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GCSE: Algebra

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1,063 GCSE Algebra essays

Marked by Teachers essays 15
Peer Reviewed essays 4

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
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 18/12/1999
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
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 18/12/1999
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 18/12/1999
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 18/12/1999
opposite corners

3 star(s)

This is a good investigation into the difference between the products of opposite corners in a grid. It is well structured and supported by algebra. There are good patterns identified.…
- Essay length: 10875 words
- Submitted: 21/04/2008
- Marked by teacher: Cornelia Bruce 18/12/1999
Opposite Corners of a Square on a Number Grid

3 star(s)

There is some good investigative work carried out here. However the mathematical content is fairly limited. Generally there should be some evidence of not only the calculation of an nth…
- Essay length: 1196 words
- Submitted: 04/11/2007
- Marked by teacher: Cornelia Bruce 18/12/1999
Number Grid Aim: The aim of this investigation is to formulate an algebraic equation that works out the product of multiplying diagonally opposite corners of a particular shape and finding the difference between the results

3 star(s)

This is a well written piece of work with only a couple of minor errors. This piece of work shows a good application of some algebraic techniques. There are specific…
- Essay length: 4565 words
- Submitted: 18/08/2006
- Marked by teacher: Cornelia Bruce 18/12/1999
I am going to investigate taking a square of numbers from a grid, multiplying the opposite corners and finding the difference of these two results. To start I used a 5x5 grid:

3 star(s)

This is a solid investigation. There are patterns identified and developed with the use of algebra. This algebra however is kept to a fairly basic level. The algebra is clearly…
- Essay length: 2963 words
- Submitted: 19/12/2005
- Marked by teacher: Cornelia Bruce 18/12/1999

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.

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GCSE: Algebra

1,063 GCSE Algebra essays

T-total coursework

opposite corners

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.

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

OPPOSITE CORNERS

opposite corners

Opposite Corners of a Square on a Number Grid

Number Grid Aim: The aim of this investigation is to formulate an algebraic equation that works out the product of multiplying diagonally opposite corners of a particular shape and finding the difference between the results

I am going to investigate taking a square of numbers from a grid, multiplying the opposite corners and finding the difference of these two results. To start I used a 5x5 grid: