Download Exam 1 Review 1. Describe visually, symbolically, and verbally two

Exam 1 Review
1. Describe visually, symbolically, and verbally two ways to determine the difference
between 1032five and 343five. Do not change out of base five!
2. Explain how the distributive property of multiplication over addition is illustrated
visually in a rectangular array model using base ten pieces.
3. From our algebra experience, we know that
(x + 3) × (x + 2) = x 2 + 2x + 3x + 6 = x 2 + 5x + 6 . Explain how this “foiling”
technique can be described in terms of (a) a rectangular array model, and (b) the
distributive property of multiplication over addition.
4. Determine whether the set of all whole numbers whose units digits are 6 is closed
under multiplication. Explain your reasoning.
{6, 16, 26, 36, 46, … }
5. Jimmy is given the problem 1233five −323five. Based on his sketches of the base five
pieces below, he gives the solution 111five.
Difference:
What error is Jimmy making? Explain how you would help this student understand how
to resolve this issue.
6. There are 78 people around a table. Each person shakes hands with the people to his or her immediate right and left. How many handshakes take place? Assume no duplicates. Write a general formula for the number of handshakes if there are n people around the table. Explain how you came up with your formula. 7. Find a pattern to extend the following figure of tiles. Figure
1st
2nd
3rd
4th
3
7
12
18
Write a general formula for the number of tiles in the nth figure. Describe the
connection between your formula and the tile pattern.
8. If the fourth number in a geometric sequence is 54 and the fifth number is 162, what is the first number in the sequence? 9. Use the method of finite differences to find the next number in the following
sequence: 1, 7, 27, 66, 129