12.1: Cumulative Review

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

Chapter 1 Whole Numbers

No exercises.

Chapter 2 The Language of Algebra

Simplify:

$1.5(3+2·6)-8^2$

Solve:

$2.17=y-13$

$3.p+14=23$

Translate into an algebraic expression.

$4.11$ less than the product of $7$ and $x.$

Translate into an algebraic equation and solve.

$5.$The difference of $y$ and $7$ gives $84.$

$6.$Find all the factors of $72.$

$7.$Find the prime factorization of $132.$

$8.$Find the least common multiple of $12$ and $20.$

Chapter 3 Integers

Simplify:

$9.\left|8-9\right|-\left|3-8\right|$

$10.\mathrm{-2}+4(\mathrm{-3}+7)$

$11.27-(\mathrm{-4}-7)$

$12.28÷\left(\mathrm{-4}\right)-7$

Translate into an algebraic expression or equation.

$13.$The sum of $\mathrm{-5}$ and $13,$ increased by $11.$

$14.$The product of $\mathrm{-11}\text{and}8.$

$15.$The quotient of $7$ and the sum of $\mathrm{-4}\text{and}m\text{.}$

$16.$The product of $\mathrm{-3}$ and is $\mathrm{-51}.$

Solve:

$17.\mathrm{-6}r=24$

Chapter 4 Fractions

$18.$Locate the numbers on a number line. $\frac{7}{8},\frac{5}{3},3\frac{1}{4},5.$

Simplify:

$19.\frac{21p}{57q}$

$20.\frac{3}{7}·\left(-\frac{28}{45}\right)$

$21.\mathrm{-6}\frac{3}{4}÷\frac{9}{2}$

$22.\mathrm{-3}\frac{3}{5}÷6$

$23.\mathrm{-4}\frac{2}{3}\left(-\frac{6}{7}\right)$

$24.\frac{\mathrm{-2}\frac{1}{4}}{-\frac{3}{8}}$

$25.\frac{7·8+4(7-12)}{9·6-2·9}$

$26.-\frac{23}{36}+\frac{17}{20}$

$27.\frac{\frac{1}{2}+\frac{1}{3}}{\frac{3}{4}-\frac{1}{3}}$

$28.3\frac{5}{8}-2\frac{1}{2}$

$29.-\frac{2}{3}r=24$

Chapter 5 Decimals

Simplify:

$30.24.76-7.28$

$31.12.9+15.633$

$32.\left(\mathrm{-5.6}\right)\left(0.25\right)$

$33.\mathrm{\$6.29}÷12$

$34.\frac{3}{4}\left(13.44-9.6\right)$

$35.\sqrt{64}+\sqrt{225}$

$36.\sqrt{121x^2{y}^2}$

$37.$Write in order from smallest to largest: $\frac{5}{8},0.75,\frac{8}{15}$

Solve:

$38.\mathrm{-8.6}x=34.4$

$39.$Using $3.14$ as the estimate for pi, approximate the (a) circumference and (b) area of a circle whose radius is $8$ inches.

$40.$Find the mean of the numbers, $18,16,20,12$

$41.$Find the median of the numbers, $24,29,27,28,30$

$42.$Identify the mode of the numbers, $6,4,4,5,6,6,4,4,4,3,5$

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

Chapter 6 Percents

$44.$Convert $\text{14.7\%}$ to (a) a fraction and (b) a decimal.

Translate and solve.

$45.63$ is $35\%$ of what number?

$46.$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?

$47.$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?

$48.$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?

$49.$Alan invested $\text{\$23,000}$ in a friend’s business. In $5$ years the friend paid him the $\text{\$23,000}$ plus $\text{\$9,200}$ simple interest. What was the rate of simple interest per year?

Solve:

$50.\frac{9}{p}=\frac{\mathrm{-6}}{14}$

Chapter 7 The Properties of Real Numbers

$51.$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:

$52.\left(\frac{8}{15}+\frac{4}{7}\right)+\frac{3}{7}$

$53.3(y+3)-8(y-4)$

$54.\frac{8}{17}·49·\frac{17}{8}$

$55.$A playground is $55$ feet wide. Convert the width to yards.

$56.$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?

$57.$June walked $2.8$ kilometers. Convert this length to miles knowing $1$ mile is $1.61$ kilometer.

Chapter 8 Solve Linear Equations

Solve:

$58.y+13=\mathrm{-8}$

$59.p+\frac{2}{5}=\frac{8}{5}$

$60.48=\frac{2}{3}x$

$61.4\left(a-3\right)-6a=\mathrm{-18}$

$62.7q+14=\mathrm{-35}$

$63.4v-27=7v$

$64.\frac{7}{8}y-6=\frac{3}{8}y-8$

$65.26-4(z-2)=6$

$66.\frac{3}{4}x-\frac{2}{3}=\frac{1}{2}x-\frac{5}{6}$

$67.0.7y+4.8=0.84y-5.0$

Translate and solve.

$68.$Four less than $n$ is $13.$

Chapter 9 Math Models and Geometry

$69.$One number is $8$ less than another. Their sum is negative twenty-two. Find the numbers.

$70.$The sum of two consecutive integers is $\mathrm{-95}.$ Find the numbers.

$71.$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?

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

$73.$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.

$74.$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?

$75.$The width of a rectangle is $4$ less than the length. The perimeter is $96$ inches. Find the length and the width.

$76.$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:

$77.\left(8m^2+12m-5\right)-\left(2m^2-7m-1\right)$

$78.p^3·p^{10}$

$79.{\left(y^4\right)}^3$

$80.{\left(3a^5\right)}^3$

$81.{\left(x^3\right)}^5{\left(x^2\right)}^3$

$82.\left(\frac{2}{3}{m}^3{n}^6\right)\left(\frac{1}{6}{m}^4{n}^4\right)$

$83.\left(y-4\right)\left(y+12\right)$

$84.\left(3c+1\right)\left(9c-4\right)$

$85.\left(x-1\right)\left(x^2-3x-2\right)$

$86.{\left(8x\right)}^0$

$87.\frac{{\left(x^3\right)}^5}{{\left(x^2\right)}^4}$

$88.\frac{32a^7{b}^2}{12a^3{b}^6}$

$89.\left(a{b}^{\mathrm{-3}}\right)\left(a^{\mathrm{-3}}{b}^6\right)$

$90.$Write in scientific notation: $\text{(a)}\mathrm{4,800,000}\text{(b)}0.00637$

Factor the greatest common factor from the polynomial.

$91.3x^4-6x^3-18x^2$

Chapter 11 Graphs

Graph:

$92.y=4x-3$

$93.y=\mathrm{-3}x$

$94.y=\frac{1}{2}x+3$

$95.x-y=6$

$96.y=\mathrm{-2}$

$97.$Find the intercepts. $2x+3y=12$

Graph using the intercepts.

$98.2x-4y=8$

$99.$Find the slope of the line shown.

$100.$Use the slope formula to find the slope of the line between the points $(\mathrm{-5},\mathrm{-2}),(3,2).$

$101.$Graph the line passing through the point $(\mathrm{-3},4)$ and with slope $m=-\frac{1}{3}.$