Chapters 1-4 Cumulative Test
1. Shade the region in the Venn Diagram below to represent the set (A B)  (BC) .
A
B
C
U
2. Given the universal set of {x 0  x  20} and sets A, B,, and C as defined below, place
all of the numbers from the universal set in the appropriate location on the Venn
Diagram below.
A = {2, 4, 0, 1, 3, 5, 6}, B = {10, 11, 12, 1, 2, 7, 6, 14}, C = {18, 19, 6, 11, 16, 12, 9,
8}
A
B
C
U
3.
4.
5.
6.
What bases x and y make the equation 32x = 23y true?
Write out the first 14 base 3 numbers beginning at 1.
Illustrate the addition problem 3 + 4 using a measurement model.
Rewrite the number 223 in each of the number systems described below.
a. Babylonian:
b. Roman:
c. Egyptian:
d. Mayan
7. Of the 4 number systems listed in problem 6,
a. in which systems does order matter?
b. in which systems is place value used?
8. Identify what subtraction problem and what conceptual approach is illustrated in each
of the following problems.
a.
??
b.
c.
4
6
7
0
1
2
3
4
5
6
7
9. Identify and explain 2 different approaches to whole number multiplication.
10. For each of the following problems, determine whether they are an example of
partitive or measurement division and explain your reasoning.
a. An airplane is gaining altitude at a rate of 400 feet per second, how long will it
take the plane to reach a cruising altitude of 32000 feet?
b. Juan has decided to give his baseball card collection of 364 cards to his brothers
and cousins (7 altogether). If he divides them evenly, how many cards will each
relative receive?
c. Ms. Tanaka has 57 pipe cleaners for her class project. She knows that each student
will need 3 pipe cleaners to do the project she has planned. How many students
can do the project?
11. Find a subset of whole numbers, call it A, that is closed for division but not closed for
addition.
12. Explain how you could determine which of the following is larger without using a
calculator.
2015
530
13. List Polya’s four steps to solving problems.
14. Identify a non-mathematical problem that could be solved using Polya’s four steps
and explain how these steps could be used to solve this problem.
15. The figures below are polygons and the dotted lines are diagonals.
a. How many diagonals does a 10 sided polygon have?
b. How many diagonals does a 100 sided polygon have?
c. Identify the strategies used to solve parts a and b.
16. Compute each of the following mentally and describe the method used.
a. 77 + 98
b. 224  4
c. 49  7
17. Sketch and explain how base 10 blocks could be used to illustrate
23 14
18. Use and explain an intermediate algorithm to compute the following sum 374 + 267.
19. Sketch and explain how base 10 blocks could be used to illustrate the following
operation 538  4 .
20. Use the problem 43 – 27 to explain how the standard algorithm for subtraction and
the “subtract from the base” algorithm require different thought processes.