Redwood High School. Department of Mathematics REALLY hard worker's name:_________________________Avanced Algebra 2016-17 Prep for Final Exam S1 . SHOW YOUR WORK to obtain full credit

MOST PROBLEMS DO NOT HAVE SPACE , WORK ON ADDITIONAL PAPER AND STAPLE IT IN THE BACK for all graphs indicate a) domain, b) vertical asymptote , c) holes, d) y and x intercepts if they exist, and e) end behavior

Solve the system by graphing.1) 3x - 2y = 11

2x + 4y = 34

Factor the polynomial completely.2) 15z2 + 8z - 16 2)

Express the function in the form f(x) = a(x - h)2 + k and indicate the vertex. DO NOT GRAPH3) f(x) = x2 + 4x - 9 3)

Simplify the power of i.4) i61 4)

Factor the polynomial.5) 6x2 + 17x + 12 5)

Find the number of solutions and classify the system as independent, inconsistent, or dependent.6) 2x - y = 4

x + 3y = 26)

7) 9 = 4x + 3y-9y - 12x = -27

7)

Use the discriminant to determine the number of real solutions.8) (6x - 9)2 = -3 8)

Simplify the power of i.9) i63 9)

1

Graph the polynomial function. Factor first if the expression is not in factored form.10) f(x) = 3x(x + 1)2(x + 2)2 10)

Solve the problem.11) The amount of particulate matter left in solution during a filtering process is given by the

equation P = 500(2)-0.6n, where n is the number of filtering steps. Find the amounts left forn = 0 and n = 5. (Round to the nearest whole number.)

11)

Factor the polynomial completely.12) 12x3 - 972x 12)

Solve the quadratic equation.13) 3x2 = 9x 13)

14) x2 + 4x + 4 = 17 14)

Solve the system by substitution.15) x + 4y = 9

2x + 4y = 1415)

Factor the trinomial completely.16) 9x2 + 18x + 8 16)

Solve the system by any method.17) -4x - 3y = -60

-8x = -62 + 6y17)

2

Graph. Indicate X and Y intercepts, and coordinates of the vertex18) y = x2 - 2x - 8 18)

19) y = -3x2 + 2x + 1 19)

Use division to find the quotient and the remainder.20) 6x3 + 15x2 - 4x + 15 is divided by x + 3 20)

21) x4 + 81 is divided by x - 3 21)

Find all of the real and imaginary zeros for the polynomial function.22) f(x) = x3 - 8x2 + x - 8 22)

Solve the problem.23) An initial investment of $480 is appreciated for 2 years in an account that earns 12%

interest, compounded quarterly. Find the amount of money in the account at the end of theperiod.

23)

24) Austin invested $12,000 in an account at 6% compounded quarterly. Find the amount inAustin's account after a period of 6 years.

24)

25) The sales of a mature product (one which has passed its peak) will decline by the functionS(t)= Soe-at, where t is time in years. Find the sales after 11 years if a = 0.12 andSo = 60,400. (Round to the nearest whole number.)

25)

3

26) 1x + 4

+2

x + 3=

-1x2 + 7x + 12

26)

Solve the problem.27) A vendor has learned that, by pricing pretzels at $1.00, sales will reach 136 pretzels per

day. Raising the price to $1.50 will cause the sales to fall to 116 pretzels per day. Thenumber of pretzels, N, is a linear function of the price, x. Write a linear function thatmodels the number of pretzels sold per day when the price is x dollars each.

27)

Find the function value.28) Let f(x) = 41-x. Find f(4). 28)

Determine which of the rational functions given below has the following feature(s). (1 point each)

29) x-intercepts: -5 and -2, y-intercepts: 58 , vertical asymptote: x = 4, horizontal asymptote: y = 1 29)

A) f(x) = (x + 5)(x + 2)(x - 4)

B) f(x) = (x - 5)(x - 2)(x + 4)2

C) f(x) = (x + 5)(x + 2)(x - 4)2

D) f(x) = (x - 5)(x - 2)(x + 4)

30) The vertical asymptote is x = 3 30)

A) f(x) = x - 3x + 9

B) f(x) = 3x - 1x + 9

C) f(x) = x + 9x - 3

D) f(x) = x + 9x + 3

31) The x-intercept is 4 31)

A) f(x) = x - 4x + 9

B) f(x) = x + 9x - 4

C) f(x) = x + 4x + 9

D) f(x) = 4x - 1x + 9

32) The horizontal asymptote is y = 3 32)

A) f(x) = 3x - 1x + 9

B) f(x) = 3x - 3

C) f(x) = 3x2 - 1x + 9

D) f(x) = x + 3x + 9

33) There is a "hole" in its graph at x = 4 33)

A) f(x) = 4x - 1x + 9

B) f(x) = x + 4(x + 9)(x + 4)

C) f(x) = (x - 4)(x + 9)(x + 5)(x - 4)

D) f(x) = x + 9x - 4

34) x-intercepts: 2 and 4, y-intercept: 8, vertical asymptote: x = 1, horizontal asymptote: y = 1 34)

A) f(x) = (x - 2)(x - 4)(x - 1)2

B) f(x) = (x + 2)(x + 4)(x + 1)

C) f(x) = (x - 2)(x - 4)(x - 1)

D) f(x) = (x + 2)(x + 4)(x + 1)2

4

Find the function value.

35) Let f(x) = 13

x. Find f(-3). 35)

Find the x- and y-intercepts of f(x), end behavior, label the points and axis, and graph the function.36) f(x) = -x2(x + 4)(x2 - 1) 36)

37) f(x) = 2x3(x - 4)3 37)

38) Zeros: -5, -6, 6; degree 3 38)

Perform the indicated operations and simplify the result. Leave the answer in factored form.

39) x2 + 8x + 15x2 + 11x + 30

·x2 + 6x

x2 - 5x - 2439)

40)x2 - 6x + 9

7x - 218x - 24

56

40)

41) 4x2x - 1

-4x

x - 141)

42) 2x2 + 2x = 40 Solve by completing the square, 42)

Graph the function Indicate X and Y intercepts, and vertex,43) f(x) = (x + 1)2 + 6 43)

Factor the polynomial completely, given that the binomial is a factor.44) x - 9, x3 + 7x2 - 80x - 576 44)

5

45) -Sketch the graph of the function. Label clearly both X and Y intercepts f(x) = - 3(x +1)(x -3)3(x + 3i)(x - 3i)

Use any method to find the function value.46) f(x) = 4x5 - 4x4 + 4x3 - x + 3; find f(3). 46)

Perform the indicated operations and write the answer in the form a + bi, where a and b are real numbers.47) (6 - 9i) + (2 + 5i) 47)

Perform the indicated operations and write the answer in the form a + bi, where a and b are real numbers. (48) (9 + 9i) - (-4 + i) 48)

49) (2 + 6i)2 49)

SImplify or rrite the expression in the standard form a + bi.

50) 4 + 3i8 - 4i

50)

Graph the function . Indicate X and Y intercepts, and vertex,51) f(x) = 2x2 - 4x + 7 51)

Solve the quadratic equation by any method52) 5x2 = 25x 52)

53) 6x2 + 12x + 5 = 0 53)

Graph the function.

54) f(x) = x2 - 7x + 10x2 - 2

55) f(x) = 2xx - 1

6

Graph the function. Indicate domain, range, asymptote and intercepts,

56) f(x) = 4x+ 1 56)

List the potential rational zeros of the polynomial function. Do not find the zeros.57) f(x) = 11x3 - x2 + 7 57)

58) f(x) = -2x3 + 3x2 - 2x + 8 58)

Factor the polynomial function COMPLETELY and use it to find all the zeros of the function. Then Find the x- andy-intercepts of f(x), end behavior, label the points and axis, and graph the function.

59) f(x) = x3 + 6x2 - x - 6 59)

60) f(x) = x4 + x2 - 20 60)

Graph the function. Indicate domain, range, asymptote and intercepts,

61) f(x) = ( 12

)x + 1

61)

Solve the problem.62) The function D(h) = 9(2.718)-0.4h can be used to determine the milligrams D of a certain

drug in a patient's bloodstream h hours after the drug has been given. How manymilligrams,rounded to two decimal places, will be present after 12 hours?

62)

7

63) Four bacteria are placed in a petri dish. The population will double every day. The formulafor the number of bacteria in the dish on day t is

N(t) = 4(2)twhere t is the number of days after the four bacteria are placed in the dish. How manybacteria are in the dish eight days after the four bacteria are placed in the dish?

63)

Graph the function.

64) f(x) = x2 - 4x + 3(x - 2)2

65) f(x) = x2 - 3x(x - 1)2

Solve the equation.

66) 2y + 3y

=32

66)

67) Sketch the graph of the polynomial function. Label clearly both X and Y intercepts f(x) = -3x3(x - 2)(x -3)44(x - 1)(x +2)4(x +5)5

Graph the function.

68) f(x) = 2xx + 4

68)

8

69) f(x) = x2 + x - 30x2 - x - 20

69)

Factor the polynomial completely , given that the binomial is a factor.70) x - 8, x3 - 2x2 - 39x - 72 70)

Factor completely.71) 2x2 - 18 71)

72) x4 - 25 72)

Decide whether or not the second polynomial is a factor of the first.73) 8x4 + 31x3 - 4x2 + x + 4; x + 4 73)

Graph the function.

74) f(x) = x2 + 4x - 5(x - 2)2

74)

75) f(x) = x2 + x - 6x2 - x - 2

9

Use the compound interest formulas A = P 1 + rn

nt

76) Suppose that you have $4000 to invest. Which investment yields the greater return over 9years: 7.2% compounded monthly or 7.3% compounded quarterly?

76)

77) f(x) = x4

x2 + 4

Find the equation and sketch the graph of the function.

78) A rational function that passes through 0, 13

, has the x-axis as as a horizontal asymptote, and has the line

x = - 3 as its only vertical asymptote.

Evaluate the exponential expression.79) -130 79)

80) 272/3 80)

Find the least common multiple.81) x2 + 7 x + 6 , x + 6 81)

Use any method to find the function value.82) f(x) = 3x5 - 4x4 + 4x3 - x + 5; find f(2). 82)

Find the quotient and the remainder.83) 12x3 + 11x2 - 20x + 8 divided by 3x - 1 83)

Solve the rational equation.

84) 5 - xx

+34

=7x

84)

10

85) x6

+2x9

=x54

85)

Perform the indicated operations and simplify the result. Leave the answer in factored form.86)

15x - 157

5x - 528

86)

87)5x

+6x2

25x2

-36x

87)

Solve the equation.

88) 10x - 2

= 1 + 12x + 2

88)

89) 3y + 3

-8

y - 3=

2y2 - 9

89)

Find all of the real and imaginary zeros for the polynomial function.90) f(x) = x3 - 6x2 + x - 6 90)

91) f(x) = x3 - 3x2 - 36x + 108 91)

92) f(x) = 6x3 + 22x2 + 10x - 6 92)

Form a polynomial (write it both in factor and in general forms) whose zeros and degree are given.93) Zeros: -5, -3, 3; degree 3 93)

94) Zeros: -3, multiplicity 2; -5, multiplicity 2; degree 4 94)

11

Graph the polynomial function. Factor first if the expression is not in factored form.95) f(x) = (3x - 1)(x + 1)2 95)

96) f(x) = x(x2 - 4)(x + 1)3 96)

97) f(x) = x3 + 4x2 - x - 4 97)

Find the x- and y-intercepts of f(x), end behavior, label the points and axis, and graph the function.98) f(x) =- 2x3(x + 1)3(x -5)(x +2)4(x +1)3 98)

12

Answer KeyTestname: ADV ALG S1 FE PREP V2.0.

1) {(7, 5)}2) (3z + 4)(5z - 4)3) f(x) = (x + 2)2 - 13

vertex: (-2, -13)4) i5) (2x + 3)(3x + 4)6) Independent7) Dependent8) No real solutions9) -i

10)

11) 500; 6312) 12x(x + 9)(x - 9)13) 0, 314) -2 ± 1715) {(5, 1)}16) (3x + 4)(3x + 2)17)18)

13

Answer KeyTestname: ADV ALG S1 FE PREP V2.0.

19)

20) 6x2 - 3x + 5; remainder 021) x3 + 3x2 + 9x + 27; remainder 16222) 8, -i, i23) $608.0524) $17,154.0325) 16,13526) no solution27) N(x) = -40x + 176

28) 164

29) C30) C31) A32) A33) C34) A35) 2736) x-intercepts: -4, -1, 0, 1; y-intercept: 037) x-intercepts: 0, 4; y-intercept: 038) f(x) = x3 - 36x + 5x2 - 180 for a = 1

39) xx - 8

40) 141) 4x42) -5, 4

14

Answer KeyTestname: ADV ALG S1 FE PREP V2.0.

43)

44) (x - 9)(x + 8)(x + 8)45)46) 75647) 8 - 4i48) 13 + 8i49) -32 + 24i

50) 14

+ 12 i

51) vertex (1, 5)intercept (0, 7)

52) 0, 5

53) -6 ± 6 6

15

Answer KeyTestname: ADV ALG S1 FE PREP V2.0.

54)

55)

56)

57) ± 111

, ± 711

, ± 1, ± 7

58) ± 12

, ± 1, ± 2, ± 4, ± 8

59) {1, -1, -6}60) -2, 2; (x + 2)(x - 2)(x2 + 5)

16

Answer KeyTestname: ADV ALG S1 FE PREP V2.0.

61)

62) 0.07 mg63) 102464)

65)

66) {-6}67)

17

Answer KeyTestname: ADV ALG S1 FE PREP V2.0.

68)

69)

70) (x - 8)(x + 3)(x + 3)71) 2(x + 3)(x - 3)72) (x2 + 5)(x2 - 5)73) Yes74)

18

Answer KeyTestname: ADV ALG S1 FE PREP V2.0.

75)

76) $4000 invested at 7.3% compounded quarterly over 9 years yields the greater return.77)

78) y = 1x + 3

79) -180) 981) (x + 6 )(x + 1 )82) 6783) 4x2 + 5x - 5; remainder 384) {-8}85) {0}86) 12

87) 5x + 625 - 36x

88) {6, -8}89) -790) 6, -i, i91) -6, 3, 6

92) - 1, - 3, 13

93) f(x) = x3 - 9x + 5x2 - 45 for a = 194) f(x) = x4 - 18x2 + 81

19

Answer KeyTestname: ADV ALG S1 FE PREP V2.0.

95)

96)97)

98) x-intercepts: 0, -1; y-intercept: 0

20