# Algebra 1 – distance

Q: To the nearest tenth, what is the distance between the points (-6,2) and (6,5)?

(Use the distance formula, and round to the nearest tenth.)
My TI-84 Plus program DISTANCE will find this value. 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: Bob has ten different books, but must choose only three to bring along on his vacation. In how many ways can Bob choose three books?

Explanation: This is a combination (not permutation) problem, because the order of the books in Bob’s bag does not matter.  Find the nCr function on your calculator and enter ’10 nCr 3′.  On the TI-84 Plus, nCr is in MATH, PRB, 3.  Or, do this by hand using the formula for nCr. 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.

# Geometry – Volume

Q: What is the maximum number of boxes with dimensions 4”x5”x8” that can be packed into one large box with dimensions 20”x20”x24”?

Explanation: First, decide that a whole number of small boxes will entirely fill the large box.  To do this, look at the dimensions and match them.  4″ fits into 20″ five times.  5″ fits into 20″ four times.  8″ fits into 24″ three times.  That means, you’ll get five rows of small boxes, four boxes per row, and three layers deep.  So, the quickest way to get the answer is to multiply 5x4x3 = 60.

BUT if you don’t notice that, just do (large volume)/(small volume).

Large volume = 20x20x24 = 9600

Small volume = 4x5x8 = 160

(large volume)/(small volume) = 9600/160 = 60 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.

# Geometry – Volume

Q: Two rectangular prisms have the same volume. Prism 1 has dimensions 4 ft, 5 ft, and 7 ft. Prism 2 has dimensions 14 ft, 4 ft, and x ft. What is the value of x?

Explanation:  Volume of a rectangular prism = (L)(W)(H)

Volume 1 = (4)(5)(7) = 140

Volume 2 = (14)(4)(x) = 56x

Since the volumes are equal, 56x = 140.  x = 2.5 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 – remainders

If summer begins on a Tuesday and ends 100 days later, on which day of the week does summer end?

Explanation:  A week has 7 days.  Dividing 100 by 7, you get 14 remainder 2.  That’s 14 weeks and 2 days.  Beginning on a Tuesday, 14 weeks later would land on a Tuesday too.  Two more days brings you to Thursday. 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.

# Geometry – circles

Q: The area of a 45 degree sector of circle M is 100 square units. What is the area of circle M?

Answer: 800 square units

Explanation:  The 45° sector is exactly 1/8 of the circle. (45/360 = 1/8)

100 = 1/8 of the area of the whole circle.

The area of the whole circle is 800. 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.

# 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? 