Final Exam Review ProblemsMath 410

Spring 2013

Solve the equation.1) 2(2n - 2) = 3(n + 4)

A) 8 B) 10 C) -8 D) 16

1)

2) -0.3(x - 9) + x = 0.5(3 - x)

A) -0.67 B) 3.5 C) -1 D) -6

2)

1

Solve the equation for the indicated variable.3) 5x - 2y = 13 for y

A) y = 5x + 132

B) y = 5x + 13-2

C) y = 5x - 13-2

D) y = 5x - 132

3)

Solve the inequality. Graph the solution set and write it in interval notation.

4) 3(4x - 1)5

> 3

-5 -4 -3 -2 -1 0 1 2 3 4 5-5 -4 -3 -2 -1 0 1 2 3 4 5

A) - 32 , ∞

-5 -4 -3 -2 -1 0 1 2 3 4 5-5 -4 -3 -2 -1 0 1 2 3 4 5

B) -∞, 32

-5 -4 -3 -2 -1 0 1 2 3 4 5-5 -4 -3 -2 -1 0 1 2 3 4 5

C) -∞, - 32

-5 -4 -3 -2 -1 0 1 2 3 4 5-5 -4 -3 -2 -1 0 1 2 3 4 5

4)

2

D) 32 , ∞

-5 -4 -3 -2 -1 0 1 2 3 4 5-5 -4 -3 -2 -1 0 1 2 3 4 5

Solve.5) The house numbers of two adjacent homes are two consecutive even

numbers. If their sum is 394, find the house numbers.

A) 196, 198 B) 197, 199 C) 196, 392 D) 195, 197

5)

Solve. If needed, round money amounts to two decimal places and all other amounts toone decimal place.

6) The owners of a candy store want to sell, for $6 per pound, a mixture ofchocolate-covered raisins, which usually sells for $3 per pound, andchocolate-covered macadamia nuts, which usually sells for $8 per pound.They have a 40-pound barrel of the raisins. How many pounds of the nutsshould they mix with the barrel of raisins so that they hit their target valueof $6 per pound for the mixture?

A) 64 lb B) 56 lb C) 60 lb D) 52 lb

6)

3

7) The manager of a coffee shop has one type of coffee that sells for$7 per pound and another type that sells for $13 per pound. Themanager wishes to mix 90 pounds of the $13 coffee to get amixture that will sell for $9 per pound. How many pounds of the$7 coffee should be used?

7)

8) At a gourmet nut shop, nuts are sold in bulk. Cashews sell for$1.40 per pound and macadamia nuts sell for $8.45 per pound. Leewishes to purchase 5 pounds of mixed nuts by mixing 3.5 poundsof cashews and 1.5 pounds of macadamia nuts. What will be theprice per pound of the mixture?

8)

Solve.9) If two planes leave an airport at the same time with one flying west at 730

miles per hour and the other flying east at 470 miles per hour, how longwill it take them to be 4800 miles apart?

A) 5 hr B) 3.5 hr C) 4 hr D) 3 hr

9)

4

Solve. If needed, round money amounts to two decimal places and all other amounts toone decimal place.

10) The radiator in a certain make of car needs to contain 50 liters of 40%antifreeze. The radiator now contains 50 liters of 20% antifreeze. Howmany liters of this solution must be drained and replaced with 100%antifreeze to get the desired strength?

A) 16.7 L B) 25 L C) 12.5 L D) 20 L

10)

Graph.11) y = 5

x-5 5

y

5

-5

x-5 5

y

5

-5

11)

5

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

D)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

12) 7x + y = 2

x-5 5

y5

-5

x-5 5

y5

-5

12)

6

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

Find the slope of the line.13)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

A) 13 B) 3 C) - 1

3 D) - 3

13)

7

14) Through (-7, 9) and (8, 4)

A) - 3 B) 13 C) 13 D) - 1

3

14)

15) x = -1

A) 1 B) undefined C) -1 D) 0

15)

Provide an appropriate response.16) Determine whether the graphs of 4x - y = - 10 and y = 1

4x + 15 are

parallel lines, perpendicular lines, or neither.

A) neither B) perpendicular C) parallel

16)

8

Find an equation for the line. Write the equation in slope intercept form.17) With slope of - 2

9, through (2, 5)

A) 9x + 2y = -49 B) 2x + 9y = 49C) 2x - 9y = 49 D) 2x + 9y = -49

17)

Simplify the exponential expression. Write the result using only positive exponents.

18) x3y2x4y-2

2

A) y16x2

B) y6x2

C) y8x2

D) y16x

18)

9

Raise to the power or find the root. Assume that all variables represent positive numbers.Write with only positive exponents.

19) 23x1/4y5x1/4

1/3

A) 2y5 B) 2y5/3 C) y5/3 D) 2y3/5

19)

Perform the indicated operation.20) (4x3 + 4x2 + 5x + 7) + (8x3 + 5x - 3)

A) 8x3 + 9x2 + 2x + 7 B) 12x3 + 9x2 - 3x + 7C) 12x3 + 10x + 4 D) 12x3 + 4x2 + 10x + 4

20)

10

21) Subtract (6x + 3) from the sum of (9x2 + 9x + 1) and (x3 - 7).

A) x3 - 9x2 - 3x - 9 B) x3 - 9x2 - 3x + 9C) -x3 - 9x2 - 3x + 9 D) x3 + 9x2 + 3x - 9

21)

Multiply.

22) 2x + 49 2x - 4

9

A) 4x2 - 169 x - 16

81 B) 4x2 - 1681

C) 4x2 + 169 x - 16

81 D) 4x2 - 89

22)

11

23) (6x - 11)2

A) 36x2 + 121 B) 6x2 + 121C) 6x2 - 132x + 121 D) 36x2 - 132x + 121

23)

Divide.

24) 4x2 + 2xy - 9x8xy

A) x2y

+ 4 - 98y B) 1

2y + 1

4 - 9x

8y

C) x2y

+ 14

- 98y D) x

2y + 1

4y - 9

8

24)

Factor the polynomial completely.25) y2 + 40y + 400

A) prime B) (y - 20)2C) (y + 20)2 D) (y + 20)(y - 20)

25)

12

26) 7t2 - t - 4

A) (7t + 5)(t - 36) B) (7t - 36)(t + 5)C) (7t - 5)(t + 36) D) (7t + 36)(t - 5)

26)

Solve the equation.27) 2x(2x - 7)(8x + 3) = 0

A) 0, 37

, - 83

B) 0, - 72

, 38

C) 0, 72

, - 38

D) 72

, - 38

27)

13

Simplify the rational expression.

28) x + 3x3 + 27

A) 1x2 - 3x + 9

B) 1x2 - 9

C) 1x - 3 D) 1

x2 + 3x + 9

28)

Perform the indicated operation and simplify if possible.

29) y2 - 7y + 103y + 6

· y + 23y - 15

A) y - 29 B) (y - 2)(y - 5)

9(y + 5)

C) y + 29 D) y - 5

9

29)

14

30) 5aa2 + 9a + 20

- 2a + 4

A) 3a - 10(a - 5)(a + 4) B) 3a - 10

(a + 5)(a + 4)

C) 3a + 10(a - 5)(a + 4) D) 3a + 10

(a + 5)(a + 4)

30)

31) x2 - 9x2 - 3x

÷ x2 + 7x + 13x - 6

A) (x - 3)(x2 + 7x + 1)3x(x - 2) B) 3(x - 3)(x - 2)

x(x2 + 7x + 1)

C) 3(x + 3)(x - 2)x(x2 + 7x + 1)

D) (x + 3)(x2 + 7x + 1)3x(x - 2)

31)

15

Solve the equation.

32) 4y - 4

= 6y + 4

A) - 20 B) - 45 C) 4 D) 20

32)

Simplify the complex fraction.

33)

9a

+ 9

9a

- 9

A) 1 + a1 - a B) 9(1 + a)

1 - a C) a29 - a2 D) 9 - a2

33)

16

Rationalize the denominator. Assume that all variables represent positive numbers.

34) x - 1x + 1

A) x + 1x - 1 B) -1

C) x - 2 x + 1x - 1 D) -2 x

34)

Perform the indicated operations. Assume that all variables represent positive numbers.35) ( 10 + 2)( 10 - 2)

A) 8 B) 6 C) 10 - 2 2 D) 14

35)

17

Solve the problem.36) Find the distance between the points (7, 4) and (5, -7).

A) 9 units B) 117 unitsC) 5 5 units D) 117 13 units

36)

37) Find the midpoint of the line segment whose endpoints are (-6, 2), (-9,-7).

A) (-15, -5) B) - 152 , - 5

2

C) (3, 9) D) 32 , 9

2

37)

18

Solve the equation using the square root property.38) (x + 2)2 = 10

A) -2 - 10, -2 + 10 B) 8C) 2 - 10, 2 + 10 D) - 10, 10

38)

Solve the equation by completing the square.39) x2 + 18x = -62

A) 9 + 19 B) -18 + 62C) 9 - 62, 9 + 62 D) -9 - 19, -9 + 19

39)

Use the quadratic formula to solve the equation.40) 3x2 - 5x - 8 = 0 40)

19

41) 4x2 = -10x - 2 41)

42) x(x - 10) = 5 42)

20

Answer KeyTestname: UNTITLED1

1)D2)C3)D4)D5)A6)C7) 180 pounds8) $3.529)C10)C11)A12)B13)D14)D15)B16)A17)B18)C19)B20)D21)D22)B23)D24)C25)C26)B27)C28)A29)A30)B31)C32)D33)A34)C35)B36)C37)B38)A39)D

21

Answer KeyTestname: UNTITLED1

40) 83

, -1

41) -5 - 174

, -5 + 174

42) 5 - 30, 5 + 30

22