# 0.1 Cumulative review

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Note: Answers to the Cumulative Review can be found in the Supplemental Resources. Please visit http://openstaxcollege.org to view an updated list of the Learning Resources for this title and how to access them.

No exercises.

## Chapter 2 the language of algebra

Simplify:

$1.\phantom{\rule{0.4em}{0ex}}5\left(3+2·6\right)-{8}^{2}$

Solve:

$2.\phantom{\rule{0.4em}{0ex}}17=y-13$

$3.\phantom{\rule{0.4em}{0ex}}p+14=23$

Translate into an algebraic expression.

$4.\phantom{\rule{0.4em}{0ex}}11$ less than the product of $7$ and $x.$

Translate into an algebraic equation and solve.

$5.\phantom{\rule{0.2em}{0ex}}$ Twice the difference of $y$ and $7$ gives $84.$

$6.\phantom{\rule{0.2em}{0ex}}$ Find all the factors of $72.$

$7.\phantom{\rule{0.2em}{0ex}}$ Find the prime factorization of $132.$

$8.\phantom{\rule{0.2em}{0ex}}$ Find the least common multiple of $12$ and $20.$

## Chapter 3 integers

Simplify:

$9.\phantom{\rule{0.4em}{0ex}}|8-9|-|3-8|$

$10.\phantom{\rule{0.4em}{0ex}}-2+4\left(-3+7\right)$

$11.\phantom{\rule{0.4em}{0ex}}27-\left(-4-7\right)$

$12.\phantom{\rule{0.4em}{0ex}}28÷\left(-4\right)-7$

Translate into an algebraic expression or equation.

$13.\phantom{\rule{0.2em}{0ex}}$ The sum of $-5$ and $13,$ increased by $11.$

$14.\phantom{\rule{0.2em}{0ex}}$ The product of $-11\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}8.$

$15.\phantom{\rule{0.2em}{0ex}}$ The quotient of $7$ and the sum of $-4\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}m\text{.}$

$16.\phantom{\rule{0.2em}{0ex}}$ The product of $-3$ and is $-51.$

Solve:

$17.\phantom{\rule{0.4em}{0ex}}-6r=24$

## Chapter 4 fractions

$18.\phantom{\rule{0.2em}{0ex}}$ Locate the numbers on a number line. $\frac{7}{8},\frac{5}{3},3\frac{1}{4},5.$

Simplify:

$19.\phantom{\rule{0.4em}{0ex}}\frac{21p}{57q}$

$20.\phantom{\rule{0.4em}{0ex}}\frac{3}{7}·\left(-\frac{28}{45}\right)$

$21.\phantom{\rule{0.4em}{0ex}}-6\frac{3}{4}÷\frac{9}{2}$

$22.\phantom{\rule{0.4em}{0ex}}-3\frac{3}{5}÷6$

$23.\phantom{\rule{0.4em}{0ex}}-4\frac{2}{3}\phantom{\rule{0.2em}{0ex}}\left(-\frac{6}{7}\right)$

$24.\phantom{\rule{0.4em}{0ex}}\frac{-2\frac{1}{4}}{-\frac{3}{8}}$

$25.\phantom{\rule{0.4em}{0ex}}\frac{7·8+4\left(7-12\right)}{9·6-2·9}$

$26.\phantom{\rule{0.4em}{0ex}}-\frac{23}{36}+\frac{17}{20}$

$27.\phantom{\rule{0.4em}{0ex}}\frac{\phantom{\rule{0.2em}{0ex}}\frac{1}{2}+\frac{1}{3}\phantom{\rule{0.2em}{0ex}}}{\frac{3}{4}-\frac{1}{3}}$

$28.\phantom{\rule{0.4em}{0ex}}3\frac{5}{8}-2\frac{1}{2}$

$29.\phantom{\rule{0.4em}{0ex}}-\frac{2}{3}r=24$

## Chapter 5 decimals

Simplify:

$30.\phantom{\rule{0.4em}{0ex}}24.76-7.28$

$31.\phantom{\rule{0.4em}{0ex}}12.9+15.633$

$32.\phantom{\rule{0.4em}{0ex}}\left(-5.6\right)\left(0.25\right)$

$33.\phantom{\rule{0.4em}{0ex}}6.29÷12$

$34.\phantom{\rule{0.4em}{0ex}}\frac{3}{4}\left(13.44-9.6\right)$

$35.\phantom{\rule{0.4em}{0ex}}\sqrt{64}+\sqrt{225}$

$36.\phantom{\rule{0.4em}{0ex}}\sqrt{121{x}^{2}{y}^{2}}$

$37.\phantom{\rule{0.2em}{0ex}}$ Write in order from smallest to largest: $\frac{5}{8},0.75,\frac{8}{15}$

Solve :

$38.\phantom{\rule{0.4em}{0ex}}-8.6x=34.4$

$39.\phantom{\rule{0.2em}{0ex}}$ Using $3.14$ as the estimate for pi, approximate the (a) circumference and (b) area of a circle whose radius is $8$ inches.

$40.\phantom{\rule{0.2em}{0ex}}$ Find the mean of the numbers, $18,16,20,12$

$41.\phantom{\rule{0.2em}{0ex}}$ Find the median of the numbers, $24,29,27,28,30$

$42.\phantom{\rule{0.2em}{0ex}}$ Identify the mode of the numbers, $6,4,4,5,6,6,4,4,4,3,5$

$43.\phantom{\rule{0.2em}{0ex}}$ Find the unit price of one t-shirt if they are sold at $3$ for $\text{28.97}.$

## Chapter 6 percents

$44.\phantom{\rule{0.2em}{0ex}}$ Convert $\text{14.7%}$ to (a) a fraction and (b) a decimal.

Translate and solve.

$45.\phantom{\rule{0.4em}{0ex}}63$ is $35%$ of what number?

$46.\phantom{\rule{0.2em}{0ex}}$ The nutrition label on a package of granola bars says that each granola bar has $180$ calories, and $81$ calories are from fat. What percent of the total calories is from fat?

$47.\phantom{\rule{0.2em}{0ex}}$ Elliot received $\text{510}$ commission when he sold a $\text{3,400}$ painting at the art gallery where he works. What was the rate of commission?

$48.\phantom{\rule{0.2em}{0ex}}$ Nandita bought a set of towels on sale for $\text{67.50}.$ The original price of the towels was $\text{90}.$ What was the discount rate?

$49.\phantom{\rule{0.2em}{0ex}}$ Alan invested $\text{23,000}$ in a friend’s business. In $5$ years the friend paid him the $\text{23,000}$ plus $\text{9,200}$ interest. What was the rate of interest?

Solve:

$50.\phantom{\rule{0.4em}{0ex}}\frac{9}{p}=\frac{-6\phantom{\rule{0.2em}{0ex}}}{14}$

## Chapter 7 the properties of real numbers

$51.\phantom{\rule{0.2em}{0ex}}$ List the (a) whole numbers, (b) integers, (c) rational numbers, (d) irrational numbers,

(e) real numbers $-5,-2\frac{1}{4},-\sqrt{4},0.\overline{25},\frac{13}{5},4$

Simplify:

$52.\phantom{\rule{0.4em}{0ex}}\left(\frac{8}{15}+\frac{4}{7}\right)+\frac{3}{7}$

$53.\phantom{\rule{0.4em}{0ex}}3\left(y+3\right)-8\left(y-4\right)$

$54.\phantom{\rule{0.4em}{0ex}}\frac{8}{17}·49·\frac{17}{8}$

$55.\phantom{\rule{0.2em}{0ex}}$ A playground is $55$ feet wide. Convert the width to yards.

$56.\phantom{\rule{0.2em}{0ex}}$ Every day last week Amit recorded the number of minutes he spent reading. The recorded number of minutes he read each day was $48,26,81,54,43,62,106.$ How many hours did Amit spend reading last week?

$57.\phantom{\rule{0.2em}{0ex}}$ June walked $2.8$ kilometers. Convert this length to miles knowing $1$ mile is $1.61$ kilometer.

## Chapter 8 solve linear equations

Solve:

$58.\phantom{\rule{0.4em}{0ex}}y+13=-8$

$59.\phantom{\rule{0.4em}{0ex}}p+\frac{2}{5}=\frac{8}{5}$

$60.\phantom{\rule{0.4em}{0ex}}48=\frac{2}{3}x$

$61.\phantom{\rule{0.4em}{0ex}}4\left(a-3\right)-6a=-18$

$62.\phantom{\rule{0.4em}{0ex}}7q+14=-35$

$63.\phantom{\rule{0.4em}{0ex}}4v-27=7v$

$64.\phantom{\rule{0.4em}{0ex}}\frac{7}{8}y-6=\frac{3}{8}y-8$

$65.\phantom{\rule{0.4em}{0ex}}26-4\left(z-2\right)=6$

$66.\phantom{\rule{0.4em}{0ex}}\frac{3}{4}\phantom{\rule{0.2em}{0ex}}x-\frac{2}{3}=\frac{1}{2}x-\frac{5}{6}$

$67.\phantom{\rule{0.4em}{0ex}}0.7y+4.8=0.84y-5.3$

Translate and solve.

$68.\phantom{\rule{0.2em}{0ex}}$ Four less than $n$ is $13.$

## Chapter 9 math models and geometry

$69.\phantom{\rule{0.2em}{0ex}}$ One number is $8$ less than another. Their sum is negative twenty-two. Find the numbers.

$70.\phantom{\rule{0.2em}{0ex}}$ The sum of two consecutive integers is $-95.$ Find the numbers.

$71.\phantom{\rule{0.2em}{0ex}}$ Wilma has $\text{3.65}$ in dimes and quarters. The number of dimes is $2$ less than the number of quarters. How many of each coin does she have?

$72.\phantom{\rule{0.2em}{0ex}}$ Two angles are supplementary. The larger angle is $24\text{°}$ more than the smaller angle. Find the measurements of both angles.

$73.\phantom{\rule{0.2em}{0ex}}$ One angle of a triangle is $20\text{°}$ more than the smallest angle. The largest angle is the sum of the other angles. Find the measurements of all three angles.

$74.\phantom{\rule{0.2em}{0ex}}$ Erik needs to attach a wire to hold the antenna to the roof of his house, as shown in the figure. The antenna is $12$ feet tall and Erik has $15$ feet of wire. How far from the base of the antenna can he attach the wire? $75.\phantom{\rule{0.2em}{0ex}}$ The width of a rectangle is $4$ less than the length. The perimeter is $96$ inches. Find the length and the width.

$76.\phantom{\rule{0.2em}{0ex}}$ Find the (a) volume and (b) surface area of a rectangular carton with length $24$ inches, width $18$ inches, and height $6$ inches.

## Chapter 10 polynomials

Simplify:

$77.\phantom{\rule{0.4em}{0ex}}\left(8{m}^{2}+12m-5\right)-\left(2{m}^{2}-7m-1\right)$

$78.\phantom{\rule{0.4em}{0ex}}{p}^{3}·{p}^{10}$

$79.\phantom{\rule{0.4em}{0ex}}{\left({y}^{4}\right)}^{3}$

$80.\phantom{\rule{0.4em}{0ex}}{\left(3{a}^{5}\right)}^{3}$

$81.\phantom{\rule{0.4em}{0ex}}{\left({x}^{3}\right)}^{5}{\left({x}^{2}\right)}^{3}$

$82.\phantom{\rule{0.4em}{0ex}}\left(\frac{2}{3}{m}^{3}{n}^{6}\right)\left(\frac{1}{6}{m}^{4}{n}^{4}\right)$

$83.\phantom{\rule{0.4em}{0ex}}\left(y-4\right)\left(y+12\right)$

$84.\phantom{\rule{0.4em}{0ex}}\left(3c+1\right)\left(9c-4\right)$

$85.\phantom{\rule{0.4em}{0ex}}\left(x-1\right)\left({x}^{2}-3x-2\right)$

$86.\phantom{\rule{0.4em}{0ex}}{\left(8x\right)}^{0}$

$87.\phantom{\rule{0.4em}{0ex}}\frac{{\left({x}^{3}\right)}^{5}}{{\left({x}^{2}\right)}^{4}}$

$88.\phantom{\rule{0.4em}{0ex}}\frac{32{a}^{7}{b}^{2}}{12{a}^{3}{b}^{6}}$

$89.\phantom{\rule{0.4em}{0ex}}\left(a{b}^{-3}\right)\left({a}^{-3}{b}^{6}\right)$

$90.\phantom{\rule{0.2em}{0ex}}$ Write in scientific notation: $\text{(a)}\phantom{\rule{0.2em}{0ex}}4,800,000\phantom{\rule{0.5em}{0ex}}\text{(b)}\phantom{\rule{0.2em}{0ex}}0.00637$

Factor the greatest common factor from the polynomial.

$91.\phantom{\rule{0.4em}{0ex}}3{x}^{4}-6{x}^{3}-18{x}^{2}$

## Chapter 11 graphs

Graph:

$92.\phantom{\rule{0.4em}{0ex}}y=4x-3$

$93.\phantom{\rule{0.4em}{0ex}}y=-3x$

$94.\phantom{\rule{0.4em}{0ex}}y=\frac{1}{2}x+3$

$95.\phantom{\rule{0.4em}{0ex}}x-y=6$

$96.\phantom{\rule{0.4em}{0ex}}y=-2$

$97.\phantom{\rule{0.2em}{0ex}}$ Find the intercepts. $2x+3y=12$

Graph using the intercepts.

$98.\phantom{\rule{0.4em}{0ex}}2x-4y=8$

$99.\phantom{\rule{0.2em}{0ex}}$ Find slope. $100.\phantom{\rule{0.2em}{0ex}}$ Use the slope formula to find the slope of the line between the points $\left(-5,-2\right),\left(3,2\right).$

$101.\phantom{\rule{0.2em}{0ex}}$ Graph the line passing through the point $\left(-3,4\right)$ and with slope $m=-\frac{1}{3}.$

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