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AS and A Level: Core & Pure Mathematics

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161 AS and A Level Core & Pure Mathematics essays

Marked by Teachers essays 3

C3 Coursework - different methods of solving equations.

5 star(s)

An excellent piece of work with no errors giving clear explanations of the use of decimal search, iterations and Newton-Raphson numerical methods to solve equations. 5 stars…
- Essay length: 3460 words
- Submitted: 05/02/2012
- Marked by teacher: Mick Macve 18/03/2012
The Gradient Function

5 star(s)

Generally an excellent piece of work with some sophisticated results. A good conversational style describes clearly why he is following particular lines of investigation.…
- Essay length: 6489 words
- Submitted: 10/09/2009
- Marked by teacher: Mick Macve 18/03/2012
Estimate a consumption function for the UK economy explaining the economic theory and statistical techniques you have used.

3 star(s)

The author recognises the importance of consumption to the UK economy and models it well. However, explanation of statistics is poor, even though the conclusions are generally accurate. The application…
- Essay length: 4377 words
- Submitted: 28/01/2005
- Marked by teacher: Nick Simmons 28/02/2012
Numerical solutions of equations
- Essay length: 2743 words
- Submitted: 24/03/2012
Mathematical equations can be solved in many ways; however some equations cannot be solved algebraically. I am going to show the three methods of solving these types of equations numerically
- Essay length: 1386 words
- Submitted: 15/02/2012
This coursework is about finding the roots of equations by numerical methods.
- Essay length: 1797 words
- Submitted: 25/06/2011
Exponential decay:The objective of this experiment is to get the trend line of heart rate and to determine the decay constant of this decay.
- Essay length: 833 words
- Submitted: 18/05/2011
In my coursework I will be using three equations to investigate their solutions using three numerical methods which are: change of sign using Newton-Raphson by finding the fixed point iteration fixed point iteration after rearranging the equa
- Essay length: 1816 words
- Submitted: 10/05/2011
C3 Numerical Solutions to Equations
- Essay length: 1225 words
- Submitted: 25/04/2011
Investigation of circumference ratio - finding the value of pi.
- Essay length: 930 words
- Submitted: 27/02/2011

Differentiation and intergration

1 It is easy to get differentiation and integration the wrong way round. Remember that the power gets smaller when differentiating.
2 Differentiation allows you to find the gradient of a tangent at any point on a curve. The first derivative describes the rate of change.
3 If a function is increasing then the first derivative is positive, if a function is decreasing, then the first derivative is negative.
4 When asked to find the area under a curve, it is asking you to integrate that curve between two points. Even if you don’t know the points, pick two numbers. You’ll get marks for methods.
5 When referring to a min/max/stationary point, the gradient equals 0. Differentiate the curve and set this to equal 0. The second derivative tells you whether it is a maximum or minimum. If the second derivative is positive, the point is a minimum, if the second derivative is negative, then the point is a maximum.

Quadratics and circles

1 When solving a quadratic inequality, always draw a picture. The inequality is less than 0, where the curve is below the x-axis and bigger than 0 when the curve is above the x-axis.
2 Sometimes in part (a) of a question you are asked to find something, for example a radius. In part (b) you might be then asked to use the radius that you found. If you couldn’t do part (a), don’t give up, choose a random radius.

Straight lines

1 To find the distance of a straight line, draw the straight line with the co-ordinates. Then make a right angle triangle, find the lengths of the horizontal and vertical lines, then use Pythagoras.
2 When a question asks you for a straight line. The first thing to do is to write down the equation of a straight line. Then find out what information you know, and what information you need. Even if you don’t understand the whole question, it is important to start.

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AS and A Level: Core & Pure Mathematics

161 AS and A Level Core & Pure Mathematics essays

C3 Coursework - different methods of solving equations.

The Gradient Function

Estimate a consumption function for the UK economy explaining the economic theory and statistical techniques you have used.

Numerical solutions of equations

Mathematical equations can be solved in many ways; however some equations cannot be solved algebraically. I am going to show the three methods of solving these types of equations numerically

This coursework is about finding the roots of equations by numerical methods.

Exponential decay:The objective of this experiment is to get the trend line of heart rate and to determine the decay constant of this decay.

In my coursework I will be using three equations to investigate their solutions using three numerical methods which are: change of sign using Newton-Raphson by finding the fixed point iteration fixed point iteration after rearranging the equa

C3 Numerical Solutions to Equations

Investigation of circumference ratio - finding the value of pi.