Wednesday, February 20, 2008
Saturday, February 16, 2008
Friday, February 15, 2008
Median, Quartiles, Boxplot
The following 2 videos explain how the boxplot is drawn from the median and quartile values of a set of data. Watch the videos to prepare yourself for our lesson next Monday.
Thursday, February 14, 2008
Survey to find out your most difficult topics in E Math and Add Math
Dear students,
Can you do the 2 surveys on the right-hand side by 21 Feb?
Can you do the 2 surveys on the right-hand side by 21 Feb?
How anxious (worried) are you over math?
Hi everyone
I found this in the internet and thought perhaps you do this self-test to see where you are in your anxiety level over math.
Rate your answers from 1 to 5; add them up and check your score below.
(1) = Disagree, (5) = Agree.
1. I cringe (become fearful) when I have to go to math class. 1 2 3 4 5
2. I am uneasy about going to the board in a math class. 1 2 3 4 5
3. I am afraid to ask questions in math class. 1 2 3 4 5
4. I am always worried about being called on in math class. 1 2 3 4 5
5. I understand math now, but I worry that it's going to get really difficult soon.1 2 3 4 5
6. I tend to "black out" (or get lost) in math class. 1 2 3 4 5
7. I fear math tests more than any other kind. 1 2 3 4 5
8. I don't know how to study for math tests. 1 2 3 4 5
9. It's clear to me in math class, but when I go home it's like I was never there. 1 2 3 4 5
10. I'm afraid I won't be able to keep up with the rest of the class. 1 2 3 4 5
CHECK YOUR SCORE:
40-50 Sure thing, you have math anxiety.
30-39 No doubt! You're still fearful about math.
20-29 On the fence!.
10-19 Wow! Loose as a goose!
[http://www.mathpower.com/anxtest.htm]
When done, please post your SCOREs and say something about what you think about your SCORE.
Do this by 16 Feb.
I found this in the internet and thought perhaps you do this self-test to see where you are in your anxiety level over math.
Rate your answers from 1 to 5; add them up and check your score below.
(1) = Disagree, (5) = Agree.
1. I cringe (become fearful) when I have to go to math class. 1 2 3 4 5
2. I am uneasy about going to the board in a math class. 1 2 3 4 5
3. I am afraid to ask questions in math class. 1 2 3 4 5
4. I am always worried about being called on in math class. 1 2 3 4 5
5. I understand math now, but I worry that it's going to get really difficult soon.1 2 3 4 5
6. I tend to "black out" (or get lost) in math class. 1 2 3 4 5
7. I fear math tests more than any other kind. 1 2 3 4 5
8. I don't know how to study for math tests. 1 2 3 4 5
9. It's clear to me in math class, but when I go home it's like I was never there. 1 2 3 4 5
10. I'm afraid I won't be able to keep up with the rest of the class. 1 2 3 4 5
CHECK YOUR SCORE:
40-50 Sure thing, you have math anxiety.
30-39 No doubt! You're still fearful about math.
20-29 On the fence!.
10-19 Wow! Loose as a goose!
[http://www.mathpower.com/anxtest.htm]
When done, please post your SCOREs and say something about what you think about your SCORE.
Do this by 16 Feb.
Wednesday, February 13, 2008
Applications of differentiation
Finding the equations of tangents to curves
To obtain the equation of the tangent to a curve with equation y = f(x), we need to be able to differentiate f(x).
The following steps show how to find the equation of the tangent to the curve with given equation at the point where x is given.
Step 1:-
Differentiate y or find dy/dx
This would give the gradient function of the curve.
Substituting the given value of x would give the value of the gradient of the tangent to the curve at the point.
Hence the equation of the tangent would begin with y = m x + c where m is the value of the gradient found.
Step 2:-
Find the y-coordinate of the point with the given value of x. The values of x and y are needed to be substituted into the equation y = m x + c to calculate the value of c.
Hence the equation of the tangent would be obtained.
Worked example:-
Find the equation of the tangent to the curve with equation
y = 3x^2 + 2x - 5 at the point where x = - 2.
Step 1:-
dy/dx = 6x + 2
At x = -2, dy/dx = - 10
Hence y = - 10 x + c ---------equation [1]
Step 2:-
When x = - 2, y = 3
Substitute these values into equation [1]
Hence c = - 17
And the equation of the tangent is y = - 10 x – 17
To obtain the equation of the tangent to a curve with equation y = f(x), we need to be able to differentiate f(x).
The following steps show how to find the equation of the tangent to the curve with given equation at the point where x is given.
Step 1:-
Differentiate y or find dy/dx
This would give the gradient function of the curve.
Substituting the given value of x would give the value of the gradient of the tangent to the curve at the point.
Hence the equation of the tangent would begin with y = m x + c where m is the value of the gradient found.
Step 2:-
Find the y-coordinate of the point with the given value of x. The values of x and y are needed to be substituted into the equation y = m x + c to calculate the value of c.
Hence the equation of the tangent would be obtained.
Worked example:-
Find the equation of the tangent to the curve with equation
y = 3x^2 + 2x - 5 at the point where x = - 2.
Step 1:-
dy/dx = 6x + 2
At x = -2, dy/dx = - 10
Hence y = - 10 x + c ---------equation [1]
Step 2:-
When x = - 2, y = 3
Substitute these values into equation [1]
Hence c = - 17
And the equation of the tangent is y = - 10 x – 17
Tuesday, February 5, 2008
Monday, February 4, 2008
Cramer's Rule
Hi everyone.
I have discovered another way to solve simultaneous equations using matrices.
It's called the Cramer's Rule.
Look at the following example to study how Cramer's Rule is used to solve the simultaneous equations below:-
5x + 3y= −11
2x + 4y = −10
Worked solution
D = det of
5 3
2 4
= 20 − 6 = 14
Dx = det of
−11 3
- 10 4
= −44 + 30 = −14
Dy = det of
5 −11
2 -10
= −50 + 22 = −28
Therefore,
x = Dx/D = −14/ 14 = −1
and y = Dy/D = −28/14 = −2
Now it's your turn to use Cramer's Rule to solve the following simultaneous equations.
- x + 5y = 4
2x + 5y = - 2
Work out D, Dx and Dy and then the solutions x and y. Post these as your comments. You have until 10 Feb to do this.
I have discovered another way to solve simultaneous equations using matrices.
It's called the Cramer's Rule.
Look at the following example to study how Cramer's Rule is used to solve the simultaneous equations below:-
5x + 3y= −11
2x + 4y = −10
Worked solution
D = det of
5 3
2 4
= 20 − 6 = 14
Dx = det of
−11 3
- 10 4
= −44 + 30 = −14
Dy = det of
5 −11
2 -10
= −50 + 22 = −28
Therefore,
x = Dx/D = −14/ 14 = −1
and y = Dy/D = −28/14 = −2
Now it's your turn to use Cramer's Rule to solve the following simultaneous equations.
- x + 5y = 4
2x + 5y = - 2
Work out D, Dx and Dy and then the solutions x and y. Post these as your comments. You have until 10 Feb to do this.
Matrices and Solving Linear Equations
Solving simultaneous linear equations using matrices.
Solve - x + 5y = 4
2x + 5y = - 2
by matrix method.
By posting your answers as comments, write about the following.
What do you need to do to solve the simultaneous equation above using matrices?
Work out the answers to x and y.
Do this by 7 Feb.
Solve - x + 5y = 4
2x + 5y = - 2
by matrix method.
By posting your answers as comments, write about the following.
What do you need to do to solve the simultaneous equation above using matrices?
Work out the answers to x and y.
Do this by 7 Feb.
Saturday, February 2, 2008
Are you okay with matrices?
Hello, we have learnt matrices together in class and now I hope you will take the following quiz on matrices to check how well you have learnt the topic.
1) When adding matrices of the same orders/dimensions, will the answer have the order/dimension of the matrices?
2) When multiplying, do matrices need to be of the same orders/dimensions?
3) Can you multiply a matrix by something other than another matrix?
4) When adding matrices, do you add different positions together?
If any of your answers is a "no", please write to explain why you say so.
Post your answers to these 4 questions by 5 Feb.
1) When adding matrices of the same orders/dimensions, will the answer have the order/dimension of the matrices?
2) When multiplying, do matrices need to be of the same orders/dimensions?
3) Can you multiply a matrix by something other than another matrix?
4) When adding matrices, do you add different positions together?
If any of your answers is a "no", please write to explain why you say so.
Post your answers to these 4 questions by 5 Feb.
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