Algebra 2/Trig First Semester Final Exam ____________________________________________________________________________
1
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
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14. Determine the solution to the system.y ≥ x − 1
3x + y ≤ −5
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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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b5a + 5c = 66
a + c = 9
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c8a + 5c = 57
a + c = 9
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da = c − 9
8a + 5c = 57
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16. Solve the system.
x − 4y − 3z = 13
4x − 5y + 5z = −28
5x + 3y − 4z = 45
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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
7
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