Prealgebra

A | Cumulative Review

PrealgebraA | Cumulative Review

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:

$1.5(3+2·6)−821.5(3+2·6)−82$

Solve:

$2.17=y−132.17=y−13$

$3.p+14=233.p+14=23$

Translate into an algebraic expression.

$4.114.11$ less than the product of $77$ and $x.x.$

Translate into an algebraic equation and solve.

$5.5.$Twice the difference of $yy$ and $77$ gives $84.84.$

$6.6.$Find all the factors of $72.72.$

$7.7.$Find the prime factorization of $132.132.$

$8.8.$Find the least common multiple of $1212$ and $20.20.$

Chapter 3 Integers

Simplify:

$9.|8−9|−|3−8|9.|8−9|−|3−8|$

$10.−2+4(−3+7)10.−2+4(−3+7)$

$11.27−(−4−7)11.27−(−4−7)$

$12.28÷(−4)−712.28÷(−4)−7$

Translate into an algebraic expression or equation.

$13.13.$The sum of $−5−5$ and $13,13,$ increased by $11.11.$

$14.14.$The product of $−11and8.−11and8.$

$15.15.$The quotient of $77$ and the sum of $−4andm.−4andm.$

$16.16.$The product of $−3−3$ and is $−51.−51.$

Solve:

$17.−6r=2417.−6r=24$

Chapter 4 Fractions

$18.18.$Locate the numbers on a number line. $78,53,314,5.78,53,314,5.$

Simplify:

$19.21p57q19.21p57q$

$20.37·(−2845)20.37·(−2845)$

$21.−634÷9221.−634÷92$

$22.−335÷622.−335÷6$

$23.−423(−67)23.−423(−67)$

$24.−214−3824.−214−38$

$25.7·8+4(7−12)9·6−2·925.7·8+4(7−12)9·6−2·9$

$26.−2336+172026.−2336+1720$

$27.12+1334−1327.12+1334−13$

$28.358−21228.358−212$

$29.−23r=2429.−23r=24$

Chapter 5 Decimals

Simplify:

$30.24.76−7.2830.24.76−7.28$

$31.12.9+15.63331.12.9+15.633$

$32.(−5.6)(0.25)32.(−5.6)(0.25)$

$33.6.29÷1233.6.29÷12$

$34.34(13.44−9.6)34.34(13.44−9.6)$

$35.64+22535.64+225$

$36.121x2y236.121x2y2$

$37.37.$Write in order from smallest to largest: $58,0.75,81558,0.75,815$

Solve:

$38.−8.6x=34.438.−8.6x=34.4$

$39.39.$Using $3.143.14$ as the estimate for pi, approximate the (a) circumference and (b) area of a circle whose radius is $88$ inches.

$40.40.$Find the mean of the numbers, $18,16,20,1218,16,20,12$

$41.41.$Find the median of the numbers, $24,29,27,28,3024,29,27,28,30$

$42.42.$Identify the mode of the numbers, $6,4,4,5,6,6,4,4,4,3,56,4,4,5,6,6,4,4,4,3,5$

$43.43.$Find the unit price of one t-shirt if they are sold at $33$ for $28.97.28.97.$

Chapter 6 Percents

$44.44.$Convert $14.7%14.7%$ to (a) a fraction and (b) a decimal.

Translate and solve.

$45.6345.63$ is $35%35%$ of what number?

$46.46.$The nutrition label on a package of granola bars says that each granola bar has $180180$ calories, and $8181$ calories are from fat. What percent of the total calories is from fat?

$47.47.$Elliot received $510510$ commission when he sold a $3,4003,400$ painting at the art gallery where he works. What was the rate of commission?

$48.48.$Nandita bought a set of towels on sale for $67.50.67.50.$ The original price of the towels was $90.90.$ What was the discount rate?

$49.49.$Alan invested $23,00023,000$ in a friend’s business. In $55$ years the friend paid him the $23,00023,000$ plus $9,2009,200$ interest. What was the rate of interest?

Solve:

$50.9p=−61450.9p=−614$

Chapter 7 The Properties of Real Numbers

$51.51.$List the (a) whole numbers, (b) integers, (c) rational numbers, (d) irrational numbers,

(e) real numbers $−5,−214,−4,0.25¯,135,4−5,−214,−4,0.25¯,135,4$

Simplify:

$52.(815+47)+3752.(815+47)+37$

$53.3(y+3)−8(y−4)53.3(y+3)−8(y−4)$

$54.817·49·17854.817·49·178$

$55.55.$A playground is $5555$ feet wide. Convert the width to yards.

$56.56.$Every day last week Amit recorded the number of minutes he spent reading. The recorded number of minutes he read each day was $48,26,81,54,43,62,106.48,26,81,54,43,62,106.$ How many hours did Amit spend reading last week?

$57.57.$June walked $2.82.8$ kilometers. Convert this length to miles knowing $11$ mile is $1.611.61$ kilometer.

Chapter 8 Solve Linear Equations

Solve:

$58.y+13=−858.y+13=−8$

$59.p+25=8559.p+25=85$

$60.48=23x60.48=23x$

$61.4(a−3)−6a=−1861.4(a−3)−6a=−18$

$62.7q+14=−3562.7q+14=−35$

$63.4v−27=7v63.4v−27=7v$

$64.78y−6=38y−864.78y−6=38y−8$

$65.26−4(z−2)=665.26−4(z−2)=6$

$66.34x−23=12x−5666.34x−23=12x−56$

$67.0.7y+4.8=0.84y−5.367.0.7y+4.8=0.84y−5.3$

Translate and solve.

$68.68.$Four less than $nn$ is $13.13.$

Chapter 9 Math Models and Geometry

$69.69.$One number is $88$ less than another. Their sum is negative twenty-two. Find the numbers.

$70.70.$The sum of two consecutive integers is $−95.−95.$ Find the numbers.

$71.71.$Wilma has $3.653.65$ in dimes and quarters. The number of dimes is $22$ less than the number of quarters. How many of each coin does she have?

$72.72.$Two angles are supplementary. The larger angle is $24°24°$ more than the smaller angle. Find the measurements of both angles.

$73.73.$One angle of a triangle is $20°20°$ more than the smallest angle. The largest angle is the sum of the other angles. Find the measurements of all three angles.

$74.74.$Erik needs to attach a wire to hold the antenna to the roof of his house, as shown in the figure. The antenna is $1212$ feet tall and Erik has $1515$ feet of wire. How far from the base of the antenna can he attach the wire?

$75.75.$The width of a rectangle is $44$ less than the length. The perimeter is $9696$ inches. Find the length and the width.

$76.76.$Find the (a) volume and (b) surface area of a rectangular carton with length $2424$ inches, width $1818$ inches, and height $66$ inches.

Chapter 10 Polynomials

Simplify:

$77.(8m2+12m−5)−(2m2−7m−1)77.(8m2+12m−5)−(2m2−7m−1)$

$78.p3·p1078.p3·p10$

$79.(y4)379.(y4)3$

$80.(3a5)380.(3a5)3$

$81.(x3)5(x2)381.(x3)5(x2)3$

$82.(23m3n6)(16m4n4)82.(23m3n6)(16m4n4)$

$83.(y−4)(y+12)83.(y−4)(y+12)$

$84.(3c+1)(9c−4)84.(3c+1)(9c−4)$

$85.(x−1)(x2−3x−2)85.(x−1)(x2−3x−2)$

$86.(8x)086.(8x)0$

$87.(x3)5(x2)487.(x3)5(x2)4$

$88.32a7b212a3b688.32a7b212a3b6$

$89.(ab−3)(a−3b6)89.(ab−3)(a−3b6)$

$90.90.$Write in scientific notation: $(a)4,800,000(b)0.00637(a)4,800,000(b)0.00637$

Factor the greatest common factor from the polynomial.

$91.3x4−6x3−18x291.3x4−6x3−18x2$

Chapter 11 Graphs

Graph:

$92.y=4x−392.y=4x−3$

$93.y=−3x93.y=−3x$

$94.y=12x+394.y=12x+3$

$95.x−y=695.x−y=6$

$96.y=−296.y=−2$

$97.97.$Find the intercepts. $2x+3y=122x+3y=12$

Graph using the intercepts.

$98.2x−4y=898.2x−4y=8$

$99.99.$Find the slope of the line shown.

$100.100.$Use the slope formula to find the slope of the line between the points $(−5,−2),(3,2).(−5,−2),(3,2).$

$101.101.$Graph the line passing through the point $(−3,4)(−3,4)$ and with slope $m=−13.m=−13.$