## Tuesday, February 14, 2012

### More Practice on Chapter 7

Today in math class we did different kinds of questions that will be on the test.

First we were given a question to find the area of rectangle with a missing piece using polynomials.

There are two ways to figuring out the area of this shape. First way is to break up the shape into 3 pieces, and add Areas 1 and 2, and subtract area 3.

The second way is to pretend the missing piece is there (area 1) so it makes a whole rectangle, then subtract area 2 (missing piece) to area 1. I chose to do this method because it seemed like a faster way for me.

l = 8x - 4 + 4x + 9 = 12x +5
w = 6x + 2 + 3x - 5 = 9x - 3

A1 = lw
= (12x + 5)(9x -3)
= (12x)(9x) + (12x)(-3) + (5)(9x) + (5)(-3)
= 108x^ - 36x + 45x - 15

A2 = lw
= (8x - 4)(3x -5)
= (8x)(3x) + (8x)(-5) + (-4)(3x) + (-4)(-5)
= 24x^ - 40x -12x + 20
= 24x^ - 52x + 20

A1 - A2
= 108x^ + 9x -15 - (24x^ - 52x + 20)
= 108x^ +9x - 15 -24x^ +52x - 20
= 84x^ + 61x -35

Therefore, the area of the shape is 84x^ + 61x - 35.

The second question was a triangle. This was much simpler because it didn't contain a missing piece.

A = bh/2
= (8x +4)(5x)/2
= (8x)(5x) + (4)(5x)
= 40x^ + 20x/2
= 40x^/2 + 20x/2
= 20x^ + 10x

The area of the triangle is 20x^ + 10x.

The third question was to find the width of the rectangular prism.

V = lwh
48x³ = (2x)(w)(3x)
48x³ = 6x^
w = 48x³/6x^
w = 8x

The width of the rectangular prism is 8x.

The fourth question is similar to the first one, except with different values. Again, I used the A1-A2 method.

Step 1

Step 2

Step 3

The area of the shape is 26x^ - 35x - 12.

The fifth question is finding the ratio of the rectangle to the circle. This won't be on the test but it's better to know it now for future references.

r = d/2
r = 6x/2
r = 3x

rectangle / circle
= lw / pi r^
= 6x(12x) / pi(3x)^
= 72x^/pi 9x^
= 8 / pi

The last question was to find the ratio of the small circle to the large circle.

So/Lo = pi r^/pi r^
= pi(2x)^/pi(4x)^
= 4x^/16x^
= 4/16
= 1/4

Solve:
1. 3(5x + 3) - (10x - 6)
= 15x +9 - 10x + 6
= 5x + 15

2. (1/2t)^ 3t
= (1/2t)(1/2t)(3t)
= 1/4t^(3t)
= 3/4t³

Remember:
Always use the FOIL(First, Outside, Inside, Last) method when multiplying