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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.
Simplify:
$1.\phantom{\rule{0.4em}{0ex}}5(3+2\xb76)-{8}^{2}$
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 $20.$
Simplify:
$9.\phantom{\rule{0.4em}{0ex}}\left|8-9\right|-\left|3-8\right|$
$10.\phantom{\rule{0.4em}{0ex}}\mathrm{-2}+4(\mathrm{-3}+7)$
$11.\phantom{\rule{0.4em}{0ex}}27-(\mathrm{-4}-7)$
$12.\phantom{\rule{0.4em}{0ex}}28\xf7\left(\mathrm{-4}\right)-7$
Translate into an algebraic expression or equation.
$13.\phantom{\rule{0.2em}{0ex}}$ The sum of $\mathrm{-5}$ and $13,$ increased by $11.$
$14.\phantom{\rule{0.2em}{0ex}}$ The product of $\mathrm{-11}\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}8.$
$15.\phantom{\rule{0.2em}{0ex}}$ The quotient of $7$ and the sum of $\mathrm{-4}\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}m\text{.}$
$16.\phantom{\rule{0.2em}{0ex}}$ The product of $\mathrm{-3}$ and is $\mathrm{-51}.$
Solve:
$17.\phantom{\rule{0.4em}{0ex}}\mathrm{-6}r=24$
$18.\phantom{\rule{0.2em}{0ex}}$ Locate the numbers on a number line. $\frac{7}{8},\frac{5}{3},3\frac{1}{4},5.$
Simplify:
$19.\phantom{\rule{0.4em}{0ex}}\frac{21p}{57q}$
$20.\phantom{\rule{0.4em}{0ex}}\frac{3}{7}\xb7\left(-\frac{28}{45}\right)$
$21.\phantom{\rule{0.4em}{0ex}}\mathrm{-6}\frac{3}{4}\xf7\frac{9}{2}$
$22.\phantom{\rule{0.4em}{0ex}}\mathrm{-3}\frac{3}{5}\xf76$
$23.\phantom{\rule{0.4em}{0ex}}\mathrm{-4}\frac{2}{3}\phantom{\rule{0.2em}{0ex}}\left(-\frac{6}{7}\right)$
$24.\phantom{\rule{0.4em}{0ex}}\frac{\mathrm{-2}\frac{1}{4}}{-\frac{3}{8}}$
$25.\phantom{\rule{0.4em}{0ex}}\frac{7\xb78+4(7-12)}{9\xb76-2\xb79}$
$26.\phantom{\rule{0.4em}{0ex}}-\frac{23}{36}+\frac{17}{20}$
$27.\phantom{\rule{0.4em}{0ex}}\frac{\phantom{\rule{0.2em}{0ex}}\frac{1}{2}+\frac{1}{3}\phantom{\rule{0.2em}{0ex}}}{\frac{3}{4}-\frac{1}{3}}$
$28.\phantom{\rule{0.4em}{0ex}}3\frac{5}{8}-2\frac{1}{2}$
$29.\phantom{\rule{0.4em}{0ex}}-\frac{2}{3}r=24$
Simplify:
$30.\phantom{\rule{0.4em}{0ex}}24.76-7.28$
$31.\phantom{\rule{0.4em}{0ex}}12.9+15.633$
$32.\phantom{\rule{0.4em}{0ex}}\left(\mathrm{-5.6}\right)\left(0.25\right)$
$33.\phantom{\rule{0.4em}{0ex}}\mathrm{\$6.29}\xf712$
$34.\phantom{\rule{0.4em}{0ex}}\frac{3}{4}\left(13.44-9.6\right)$
$35.\phantom{\rule{0.4em}{0ex}}\sqrt{64}+\sqrt{225}$
$36.\phantom{\rule{0.4em}{0ex}}\sqrt{121{x}^{2}{y}^{2}}$
$37.\phantom{\rule{0.2em}{0ex}}$ Write in order from smallest to largest: $\frac{5}{8},0.75,\frac{8}{15}$
Solve :
$38.\phantom{\rule{0.4em}{0ex}}\mathrm{-8.6}x=34.4$
$39.\phantom{\rule{0.2em}{0ex}}$ 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 $\text{\$28.97}.$
$44.\phantom{\rule{0.2em}{0ex}}$ 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:
$50.\phantom{\rule{0.4em}{0ex}}\frac{9}{p}=\frac{\mathrm{-6}\phantom{\rule{0.2em}{0ex}}}{14}$
$51.\phantom{\rule{0.2em}{0ex}}$ List the (a) whole numbers, (b) integers, (c) rational numbers, (d) irrational numbers,
(e) real numbers $\mathrm{-5},\mathrm{-2}\frac{1}{4},-\sqrt{4},0.\overline{25},\frac{13}{5},4$
Simplify:
$52.\phantom{\rule{0.4em}{0ex}}\left(\frac{8}{15}+\frac{4}{7}\right)+\frac{3}{7}$
$53.\phantom{\rule{0.4em}{0ex}}3(y+3)-8(y-4)$
$54.\phantom{\rule{0.4em}{0ex}}\frac{8}{17}\xb749\xb7\frac{17}{8}$
$55.\phantom{\rule{0.2em}{0ex}}$ 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.
Solve:
$58.\phantom{\rule{0.4em}{0ex}}y+13=\mathrm{-8}$
$59.\phantom{\rule{0.4em}{0ex}}p+\frac{2}{5}=\frac{8}{5}$
$60.\phantom{\rule{0.4em}{0ex}}48=\frac{2}{3}x$
$61.\phantom{\rule{0.4em}{0ex}}4\left(a-3\right)-6a=\mathrm{-18}$
$62.\phantom{\rule{0.4em}{0ex}}7q+14=\mathrm{-35}$
$63.\phantom{\rule{0.4em}{0ex}}4v-27=7v$
$64.\phantom{\rule{0.4em}{0ex}}\frac{7}{8}y-6=\frac{3}{8}y-8$
$65.\phantom{\rule{0.4em}{0ex}}26-4(z-2)=6$
$66.\phantom{\rule{0.4em}{0ex}}\frac{3}{4}\phantom{\rule{0.2em}{0ex}}x-\frac{2}{3}=\frac{1}{2}x-\frac{5}{6}$
$67.\phantom{\rule{0.4em}{0ex}}0.7y+4.8=0.84y-5.3$
Translate and solve.
$68.\phantom{\rule{0.2em}{0ex}}$ Four less than $n$ is $13.$
$69.\phantom{\rule{0.2em}{0ex}}$ 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 $\mathrm{-95}.$ 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 $24\text{\xb0}$ more than the smaller angle. Find the measurements of both angles.
$73.\phantom{\rule{0.2em}{0ex}}$ One angle of a triangle is $20\text{\xb0}$ 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.
Simplify:
$77.\phantom{\rule{0.4em}{0ex}}\left(8{m}^{2}+12m-5\right)-\left(2{m}^{2}-7m-1\right)$
$78.\phantom{\rule{0.4em}{0ex}}{p}^{3}\xb7{p}^{10}$
$79.\phantom{\rule{0.4em}{0ex}}{\left({y}^{4}\right)}^{3}$
$80.\phantom{\rule{0.4em}{0ex}}{\left(3{a}^{5}\right)}^{3}$
$81.\phantom{\rule{0.4em}{0ex}}{\left({x}^{3}\right)}^{5}{\left({x}^{2}\right)}^{3}$
$82.\phantom{\rule{0.4em}{0ex}}\left(\frac{2}{3}{m}^{3}{n}^{6}\right)\left(\frac{1}{6}{m}^{4}{n}^{4}\right)$
$83.\phantom{\rule{0.4em}{0ex}}\left(y-4\right)\left(y+12\right)$
$84.\phantom{\rule{0.4em}{0ex}}\left(3c+1\right)\left(9c-4\right)$
$85.\phantom{\rule{0.4em}{0ex}}\left(x-1\right)\left({x}^{2}-3x-2\right)$
$86.\phantom{\rule{0.4em}{0ex}}{\left(8x\right)}^{0}$
$87.\phantom{\rule{0.4em}{0ex}}\frac{{\left({x}^{3}\right)}^{5}}{{\left({x}^{2}\right)}^{4}}$
$88.\phantom{\rule{0.4em}{0ex}}\frac{32{a}^{7}{b}^{2}}{12{a}^{3}{b}^{6}}$
$89.\phantom{\rule{0.4em}{0ex}}\left(a{b}^{\mathrm{-3}}\right)\left({a}^{\mathrm{-3}}{b}^{6}\right)$
$90.\phantom{\rule{0.2em}{0ex}}$ Write in scientific notation: $\text{(a)}\phantom{\rule{0.2em}{0ex}}\mathrm{4,800,000}\phantom{\rule{0.5em}{0ex}}\text{(b)}\phantom{\rule{0.2em}{0ex}}0.00637$
Factor the greatest common factor from the polynomial.
$91.\phantom{\rule{0.4em}{0ex}}3{x}^{4}-6{x}^{3}-18{x}^{2}$
Graph:
$92.\phantom{\rule{0.4em}{0ex}}y=4x-3$
$93.\phantom{\rule{0.4em}{0ex}}y=\mathrm{-3}x$
$94.\phantom{\rule{0.4em}{0ex}}y=\frac{1}{2}x+3$
$95.\phantom{\rule{0.4em}{0ex}}x-y=6$
$96.\phantom{\rule{0.4em}{0ex}}y=\mathrm{-2}$
$97.\phantom{\rule{0.2em}{0ex}}$ 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 $(\mathrm{-5},\mathrm{-2}),(3,2).$
$101.\phantom{\rule{0.2em}{0ex}}$ Graph the line passing through the point $(\mathrm{-3},4)$ and with slope $m=-\frac{1}{3}.$
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