Study Guide for Exam 2

Study Guide for Exam 2

Note that this is a study guide, not a sample exam - it is much longer than your exam will be. However, the ideas and the question types represented here (along with your homework and activities) will help prepare you for your exam.

Note that from 3.1, you will be expected to be familiar with the first four symbols of the Egyptian numeration system (staff, yoke, scroll and lotus flower) and Babylonian (base 60) system.

This exam covers material from 3.1 to 4.2.

1. Determine all values for the digit d that make the number 4,3d1 divisible by 3. If none exist, indicate so.

2. Compute the checksum to determine if the following could be a valid credit card number:

6011 3047 5012 2202

3. Write the Indo-Arabic equivalent of the following:

(a)

(b) Note: the table boundaries indicate place value, so you don't have to guess.

4. Write the number 37,395 in the Babylonian numeration system.

5. Write the number 2342 in the Egyptian numeration system.

6. Convert to base ten.

(a) 130_five
(b) 555_six
(c) E9_twelve
(d) 2004_five
(e) 2134_six
(f) 1TE6_twelve
(g) 312_four

7. Convert the decimal to the given base.

(a) 2,874 to base five
(b) 329 to base six
(c) 46 to base twelve
(d) 215 to base five
(e) 215 to base six
(f) 215 to base twelve
(g) 215 to base four

8. Illustrate and explain how an alien from a base four world would gather these pebbles in groups for counting. What base four number represents the number of pebbles?

9. Sketch the solution to the following problems using place value cards or using mats, strips, and units. Draw a square for a mat, a vertical line for a strip, and a dot for a unit. Remember that a numeral with no subscript is understood to be base ten.

(a)
221_four
+ 131_four
-----------
(b)
301_four
- 102_four
-----------
(c) 25 + 37
(d) 313_four + 33_four
(e) 25_six + 43_six
(f) 65 - 28
(g) 412_five - 31_five

10. Fill in the missing blanks of this base ten addition problem.

   (a)   5    4    8
          3   (b)   2
+ 4    5    8   (c)
    7   (d)   0    5

11. Fill in the missing blanks of this base ten subtraction problem.

    3     (a)   (b)    5
-          4      5     7
    2     8      6    (c)

12. Name the base that the following calculations are written in. Explain your reasoning.

(a)
    321
+ 313
1300
(b)
   286
+ 578
   842
(c)
   632
- 456
198
(d)
     234
+ 443
   1121
(e)
     234
+ 443
   1232
(f)
     233
+ 331
   1230

13. Carry out these calculations using base five notation. All numerals are already written in base five so that no subscripts are needed. You may do your work in base five if you show all steps (including scratch work), or you may use place value cards or mats, strips, and units. Do not convert into base ten to perform the calculations, although you may check your answers this way if you wish.

(a)
24
x 3
(b)

(c) 143
x 31

14. Construct a factor tree for the given number. Use this to determine the prime power representation of the number.

(a) 65
(b) 170
(c) 200

15. Identify the number as prime, composite, or unit. If it is composite, give the prime factorization. If it is prime, explain how you determined this. If it is prime, what is the smallest number of factors you need to check to determine this? Why? List them.

(a) 42
(b) 53
(c) 1
(d) 157
(e) 627

16. Suppose you have a Sieve of Eratosthenes that goes to 900. What is the smallest number that you would circle and not find any of its multiples to cross off? Explain.

17. What can you say about a number that has exactly two factors? Give an example.

18. What can you say about a number that has exactly three factors? Give an example.

19. Determine whether or not the first number is divisible by the second number by using the appropriate divisibility test (not by just checking it in your calculator, although you can check your answer this way). Explain what test you used and how you used it.

(a) 263,418 by 3
(b) 703 by 3
(c) 1,358,082 by 11
(d) 87,405,783 by 11

20. Recall that the checksum for an ISBN is found by multiplying the sequence of 10 digits by the respective numbers 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 and then adding the products. The checksum must be a multiple of 11. Explain why the checksum for an ISBN might need an X in the last digit.

21. What calculation is represented in the following sequence of sketches? Give the number sentence for the calculation (for example, 5 – 3 = 2 is a number sentence) and give the base that the calculation is in.

22. Let a = 2³ * 3⁴ * 5¹ * 7².

(a) Is 2² * 3¹ * 5¹ a factor of a? Why or why not?
(b) Is 2¹ * 3⁵ * 7² a factor of a? Why or why not?

23a. Look at the following Chapter 3 review questions in your text: 1a, 4-6, 8, 9, 13, 15.
23b. Look at the following Chapter 3 chapter test questions in your text: 1, 2, 5-8, 14, 16.
23c. Look at the following Chapter 4 review questions in your text: 2, 7, 9, 10, 12 - 14.
23d. Look at the following Chapter 4 chapter test questions in your text: 1, 2ab, 3, 5, 9, 10ab.

Look at the solutions

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