Algebra 2/Trig First Semester Final Exam ____________________________________________________________________________

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DO NOT mark on this test. Fill in the appropriate answers on your scantron.

1. The literature club is printing a storybook to raise money. The print shop charges $3 for each book and $60 to create the film. How many books can the club print if their budget is $540?a 175 b 160 c 165 d 180

2. Solve: 5b − 12 < 6b + 15a b > −27 b b > 27 c b = −3 d b < 17

3. Solve: x − 3 < 5 or x + 4 > 14a 8 < x < 10 b x < 8 or x > 10 c x > 10 d x < 8

4. Solve: x + 3| | > 3a x < −6 or x > 0 b x < −6 or x < 0 c −6 < x < 0 d −6 > x > 0

5. Graph: f(x) = 2x − 1a c

b d

6. Find the slope of the line that passes through: (−4,3) and (8,−7).

a −1 b15

c −56

d −65

2

7. Find the x- and y-intercepts of: −5x + y = −10a x-int: (2,0)

y-int: (0,-10)b x-int: (-10,0)

y-int: (0,5)c x-int: (-10,0)

y-int: (0,2)d x-int: (5,0)

y-int: (0,-10)

8. Write the slope-intercept form of the line that passes through (−4,−1) and has a slope of 3.a y = 3x − 11 b y = −3x + 11 c y = 3x + 11 d y = −3x − 11

9. Write the equation of the line that goes through (1,−5) and is parallel to 2x − 2y = −2a y = x − 6 b y = −x − 6 c y = −x + 6 d y = x + 6

10. Graph: 6x − 5y = −30a c

b d

11. A rental car agency charges $18 per day plus $0.09 per mile to rent a certain car. Another agency charges $20 a day plus $0.06 per mile to rent the same car. How many miles per day will have to be driven for the cost of the car to be the same? a 666.67 mi/day b 1266.67 mi/day c 126.67 mi/day d 66.67 mi/day

3

12. Graph: 4x − 7y < −28a c

b d

13. Graph. x ≥ −1

y ≤ −6

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Ì

Ó

ÔÔÔÔÔÔÔÔÔÔ

a c

b d

4

14. Determine the solution to the system.y ≥ x − 1

3x + y ≤ −5

Ï

Ì

Ó

ÔÔÔÔÔÔÔÔÔÔ

a c

b d

15. Mr. Frankel bought 9 tickets to a puppet show and spent $57. He bought a combination of child tickets for $5 each and adult tickets for $8 each. Which system of equations below will determine the number of adult tickets, a, and child tickets, c, he bought?

aa + c = 513

a + c = 9

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Ó

ÔÔÔÔÔÔÔÔÔÔ

b5a + 5c = 66

a + c = 9

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Ì

Ó

ÔÔÔÔÔÔÔÔÔÔ

c8a + 5c = 57

a + c = 9

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Ó

ÔÔÔÔÔÔÔÔÔÔ

da = c − 9

8a + 5c = 57

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Ó

ÔÔÔÔÔÔÔÔÔÔ

16. Solve the system.

x − 4y − 3z = 13

4x − 5y + 5z = −28

5x + 3y − 4z = 45

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Ì

Ó

ÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔ

a value z is -3 b value of y is 2 c value of x is 4 d none of these

17. Find the determinant of A. A = −2 3

6 5

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇˙̇˙̇˙̇˙̇˙̇

a 28 b -28 c -19 d 8

5

18. Find the inverse of A. A = 5 7

−2 −2

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇˙̇˙̇˙̇˙̇˙̇

a−2 −7

2 5

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇˙̇˙̇˙̇˙̇˙̇

b−2 7

−2 5

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇˙̇˙̇˙̇˙̇˙̇

c−1 / 2 −7 / 4

1 / 2 5 / 4

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇˙̇˙̇˙̇˙̇˙̇

d5 / 4 −7 / 4

1 / 2 −1 / 2

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇˙̇˙̇˙̇˙̇˙̇

19. Perform the matrix operations.

0 9

−4 7

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇˙̇˙̇˙̇˙̇˙̇

⋅

4 6

3 −2

4 8

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇˙̇˙̇˙̇˙̇˙̇˙̇˙̇˙

a

0

54

−16

−18

0

56

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇˙̇˙̇˙̇˙̇˙̇˙̇˙̇˙

b0 −18

−12 −14

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇˙̇˙̇˙̇˙̇˙̇

c−16 42 8

0 27 72

È

Î

ÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇˙̇˙̇˙̇˙̇˙

d not possible

20. Perform the matrix operation.

3 −2 3

4 5

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇˙̇˙̇˙̇˙̇˙̇

+ 4 6

0 −1

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇˙̇˙̇˙̇˙̇˙̇

a2 9

4 4

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇˙̇˙̇˙̇˙̇˙̇

b−2 15

12 14

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇˙̇˙̇˙̇˙̇˙̇

c not possible d−10 3

12 16

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇˙̇˙̇˙̇˙̇˙̇

21. Find all of the zeroes of the function. f(x) = 5(−4x + 4)(4x − 7)(−7x + 8)

a −5,−354

,−407

b 1,74

,87

c −1,−74

,−87

d 5,354

,407

22. How many solutions will the function f(x) = 2x4 + 3x3 − 3x2 + 3x − 5 have?a 2 b 3 c 4 d not enough info

23. Use completing the square to find c so that x2 − 16x + c is a perfect square trinomial.a -64 b -8 c -32 d 64

24. What are the real zeroes of f(x) = x3 − 8x2 − 23x + 30a -3, -1, 10 b 3, 1, 10 c -3, 1, -10 d -3, 1, 10

25. Which of the following is 48 in simplest radical form?

a 6 8 b 4 3 c 16 3 d 24

6

26. Graph: y = x2 + 3x − 2a c

b d

27. Write the quadratic equation in standard form. y = (x − 2)2 − 3

a y = −x2 + 4x − 7 b y = x2 − 4x + 1 c y = −x2 − 4x − 7 d y = x2 + 4x + 1

28. Factor the expression: 36y2 − 49a (36y + 1)(y − 49) b (6y + 7)(6y − 7) c (6y − 7)(6y − 7) d (6y + 7)(6y + 7)

29. Solve: x2 + 6x = 0a 0, 6 b -6, 6 c -6, 5 d 0, -6

30. What are the x-intercepts of the graph y = x2 + 16x + 63a 3, 21 b -9, -7 c -21, -3 d 9, 7

31. Solve: 2x2 − 11 = 7a 4, -4 b 3, -3 c 2, -2 d no real sol.

32. Find the roots. f(x) = x2 + 6x + 13a 3 ± 4i b −3 ± 4i c 3 ± 2i d −3 ± 2i

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33. Solve by square roots: (6x − 3)2 = 66

a3 ± 66

6b

3 ± 6612

c−3 ± 66

6d

−3 ± 6612

34. Find the zeroes of the function using quadratic formula.. f(x) = 2x2 + 7x + 1

a7 ± 41

4b

−7 ± 574

c7 ± 57

4d

−7 ± 414

35. Solve. x3 − x2 = 0a 1, -1 b 0, 1 c 1, -2 d 0, -1

36. Solve. 2x2 + x = −3

a1 ± i 25

4b

−1 ± i 254

c1 ± i 23

4d

−1 ± i 234

37. Evaluate f(5) if f(x) = 8x3 + 5x2 + 9x − 3a f(5) = 212 b f(5) = 1167 c f(5) = 1157 d f(5) = 1170

38. Simplify: (4m5 + 4m4 − 2) + (5m5 + 5m − 3)

a 9m5 + 9m4 − 5 c 9m5 + 4m4 + 5m − 5

b −m5 + 4m4 − 5m + 1 d −m5 + 4m4 + 5m + 1

39. Simplify. (−4x2 − 3x − 3) − (x2 − 5x − 8)

a −5x2 − 8x − 11 b −5x2 + 2x − 11 c −5x2 + 2x + 5 d −5x2 − 2x + 5

40. Estimate the real zeroes of the function graphed below.

a 2 b -3, -1, 1 c 2, -3, -1, 1 d -1, 1, 3

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41. Simplify. (x − 3)(x2 + 3x − 6)

a x3 − 6x2 − 15x + 18 b x3 − 3x + 18 c x3 + 3x2 + 18 d x3 − 15x + 18

42. Factor completely. 4x3 + 8x2 + 16xa 4x(x + 2)(x + 4) b 4(x3 + 2x2 + 4x) c 4x(x2 + 2x + 4) d x(4x2 + 8x + 16)

43. Factor. 125y3 − 64

a (5y − 4)3c (5y − 4)(25y2 + 20y + 16)

b (5y − 4)(5y2 + 20y + 16) d (5y − 4)(25y2 − 20y + 16)

44. Simplify completely: 16x2 y2

28x7y

a8x5 y14

c8y

14x5

b4y2

7x5 yd

4y

7x5

45. Simplify completely: 2x3yÊ

ËÁÁÁ

ˆ

¯˜̃˜

3

a 2x27y3c 6x9y3

b 8x9y3d 8x27y3

ID: A

1

DO NOT mark on this test. Fill in the appropriate answers on your scantron.Answer Section

1. ANS: A PTS: 1 2. ANS: B PTS: 1 3. ANS: B PTS: 1 4. ANS: A PTS: 1 5. ANS: A PTS: 1 6. ANS: B PTS: 1 7. ANS: A PTS: 1 8. ANS: A PTS: 1 9. ANS: D PTS: 1 10. ANS: B PTS: 1 11. ANS: B PTS: 1 12. ANS: C PTS: 1 13. ANS: B PTS: 1 14. ANS: A PTS: 1 15. ANS: C PTS: 1 16. ANS: D PTS: 1 17. ANS: B PTS: 1 18. ANS: C PTS: 1 19. ANS: D PTS: 1 20. ANS: B PTS: 1 21. ANS: B PTS: 1 22. ANS: C PTS: 1 23. ANS: D PTS: 1 24. ANS: A PTS: 1 25. ANS: B PTS: 1 26. ANS: B PTS: 1 27. ANS: B PTS: 1 28. ANS: B PTS: 1 29. ANS: D PTS: 1 30. ANS: B PTS: 1 31. ANS: B PTS: 1 32. ANS: A PTS: 1 33. ANS: C PTS: 1 34. ANS: A PTS: 1 35. ANS: B PTS: 1 36. ANS: B PTS: 1 37. ANS: B PTS: 1 38. ANS: C PTS: 1 39. ANS: C PTS: 1 40. ANS: D PTS: 1 41. ANS: D PTS: 1 42. ANS: C PTS: 1

ID: A

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43. ANS: C PTS: 1 44. ANS: D PTS: 1 45. ANS: B PTS: 1