Algebraic Vocabulary (Edexcel IGCSE Maths)

Spec point — 2.1A

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
  • $\frac{6y}{5t}$
  • 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

Exam Hint

• Knowing the differences between an expression, an equation and a formula will help you to understand the wording of exam questions.

Worked Example (a) From the list below, write down

(i) an expression,

(ii) an equation.

2x + 5 = 4 7*x *– 9 x = vt – w

Answer:

(i)

An expression does not have an equals sign

Final answer: 7x – 9 is the expression

(ii)

An equation has an equals sign and can be solved

Final answer: 2x + 5 = 4 is the equation

(b) If x = 10, v = 2 and w = 3, use the formula shown to write an equation in t.

Answer:

*x *= vt – w is the formula shown (a group of different quantities forming a relationship)

Substitute x = 10, v = 2 and w = 3 into the formula

Final answer: 10 = 2t** – 3