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.

1,062 GCSE Algebra essays

  • Marked by Teachers essays 23
  • Peer Reviewed essays 4
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  5. 107
  1. Marked by a teacher

    T-total coursework

    5 star(s)

    An excellent piece of work taking a simple idea and generating some complex algebraic formulae and expressions. 5 stars.…

    • Essay length: 2995 words
    • Submitted: 15/07/2010
    • Marked by teacher: (?) Mick Macve 18/03/2012
  2. Marked by a teacher

    opposite corners

    5 star(s)

    This is a very well structured investigation. The relationships are clearly described through written, numeric and algebraic explanation. There are specific strengths and improvements suggested throughout. …

    • Essay length: 1638 words
    • Submitted: 08/03/2007
    • Marked by teacher: (?) Cornelia Bruce 18/04/2013
  3. Marked by a teacher

    I am going to investigate the difference between the products of the numbers in the opposite corners of any rectangle that can be drawn on a 100 square (10x10) grid

    4 star(s)

    ****
    This is a well thought out and constructed algebraic investigation. There is a good use of a general formula to generalise the relationships discovered. Specific strengths and improvements have…

    • Essay length: 1629 words
    • Submitted: 21/02/2013
    • Marked by teacher: (?) Cornelia Bruce 18/07/2013
    • Awarding body: Edexcel (for GCSEs)
  4. Marked by a teacher

    Number grids. In this investigation I have been attempting to work out a formula that will find the difference between the products of the top left and bottom right of a number grid and the top right and bottom left of a number grid.

    4 star(s)

    A well written piece of work with only a couple of minor errors. This piece of work shows an excellent application of multiplying double brackets. 4 stars ****…

    • Essay length: 941 words
    • Submitted: 26/11/2011
    • Marked by teacher: (?) Mick Macve 18/03/2012
  5. Marked by a teacher

    T-TOTALS

    4 star(s)

    ****
    This is an incredibly well structured and demonstrated algebraic investigation. The staging of the investigation allows for the concepts to be developed throughout. Specific strengths and improvements are suggested…

    • Essay length: 1156 words
    • Submitted: 17/02/2011
    • Marked by teacher: (?) Cornelia Bruce 18/07/2013
  6. Marked by a teacher

    Opposite Corners. In this coursework, to find a formula from a set of numbers with different square sizes in opposite corners is the aim. The discovery of the formula will help in finding solutions to the tasks ahead as well as patterns involving Opposite

    4 star(s)

    This is a well thought out and demonstrated algebraic investigation. To further develop this a general form for other rectangles within the grid (not just squares) should be investigated. …

    • Essay length: 2865 words
    • Submitted: 01/07/2010
    • Marked by teacher: (?) Cornelia Bruce 18/04/2013
  7. Marked by a teacher

    Opposite Corners

    4 star(s)

    This is an excellent pieces of mathematical investigation. It is well structured moving from the concrete to the algebraic easily. The are a few small mathematical errors which limit the…

    • Essay length: 2183 words
    • Submitted: 02/05/2009
    • Marked by teacher: (?) Cornelia Bruce 18/04/2013
  8. Marked by a teacher

    I am going to investigate by taking a square shape of numbers from a grid, and then I multiply the opposite corners to find the difference of these two results. Firstly I am going to start with a 10x10 grid

    4 star(s)

    ****
    This is a very well structured investigation. All mathematical working is correct and appropriately tested throughout. Specific strengths and improvements are suggested throughout. This is a good example of…

    • Essay length: 3671 words
    • Submitted: 18/08/2006
    • Marked by teacher: (?) Cornelia Bruce 18/07/2013
  9. Marked by a teacher

    Maths coursework- stair totals. I shall be investigating the total and difference in sets of stairs in different grid sizes. I will be investigating the relationship between stair totals on different grids.

    3 star(s)

    ***
    This mathematical investigation makes good use of algebraic expressions to analyse the relationship between numbers within varying grid sizes. It has a reasonable structure and the algebraic simplification is…

    • Essay length: 1525 words
    • Submitted: 10/01/2010
    • Marked by teacher: (?) Cornelia Bruce 18/07/2013
  10. Marked by a teacher

    OPPOSITE CORNERS

    3 star(s)

    This is a basic opposite corners investigation. It uses good concrete examples to make and test predictions but is limited by the only basic use of algebra. Specific strengths and…

    • Essay length: 2281 words
    • Submitted: 05/10/2009
    • Marked by teacher: (?) Cornelia Bruce 18/04/2013

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