Contemporary Mathematics

# Chapter Review

### 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: $\text{−4}, \frac{2}{7}, \text{15}, \text{97.5}, \text{0}, \sqrt{122}$.
8 .
Plot the following on the same number line:
${1, 5, −2, 0}$.
9 .
What two numbers have absolute value of 18?
10 .
Calculate $14 - ( - 12)$.
11 .
Calculate $( - 19) \times 4$.
12 .
Calculate $( - 240) \div ( - 12)$.
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 . ${(8 - 1)^3}\, \text{− 3}\, \times 9$ 18 . $120 - (51 + 12) \div {3^2}$ ##### 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 $\frac{3}{10} \div \frac{12}{25}$ 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 $\frac{3}{{8 \,+ \,\sqrt {34} }}$ 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 $\left( {9.15 \times {{10}^3}} \right) \div \left( {3 \times {{10}^8}} \right)$. 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?
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