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Chapter Review

Prime and Composite Numbers

1 .
Identify which of the following numbers are prime, composite, or neither:
201, 34, 17, 1, 37.
2 .
Find the prime factorization of 500.
3 .
Find the greatest common divisor of 80 and 340.
4 .
Find the greatest common divisor of 30, 40, and 70.
5 .
Find the least common multiple of 45 and 60.
6 .
Bella and JJ volunteer at the zoo. Bella volunteers every 8 days, while JJ volunteers every 14 days. How many days pass between days they volunteer together?

The Integers

7 .
Identify all the integers in the following list: −4 , 2 7 , 15 , 97.5 , 0 , 122 .
8 .
Plot the following on the same number line:
1 , 5 , 2 , 0 .
9 .
What two numbers have absolute value of 18?
10 .
Calculate 14 ( 12 ) .
11 .
Calculate ( 19 ) × 4 .
12 .
Calculate ( 240 ) ÷ ( 12 ) .
13 .
Six students rent a house together. The total monthly rent (including heat and electricity) is $3,120. If they all pay an equal amount, how much does each student pay?

Order of Operations

14 .
Calculate 5 × 3 ( 12 ) .
15 .
Calculate 4 2 × 6 + 2 3 .
16 .
( 4 6 ) × 2
17 .
( 8 1 ) 3 − 3 × 9
18 .
120 ( 51 + 12 ) ÷ 3 2

Rational Numbers

19 .
Reduce 90 153 to lowest terms.
20 .
Convert 430 25 to a mixed number and reduce to lowest terms.
21 .
Convert 9 5 to decimal form.
22 .
Convert 5 11 to decimal form.
23 .
Calculate 4 15 + 9 10 and reduce to lowest terms.
24 .
Compute 3 10 ÷ 12 25 and reduce to lowest terms.
25 .
Determine 30% of 400.
26 .
18 is what percent of 40?
27 .
In Professor Finnegan’s Science Fiction course, there are 60 students. Of those, 15% say they’ve read A Hitchhiker’s Guide to the Galaxy. How many of the students have read that book?

Irrational Numbers

28 .
Simplify the square root by expressing it in lowest terms: 275 .
29 .
Calculate 4 13 15 13 without a calculator. If not possible, explain why.
30 .
Calculate ( 2.3 5 ) × ( 4.2 3 ) without a calculator. If not possible, explain why.
31 .
Rationalize the denominator of 6 22 , and simplify the fraction.
32 .
Find the conjugate of 4 7 + 3 and find the product of 4 7 + 3 and its conjugate.
33 .
Rationalize the denominator of 3 8 + 34 and simplify the fraction.

Real Numbers

34 .
Identify the numbers of the following list as a natural number, an integer, a rational number, or a real number: 37 , −0.43, 18, −43, 12 π .
35 .
Identify the property of real numbers illustrated here: 14 + 19 = 19 + 14 .
36 .
Identify the property of real numbers illustrated here: 87.4 + 0 = 87.4 .
37 .
Identify the property of real numbers illustrated here: 2 × ( 31 12 ) = 2 31 2 × 12 .
38 .
Identify the property of real numbers illustrated here: 98 × 41 = 41 × 98 .
39 .
Use mental math to calculate 21 × 99 .

Clock Arithmetic

40 .
Determine 74 modulo 9.
41 .
Use clock arithmetic to calculate 13 + 25 .
42 .
Use clock arithmetic to calculate 4 × 8 .
43 .
It is Wednesday. What day of the week will it be in 44 days?
44 .
It is 4:00. What time will it be in 100 hours?
45 .
Security guards with Acuriguard submit a report on campus activity every 4 days. If they make a report on a Monday, what day of the week will it be after 10 more reports?

Exponents

46 .
Use exponent rules to simplify 17 8 × 17 3 .
47 .
Use exponent rules to simplify 15 9 15 5 .
48 .
Use exponent rules to simplify ( 3 k ) 6 .
49 .
Use exponent rules to simplify ( y 4 ) 11 .
50 .
Use exponent rules to simplify ( 51 3 ) 6 .
51 .
Use exponent rules to simplify ( 3 x 4 5 ) 7 .
52 .
Rewrite 5 2 x 4 without a denominator.
53 .
Rewrite 16 z 9 without negative exponents.

Scientific Notation

54 .
Convert 0.0000452 to scientific notation.
55 .
Convert 3.01 × 10 5 to standard notation.
56 .
Convert 42.9 × 10 9 to scientific notation.
57 .
Calculate 4.51 × 10 5 9.11 × 10 4 .
58 .
Calculate ( 9.15 × 10 3 ) ÷ ( 3 × 10 8 ) .
59 .
The Sextans Dwarf Spheroidal Galaxy has diameter 8,400 light years (ly). Express this in Scientific notation.
60 .
The Reticulum II Galaxy has diameter 3.78 × 10 2 light years (ly), while the Andromeda Galaxy has a diameter of 2 × 10 5 . How many times bigger is the Andromeda Galaxy compared to the Reticulum II Galaxy?

Arithmetic Sequences

61 .
Determine the common difference of the following sequence: {19, 13, 7, 1, -5, …}.
62 .
Find the 25th term, a 25 , of the arithmetic sequence with a 1 = 13 and d = 1.7 .
63 .
Find the first term and the common difference of the arithmetic sequence with 8th term b 8 = 50 and 15th term b 15 = 106 .
64 .
Find the sum of the first 30 terms, s 30 , for the arithmetic sequence with first term a 1 = 4 and common difference d = 3.5 .
65 .
Jem makes a stack of 5 pennies. Each day, Jem adds three pennies to the stack. How many pennies are in the stack after 10 days?

Geometric Sequences

66 .
Determine the common ratio of the following geometric sequence: {6, 18, 54, 162, …}.
67 .
Find the 6th term, c 6 , of the geometric sequence with c 1 = 400 and r = 0.25 .
68 .
Find the sum of the first 12 terms, s 12 , for the geometric sequence with first term a 1 = 4 and common ratio r = 1.25 .
69 .
Carolann and Tyler deposit $8,500 in an account bearing 5.5% interest compounded yearly. If they do not deposit any more money in that account, how much will be in the account after 15 years?
70 .
The total number of ebooks sold in 2013 was 242 million ( a 1 = 242 ). Each year, the number of ebooks sold has declined by 3% ( r = 0.97 ). How many ebooks were sold between 2013 and 2022?
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