Maths behind the dance

Dancing vary a lot in the different types there are. Is any type of dance that uses maths? Give examples of the maths in the things we love to do and we are so good at.

Confidence with the use of blog

Virtual Classroom by Fariel Mohan
Did the virtual classroom helped improved your confidence in Maths?
Has the virtual classroom help your understanding in Maths?
Would you recommend a student to use this virtual classroom?
Do you feel you were included and involved when you answered or asked questions?
Was the flexibility of using at any time significant to you?
In explaining or making a comment, did you ever had to stop and ask yourself how can I really explain what I am trying to say?
Did you ever felt good at helping someone by correcting their error or suggesting what might be the error?
Did you feel you were included and involved in the teaching of this course?
Being able to ask a question whenever you want, was this useful?
Was it helpful to you to use anonymous names?

Trig Calculus

1. ∫5sinb db
2. ∫5cosm dm
3. ∫5sinb + 9b^4 db
4. ∫5/x dx
5. Find the derivative of the following

Let f(t) = 5 cos t , f(x) = sin x, Let f(x) = 3cos x + 5x, Let f(t) = 2t + sin t. f(t) = 1/t2 - sin t, Let f(x) = sin x - cos x. Let f(x) = 2sin x + 3cos x. Let f(x) = 4sin x + 1/x.
Let f(t) = -3sin t + 1/2 cos t.

6. Find the integration of the following
Let f(t) = 5 cos t , f(x) = sin x, Let f(x) = 3cos x + 5x, Let f(t) = 2t + sin t. f(t) = 1/t2 - sin t, Let f(x) = sin x - cos x. Let f(x) = 2sin x + 3cos x. Let f(x) = 4sin x + 1/x. Let f(t) = -3sin t + 1/2 cos t.

Real Life ie rate of change

1. The displacement s of a piston during each 8-s is given by s = 8t -t^2. For what value of t is the velocity of the piston 4?
2. The distance s travelled by a subway train after the brakes are applied is given by s = 20t -2t^2 How far does it travel after the brakes are applied in coming to a stop?
3. Water is being drained from a pond such that the volume V of water in the pond after t hours is given by V = 50t(60-t^2). Find the rate at which the pond is being drained after 4 hours.
4. The electric field E at a distance r from a point charge is E=k/r^2 where k is a constant. Find an expression for the instantaneous rate of change of the electric field with respect to r.
5. The altitude h of a certain rocket as a function of the time t after launching is given by h = 550t - 4.9 t^2. What is the maximum altitude the rocket attains?
6. The blade of a saber saw moves vertically up and down and its displacement is given by y = 1.85 sin t. Find the velocity of the blade for t=0.2
7. Differentiate y = 7sin x + 4x^2 +1

Review Questions

Integrate the following DO NOT FORGET THE +c
1. dy/dx = 5x^3 + 2x^2 + 5
2. dy/dx = 6x + 1
3. dy/dx = 2
4. dy/dx = 8x^5 - 5x^3 + 4x
5. dy/dx = 7x^2 + 3x + 4

6. A particle moves in a straight line and at point P, it's velocity is given as v = 7t^2 - 5t +3. The particle comes to rest at point Q.1. What is the acceleration at Q if it arrives at Q when t=7?2. How far does the particle travel in t=1 to t=4?

7. Find dy/dx of the following:

1. y = 6x^3 + 4x^2 - 5x
2. y = x^-3 + 16
3. y = 4x + 4
4. y = 3x^4 + 3(x^2 + 5)
5. y + 6 = 4x + 9y - 3x^2


8. A curve has equation y = 4/(2)^.5, find dy/dx
9. A curve is such that dy/dx = 16/x^3 and (1,4) is a point on the curve, find the equation of the curve.
10. y = 6theta - 2sin theta, find dy/dx
11. The equation of a curve is y = 2x + 8/x^2, find dy/dx and d^2ydx^2
12. A curve is such that dy/dx = 2x^2 -5. Given that the point (3,8) lies on the curve, find the equation of the curve.

Questions

1. A rectangle is to have a perimeter 26cm and a length x cm. If the width x equals 3cm, find the length and hence the Area of the rectangle. Find dA/dx and hence find the width of the rectangle giving the maximum area.
2. Solve for p and r given 3p + 2r = 7 and p^2 - 2r = 11
3. Solve 8x^2 + 3y^2 = 50 and 2x + y = 5
4. Write the expression 9x^2 - 9x + 1 in the form a(x + b)^2 + c, where a,b and c are constants. Hence state whether the function y = 9x^2 - 9x + 1 has a maximun or minimum value. State the value of x at which this maximum or minimum value occurs
5. EFGH is a parallelogram with EF = 6cm EH = 4.2cm, and angle FEH = 70 degrees. Calculate the length of HF. Calculate the area of the parallelogram EFGH.
6. A vertical tover FT has a vertical antenna TW mounted on top of the tower. A point P is on the same horizontal ground as F such that PF = 28 m and the angle of elevation of T and W from P are 40 and 54 resp. Calculate the length of the antenna TW.
7. A vertical pole AD and a vertical tower BC stands on horizontal ground XABY. The height of the pole is 2.5 m and the angle of depressionn of B from D is 15 degrees abd the angle of elevation of C from D is 20 degrees. DE is a horizontal line. Calculate AB and the height of the tower BC.
8. Find the coordinates of the stationary points on the graph of y = x^3 - 12 x - 12.
9. Factorise x^2 + x -12
10. Evaluate (5x^2 + 4x + 1) + (-7x + 2)
11. Factorise 5x^2 + 13x - 6
12. Simplify (8x^4 - 2x^2)/2x^2
13. Factorise 3x^2 - 48
14. KNM is a right angle triangle with KNL also being a right angle triangle. AN = 6 cm and NM = 15.6 cm and angle KLN is 52 degrees. KLM is a straight line. Calculate the size of angle KMN and the length LM
15. F(x) = 3x^2 - 12x + 5. Write in the form a(x + b)^2 + c, where a,b and c are constants. Hence determine the minimum value of f(x) and the coordinates of the minimum point.
16. y = 6x^2 + 32/x^3, find dy/dx
17. y = x^2 + 54/x, find dy/dx
18. y = 1 + 4x^3, find dy/dx
19. Find the coordinates of the stationary points on the graph of y = x^2 + x^3.
20. The curve y = 27 - x^2 has the points P and S on the curve. The point R and Q lie on the x-axis and PQRS is a rectangle. The length of OQ is t units. Find the length of PQ in terms of t and show the area of PQRS is A = 54t - 2t^3. Find the value of t for which A has a stationary value. What is the stationary value of A and determine its nature (max or min)

Graphs Project

The graph project was an individual project, if group the quantities must be multiplied, so 4457, 255, 133, 2282, 4420 redo or the project which is 1 student will be divided by 5.

This project was suppose to be the 3 sections:

• Show a graph being used in real life for 3 cases
• In graphs line and curve identify keep points and explain what they signify
• Show how 2 graphs can be used to solve (intersection) and take some points from a lab or internet and plot the graph

Generally speaking very little time was spent on this project so it is reflected. If anyone wants to add to their project, do so before start of exam (mon)

Leave with admin assistant and write added to project

So far 60 projects was collected

So far 84 blog users and 1 manual user

So far 95 quiz were done