Free Printable Semester #2 Final (Study Guide) MA

1.

Find the common difference: 1, 201, 401, 601, ...

a)

d = 100

b)

d = 101

c)

d = 200

d)

d = 201

2.

Find the next three terms in the arithmetic sequence: -3, -8, -13, -18, ...

a)

-20, -24, -28

b)

-21, -25, -29

c)

-23, -28, -33

d)

-24, -29, -32

3.

Find a₂₆ in the arithmetic sequence: -15, -35, -55, -75, ...

a)

-515

b)

-490

c)

-535

d)

460

4.

What are the next 3 terms in the following geometric sequence:

512, 256, 128, ___, ___, ___, ...

a)

1024, 2048, 4096

b)

32, 8, 2

c)

64, 32, 16

d)

92, 66, 38

5.

Write the explicit formula for the geometric sequence.

a)

a_n = 4(3)^n-1

b)

a_n = 3(4)^n-1

c)

a_n = -4(3)^n-1

d)

a_n = 3(-4)^n-1

6.

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

a)

20, 100, 500, 2500

b)

5, 20, 80, 320

c)

4, 20, 100, 500

d)

4, 9, 14, 19

7.

A geometric sequence has a common ration(r) of 3 and the 8th term (a₈) is 13,122. What is the first term of the sequence (a₁)?

a)

3

b)

6

c)

18

d)

2

8.

Evaluate the arithmetic series described:
2 + (-2) + (-6) + (-10)..., S₁₀

a)

-160

b)

-328

c)

-320

d)

-336

9.

Evaluate the arithmetic series described:
a₁ = 12, a_n = 64, Find S₁₄

a)

1082

b)

532

c)

541

d)

1064

10.

Evaluate the geometric series below:
a₁ = -2, a_n = -1458, r = 3

a)

-2186

b)

-2408

c)

1

d)

-2703

11.

Evaluate the geometric series below:
4 - 8 - 16 - 32..., S₇

a)

195

b)

172

c)

202

d)

145

12.

What type of function is f(x)=2(1/7)^x ?

a)

Exponential Growth

b)

Linear

c)

Exponential Decay

d)

None of the Abovee

13.

What type of function is y = 7(5/4)^x?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None of the above

14.

The amount of ants in a colony, f, that is decaying can be modeled by f(x) = 800(.87)^x, where x is the number of days since the decay started. By what percentage is the colony decaying?

a)

87%

b)

13%

c)

800%

d)

8.7%

15.

What is the increasing interval on the function shown?

a)

$\left(-\infty,\ 1\right)$

b)

$\left(-\infty,\ 2\right)$

c)

$\left(2,\ \infty\right)$

d)

$\left(1,\ \infty\right)$

16.

What is the decreasing interval on the function shown?

a)

$\left(-\infty,\ 1\right)$

b)

$\left(-\infty,\ 2\right)$

c)

$\left(2,\ \infty\right)$

d)

$\left(1,\ \infty\right)$

17.

Describe the end behavior of the graph.

a)

x → -∞, f(x) → ∞ and x→∞, f(x) →⁻∞

b)

x → -∞, f(x) → ∞ and x→∞, f(x) →∞

c)

x → -∞, f(x) → ∞ and x→∞, f(x) → 0

d)

x → -∞,f(x) → -∞and x→ ∞, f(x) → ∞

18.

How has the function $7\left(3\right)^x-5$ been transformed from the parent function $7\left(3\right)^x$ ?

a)

Shifted up 5

b)

Shifted down 5

c)

Reflection over the x-axis

d)

Reflection over the y-axis

19.

How has the function $-5\left(3\right)^x$ been transformed from the parent function $5\left(3\right)^x$ ?

a)

Shifted up 5

b)

Shifted down 5

c)

Reflection over the x-axis

d)

Reflection over the y-axis

20.

What is the y-intercept of $g\left(x\right)=0.9\left(2\right)^x$ ?

a)

$\infty$

b)

2

c)

0.9

d)

1

21.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

22.

What does the a in y=a(1+r)^x represent?

a)

Time

b)

Rate

c)

Slope

d)

Initial Amount

23.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

24.

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

a)

$23,219.72

b)

$136.72

c)

$51,710.94

d)

$16,710.94

25.

Rewrite log₂8 = 3 in exponential form

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

26.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

27.

log ₃9 =

a)

1/2

b)

2

c)

1/3

d)

3

28.

log (1/10,000)

a)

1/4

b)

-4

c)

1000

d)

-1000

29.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

30.

Solve the log by using change of base )

log₄32

a)

8

b)

5/2

c)

2/5

d)

3/2

31.

Solve ln e

a)

10

b)

1

c)

5

d)

3

32.

Solve ln 1

a)

10

b)

4

c)

0

d)

1

33.

Write log_b(xy) as two logs

a)

log_bx+log_by

b)

log_bx-log_by

c)

log_bx*log_by

d)

log_bx/log_by

34.

Write log_b(x/y) as two logs

a)

log_bx-log_by

b)

log_bx+log_by

c)

log_bx*log_by

d)

log_bx/log_by

35.

Rewrite log_b(xⁿ)

a)

nlog_bx

b)

(log_bx)ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

36.

Rewrite as a single logarithm:

\log3\ +\ \log7

a)

log 10

b)

log 21

c)

log 3/7

d)

log 3/log 7

37.

Rewrite as a single logarithm:

\log_260\ -\ \log_210

a)

$\log_26$

b)

$\log_250$

c)

$\frac{\log_260}{\log_210}$

d)

$\log_270$

38.

BONUS: Expand log₆(5x³/y).

a)

log₆5x³-log₆y

b)

log₆5+log₆x³-log₆y

c)

log₆5+3log₆x-log₆y

39.

Solve 8 = 2^5x+7

a)

⅘

b)

¼

c)

-⅘

d)

-¼

40.

Solve 3³ = 3^{4x + 2}

a)

¼

b)

-¼

c)

½

d)

-½

41.

Sovle for x:
5^{-3x - 1} = 25

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

42.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

43.

log₄(3x-1)=log₄(2x+3)

a)

4

b)

3

c)

1

d)

8

44.

570° is found in which quadrant?

a)

Quadrant 1

b)

Quadrant 2

c)

Quadrant 3

d)

Quadrant 4

45.

Find a coterminal angle to 5°.

a)

365°

b)

255°

c)

-220°

d)

-365°

46.

What are the negative and positive coterminal angles of 240°?

a)

540°, -120°

b)

600°, -120°

c)

425°, -240°

d)

120°, -135°

47.

Convert π/3 radians to degrees

a)

60⁰

b)

30⁰

c)

90⁰

d)

45⁰

48.

What is 90 degrees in radians?

a)

π/4

b)

π/2

c)

π/6

d)

3π/2

49.

Which is a coterminal angle to the angle shown?

a)

25

b)

-205

c)

335

d)

516

50.

Solve for DE

a)

36.5

b)

18.8

c)

8.5

d)

7.9

51.

Find m∠N

a)

14

b)

65

c)

76

d)

53

52.

A 16 foot ladder leans against a building. If the angle the ladder makes with the ground is 68°, how high up the building does the ladder reach?

a)

39.6

b)

6.0

c)

14.8

d)

13.6

53.

Find m<B

a)

A

b)

B

c)

C

d)

D

54.

What is the height of the tree? Round the the nearest foot.

a)

38 ft

b)

63 ft

c)

20 ft

d)

98 ft

55.

Solve for the missing angle.

a)

50.5 degrees

b)

12.7 degrees

c)

36.9 degrees

d)

72.2 degrees

56.

What is the reference angle for -30°?

a)

150°

b)

30°

c)

80°

d)

60°

57.

What is the reference angle for 2pi/3

a)

pi/4

b)

7pi/6

c)

4pi/3

d)

pi/3

58.

$\tan\ 300\degree$ = ______

a)

$\frac{1}{\sqrt{3}}\ or\ \frac{\sqrt{3}}{3}$

b)

$-\ \frac{1}{\sqrt{3}}\ or\ \ -\frac{\sqrt{3}}{3}$

c)

$\sqrt{3}$

d)

$-\sqrt{3}$

59.

If $\sin\theta\ =\frac{3}{5}$ and $\frac{\pi}{2}\le\theta\le\frac{3\pi}{2}$ , find $\cos\theta$

a)

$\frac{4}{5}$

b)

$-\frac{4}{5}$

c)

$\frac{3}{4}$

d)

$-\frac{3}{4}$

60.

\sin225\degree

=_______

a)

$\frac{1}{2}$

b)

$-\frac{1}{2}$

c)

$\frac{1}{\sqrt{2}}$

d)

$-\frac{1}{\sqrt{2}}$

61.

$\sin\ \frac{5\pi}{3}$ = _______

a)

$\frac{\sqrt{3}}{2}$

b)

$-\frac{\sqrt{3}}{2}$

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

62.

$\cos\ \frac{5\pi}{6}$ = _______

a)

$\frac{\sqrt{3}}{2}$

b)

$-\frac{\sqrt{3}}{2}$

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

63.

$\tan\ \frac{7\pi}{6}$ = _____

a)

$\frac{1}{\sqrt{3}}$

b)

$-\frac{1}{\sqrt{3}}$

c)

$\sqrt{3}$

d)

$-\sqrt{3}$

64.

Use the Law of Sines to solve for BC

a)

33

b)

24

c)

12

d)

29

65.

In ΔABC, m<C = 53, m<B = 44 and AC = 7. Find AB to nearest tenth.

a)

3.9

b)

6.1

c)

6.8

d)

8.0

66.

Use Law of Cosines to find angle T

a)

62.2°

b)

53.1°

c)

59.5°

d)

64.7°

67.

Use Law of Cosines to find angle T

a)

62.2°

b)

53.1°

c)

59.5°

d)

64.7°

68.

Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them. The angle of elevation from Amanda to the bird is 55 degrees, and from Jamie to the bird is 63 degrees. How far away, to 2 decimal places, is the bird from Amanda?

a)

25.23 ft

b)

23.19 ft

c)

22.15 ft

d)

20.85 ft

69.

a)

y = sin x

b)

y = - sin x

c)

y = cos x

d)

y = - cos x

70.

a)

y = sin x

b)

y = - sin x

c)

y = cos x

d)

y = - cos x

71.

what is the amplitude of

y = -3sin (7x) -2

a)

7

b)

-2

c)

3

d)

-3

72.

What is the period of
y= 4 cos (5x)

a)

2π/5

b)

π

c)

5

d)

5π

73.

If $\sin\theta=\frac{4}{5}$ , find $\csc\theta$ .

a)

$\frac{9}{5}$

b)

$\frac{5}{4}$

c)

$\frac{1}{5}$

d)

$\frac{1}{4}$

74.

If $\tan\theta=\frac{5}{3}$ , find $\sec\theta$ .

a)

$0.65$

b)

$1.63$

c)

$1.94$

d)

$0.94$

75.

If $\cos\theta=\frac{3}{5}$ , find $\csc\theta$ .

a)

$1.58$

b)

$0.63$

c)

$0.80$

d)

$1.25$

Semester #2 Final (Study Guide) MA

Total questions: 75

Worksheet time: 5hrs 41mins

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