Infinite Algebra 2 - FINAL Review

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ALG 3 - Functions, Quads, Polys, Logs + SS.

Name___________________________________

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FINAL Review

Date________________ Period____

Solve each system by substitution. 1) y = -6 x - 8 y = 6x - 8

2) y = -3 x + 1 -8 x + 3 y = -14

Solve each system by elimination. 3) 3 x + y = -14 6 x + 7 y = -8

4) -30 x + 45 y = 3 24 x - 36 y = 0

Solve each system by substitution. 5) z - y = 7 3 x + 5 y + 2z = 1 -5 x - 3 y - 5z = -17

Evaluate each function. 6) w(a) = 3 -a - 2; Find w(-1)

7) g(n) = 3 × 2 2n; Find g(-2)

8) k(a) = -2a + 4; Find k(3 - a)

9) w(n) = n 2 - 2; Find w(a - 2)

Perform the indicated operation. 10) h(n) = -4n - 1 g(n) = 2n - 1 Find (h - g)(n)

11) f ( x) = 2 x 2 + 2 g( x) = -2 x + 4 Find ( f g)( x)

12) f ( x) = -3 x 2 + 5 x g( x) = 2 x - 2 Find ( f + g)( x)

13) f (t) = -2t - 3 g(t) = t 2 - 3t Find ( f × g)(t)

Change to VERTEX FORM. Sketch the graph of each function. State the DOMAIN and RANGE. Solve for the ROOTS. Name the type of roots and how many. 14) y = x 2 - 6 x + 10

15) y = -2 x 2 - 8 x - 4

y

y 5

6 5.5 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 -1

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

1

2

3

4

5 x

-1 -2 -3 -4 1

2

3

4

-5

5 x

Worksheet by Kuta Software LLC

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Find the VERTEX. Sketch the graph of each function. State the DOMAIN and RANGE. Solve for the ROOTS. Name the type of roots and how many. 16) y = -2( x - 2) 2 - 1

17) y =

y -3 -2 -1

1

2

3

4

5

6

7 x

1( x - 4) 2 - 1 2

y

-1

4

-2

3

-3 2 -4 1

-5 -6

1

-7

2

3

4

5

6

7 x

-1

-8 -2 -9 -3

-10

-4

Solve each equation by taking square roots. Name the type of roots and how many. 18) m 2 = 72

19) -5r 2 = 60

20) 10r 2 = 250

Solve each equation by factoring. 21) x 2 + 2 x = 0

22) x 2 - 4 x - 2 = -5

23) (v - 2)(7v - 3) = 0

24) 2n 2 - 7n + 6 = 0

Solve each equation with the quadratic formula. Then state the type of roots and how many. 25) 3k 2 + 4k + 9 = 0

26) 6 x 2 - 30 = -11 x

Find the roots and their multiplicitues, then sketch the graph of each function. 27) f ( x) = - x 4 + x 2 + x - 3

28) f ( x) = x 3 - 3 x 2

y

-8

-6

-4

y

8

8

6

6

4

4

2

2

-2

2

4

6

8 x

-8

-6

-4

-2

2

-2

-2

-4

-4

-6

-6

-8

-8

4

6

8 x

Worksheet by Kuta Software LLC

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Find f(2), f(-1) and 3f(0). What is the absolute maximum value, absolute minimum, and the relative maxima or minima. Then state where the function is increasing or decreasing. 29) f ( x) = x 4 - x 2 - 2 y 8 6 4 2 -8

-6

-4

-2

2

4

6

8 x

-2 -4 -6 -8

Factor and use quadratic methods to solve for the roots. Then state the type of roots and how many. 30) x 2 (5 x - 4)( x + 1) = 0 31) x 4 + 2 x 2 - 63 = 0 32) 3 x 3 + 3 x 2 - 2 x - 2 = 0 33) x 4 + 27 x = 0 34) x 3 - 8 = 0 Use the Rational Root Theorem and quadratic methods to solve for the roots. Then state the type of roots and how many. 35) 2 x 3 + 7 x 2 + 7 x + 2 = 0 36) 3 x 3 + 5 x 2 + x - 1 = 0 Write a polynomial function of least degree with integral coefficients that has the given zeros. 37) 1 mult. 2, -

1 5

38) 0,

3 , 1 5

Sketch the graph of each function. State the domain and range. 39) y = 2 ×

1 x +1 3

40) y = 3 × 2 x

()

y 20

y 20

18

18

16

16

14

14

12

12

10

10

8

8

6

6

4

4

2

2 -6 -6

-4

-2

2

4

6

x

-4

-2

2

4

6

x Worksheet by Kuta Software LLC

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Simplify. 3

41) 750 x 5 y 7 z 42) 112m 2 np 4 Simplify. Your answer should contain only positive exponents with no fractional exponents in the denominator. 4 3

43) 4 p × 2 p

3 2

()

44) x Simplify.

7 4

45)

1 3 3 4

3n 4n 2

46) (216n

1 6 3

)

Solve each equation. 47) 2 2 - 2 x = 32 49) 36 -1 + n = 1

()

1 48) 5

2v

50) 125

= 25 -2r

( )

1 × 625

2r + 1

= 25

Solve each equation. Round your answers to the nearest ten-thousandth. 51) 15 m = 44

52) e k + 9 = 0.6

53) e x = 31 Solve each equation.

54) e -9n = 4

55) log 7 (-r - 6) = log 7 (r + 2)

56) log 16 (-6 p - 1) = log 16 ( p 2 - 28)

57) log 11 a = 0

58) ln p = -2

59) log 6 (n - 3) = 1

60) 10 ln (r - 3) = 30

61) log x - log ( x + 3) = 1

62) log 7 10 - log 7 ( x - 8) = 1

63) log 8 ( x 2 - 2) + log 8 4 = 1

64) log 9 ( x + 6) - log 9 3 = log 9 23

Find the common difference, the 52nd term, and the explicit formula.

Find the common ratio, the 8th term, and the explicit formula.

65) 7, 4, 1, -2, ... Find the missing term or terms in each arithmetic sequence.

66) -2, 12, -72, 432, ... Find the missing term or terms in each geometric sequence.

67) ..., 30, ___, ___, 42, ... Evaluate each arithmetic series described.

68) ..., 3, ___, ___, ___, 1875, ... Evaluate each geometric series described.

69) a1 = 5, d = 3, n = 40

70) 2 + 10 + 50 + 250..., n = 6

Evaluate each arithmetic series described.

Evaluate each geometric series described.

35

71)

S

9

(10m - 18)

72)

m=1

S -3 × 3

n=1

-4-

n-1 Worksheet by Kuta Software LLC

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Answers to FINAL Review (1, -2) 3) (-6, 4)

1) (0, -8) 5) (-2, -1, 6)

2) 6) 1

9) a 2 - 4a + 2 13) -2t 3 + 3t 2 + 9t

10) -6n 14)

4) No solution 8) -2 + 2a

3 16 11) 8 x 2 - 32 x + 34 7)

12) -3 x 2 + 7 x - 2

15)

y

y

6 4 5 2

4 3

-8

-6

-4

2

16) -4

-4 1

2

17)

y -2

2

4

3

4

5 x

18) {6 2 , -6 2 } 2 irrational

y 4 3 2 1

6 x

-2 -4 -6

-1 -2 -3 -4

-8 -10

1 2 3 4 5 6 7 x

{ }

-2 + i 23 -2 - i 23 , } 2 complex 3 3 28)

y

-2 -4 -6 -8

29)

y

8 6 4 2 -8 -6 -4 -2

{ }

3 ,2 2 3 10 26) { , - } 2 rational 2 3 24)

7

27)

21) {-2, 0}

20) {5, -5} 2 rational

19) {2i 3 , -2i 3 } 2 imaginary 22) {1, 3} 3 23) 2, 25) {

2 x -2

1 -1

-2

y

8 6 4 2 2 4 6 8 x

-8 -6 -4 -2 -2 -4 -6 -8

4 5

30) {0 mult. 2, , -1} 3/4 rational

8 6 4 2 2 4 6 8 x

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8 x

31) { 7 , - 7 , 3i, -3i} 2 irrational, 2 imaginary

6 6 ,} 2 irrational, 1 rational 3 3 3 + 3i 3 3 - 3i 3 33) {0, -3, , } 2 rational, 2 complex 2 2 34) {2, -1 + i 3 , -1 - i 3 } 1 rational, 2 complex p 1 1 1 35) { , 2, -2, 1, -1, , - } {-2, - , -1} 3 rational q 2 2 2 p 1 1 1 37) f ( x) = 5 x 3 - 9 x 2 + 3 x + 1 36) { , 1, 1, , - } { , -1 mult. 2} 3 rational q 3 3 3 Worksheet by Kuta Software LLC 3 2 ( ) 38) f xXK]uOtEaG = 5 x mSEodfatYwHawrVeo - 8 x + 3 x cLkL^Cw.Q W nAQlcld ^r_iOgTh_tosI YrZeIsIearpvRezdI.x -5- P oMYadd^eJ UwBiotYhR fICn^fIiPn^iUtZeV PAXlCgneDbmrjaT a2i. ©I l2w0x1U5M 32) {-1,

( (

)

)

39)

3

40)

y 20 18 16 14 12 10 8 6 4 2 -6 -4 -2

20 18 16 14 12 10 8 6 4 2 2 4 6

-6 -4 -2

x

2

42) 4 p m 7n 43) 8 p 46) 6n 2

{ }

3 7 54) -0.154 1 50) -

58)

{}

62)

{}

41) 5 xy 2 6 x 2 yz

y

17 6

2 4 6

44) x

x

1 4

3 4

3 2 51) 1.3974

48) {-1}

3n 4n 49) {1}

52) -9.5108

53) 3.434

55) No solution. 59) {9}

56) {-9} 60) {e 3 + 3}

57) {1} 61) No solution.

63) {2, -2}

64) {63}

{ }

47) -

45)

e2

66 7

65) Common Difference: d = -3 a52 = -146 Explicit: an = 10 - 3n 67) 34, 38 71) 5670

68) 15, 75, 375 72) -29523

66) Common Ratio: r = -6 a8 = 559872 Explicit: an = -2 × (-6) n - 1 69) 2540 70) 7812

Worksheet by Kuta Software LLC

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