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GCSE: Algebra

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Top tips to remember when doing algebra

  1. 1 When solving a quadratic equation, try factorising first and then use the formula. Only use completing the square if a question specifically asks you to do so.
  2. 2 After solving an equation, substitute the values back into the original equation to see if you are correct.
  3. 3 You need to know the difference between an expression, an equation, an identity and a formula. An expression doesn’t have an equals sign, e.g. 3x – 1. An identity is true for every value of x, e.g. 5x + 2x = 7x. An equation only works for particular values of x, e.g. x2 – 4 = 0 is only true for x=-2 or x = 2. A formula is a connection between two or more variables, e.g. A = 3.14r2
  4. 4 When using expressions like 5y2, remember that the power comes first and then the multiplication. So if y = 2, don’t do 5x2 and then square the answer to get 100; square first to get 4 and then multiply by 5 to get 20.
  5. 5 When collecting like terms, always look at the plus or minus sign that comes before each term. For example 4x + 8y +3x – 2y = 5x + 6y

Important words in GCSE Maths questions

  1. 1 Write down means that there is no working out to do and it’s probably quite easy.
  2. 2 Calculate means that you need to do some arithmetic. You could get this question in a non-calculator paper.
  3. 3 Prove means that your working is going to be marked so you need to write down everything that you do giving reasons at every step.
  4. 4 Evaluate means that the answer is going to be a number.
  5. 5 Estimate means that you don’t have to give an exact answer. This will probably be in a non-calculator paper and so you are allowed to use approximations.

Common algebra mistakes

  1. 1 (x+3)2 =x2 + 9 is wrong.

    It should be (x+3)2 = (x + 3)(x + 3) = x2+6x + 9
  2. 2 It is a common mistake for student to write x+3(x+2) when they mean (x+3)(x+2). These are different.
  3. 3 When cancelling terms in algebraic fractions, it’s important to remember that addition and division are NOT inverses of each other.
  4. 4 When solving an equation you need to apply inverse operations in the reverse order.
  5. 5 When factorising quadratic expressions in order to solve equations, it’s a common mistake not to check that the right hand side of the equation is zero.

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