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Review for exam 2 – numeration systems and some geometry
Spring 2011, MA118, McAllister
1. Complete the chart to indicate whether each of the numeration systems has each of the traits
on the left. Write a YES or NO in each box.
Babylonian
Roman
Mayan
Indio-Arabic
Egyptian
ZERO?
PLACE
VALUE?
ADDITIVE
SYSTEM?
WHAT
BASE?
2. Briefly discuss the value of teaching and learning about other numeration systems besides our
own. List at least two reasons.
3. Convert each Roman numeral into Indo-Arabic numerals and each Indo-Arabic number into
Roman numerals.
a. MMCCCLXXVII
b. MMCMXCIX
c. 3495
d. 1987
4. a. Make a base 7 place value chart with at least 4 place values:
b. Convert 89510 to base 7. Show your work. c. Convert 64137 to base 10. Show your work.
5. Compute the following base 7 numbers as indicated using any algorithm. Leave the answers
in the base the original numbers are given in.
a 5647 + 4347 = _______
b 6217 – 5547 = _______
6. In the figure below, line l and m are parallel. Using the given information, determine the
measure of all of the angles in the figure.
65
 c
120

h
i
a
d e
f
g
b
j
k
7. Determine if the following statements are true or false. Indicate a true statement by writing the word
‘true’ in the blank before the statement and a false statement by writing the word ‘false’ in the blank.
__________a. Every equilateral triangle is acute, but not every acute triangle is equilateral.
__________b. Every square is a rectangle, and every rectangle is a square.
__________c. It is possible to have a right scalene triangle.
__________d. Octagons have six sides and look like a stop sign.
__________e. A kite has two pairs of congruent adjacent sides.
__________f. A triangle has at most two acute angles.
__________g. It is possible to have a right equilateral triangle.
__________h. Two angles are complementary if the sum of their measures is 180.