• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Maths coursework: gradient function

Extracts from this document...

Introduction

Jatinder Minhas                         

Maths Coursework

  1. Draw a graph of y = x2 for values of x from 0 to 4. Obtain the gradient of the tangent at different points. Record the results.

To conduct this question I first had to obtain the values of y = x2 for values of x from 0 to 4. This is shown below. I decided to use values more accurate and precise values of x to enable me to obtain a more accurate curve and thus enabling me to obtain a more accurate gradient. I took the values of y = x2 and then plotted them on the graph. I rounded the values to two decimal places to enable me to plot the point as accurately as possible on my scale.

y

y = x2

0.0

0.0image00.png

0.25

0.0625

0.5

0.25

0.75

0.5625

1.0

1.0

1.25

1.5625

1.5

2.25

1.75

3.0625

2.0

4.0

2.25

5.0625

2.5

6.25

2.75

7.5625

3.0

9.0

3.25

10.5625

3.5

12.25

3.75

14.025

4.0

16.0

I then joined up the points with a flexi-curve.

...read more.

Middle

4

Gradient

2

4

6

8

Even though I used an accurate method, which was the tangent method I felt that I could have, improved and found the gradients using a method, which could check and maybe even improve values of the gradients. This method is called the small increment method and is shown below. This method is calculated first by taking a point on the x axis and then square rooting it. You then take another point that is close to the original point and you then square root the x axis point and you follow the method below. Though one rule is that the original point must always remain the same.

Using the small increment method the results for my calculations were;

Point on line

1

2

3

4

Gradient

2

4

6

8

These results were the same as the results found using the tangent method.

...read more.

Conclusion

"1">

11.390625

2.5

2.5

2.5

15.625

2.75

2.75

2.75

20.796875

3.0

3.0

3.0

27.0

3.25

3.25

3.25

34.328125

3.5

3.5

3.5

42.875

3.75

3.75

3.75

52.734375

4.0

4.0

4.0

64.0

I then used these values and I plotted a graph. I then joined the points up to create a curve. I then drew the tangents as accurately as possible and worked out the gradients.

y = x1

Point on line

1

2

3

4

Gradient

1

2

3

4

y = x3

Point on line

1

2

3

4

Gradient

1

12

27

48

I then used the small increment method for the calculation of the gradient and I acquired the results;

y = x1

Point on line

1

2

3

4

Gradient

1

2

3

4

y = x3

Point on line

1

2

3

4

Gradient

3

12

24

42

...read more.

This student written piece of work is one of many that can be found in our GCSE Gradient Function section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Gradient Function essays

  1. Peer reviewed

    The Gradient Function Coursework

    5 star(s)

    Graph x-coordinate of Point y-coordinate of Point Gradient (m) y=x� 1 1 2 y=x� 2 4 4 y=x� 3 9 6 y=2x� 1 2 4 y=2x� 2 8 8 y=2x� 3 18 12 The gradient function for the range of graphs y=ax� would be m=2ax, where x is the x-coordinate of the point at which the gradient should be determined.

  2. Curves and Gradients Investigation

    - x³ (expand brackets) h = 3x²h + 3xh² + h³ (cancel x³) h = 3x² + 3xh + h² (cancel h) as h tends to 0 GF tends to 3x² 2. y = x4 Gradient = (x + h)

  1. The Gradient Function

    To find the next point on the graph, you must multiply the tangent, by the place value of 'a'. As we are investigating the curve of y=3x2, you must multiply 0.8 by 3. So the first set of co-ordinates will be (0.8, 1.92).

  2. The Gradient Function Investigation

    Also, the power of X in the gradient function (e.g. 9x�) is one less than that in the graph equation (e.g. 3x�). I can therefore summarise the results from these three examples in the following formula: Gradient Function for graph y = Axn is (An)x(n-1)

  1. Maths Coursework - The Open Box Problem

    30 by 30 square Cut Out x Width 30-2x Length 10-2x Volume 1 28 28 784 2 26 26 1352 3 24 24 1728 4 22 22 1936 5 20 20 2000 6 18 18 1944 7 16 16 1792 8 14 14 1568 9 12 12 1296 10 10

  2. The Gradient Function

    I will now check the accuracy of these results using the increment method. Increment Method I will now perform the small increment method to check my gradients. I will perform the increment method for each of the curved graphs i.e.

  1. The Gradient Function

    Using my existing rule of G = anxn-1, for graphs of form axn, then if the graph is of form perhaps y=axn + bxm perhaps it is equivalent to two graphs of the form axn added together, e.g.: For y= x2 + x3, perhaps G = 2x + 3x2 I

  2. I have been given the equation y = axn to investigate the gradient function ...

    find the gradient of a tangent to a curve but if the tangent is just drawn by eye the value obtained can only be an approximation A more precise method is needed for determining the gradient of a curve whose equation is known so that further analysis can be made

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work