3.12.5: Chapter Review
Prime and Composite Numbers
Identify which of the following numbers are prime, composite, or neither: 201, 34, 17, 1, 37.
Find the prime factorization of 500 .
Find the greatest common divisor of 80 and 340 .
Find the greatest common divisor of 30,40 , and 70 .
Find the least common multiple of 45 and 60.
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
Identify all the integers in the following list: \(-4, \frac{2}{7}, 15,97.5,0, \sqrt{122}\).
Plot the following on the same number line: \(1,5,-2,0 .\)
What two numbers have absolute value of 18 ?
Calculate \(14-(-12)\).
Calculate \((-19) \times 4\).
Calculate \((-240) \div(-12)\).
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
Calculate \(5 \times 3-(-12)\).
Calculate \(4^2 \times 6+2^3\).
\((4-6) \times 2\)
\((8-1)^3-3 \times 9\)
\(120-(51+12) \div 3^2\)
Rational Numbers
Reduce \(\frac{90}{153}\) to lowest terms.
Convert \(\frac{430}{25}\) to a mixed number and reduce to lowest terms.
Convert \(\frac{9}{5}\) to decimal form.
Convert \(\frac{5}{11}\) to decimal form.
Calculate \(\frac{4}{15}+\frac{9}{10}\) and reduce to lowest terms.
Compute \(\frac{3}{10} \div \frac{12}{25}\) and reduce to lowest terms.
Determine \(30 \%\) of 400 .
18 is what percent of 40 ?
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
Simplify the square root by expressing it in lowest terms: \(\sqrt{275}\).
Calculate \(4 \sqrt{13}-15 \sqrt{13}\) without a calculator. If not possible, explain why.
Calculate \((2.3 \sqrt{5}) \times(4.2 \sqrt{3})\) without a calculator. If not possible, explain why.
Rationalize the denominator of \(\frac{6}{\sqrt{22}}\), and simplify the fraction.
Find the conjugate of \(4 \sqrt{7}+3\) and find the product of \(4 \sqrt{7}+3\) and its conjugate.
Rationalize the denominator of \(\frac{3}{8+\sqrt{34}}\) and simplify the fraction.
Real Numbers
Identify the numbers of the following list as a natural number, an integer, a rational number, or a real number: \(\sqrt{37},-0.43,18,-43,12 \pi\).
Identify the property of real numbers illustrated here: \(14+19=19+14\).
Identify the property of real numbers illustrated here: \(87.4+0=87.4\).
Identify the property of real numbers illustrated here: \(2 \times(\sqrt{31}-12)=2 \sqrt{31}-2 \times 12\).
Identify the property of real numbers illustrated here: \(98 \times 41=41 \times 98\).
Use mental math to calculate \(21 \times 99\).
Clock Arithmetic
Determine 74 modulo 9.
Use clock arithmetic to calculate \(13+25\).
Use clock arithmetic to calculate \(4 \times 8\).
It is Wednesday. What day of the week will it be in 44 days?
It is \(4: 00\). What time will it be in 100 hours?
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
Use exponent rules to simplify \(17^8 \times 17^3\).
Use exponent rules to simplify \(\frac{15^9}{15^{-5}}\).
Use exponent rules to simplify \((3 k)^6\).
Use exponent rules to simplify \(\left(\frac{y}{4}\right)^{11}\).
Use exponent rules to simplify \(\left(51^3\right)^6\).
Use exponent rules to simplify \(\left(\frac{3 x^4}{5}\right)^7\).
Rewrite \(\frac{5^2}{x^4}\) without a denominator.
Rewrite \(16 z^{-9}\) without negative exponents.
Scientific Notation
Convert 0.0000452 to scientific notation.
Convert \(3.01 \times 10^5\) to standard notation.
Convert \(42.9 \times 10^{-9}\) to scientific notation.
Calculate \(4.51 \times 10^5-9.11 \times 10^4\).
Calculate \(\left(9.15 \times 10^3\right) \div\left(3 \times 10^8\right)\).
The Sextans Dwarf Spheroidal Galaxy has diameter 8,400 light years (ly). Express this in Scientific notation.
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
Determine the common difference of the following sequence: \(\{19,13,7,1,-5, \ldots\}\).
Find the 25th term, \(a_{25}\), of the arithmetic sequence with \(a_1=13\) and \(d=1.7\).
Find the first term and the common difference of the arithmetic sequence with 8 th term \(b_8=50\) and 15 th term \(b_{15}=106\).
Find the sum of the first 30 terms, \(s_{30}\), for the arithmetic sequence with first term \(a_1=-4\) and common difference \(d=3.5\).
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
Determine the common ratio of the following geometric sequence: \(\{6,18,54,162, \ldots\}\).
Find the 6th term, \(c_6\), of the geometric sequence with \(c_1=400\) and \(r=0.25\).
Find the sum of the first 12 terms, \(s_{12}\), for the geometric sequence with first term \(a_1=-4\) and common ratio \(r=-1.25\).
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?
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 \(2022 ?\)