12.1: Cumulative Review

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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:

$1. 5 (3 + 2 \cdot 6) - 8^{2}$

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:

$9. | 8 - 9 | - | 3 - 8 |$

$10. −2 + 4 (−3 + 7)$

$11. 27 - (−4 - 7)$

$12. 28 \div (−4) - 7$

Translate into an algebraic expression or equation.

$13.$ The sum of $−5$ and $13,$ increased by $11 .$

$14.$ The product of $−11 and 8 .$

$15.$ The quotient of $7$ and the sum of $−4 and m .$

$16.$ The product of $−3$ and is $−51 .$

Solve:

$17. −6 r = 24$

Chapter 4 Fractions

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

Simplify:

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

$20. \frac{3}{7} \cdot (- \frac{28}{45})$

$21. −6 \frac{3}{4} \div \frac{9}{2}$

$22. −3 \frac{3}{5} \div 6$

$23. −4 \frac{2}{3} (- \frac{6}{7})$

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

$25. \frac{7 \cdot 8 + 4 (7 - 12)}{9 \cdot 6 - 2 \cdot 9}$

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

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

$28. 3 \frac{5}{8} - 2 \frac{1}{2}$

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

Chapter 5 Decimals

Simplify:

$30. 24.76 - 7.28$

$31. 12.9 + 15.633$

$32. (−5.6) (0.25)$

$33. $6.29 \div 12$

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

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

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

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

Solve:

$38. −8.6 x = 34.4$

$39.$ 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 $$28.97 .$

Chapter 6 Percents

$44.$ Convert $14.7%$ 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 $$510$ commission when he sold a $$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 $$67.50 .$ The original price of the towels was $$90 .$ What was the discount rate?

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

Solve:

$50. \frac{9}{p} = \frac{−6}{14}$

Chapter 7 The Properties of Real Numbers

$51.$ List the (a) whole numbers, (b) integers, (c) rational numbers, (d) irrational numbers,

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

Simplify:

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

$53. 3 (y + 3) - 8 (y - 4)$

$54. \frac{8}{17} \cdot 49 \cdot \frac{17}{8}$

$55.$ 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:

$58. y + 13 = −8$

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

$60. 48 = \frac{2}{3} x$

$61. 4 (a - 3) - 6 a = −18$

$62. 7 q + 14 = −35$

$63. 4 v - 27 = 7 v$

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

$65. 26 - 4 (z - 2) = 6$

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

$67. 0.7 y + 4.8 = 0.84 y - 5.0$

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 $−95 .$ Find the numbers.

$71.$ Wilma has $$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 $24 °$ more than the smaller angle. Find the measurements of both angles.

$73.$ One angle of a triangle is $20 °$ 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?

$No Alt Text$

$75.$ 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:

$77. (8 m^{2} + 12 m - 5) - (2 m^{2} - 7 m - 1)$

$78. p^{3} \cdot p^{10}$

$79. {(y^{4})}^{3}$

$80. {(3 a^{5})}^{3}$

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

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

$83. (y - 4) (y + 12)$

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

$85. (x - 1) (x^{2} - 3 x - 2)$

$86. {(8 x)}^{0}$

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

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

$89. (a b^{−3}) (a^{−3} b^{6})$

$90.$ Write in scientific notation: $(a) 4,800,000 (b) 0.00637$

Factor the greatest common factor from the polynomial.

$91. 3 x^{4} - 6 x^{3} - 18 x^{2}$

Chapter 11 Graphs

Graph:

$92. y = 4 x - 3$

$93. y = −3 x$

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

$95. x - y = 6$

$96. y = −2$

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

Graph using the intercepts.

$98. 2 x - 4 y = 8$

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

$No Alt Text$

$100.$ Use the slope formula to find the slope of the line between the points $(−5, −2), (3, 2) .$

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

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Chapter 1 Whole Numbers

Chapter 2 The Language of Algebra

Chapter 3 Integers

Chapter 4 Fractions

Chapter 5 Decimals

Chapter 6 Percents

Chapter 7 The Properties of Real Numbers

Chapter 8 Solve Linear Equations

Chapter 9 Math Models and Geometry

Chapter 10 Polynomials

Chapter 11 Graphs