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AS and A Level: Core & Pure Mathematics
161 AS and A Level Core & Pure Mathematics essays
- Marked by Teachers essays 3
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
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
- Essay length: 2743 words
- Submitted: 24/03/2012
- 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
- Essay length: 1225 words
- Submitted: 25/04/2011
- 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.
- 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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