73
- Quadratic Equations53
- Inequalities and Absolute Value41
- Ratio, Proportion and Variation19
- Functions and Graphs68
- Exponential and Logarithmic Functions20
- Sequences and the Nth Term12
- Complex Numbers11
Notes
-
Solving Simultaneous Equations 1. Work out the values of N and M(1) 8m+ 4n = 104(2) 8m + 2n = 1342n = -30n = -15(1) 8m + 4(-15) = 1048m - 60 = 1048m = 164m = 20.5(2) 8(20.5) + 2(-15) = 134164 - 30 = 104N = -15M = 20.52. Work out the values of A and...
-
Leaving Certificate Algebra Table of Contents Expressions Factorising Algebraic Fractions : Adding and Subtracting Algebraic Fractions : Multiplying and Dividing Binomial Expansions Long Division in Algebra Solving Linear Equations Solving Quadr...
-
C3 Math Edexcel I should know how to:1. Cancel down algebraic fractions2. Multiply together two or more algebraic fractions3. Divide algebraic fractions4. Add or subtract algebraic fractions5. Convert an improper fraction into a mixe...
-
Trial and Improvement The equation:x³ + 5x = 67has a solution between 3 and 4 Use a trial and improvement method to find a solution.Give the solution to one decimal place. Th The answer is always the one on its own...for example:small...
-
algebra 2
-
Algebra Definition: study is the use of letters. Use of letters will allow us to write rules and formulas in a general way. letters stand for numbers, operations can be performed on them as on numbers. This leads to the study...
-
algebra 1 Algebraic Fractions When adding or subtracting algebraic fractions, the first thing to do is to put them onto a common denominator (by cross multiplying). e.g. 1 + ...
-
Algebraic & Geometric Proofs Statements Reasons 1) 5x-4 = 6 ...
-
Grade 9 Math Key Words Solving Equations Lowest Common Denominator term numerator denominator distributive property expand monomial, binomial, polynomial BEDMAS like terms, unlike terms integers coefficients variables inverse operatio...
-
Graphing Inequalities
-
Multiplying out Single Brackets. Multiplying out Single Brackets Brackets are often used in algebra, for example 3 x (x - y) is usually written as 3(x - y).Multiplying out brackets is often known as 'expanding brackets'. To expand brackets, each term...
-
Chapters 2.3, 2.4, 2.5, 2.8, 2.9, 5.3, 5.4, and 5.5 To clear decimals: 0.5 x 10 = 5: When multiplying by 10, move decimal to right twice. As decimals move into the hundredths, thousandths, and ten thousandths, you just add another zero to the original 10. To clea...
-
Algebraic Formulas
-
Checkpoint Study Guide. Inverse Variation- Multiply Numbers in table to find if it is an inverse variation equation. The graph will be two separate curved lines that don't intersect the y axis or the origin.CONSTANT: k=xyEQUATION= k/x f(x) =...
-
Linear Equations A linear equation is an algebraic equation with two variables (x & y) which refers to a line in the co-ordinate plane. There are two common forms of linear equations: 1. y = mx + c
-
Solving Simultaneous Equations 1. Work out the values of N and M(1) 8m+ 4n = 104(2) 8m + 2n = 1342n = -30n = -15(1) 8m + 4(-15) = 1048m - 60 = 1048m = 164m = 20.5(2) 8(20.5) + 2(-15) = 134164 - 30 = 104N = -15M = 20.52. Work out the values of A and...
-
Factorising Simple Expressions Factorising Simple ExpressionsFactorising is the reverse process to that of removing brackets. An expression is put into bracket by taking out common factors.ExamplesFactorise...1) 8x +12=4(2x + 3)In this example, you...
-
3. Inequalities: Theory The line below is a number line and extends to infinity in both directions. All real numbers (pos and neg) are represented by a point on the line. Picking a number, x, all values to the right of x are greater than x, ...
-
Chapter 1 - Algebraic Expressions Learning Objectives Multiply and divide integer powers Expand a single term over brackets and collect like terms Expand the product of two or three expressions Factorise linear quadratic and simpl...
-
Algebra for James
-
Simplifying Expressions and Solving Equations
-
Algebraic Fractions SAME DENOMINATOR1 + 3 = 1+38 8 8 = 4 &...
-
2*2 Simultaneous Equations What are they?1) We have 2 systems of equations.1b) This means we're basically finding 2 solutions that fit both equations.1c) Those 2 solutions will be x and y, which are 2 points, (The points of intersection)Work it...
-
Exponent Equations
-
Maths TRANSFORMATIONS TRANSLATIONSIn a translation, the amount the shape moves by is given as a vector (horizontal on the top, up and down on the bottom, minus numbers are left and down) ROTATIONSTo describe a rotation you ...
-
Solving Equasions Solving Equasions Solving equations with algebraic fractions:Solve: x+1 - x-3 Use the subtraction rule for combining fractions, and also cross multiply the denominator of th...
-
Mathematics 2.6 Apply algebraic methods in solving problems Subject content • Expanding in algebra • Expanding three brackets • Factorising algebraic expressions • Fractional and negative indices • Changing the subject of the formula • Properties of logarithms • Simplifying ra...
-
answers to discussion 1 Rearrange the formulae to make x the subject (I) p + x = r (ii) 2x + r = 4p (ii) 3x = 2p + q (iv) xy = uv (v) 3x - 7y = 4z Answers: (i) x = r - p (ii) x = 4p - r  ...
-
Matricies Types Addition Subtraction/Scalar Multiplication/Identity
-
Origins of algebra Origins of Algebra: Algebra- book written by Persian Mathematician-820 AD Bagdad Algebra means restoration/completion TIMELINE Babylon- 2000 BC: Stone tablets with basic concepts of Algebra Alexandri...
-
notes on deriving a number deriving a simple formulanumber of hours (h) 123h cost of hours 1 x 25 = 25 2 x 25 = 50 3 x 25 = 75 h x 25 = 25h call out charge50505050
-
Quadratics Solving Quadratic Equation: Factorisation Completing the square Quadratic Formula Sum and Product of the roots (x1, x2): x1 + x2 = -b/a x1 x2 = c/a Quadratic functions:
-
Simplifying expressions Key Terms: associative property of multiplication. commutative property of multiplication. distributive property. identity property.
-
Linear Programing Gradient, General Equation. Simultaneous Break even, Interpreting and Sketching Graphs Objective
-
MPC1-Equations needed
-
ALGEBRA what is algebra? Algebra is the part of mathematics in wich letters and other general symbols are used t represent numbers and quantities in formulae and equations. Algebra is really easy, the first time you see it, i...
More Introduction to Algebra and Algebraic Expressions resources
About introduction to algebra and algebraic expressions notes
GoConqr OriginalIntroduction to Algebra and Algebraic Expressions notes
These notes cover topics from writing formulae and multiplying out brackets to simultaneous equations and algebraic fractions. There are also notes on inequalities, indices and the factor and remainder theorem. They were made by GoConqr users, so their approaches and detail can vary.
How to use the notes
Start with Solving equations if you want to review how inverse operations can help solve an equation. For a look at expressions, Factorising Simple Expressions explains taking out common factors and includes examples. If you are practising simultaneous equations, the note on solving them with algebra works through a substitution example.
Read a note, then work through its examples on your own before checking the method. Return to the explanation wherever a step is unclear. If you want to test your understanding or see a topic laid out visually, switch to a quiz or mind map on the unit page. Pick a topic and explore the notes that match it.
Frequently asked questions
Which note is a good place to start?
Try Solving equations if you want to review inverse operations. If your focus is expressions, Factorising Simple Expressions introduces common factors and gives examples. For simultaneous equations, the note on solving them with algebra shows a substitution method. Choose the one closest to the topic you are practising.
Are these notes free to use?
Yes. Every note listed on this page is free to open and study, and you do not need an account. The notes were made by GoConqr users rather than GoConqr, so you can browse different approaches to topics such as equations, formulae and inequalities.
What can I do if I cannot find the note I need?
Look for a note on a related topic first. For example, the page includes separate notes on linear equations, simultaneous equations and writing formulae. If you want to make material of your own, a free account lets you create notes, quizzes, mind maps and flashcards, and save quiz scores.