1. SAT Questions

I do not know how to do all of the following:

1.Point P is the center of one face of a cube and point Q is the center of the opposite face. If the length of the shortest possible path from P to Q along the outer surface of the cube is 2root2 cnetimers what is the volume of the cube in public centimeters.

2. x^2 + 16x + a = (x+b)^2
In the equation above, a and b are constants. If the equation is true for all values of x what is the value of a?

3. In the xy-plane, line m is the reflection of line l across the x-axis. If the intersection of lines l and m is the point (r,s), which of the following must be true?
a) r=0
b) s=0
c) r=s
d) r=-s
e) rs=-1

2. Originally Posted by juliak
1.Point P is the center of one face of a cube and point Q is the center of the opposite face. If the length of the shortest possible path from P to Q along the outer surface of the cube is 2root2 cnetimers what is the volume of the cube in public centimeters.
Draw a picture. Note that the shortest path will be up one side, across a face (say, the top), and down the opposite side. Note that this will be twice the length of one face. Use this to find the length of one face. Plug this value into the volume formula for a cube.

Originally Posted by juliak
2. x^2 + 16x + a = (x+b)^2
In the equation above, a and b are constants. If the equation is true for all values of x what is the value of a?
Use what you've learned in algebra about recognizing perfect-square trinomials. Deduce from this what the value of "a" must be, to create a perfect-square trinomial.

Originally Posted by juliak
3. In the xy-plane, line m is the reflection of line l across the x-axis. If the intersection of lines l and m is the point (r,s), which of the following must be true?
a) r=0
b) s=0
c) r=s
d) r=-s
e) rs=-1
Draw a line. Reflect it in the x-axis. Look at the intersection point. See what you can conclude.