MTH070 Review Problems for Final Exam - MLC This is not a sample test. These problems are designed to get you started on your review for the test. Study the homework from the textbook and your class notes for a more complete review. Section 1.1 1. Use properties of equality to solve each of the equations. Show your steps.

a) 3y = 24 b) k5= 17 c) n−5= 35 d)

−13t

8= −26

2. Translate each sentence into an equation, using x for the unknown quantity. Solve the equation. a) If nine is added to a number, the result is negative seventeen.

b) The difference of a number and negative twelve is negative five.

Section 1.2 3. Use properties of equality to solve each of the equations. Show your steps.

a) 8x − 7 = −23 b) t7−8 = 11 c) 5(x + 3)− 7 = −8 d)

32

x −5= 56

x − 3

Section 1.3 4. Solve each equation for the given variable. a) x + 3t = 8 for x b) x + 3t = 8 for t c) 15x + 3y = 17 for y

Section 1.4 5. Solve each of the inequalities, then graph the solution on a number line. a) 7 − 2x ≥ −5 b) 5.3+ 3.5x ≤ 2.4 c) 17 ≤ 5x + 2 ≤ 32

Section 2.1 6. Nacho Daddy’s taco stand sells beef burritos. Let b represent the number of burritos purchased and c be

the cost, in dollars, for a lunch at Nacho Daddy’s. c = 4b+ 2

a) What is the cost for lunch if two burritos are purchased?

b) How many burritos can be purchased for a total lunch cost of $22? 7. A 2500 gallon water tank was completely full when it sprang a leak. Let V represent the number of

gallons of water remaining in the tank after D days. Use the table to help answer the following questions.

a) How much water remains in the tank after 65 days? b) How many days does it take for the remaining water level to reach 2175

gallons? 8. The graph shows the distance, d, in miles, Phil rode his bike during a

cross-country bicycle trip. Let t represent the number of days Phil rode. a) What was Phil’s distance after 4 days? b) How many days did it take Phil to go 500 miles?

D525456585

V24352175191516551395

time (days)

dist

ance

(mi)

6420

500

400

200

100t

d

8

600

700

MTH070 Final Review

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Section 2.2 9. a) Create a scattergram of the table at right.

b) Are the points linearly related?

10. Determine whether or not each ordered pair represents a solution of the equation the equation:

y = 3x + 2 ? (0, 2), (1, 4), (2, 9), (5, 17) Section 2.3 11. Find the slope of the line passing through each pair of points. a) (2, 5) and (6, 7) b) (−2, 4) and (2, −4) c) (2, 7) and (5, 7) d) (3, 4) and (3, 7) 12. What is the slope of the line sketched at the right?

13. Find the slope of each line whose equation is given. a) 3y +5x = 2 b) 3y + 2 = 15 c) 8y + 7x = 3 d) 5x = −15 Section 2.4 14. Graph each of the equations by hand.

a) y = 2

3x − 2 b) 3x + 4y = 24

Section 2.5 15. Find the x-intercept and y-intercept, and then use the intercept method to graph the equations by hand.

Show your work. a) 2x − 3y = −6 b) 4x + 3y −12 = 0 Section 2.6 16. Find an equation of the line that has the given slope and contains the given point. Write the equation in

slope-intercept form. Show your work. a) m = 3, (2, 7) b) m = −5, (1, −3) 17. Find an equation of the line that passes through the two given points. Show your work. Do not use

linear regression. a) (5, 4) and (6, 7) b) (−4, −8) and (−1, −2) Section 2.7 18. For the given table of values, use a graphing calculator to draw a

scatterplot, then use regression to find an equation of the line of best fit. Round decimals to three decimal places.

X 33 44 55 66 77 88 99Y 12 15 17 25 24 29 37

x1356

y-2268

x

y

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19. The percentage of Fortune 500 companies that offer pensions are shown in the table for various years. Let y be the percentage of Fortune 500 companies that offer pensions at x years after 1990.

a) Use regression on a calculator to find a linear equation for the line of best fit. Round decimals to two places.

b) Use your regression equation to predict the percentage of companies that offered pensions in 2015. c) Use your regression equation to predict the year that 75% of the companies offered pensions.

Section 2.8 20. a) Find an equation of a line that contains the point (2, −3) and is perpendicular to the graph of

x − 2y = 8 . Show your work. b) Find an equation of a line that contains the point (2, −3) and is parallel to the graph of x − 2y = 8 .

Show your work.

Section 3.1 21. Find the solution of the system by graphing the equations by hand. Then use “intersect” on your

calculator to check your solution.

a)

2y − x = 43y − 2x = 3

b)

5y − 3 = x + 210y = 2x − 20

Section 3.2 22. Solve the system by substitution. Verify your solution by checking that it satisfies both equations of the

system.

a)

y = −5x +183x − y = −2

b)

2x − y = −45y = 3x −1

Section 3.3 23. Solve the system by elimination. Verify your solution by checking that it satisfies both equations of the

system.

a)

x − y = 23x + y = 10

b)

x − y = 55x − y = 13

Section 3.4 24. Set up and solve a system of equations to answer each question.

a) Sean bought 15 pounds of a grass seed mixture for $48.71. The mixture was made up of ryegrass seed that cost $2.79 per pound and fescue seed that cost $4.75 per pound. How many pounds of each type of grass seed are in the mixture.

b) Jolene needs 10 quarts of a 27% acid solution. She is going to mix two solutions together, solution A, which is 18% acid and solution B, which is 30% acid. How much of each solution does Jolene need?

Section 4.1 25. Simplify each algebraic expression.

a) 7 y2 +5y − 3y2 + 2y d) (x +5)3+ 2x −15

Section 4.2 26. Perform the multiplications and combine any like terms.

a) −5t(2t + 3) b) (x + 3)2 c) t −5( )2 d) (x −1)(2x2 + 3x +5)

year 1995 2000 2002 2006 2009percent 35 45 40 55 62

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Section 4.3 27. Use the rules of exponents to simplify each expression.

a) t3t15 b) mt i m3 i m5t c)

10x7 y6z5

5x2 y3z3

Section 4.4 28. Use the rules of exponents to simplify each expression.

a) (xy)3 b) 2m5( )3

c)

2t3z5

tz2

⎛⎝⎜

⎞⎠⎟

4

Section 4.5 29. Use the rules of exponents to simplify each expression. There should be no negative exponents in your

answers.

a) x−3 b) −2( )−5 c)

3x2

⎛⎝⎜

⎞⎠⎟

4

d)

x−2 y5

x5 y3

⎛⎝⎜

⎞⎠⎟

−4

Section 4.6 30. Use the conversion table to convert each measurement. Round to

two decimal places. Show your work. a) 3 square kilometers into square miles. b) 450,000 cubic inches into cubic meters.

31. Write each number in scientific notation. a) 0.000 000 25 b) 5,297,000

32. Write each number in standard notation. a) 3.718×10−8 b) 4.829×109

33. Perform the indicated operations. Write your answers in scientific notation.

a) 2.3×10−7( ) 5.8×10−3( ) b)

5.712×10−17( )3.215×1011( )

Section 5.1 34. Factor out the greatest common factor. a) 14t3z5 − 28t2z3 b) 16x2 + 24x

Section 5.2 35. Factor each trinomial when possible. a) 5x2 + 40x + 75 b) 3x2 − 3x − 36

Section 5.3 36. Factor each polynomial completely. a) x2 − 49 b) x2 +14x + 49 c) 25x2 − 9y2

Section 5.4 37. Simplify each rational expression.

a)

3t3

6t2 + 9t b)

x2 +10x + 25x2 +8x +15

c)

m2 − 36m2 +12m+ 36

1 foot = 12 inches 1 yard = 3 feet 1 mile = 5280 feet 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 meter = 1000 millimeters1 kilometer = 1000 meters 1 mile = 1.609 kilometers

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13

x8

x-0.829x6

Section 6.1 38. Solve by factoring.

a) (x − 4)(2x + 3) = 0 b) x2 − x = 30 c) 8x = x2 +12 d) x2 + 6x = 16

Section 6.2 39. Simplify each of the square roots. Give simplified exact answers, not decimals.

a) 48 b)

716

c) 60

Section 6.3 40. Use square roots to solve the equation. Leave answers in simplified exact form. a) x2 − 60 = 0 b) (x +5)2 = 36 e) 5x2 = 50 41. Find the missing side length of each triangle. Leave answers as decimals rounded to two places. a) b)

42. Find the distance between the pairs of points. Show your work. a) (5, 9) and (1, 6) b) (4, −2) and (−8, 9)

Section 6.4 43. Solve by using the quadratic formula. Show your work.

a) x2 + 6x + 9 = 0 b) x2 − x − 20 = 0 c) 4x2 − 2x +1= 0

Section 6.5 44. For each equation: Find the vertex and four additional points, and graph the equations. a) y = (x −5)2 b) y = x2 − 6x + 2 Section 6.6 45. Use a graphing calculator to help you solve the following equations. Round answers to the nearest

thousandth. a) 4.23x2 −5.37 = −2.56x2 + 0.55 b) −x2 − 3x +5= 0

ANSWERS: 1. a) y = 8 b) k = 85 c) n = 40 d) t = 16 2. a) 9+ x = −17 , x = −26 b) x − (−12) = −5 , x = −17

3. a) x = −2 b) t = 133 c) x = −16

5 d) x = 3

4. a) x = 8− 3t b) t = 8− x

3 c)

y = 17

3−5x

5. a) x ≤ 6 , b) x ≤ −0.829 , c) 3≤ x ≤ 6 ,

19

x

7

MTH070 Final Review

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x

y

each square is one unit

y

x

y

x

6. a) $10 b) 5 7. a) 1,655 gallons b) 25 days

8. a) 400 miles b) 5 days 9. a) b) Yes 10. (0, 2) yes, (1, 0) no, (2, 9) no, (5, 17) yes

11. a) m =

7 − 56 − 2

=24=

12

b) m =

4 − (−4)−2 − 2

= −84= −2

c) m =

7 − 75− 2

=03= 0 d)

m =

7 − 43− 3

=30= undefined

12. m = 1

3 13. a)

m = − 5

3 b) m = 0 c)

m = − 78

d) m is undefined

14. a) b) 15. a) x-intercept: (−3, 0) y-intercept: (0, 2)

b) x-intercept: (3, 0) y-intercept: (0, 4)

16. a) y = 3x +1 b) y = −5x + 2 17. a) y = 3x −11 b) y = 2x 18. y = .357x − .857 19. a) y = 1.91x + 23.68 b) 71.43% c) x = 26.9, 2017

20. a) y = −2x +1 b) y = 1

2x − 4

21. a)

y =12

x + 2

y =23

x +1 b)

y =15

x +1

y =15

x − 2

(6, 5) No Solution - Inconsistent

x

y

y

x

y

x

x

y

MTH070 Final Review

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21

0

-4

-132 51 4 6

-5

-3

-2

-6

-7

25

20

15

5

10

64 102 8

22. a)

x = 2y = 8

b)

x = −3y = −2

23. a)

x = 3y = 1

b)

x = 2y = −3

24. a) 3.5 lb fescue, 11.5 lb rye b) 2.5 quarts of mixture A, 7.5 quarts of mixture B

25. a) 4y2 + 7 y b) 5x

26. a) −10t2 −15t b) x2 + 6x + 9 c) t

2 −10t + 25 b) 2x3 + x2 + 2x −5

27. a) t18 b) m6t+3 c) 2x5 y3z2 28. a) x

3 y3 b) 8m15 c) 16t8z12

29. a)

1x3 b)

− 132

c)

81x8 d)

x28

y8

30. a) 3km2 i

1mi2

1.6092 km2 = 1.16mi2 b) 450,000in3 i

2.543cm3

1in3 i1m3

1003cm3 = 7.37m3

31. a) 2.5×10−7 b) 5.297 ×106 32. a) .000 000 037 18 b) 4,829,000,000

33. a) 1.334×10−9 b) 1.777 ×10−28 34. a) 14t2z3 tz2 − 2( ) b) 8x(2x + 3)

35. a) 5(x + 3)(x +5) b) 3(x + 3)(x − 4) 36. a) (x + 7)(x − 7) b) (x + 7)2 c) (5x + 3y)(5x − 3y)

37. a)

t2

2t + 3 b)

x +5x + 3

c) m− 6m+ 6

38. a) x = 4, −

32

b) x = 6, − 5 c) x = 2, 6 d) x = 2, − 8

39. a) 4 3 b)

74

c) 2 15 40. a) x = ±2 15 b) x = 1, −11 c) x = ± 10

41. a) x = 15.26 b) x = 17.66 42. a) 5 b) ≈ 16.279

43. a) x = −3 b) x = 5, − 4 c) No real-number solution 44. a) b) 45. a) x = −.934, .934 b) x = −4.193, 1.193