form 3 maths

1.Maggie deposits a sum of money in a bank at an interest rate of 7% p.a.compounded half-yearly.If the interest she received after 3 years is $1834, find the principal. When calculating questions relating to compound interest, use the following formula.

圖片參考：http://upload.wikimedia.org/wikipedia/en/math/3/c/6/3c61f664e4b9ae0ea85f89dff6b52548.png

Let $x be the principal.
　 x(1+3.5%)^6=1834+x
x(1+3.5%)^6-x=1834
0.2293x=1834
　 　 　 x=8000
The principal is $8000.
2.

圖片參考：http://upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Trigonometry_triangle.svg/288px-Trigonometry_triangle.svg.png


圖片參考：http://upload.wikimedia.org/wikipedia/en/math/3/8/1/3814ef0ec01bf92e5ecff3d92a9d0b3d.png


圖片參考：http://upload.wikimedia.org/wikipedia/en/math/0/1/2/0128e296de33af22b732f384eaed1728.png


圖片參考：http://upload.wikimedia.org/wikipedia/en/math/c/0/d/c0dd18b51a2d4e39c12f9461a485e1b0.png

Sin, cos and tan are trigonometric functions.
In Form 3 Mathematics, they are commonly used when finding an angle or a side in an acute triangle.

There are 2 examples using the graph above.
Ex 1. Finding an angle using given 2 sides.
Given that a=20 and b=30, find∠A.
Use tangent function,
tan ∠A =20/30
∠A =33.69°
Ex 2. Finding a side using a given angle and a given side.
Given that a=15 and ∠A=60°, find h.
Use sine function,
sin 60°=15/h
h=15/( sin 60°)
h=17.32 or 10√3


3a.(p^2-q^2)^2-4p^2q^2
=(p^2-q^2)^2-(2pq)^2
=(p^2-q^2+2pq)(p^2-q^2-2pq)
b.16x^2-12x-49y^2-21y
=16x^2+28xy-28xy-49y^2-12x-21y
=(4x-7y-3)(4x+7y)

2012-06-14 18:41:15 補充：
The ways I use in Q2 are only for RIGHT-ANGLED triangle.

1
Let $x be the principal

x(1+3.5%)^6 - x =1834
x [ (1+3.5%)^6 -1 ] = 1834
x (1.035 ^6 -1) =1834
x =1834 / 0.22926
x=8000

Therefore, the principal is $8,000

Q2
sinθ=(opposite side)/(hypotenuse)
cosθ=(adjacent side)/(hypotenuse)
tanθ=(opposite side)/(adjacent side)
It is just depends on what information you have and what you have to find to choose which ratio you use:
Example1:
Have degree, have hypotenuse, find opposite side: so just use sin
Examlpe2:
Have opposite side, adjacent side, find θ: use tan
Example3:
Have degree, have adjacent side, find hypotenuse: use cos
Q3a
〖〖(p〗^2-q^2)〗^2-4p^2 q^2
p^4-2p^2 q^2+q^4-4p^2 q^2
-2p^2 q^2 (1+2)+p^4+q^4
Q3b
16x^2-12x-49y^2-21y
4x(4x-3)-7y(7y-3)

I sorry that I forget how to calculate Q1, but acutely I am only form2. I type so hard la, please give me the marks. Thx!