Free Printable Sem I Final Practice

1.

Calculate the length of Side AB.

a)

15

b)

20

c)

25

d)

30

2.

Calculate the length of side AB.

a)

15

b)

9

c)

20

d)

13

3.

Which law would you use to find angle A?

a)

Law of Cosines

b)

Law of right triangles

c)

Law of Sines

d)

Pythagorean Theorem

4.

Which Law would you use to solve for Angle B?

a)

Law of the Jungle

b)

Law of Cosines

c)

Law of the Gravity

d)

Law of Sines

5.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

6.

Which of the following formulas shows the Law of Cosines?

a)

c² = a² + b² - 4ac + cosA

b)

c² = a² - b² - 2abcosC

c)

c² = a² + b² - 2abcosC

d)

(cos A)/a = (cos B)/b

7.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

8.

David is building a triangular garden and needs to determine the measure of angle A to ensure the garden's design is accurate. What is the measure of angle A?

a)

50 degrees

b)

60 degrees

c)

78 degrees

d)

74 degrees

9.

Based on the given information determine the number of unique triangles that may exist.
J = 98°, j = 29, p = 6

a)

1 Triangle

b)

2 Triangles

c)

No Triangles

d)

3 Triangles

10.

Based on the given information determine the number of unique triangles that may exist.
A= 37°, a=8, b=14

a)

1 Triangle

b)

2 Triangles

c)

No Triangles

d)

3 Triangles

11.

Based on the given information determine the number of unique triangles that may exist.
B= 70°, b=85, c=88

a)

1 Triangle

b)

2 Triangles

c)

No Triangles

d)

3 Triangles

12.

In triangle ABC, find side a if:

B=70 degrees A=40 degrees and c=11

a)

11

b)

7.5

c)

70

d)

8

13.

In ΔABC, B = 45^o, a = 28 and b = 27. Find all possible values for Angle A

a)

47.2° only

b)

47.2° and 132.8°

c)

47.2° and 87.8°

d)

47.2° and 137.2°

14.

Parker needs to determine the distance from Point X to Point Y across a river. He identifies Point Z that is 920 feet from point X and 200 feet from Point Y. He measures the angle at Point Z to be 75 degrees. Calculate the distance from point X to point Y.

a)

950.34

b)

890.45

c)

915.67

d)

920.12

15.

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, and from Jamie to the bird is 63. How far away is the bird from Amanda?

a)

25.23

b)

23.19

c)

22.15

d)

20.85

16.

Clint is building a wooden swing set for his children. Each supporting end of the swing set is to be an A-frame constructed with two 10 foot long 4-by-4s joined at a 45 degree angle. To prevent the swing set form tipping over, Clint wants to secure the base of each A-frame to concrete footings. How far apart should the footings for each A-frame be?

a)

5.461 feet

b)

9.743 feet

c)

6 feet

d)

7.65 feet

17.

Find the factors of 4x²-16x-9

a)

(2x-9)(2x+1)

b)

(2x+9)(2x-1)

c)

(4x-1)(x+9)

d)

(x+1)(4x-9)

18.

Find the factors of 4x²-16x-9

a)

(2x-9)(2x+1)

b)

(2x+9)(2x-1)

c)

(4x-1)(x+9)

d)

(x+1)(4x-9)

19.

Find the measure of the angle marked in red.

a)

-230°

b)

130°

c)

230°

d)

50°

20.

Convert 100⁰ to radians

a)

5π/9

b)

π/2

c)

5π/8

d)

5π/6

21.

What is 11π/6 radians in degrees?

a)

30

b)

330

c)

360

d)

300

22.

How many radians does a circle have?

a)

360 degrees

b)

2pi radians

c)

pi radians

d)

^{2 radians}

23.

Find a coterminal angle to 5°.

a)

365°

b)

255°

c)

-220°

d)

-365°

24.

Find the measure of the angle marked in red.

a)

-200°

b)

200

c)

-110°

d)

110°

25.

Find the reference angle.

a)

-65°

b)

125°

c)

-55°

d)

55°

26.

Find the reference angle.

a)

-15°

b)

15°

c)

-165°

d)

165°

27.

Find sinA

a)

32/40

b)

32/24

c)

24/40

d)

24/32

28.

a)

A

b)

B

c)

C

d)

D

29.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

30.

What does it mean to find the inverse of a function?

a)

the x's and y's are switched

b)

the x's and y's are divided by 2

c)

the x's and y's are made negative

d)

the x's and y's are the same

31.

.
If the blue is f(x)=x^2,then the red must be

a)

g(x)=x²-5

b)

g(x)=x²+5

c)

g(x)=(x-5)²

d)

g(x)=(x+5)²

32.

What are the following transformations?
- f(x+2)

a)

reflection over the y axis and 2 units to the right

b)

reflection over the x axis and 2 units right

c)

reflection over the y axis and 2 units left

d)

reflection over the x axis and 2 units left

33.

What are the transformations of this functions compared to the parent function y = √(x)?

a)

Shifted right 5, shifted down 2, and reflected over the x-axis

b)

Reflected over the x-axis, vertical stretch, and shifted right 5

c)

Reflected over the x-axis, vertical stretch, and shifted left 5

d)

Shifted right 5, shifted down 2

34.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

35.

If f(x) = x² and g(x) = 3x - 1, find f(g(x))

a)

9x² - 6x + 1

b)

3x - 1

c)

3x² - 1

d)

9x² - 1

36.

Write the domain of $f\left(x\right)=\frac{x}{x^2-16}$

a)

$\left\{x\ne4\right\}$

b)

$\left\{x>8\right\}$

c)

$\left\{x\ne16\right\}$

d)

$\left\{x\ne-4,\ 4\right\}$

37.

Find the domain of $g\left(x\right)=\sqrt{2x-4}$

a)

$\left\{x>2\right\}$

b)

$\left\{x\ge2\right\}$

c)

$\left\{x\le2\right\}$

d)

$\left\{x\ne\sqrt[]{2}\right\}$

38.

$\frac{\sqrt{x-3}}{x+8}$ Choose the domain for which the function is defined.

a)

$x\ne3\ and\ x\le8$

b)

$x\ne3\ and\ x\ge8$

c)

$x\ne8\ and\ x\ge3$

d)

$x\ne-8\ and\ x\ge3$

39.

What are the domain restrictions $f\left(x\right)=\frac{3}{x^2+6x+5}$

a)

$x\ne-5,-1$

b)

$x\ne1,5$

c)

$x>5,\ x<1$

d)

$x<-5,\ x>-1$

40.

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

a)

(1, 4) and (4, 6)

b)

(-4, -1) and (-6, -4)

c)

(-1, -4) and (-4, -6)

d)

(4, 1) and (6, 4)

41.

Factor Completely: 3x² + 5x - 12

a)

(3x + 4)(x-3)

b)

(3x - 4)(x + 3)

c)

(3x + 3)(x -4)

d)

(3x - 3)(x + 4)

42.

What are all the possible rational roots of x³ - 4x² + 5x - 12?

a)

+-1, +-2, +-3, +-4, +-6, +-12

b)

+-1, +-2, +-3, +-4, +-6

c)

+-2, +-3, +-4, +-6, +-12

d)

+-1, +-2, +-4, +-6, +-12

43.

Find all the factors of x³ -3x² -4x +12 given that -2 is a zero.

a)

(x-2) (x+2) (x+3)

b)

(x-2) (x-2) (x+3)

c)

(x+2) (x+2) (x+3)

d)

(x-2) (x+2) (x-3)

44.

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

List the zeros for this function.

a)

x= -4, x=3, x= -2

b)

x= -4, x=3, x=2

c)

x= -4, x=-3, x=2

d)

x=4, x= -3, x= -2

45.

a)

The function has an Even degree

b)

The function has a Negative coefficient

c)

The function has an Odd degree

d)

The function has 3 real zeros

46.

a)

Positive Odd

b)

Positive Even

c)

Negative Odd

d)

Negative Even

47.

Which of the following could be the equation of this graph in factored form? (Careful-pay attention to multiplicity.)

a)

f(x) = (x-4)(x-1)²(x+2)(x+4)

b)

f(x) = (x-4)(x+1)²(x+2)(x+4)

c)

f(x) = (x-4)(x-1)²(x-2)(x+4)

d)

f(x) = (x+4)(x+1)²(x-2)(x-4)

48.

What does multiplicity of a zero mean?

a)

Look at the number of terms

b)

How many times the zero repeats

c)

Find the sum of all the coefficients

d)

Ratio your x and y

49.

What is the end-behavior of the function
y = -x³ + 6x² + 7x

a)

as x-> -∞ f(x) -> ∞
as x-> ∞ f(x) -> -∞

b)

as x-> -∞ f(x) -> ∞
as x-> ∞ f(x) -> ∞

c)

as x->-∞ f(x) -> -∞
as x-> ∞ f(x) -> ∞

d)

as x-> -∞ f(x) -> -∞
as x-> ∞ f(x) -> -∞

50.

What is the end-behavior of the function
y = x⁶ - 7x⁵ + 7x - 9

a)

as x-> -∞ f(x) -> ∞
as x-> ∞ f(x) -> -∞

b)

as x-> -∞ f(x) -> ∞
as x-> ∞ f(x) -> ∞

c)

as x->-∞ f(x) -> -∞
as x-> ∞ f(x) -> ∞

d)

as x-> -∞ f(x) -> -∞
as x-> ∞ f(x) -> -∞

51.

Which of the following could be the factored form for the equation representing the graph shown?

a)

(x+3)(x-2)(x-5)

b)

(x-5)²(x-2)(x+3)

c)

(x-3)(x+2)(x+5)²

d)

none of these

52.

What is the vertical asymptote?

a)

x=-8

b)

x=-5

c)

x=8

d)

x=5

53.

Match the graph to the correct rational equation below.

a)

f(x)=-8/(x+2) + 2

b)

f(x)=8/(x-2) + 2

c)

f(x)=1/(x+2) + 2

d)

f(x)=-1/(x+2) - 2

54.

Describe the transformations of the function.

a)

Shift up by 2 units

Reflected over the x-axis

b)

Shift down by 2 units

Reflected over the y-axis

c)

Shift up by 2 units

Reflected over the y-axis

d)

Shift left by 2 units

Reflected over the x-axis

55.

What is the equation of the rational function graphed?

a)

$f\left(x\right)=\frac{1}{x-2}$

b)

$f\left(x\right)=\frac{1}{x+2}$

c)

$f\left(x\right)=\frac{1}{x}+2$

d)

$f\left(x\right)=\frac{1}{x}-2$

56.

a)

$y\ =\ \frac{3}{x-2}$

b)

$y\ =\ \frac{3}{x-2}-4$

c)

$y\ =\ \frac{3}{x+2}-4$

d)

$y\ =\ \frac{3}{x+4}-2$

57.

Suppose you translate the graph of $y=\frac{3}{x}$ so that the new graph has asymptotes at x= -5 and y=14. What is the equation for the new graph?

a)

$y=\frac{3}{x-5}-14$

b)

$y=\frac{3}{x+5}+14$

c)

$y=\frac{3}{x-14}-5$

d)

$y=\frac{3}{x+14}+5$

58.

Select ALL the information that applies to the given rational function.

a)

V.A. at x = -3 and x = 1

b)

Hole at (1, 0)

c)

H.A. at y = 2

d)

x-intercepts at (3,0) and (1, 0)

59.

Select ALL the information that applies to the given rational function.

a)

V.A. at x = 1

b)

No Holes

c)

H.A. at y = 0

d)

y-intercept at (0, 1/2)

60.

Select ALL the information that applies to the given rational function.

a)

V.A. at x = 2

b)

No Holes

c)

H.A. at y = -1/3

d)

y-intercepts at (0, 1/2)

61.

Graph the function.

a)

b)

c)

d)

62.

Graph the function.

a)

b)

c)

d)

63.

Graph the function.

a)

b)

c)

d)

64.

Solve for x: $\frac{5}{3}-\frac{2}{x}=\frac{8}{x}$

a)

$2$

b)

$\frac{18}{5}$

c)

$\frac{26}{5}$

d)

$6$

65.

Solve: $\frac{3}{x-5}-\frac{20}{x^2-25}=\frac{2}{x+5}$

a)

$x=-5$

b)

$x=5$

c)

$\frac{5}{\left(x+5\right)\left(x-5\right)}$

d)

No Solution

66.

Solve!

a)

x = 2

b)

x = -2

c)

x = 6

d)

x = 3

67.

a)

7

b)

-3

c)

12

d)

14

68.

Solve

a)

k = 1, k = 5

b)

k = −1, k = 5

c)

k = −1, k = −3

d)

k = 1

Sem I Final Practice

Total questions: 68

Worksheet time: 5hrs 53mins

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