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MA 201: FINAL REVIEW I
2. Sets and Numeral Systems
Define the following.
set:
null set:
set equality:
cardinality:
set equivalency:
subset:
natural numbers:
less than:
reflexive property:
transitive property:
symmetric property:
1. List the elements in the following sets.
a) {x | x is an odd number between 2 and 8}
c) {z | z prime and 2 ≤ x ≤ 7}
b) {y | y is a letter in the word “pullup”}
d) {w | w < 9 and w > 10}
2. Are any of the above sets equivalent? Are any of the above sets equal? Which ones, and why?
3. Use sets to explain why 3 < 5.
4. Complete each statement to illustrate the indicated property.
a) Reflexive property: 32=
b) Transitive property: If a = b and b = c, then
c) Symmetric property: If 5 = x, then
d) Transitive property: If
and 5 = y, then x = y.
e) Symmetric property: If
, then a = b.
5. State the place value of the underlined digit.
a) 742,094,009
c) 1,000,270,695
b) 28,000,412
d) 1,230,805,300
6. Write the word name for each of the above numerals.
a)
c)
b)
d)
7. Write the binary number as a base-ten number.
a) 110
c) 10101
b) 1011
d) 111000
8. Write the base-ten number as a base-three number.
a) 312
c) 586
b) 44
d) 1300
3. Operations with Whole Numbers
Define the following.
union:
a + b:
commutative property of addition:
associative property of addition:
additive identity property:
a − b:
a · b:
commutative property of multiplication:
associative property of multiplication:
multiplicative identity property:
zero product property:
distributive property:
a ÷ b:
divisor:
dividend:
quotient:
remainder:
9. Using one of the algorithms we discussed, determine the following. Show work.
a) 29+44
i) 229+458+4951
b) 87-33
b) 7111-836
c) 45×59
c) 402×617
d) 336÷ 8
d) 14365÷ 221
e) 87+698
e) 7268+9534
f) 2315-1557
f) 2426-1995
g) 551×146
g) 36×321
h) 5374÷ 63
h) 1760÷ 38
4. Exponents and Order of Operations
Define the following.
base:
exponent:
squared:
cubed:
product of powers property:
quotient of powers property:
power of product property:
power of power property:
order of operations:
10. Find a value of x that makes the equation true.
a) 34 · 3x = 38
e) x4 = 38
b) 3x · 7x = 215
f)
5x
53
= 54
c) (7x )4 = 78
g)
2x
22
=8
d) (5x )3 = 125x
h) x4 = 212
11. Write a numerical expression that uses the order of operations to represent the problem.
a) Multiply the difference of 6 and 2 by 3.
b) Subtract the product of 5 and 6 from 35.
c) Add the difference of 18 and 14 to 11.
d) Subtract the quotient of 24 and 6 from 29.
e) Add the square of 5 to the sum of 18 and 7.
12. Evaluate the following.
a) 21 − 4 × (6 − 4)
d) 38 − 5 × (36 ÷ 12)
b) 66 − 24 − 4 × 3
e) 5 × 7 − 42
c) 3 × 42 − 20
f) 2 × (19 − 15)2 − 32 − 2 × (72 ÷ 62 )