Algebra Basics
Maths: Edexcel IGCSE Higher, topic 2.1.1
Algebra Rules
Here are some common rules of algebra:
Common rules
- ab means a × b
- abc means a × b × c
- 5a means 5 × a or a + a + a + a + a
Coefficients
- A number written before an algebraic symbol is called a coefficient.
- In the expression 3x - 4y + z, x has a coefficient of 3, y has a coefficient of -4 and z has a coefficient of 1.
Brackets
- We can expand brackets like this.
Common rules
- a² means a × a
- a4 means a × a × a × a
- ab²c means a × b × b × c
Common rules
- 1⁄2a means 0.5 × a
- 1a means 1 × a but is just written as a
Substituting Values
For the equation y = 5x² - 3x, what is y when x = 3?
Write equation
Substitute x = 3
Multiply out brackets
Multiply out brackets again
Answer
Algebraic Vocabulary
Here are some technical terms for algebra:
Term
- A term is anything which does not include a plus or minus:
- 3x²
- 5x⁄2y
Expression
- An expression is when terms are combined without an '=' sign:
- 3x
- 6c(5a - b² + 8)
Equation
- An equation is when terms are combined and a ‘=’ sign is used:
- 5x = 3y
- a + b - c = 0
Inequality
- An inequality is when inequality symbols are used (<, ≤, >, ≥):
- 5x < 3
- y ≥ 3x - 2
Identity
- An identity is when two lines are equivalent for any values of x or y.
- The identity symbol (≡) is used.
Formula
- A formula is a general rule describing a relationship:
- area of a circle = πr2
- speed = distance⁄time
Factor
- A factor is a quantity which divides an expression exactly:
- 3 is a factor of 9 and of 12
- 2x is a factor of 4x and of 8x3
Test yourself on Algebra Basics
How can 1 x a + 3 x b also be written?
How can 7(a + 2b) be expanded?
x = 2a
What is x when a = 2?x = 2a - 1
What is x when a = 5?x = 2a + 1
What is x when a = 3?