GCSE: Algebra

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Top tips to remember when doing algebra

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 After solving an equation, substitute the values back into the original equation to see if you are correct.
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 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 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 Write down means that there is no working out to do and it’s probably quite easy.
2 Calculate means that you need to do some arithmetic. You could get this question in a non-calculator paper.
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 Evaluate means that the answer is going to be a number.
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 (x+3)2 =x2 + 9 is wrong.

It should be (x+3)2 = (x + 3)(x + 3) = x2+6x + 9
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 When cancelling terms in algebraic fractions, it’s important to remember that addition and division are NOT inverses of each other.
4 When solving an equation you need to apply inverse operations in the reverse order.
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.

Marked by Teachers essays 23
Peer Reviewed essays 4

GCSE Maths questions
- Develop your confidence and skills in GCSE Maths using our free interactive questions with teacher feedback to guide you at every stage.
- Level: GCSE
- Questions: 75
T-total coursework

5 star(s)
- Word count: 2995
- Submitted: 15/07/2010
- Marked by teacher: Mick Macve 18/03/2012
opposite corners

5 star(s)
- Word count: 1638
- Submitted: 08/03/2007
- Marked by teacher: Cornelia Bruce 18/04/2013
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)
- Word count: 1629
- Submitted: 21/02/2013
- Marked by teacher: Cornelia Bruce 18/07/2013
- Awarding body: Edexcel (for GCSEs)
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)
- Word count: 941
- Submitted: 26/11/2011
- Marked by teacher: Mick Macve 18/03/2012
T-TOTALS

4 star(s)
- Word count: 1156
- Submitted: 17/02/2011
- Marked by teacher: Cornelia Bruce 18/07/2013
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)
- Word count: 2865
- Submitted: 01/07/2010
- Marked by teacher: Cornelia Bruce 18/04/2013
Opposite Corners

4 star(s)
- Word count: 2183
- Submitted: 02/05/2009
- Marked by teacher: Cornelia Bruce 18/04/2013
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)
- Word count: 3671
- Submitted: 18/08/2006
- Marked by teacher: Cornelia Bruce 18/07/2013
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)
- Word count: 1525
- Submitted: 10/01/2010
- Marked by teacher: Cornelia Bruce 18/07/2013
OPPOSITE CORNERS

3 star(s)
- Word count: 2281
- Submitted: 05/10/2009
- Marked by teacher: Cornelia Bruce 18/04/2013

GCSE: Algebra

Top tips to remember when doing algebra

Important words in GCSE Maths questions

Common algebra mistakes

GCSE Maths questions

T-total coursework

opposite corners

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

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.

T-TOTALS

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

Opposite Corners

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

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.

OPPOSITE CORNERS

Marked by a teacher

Peer reviewed

Peer reviewed