Algebraic Vocabulary (Cambridge (CIE) IGCSE International Maths)

Algebraic Vocabulary

What is a term?

• A term is either:

  • a letter (variable) on its own, or a variable raised to a power

    • For example, x  or x²

  • a number on its own

    • For example, 20

    • These are also called constants as they can't change value

  • or a number multiplied by a letter

    • For example, 5x

• The number in front of a letter is called a coefficient

  • The coefficient of x  in 6x  is 6

  • The coefficient of y  in -5y  is -5

• Terms can include powers and more than one letter, 

  • 6xy

  • 4x²

  • ab³c

What is a factor?

• A factor is any number or letter that divides a term exactly

  • There is no remainder

    • The factors of 3x  are 1, 3, x  and 3x

    • The factors of 4xy  are 1, 2, 4, x,  2x,  4x,  y,  2y,  4y,  xy,  2xy  and 4xy

• A term can be separated into factors that multiply together to give that term

  • Two factors of 5x  are 5 and x

    • 5 × x = 5x

• To factorise means to write something as a multiplication of factors

• When comparing two terms, a common factor is one that divides both

  • Compare 6xy  with 4x

    • Common factors are 1, 2, x  and 2x

    • The highest (or greatest) common factor is 2x

What is an expression?

• An expression is an algebraic statement that does not have an equals sign

  • There is nothing to solve

• An expression is made by adding, subtracting, multiplying or dividing terms

  • 2x + 5y

  • b² – 2cd

  • 

  • A single term is still an expression

• Expressions can be simplified (made easier)

  • x + x + x   simplifies to 3x

What is an equation?

• An equation is an algebraic statement with an equals sign between a left-hand side and a right-hand side

  • Both sides are equal in value

  • For example, if 2x  has the same value as 10, then 2x = 10

• An equation can be solved by finding the values of the letters that make both sides equal

  • The equation 2x = 10 is solved when x has the value of 5

    • x = 5 is called the solution

What is a formula?

• A formula is a rule, definition or relationship between different quantities, written in shorthand using letters

  • For example, weight, w,  is mass, m,  multiplied by gravitational acceleration, g

    • The formula is w = mg

• It is common to substitute numbers into a formula

  • But a formula on its own cannot be solved

• To turn a formula into an equation, more information is needed

  • For example, if w = 50 and m = 5, the formula w = mg  becomes the equation 50 = 5g