FCM — Unit #5 Rational Expressions Name: _____________________Review for Mid-Term Date: __________ Per: _____

Show all work on a separate sheet of paper for full credit!!!SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Solve the equation.1) 6x + 12 = 2x + 32 1)

2) 13(8x - 3) = 2x - 3 2)

3) 6(k - 1) - (5k - 9) = -6 3)

4) 2x5

- x3

= 2 4)

5) -80.2 - 9x = 1.7 5)

Write the following as an algebraic expression. Then simplify.6) The sum of three consecutive integers if the last integer is z. 6)

7) The perimeter of the floor plan shown.

x - 118

14

x - 3

7)

Solve.8) A diamond ring sold for $1929.60 including tax. If the tax rate where the diamond waspurchased is 7.2%, find the price of the ring before the tax was added. (Round to thenearest cent, if necessary.)

8)

Solve the formula for the specified variable.9) I = Prt for t 9)

Use the formula A = P 1 + rn

nt to find the amount requested.

10) A principal of $480 is invested in an account paying an annual interest rate of 15%. Findthe amount in the account after 8 years if the account is compounded quarterly.

10)

FCM - Review for Mid-Term V 1.0

FCM - Unit #5 Rational Expressions Review for Mid-TermSolve the inequality. Write the solution set in interval notation and graph the solution set.

11) 3z + 5 ≥ 2z + 5 11)

Graph the solution set of the inequality and write it in interval notation.12) -x < -8 12)

Solve.13) An archer has $62 to spend on a new archery set. A certain set containing a bow and

three arrows costs $42. With the purchase of this set, he can purchase additional arrowsfor $4 per arrow. Use an inequality to find the maximum number of arrows he couldobtain, including those with the set, for his $62.

13)

Solve the compound inequality. Graph the solution set.14) -8x > -8 and x + 8 > 6 14)

15) 12x - 8 < 4x or -2x ≤ -6 15)

Solve the absolute value equation.16) |5x + 8| + 4 = 6 16)

Solve the inequality. Graph the solution set.17) |6k - 8| - 3 < 6 17)

Solve the absolute value equation.18) |6x - 8| = -2 18)

FCM - Review for Mid-Term V 1.0

FCM - Unit #5 Rational Expressions Review for Mid-TermGraph the equation.

19) -4x - y = 5

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

19)

Use the vertical line test to determine whether the graph is the graph of a function.20)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

20)

21)

x-2 -1 1 2

y2

1

-1

-2

x-2 -1 1 2

y2

1

-1

-2

21)

FCM - Review for Mid-Term V 1.0

FCM - Unit #5 Rational Expressions Review for Mid-TermGraph the function by finding x- and y-intercepts.

22) 6x - 12y = 12

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

22)

Graph the equation.23) y + 5 = 0

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

23)

Find the domain and the range of the relation. Use the vertical line test to determine whether the graph is the graph ofa function.

24)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

24)

FCM - Review for Mid-Term V 1.0

FCM - Unit #5 Rational Expressions Review for Mid-Term25)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

25)

Find the indicated value.26) Find f(2) when f(x) = 4x2 + 4x + 4. 26)

Find the slope of the line.27) x - 6 = -7 27)

Determine whether the lines are parallel, perpendicular, or neither.28) 5x + 8y = 2

8x - 5y = 4028)

Solve the problem.29) The altitude above sea level of an airplane just after taking off from an airport on a high

plateau is given by the linear function y = 700x + 2233, where y is in feet and x is the timein minutes since take-off. Find and interpret the slope and y-intercept.

29)

Write an equation of the line with the given slope and containing the given point. Write the equation in the formy = mx + b.

30) Slope 4; through (-6, -8) 30)

Find an equation of the line. Write the equation in standard form.31) Undefined slope; through (-6, 3) 31)

Find an equation of the line. Write the equation using function notation.32) Through (7, 4); parallel to 7x + 4y = 81 32)

Solve the system of equations.33)

x + 6y = 1-7x + 7y = -7

33)

34)2x + 12y = -7012x + 3y = 63

34)

FCM - Review for Mid-Term V 1.0

FCM - Unit #5 Rational Expressions Review for Mid-TermGraph the piecewise defined function.

35)

f(x) = 2x - 1 if x ≤ 4-x if x > 4

x-5 5

y

5

-5

x-5 5

y

5

-5

35)

Graph the union or intersection, as indicated.36) The union of x ≥ 4 or y ≤ -3

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

36)

37) The intersection of x ≥ -3 and y > 2

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

37)

Solve the system.38)

x - y + 3z = 45x + z = 3x + 4y + z = 23

38)

FCM - Review for Mid-Term V 1.0

FCM - Unit #5 Rational Expressions Review for Mid-Term39)

3x + 4y + z = 245x - 5y - z = 45x + y + 4z = 8

39)

Solve.40) Two cars leave a city and head in the same direction. After 5 hours, the faster car is 20

miles ahead of the slower car. The slower car has traveled 210 miles. Find the speeds ofthe two cars.

40)

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to breakeven.

41) C(x) = 164x + 194,400R(x) = 326x

41)

Solve.42) Three trains one eastbound, one westbound, and one northbound leave a city at the

same time. The speed of the northbound train is 10 miles per hour greater than the speedof the eastbound train. After 3 hours, the distance between the westbound train and theeastbound train is 270 miles. Twice the speed of the westbound train is 80 miles per hourmore than the speed of the northbound train. Find the speeds of the three trains.

42)

Solve the system of linear equations using matrices.43)

7x - y + 2z = 563x + 9y - 5z = 369x - 9y + z = 24

43)

Simplify. Write the answer with positive exponents.

44) 30x-7y7

5xy-444)

Perform the indicated operation. Write the answer in scientific notation.

45) (9 × 107) (2.4 × 10-1) 45)

46) 150,000,000,000,0000.00000005 46)

Find the degree of the term.

47) -9xy5 47)

Simplify.48) If P(x) = 4x2 - 4x, find P(-2). 48)

Perform the indicated operations.

49) (6x5 - 2x4 - 6x) + (2x5 - 9x4 - 6x) 49)

FCM - Review for Mid-Term V 1.0

FCM - Unit #5 Rational Expressions Review for Mid-Term50) (5x5 - 4x4 + 8x3 + 3) - (8x5 + 7x4 + 2x3 - 5) 50)

Multiply.51) (5y + 11)(7y2 - 2y - 2) 51)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

52) (-5x + 10)(2x + 10)

A) -3x2 - 30x - 30 B) -10x2 - 30x + 100

C) -10x2 - 30x - 30 D) -3x2 - 30x + 100

52)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

53) (4x + 9y)(4x - 9y) 53)

54) (9x + 4y)2 54)

Evaluate the polynomial function.

55) If f(x) = x2 + 2x + 1, find f(a + h). 55)

Multiply.56) (x - 3)(x + 3)(x2 + 9) 56)

Factor the polynomial completely.

57) 35x5y + 45xy3 57)

58) x2 - 2x - 48 58)

59) 14x2 - 49x - 28 59)

60) 12x2y2 - 11xy2 - 15y2 60)

61) 81x2 - 4y2 61)

Solve the equation.

62) x2 + 3x = x(x - 6) 62)

Solve.63) One leg of a right triangle is 28 inches longer than the smaller leg, and the hypotenuse is

32 inches longer than the smaller leg. Find the lengths of the sides of the triangle.63)

Find the domain of the rational function.

64) f(x) = 1 - 6x

x2 - 16x + 2864)

FCM - Review for Mid-Term V 1.0

FCM - Unit #5 Rational Expressions Review for Mid-TermSimplify the rational expression.

65) x2 + 4x + 4

x2 + 9x + 1465)

Multiply or divide as indicated. Simplify completely.

66) 24x + 2412x - 4

∙ 48x - 16

6x2 - 666)

67) x2 + 7x + 10

x2 + 9x + 20 ÷ x2 + 2x

x2 + 10x + 2467)

Perform the indicated operation. Simplify if possible.

68) xx + 9

+ -6x + 9

68)

Find the LCD of the rational expressions in the list.

69) 1

48x, 1

8x2, 1

6x369)

Perform the indicated operation. Simplify if possible.

70) 3

y2 - 3y + 2 + 5

y2 - 170)

71) x

x2 - 16 - 8

x2 + 5x + 471)

Simplify.72)

x4

5x + 8

72)

73)

x - 64

x - 1x

73)

74) 9x-1 + 6y-1

5x-2 + 5y-274)

FCM - Review for Mid-Term V 1.0

FCM - Unit #5 Rational Expressions Review for Mid-TermDivide.

75) -24x8 + 36x7 - 18x5 - 24x3

-6x575)

76) (-24x2 - 22x + 7) ÷ (-4x + 1) 76)

Use synthetic division to divide.

77) (3x3 + 10x2 - 2x + 24) ÷ (x + 4) 77)

78) 12x3 - 23x2 - 11x + 13

4x - 178)

Solve the equation.

79) 2x + 3

- 4x - 3

= 8

x2 - 979)

Solve the equation for the specified variable.

80)P1V1T1

= P2V2T2

for P2 80)

Solve.81) One conveyor belt can move 1000 boxes in 9 minutes. Another can move 1000 boxes in

12 minutes. If another conveyor belt is added and all three are used, the boxes aremoved in 3 minutes. How long would it take the third conveyor belt alone to do thesame job?

81)

Find the variation equation for the variation statement.82) c varies directly as a and inversely as b; c = 4 when a = 36 and b = 54 82)

FCM - Review for Mid-Term V 1.0