### Chapter Review

##### Prime and Composite Numbers

1
.

Identify which of the following numbers are prime, composite, or neither:

201, 34, 17, 1, 37.

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: $\text{\u22124},\frac{2}{7},\text{15},\text{97.5},\text{0},\sqrt{122}$.

8
.

Plot the following on the same number line:

$1,5,-2,0$.

$1,5,-2,0$.

9
.

What two numbers have absolute value of 18?

10
.

Calculate $14-(-12)$.

11
.

Calculate $(-19)\times 4$.

12
.

Calculate $(-240)\xf7(-12)$.

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 $5\times 3-(-12)$.

15
.

Calculate ${4}^{2}\times 6+{2}^{3}$.

16
.

$(4-6)\times 2$

17
.

$(8-1{)}^{3}\phantom{\rule{thinmathspace}{0ex}}\text{\u2212 3}\phantom{\rule{thinmathspace}{0ex}}\times 9$

18
.

$120-(51+12)\xf7{3}^{2}$

##### Rational Numbers

19
.

Reduce $\frac{90}{153}$ to lowest terms.

20
.

Convert $\frac{430}{25}$ to a mixed number and reduce to lowest terms.

21
.

Convert $\frac{9}{5}$ to decimal form.

22
.

Convert $\frac{5}{11}$ to decimal form.

23
.

Calculate $\frac{4}{15}+\frac{9}{10}$ and reduce to lowest terms.

24
.

Compute $\frac{3}{10}\xf7\frac{12}{25}$ 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: $\sqrt{275}$.

29
.

Calculate $4\sqrt{13}-15\sqrt{13}$ without a calculator. If not possible, explain why.

30
.

Calculate $\left(2.3\sqrt{5}\right)\times \left(4.2\sqrt{3}\right)$ without a calculator. If not possible, explain why.

31
.

Rationalize the denominator of $\frac{6}{\sqrt{22}}$, and simplify the fraction.

32
.

Find the conjugate of $4\sqrt{7}+3$ and find the product of $4\sqrt{7}+3$ and its conjugate.

33
.

Rationalize the denominator of $\frac{3}{8\phantom{\rule{thinmathspace}{0ex}}+\phantom{\rule{thinmathspace}{0ex}}\sqrt{34}}$ 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: $\sqrt{37}$, −0.43, 18, −43, $12\pi $.

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: $2\times (\sqrt{31}-12)=2\sqrt{31}-2\times 12$.

38
.

Identify the property of real numbers illustrated here: $98\times 41=41\times 98$.

39
.

Use mental math to calculate $21\times 99$.

##### Clock Arithmetic

40
.

Determine 74 modulo 9.

41
.

Use clock arithmetic to calculate $13+25$.

42
.

Use clock arithmetic to calculate $4\times 8$.

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 ${17}^{8}\times {17}^{3}$.

47
.

Use exponent rules to simplify $\frac{{15}^{9}}{{15}^{-5}}$.

48
.

Use exponent rules to simplify $(3k{)}^{6}$.

49
.

Use exponent rules to simplify ${\left(\frac{y}{4}\right)}^{11}$.

50
.

Use exponent rules to simplify ${\left({51}^{3}\right)}^{6}$.

51
.

Use exponent rules to simplify ${\left(\frac{3{x}^{4}}{5}\right)}^{7}$.

52
.

Rewrite $\frac{{5}^{2}}{{x}^{4}}$ without a denominator.

53
.

Rewrite $16{z}^{-9}$ without negative exponents.

##### Scientific Notation

54
.

Convert $0.0000452$ to scientific notation.

55
.

Convert $3.01\times {10}^{5}$ to standard notation.

56
.

Convert $42.9\times {10}^{-9}$ to scientific notation.

57
.

Calculate $4.51\times {10}^{5}-9.11\times {10}^{4}$.

58
.

Calculate $\left(9.15\times {10}^{3}\right)\xf7\left(3\times {10}^{8}\right)$.

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 $3.78\times {10}^{2}$ light years (ly), while the Andromeda Galaxy has a diameter of $2\times {10}^{5}$. 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?