# Geometry – prism

How many vertices does a rectangular prism have?

If you have trouble drawing it or visualizing it, consider this instead:  A prism has two identical bases.  All of the vertices are along the edges of the two bases.  Since a rectangular prism has rectangles for bases, each base will have 4 vertices.  Two rectangular bases will have 8 vertices total. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# SAT – counting and ordering

Q: You are 18th in line and your friend is 34th in line. How many people are in line between you and your friend?

No, not 16! Do 34-18=16, but then subtract one. Why? The 16 includes either the person you started with (you) or the person you ended with (your friend), and you don’t want to include either person in the count. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# Algebra 2 – solving quadratic equations

Q: The length of a rectangle is 4 cm longer than the width. If the rectangle’s area is 45 cm², what is the width?

Explanation:  Call the width x.  Then, the length is x+4.

Area of a rectangle = (length)(width).

45 = x(x+4)

45 = x² + 4x

0 = x² + 4x – 45

Now, factor:

0 = (x + 9)(x – 5)

x = -9 or x = 5

Since a length can’t be negative, discard x = -9.  The only solution is x = 5.  Since ‘x’ is what we called the width, it is the answer to the question.  Just put the appropriate unit on it: 5 cm. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# SAT – Probability

Using a standard pair of dice, what is the probability of rolling two numbers with a sum of 8?

5/36

Explanation:  6 x 6 = 36 ways you can roll two dice.  Now, find the ways you can get a sum of 8:

2+6, 6+2, 3+5, 5+3, 4+4

That’s 5 ways.  So, the probability is 5/36.  