Free Printable MA Sem 2 Final Review

1.

State the number of possible triangles that can be formed using the given measurements.
$A=36\degree,\ c=30\ km,\ a=26\ km$

a)

Two Triangles

b)

One Triangle

c)

None

2.

Find c

a)

10

b)

8

c)

6.1

d)

4.9

3.

State the number of possible triangles that can be formed using the given measurements.
$B=139\degree,\ a=12\ cm,\ b=35\ cm$

a)

Two Triangles

b)

One Triangle

c)

None

4.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

5.

Solve the Triangle(s): $a=14$ , $b=6$ , $A=27\degree$

a)

no triangle possible

b)

B = 11.219^o, C = 141.781^o, c = 19.078

c)

B = 38.219^o, C = 114.781^o, c = 27.998

d)

B = 11.219^o, C = 141.781^o, c = 19.078

OR

B = 38.219^o, C = 114.781^o, c = 27.998

6.

What is the measure of angle A?

a)

$58\degree$ and $122\degree$

b)

$61\degree$ and $119\degree$

c)

$78\degree$ and $102\degree$

d)

$74\degree$ and $106\degree$

7.

What is the measure of angle A?

a)

58 degrees

b)

61 degrees

c)

78 degrees

d)

74 degrees

8.

Find the Area of the Triangle.

a)

13 in²

b)

7 in²

c)

5.2 in²

d)

9.6 in²

9.

Find the area to the nearest whole number (no units needed)

(a)

10.

Any vector with initial point (x₁, y₁) and terminal point (x₂, y₂) can be written in component form as:

a)

b)

c)

d)

11.

Write in component form.

a)

<-8, -2>

b)

<8, 2>

c)

<2, 8>

d)

<-2, -8>

12.

Find the magnitude of the vector

with initial point (-8, 7) and

terminal point (2, -5).

Round to the nearest tenth.

(a)

13.

Using scalar multiplication, find

5\overrightarrow{u}

if

\overrightarrow{u}=<2,\ 4>

a)

<7, 9>

b)

<10, 20>

c)

<-3, -1>

14.

Add

$<5,\ -2>+<-4,\ 8>$

a)

$<-9,\ 10>$

b)

$<3,\ 4>$

c)

$<1,\ 6>$

15.

Given u = <3, 7> and v =<-5, 4>, find 2u - 3v

a)

<-11,26>

b)

<8,3>

c)

<21,2>

d)

23

16.

Given vector < 5, 12>, find the unit vector.

Select 2 answers, one exact answer and one decimal answer.

a)

$<\frac{1}{5},\ \frac{1}{12}>$

b)

$<\frac{5}{13},\ \frac{12}{13}>$

c)

$<0.2,\ 0.08>$

d)

$<0.38,\ 0.92>$

17.

Write the vector u $=<-2,5>$ in component form.

a)

-2j+5i

b)

-2+5j

c)

-2i+5j

d)

-2i+0, 0+5j

18.

Find the direction angle for the vector <-8, 3>

a)

159.44°

b)

200.56°

c)

110.56°

d)

249.44°

19.

Determine the direction and magnitude of the vector 〈7,18〉

a)

Direction 21.3°
Magnitude 19.3

b)

Direction 68.7°
Magnitude 19.3

c)

Direction 21.3°
Magnitude 373

d)

Direction 68.7°
Magnitude 373

20.

Solve the system of equations using any method:
y = 4x+1
3x + 2y = 13

a)

(1, 5)

b)

(5, 1)

c)

(0.25, 2)

d)

∅

21.

Solve the following system using any method:
3x + 2y = 16
7x + y = 19

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

22.

Solve the system using any method:
8x + 4y = 12
y = -2x + 3

a)

(0,3)

b)

(3,0)

c)

No solution

d)

Infinitely many solutions

23.

Add

a)

11 8
-4 2

b)

3 2
-6 -6

c)

-3 2
-4 -6

d)

10 8
-6 2

24.

Calculate the determinant

a)

0

b)

none

c)

-32

d)

-8

25.

Multiply

a)

1 2
6 -8

b)

-3 -5
-5 -11

c)

-2 8
-6 -12

d)

2 -3
5 -2

26.

Find A−B

a)

-3 1
7 -1

b)

1 0
1 -4

c)

-4 0
6 -1

d)

not possible because rows do not match columns

27.

Calculate the determinant

a)

0

b)

-15

c)

-70

d)

10

28.

Can the operation be performed?

a)

Yes

b)

No

c)

Sometimes

d)

only your teacher knows

29.

Calculate the determinant

a)

13

b)

-3

c)

-5

d)

13

30.

On your paper show the setup for solving the system using Cramer's rule. Solve system by using Cramer's Rule. Answers are written in the following form (x,y)

$2x+3y=15$
$x-3y=3$

a)

$\left(1,6\right)$

b)

$\left(6,-1\right)$

c)

$\left(6,1\right)$

d)

$\left(-1,6\right)$

31.

On your paper show the setup for solving using Cramer's rule. Solve the system of equations using Cramer's Rule.

a)

$\left(-3,-1\right)$

b)

$\left(-6,\ 1\right)$

c)

$\left(-6,-3\right)$

d)

$\left(-3,-6\right)$

32.

Using determinants, find the area of the triangle whose vertices are (0, 0), (4, 3) and (8, 0).

a)

12

b)

21

c)

24

d)

NONE OF THE ABOVE

33.

Jeffrey wrote a matrix to represent his system of equations. What was his mistake

a)

The z's are not aligned correctly

b)

There should be a one in the top row for zero

c)

There should be a zero in the second column of the third representing the y

d)

Nothing. This is correct.

34.

Which row command is an appropriate next step?

a)

7R2 + R3 -> R3

b)

-7R1 + R3 -> R3

c)

7R3 -> R3

d)

-7R2 + R3 -> R3

35.

What is an appropriate first row command to solve this by Gaussian Elimination?

a)

2R2 + R2 -> R2

b)

-2R1 + R2 -> R2

c)

R3 +R2 --> R3

d)

2R1 + R2 --> R2

36.

Evaluate: $\sum_{n=1}^{25}9n-19$

a)

2450

b)

4888

c)

2444

d)

4900

37.

15, -85, -185, -285, ...

Find a₃₄

a)

-3285

b)

-3585

c)

-3185

d)

-3385

38.

Find the explicit rule for the sequence:

-15, -6, 3, 12, ...

a)

a_n = -15 + 9n

b)

a_n = -24 + 9n

c)

a_n = -7 + 9n

d)

a_n = -6 + 9n

39.

Evaluate.

a)

5461

b)

800

c)

4095

d)

6241

40.

Evaluate

a)

105

b)

81

c)

100

d)

106

41.

Evaluate, if it exists. $\sum_{n=1}^{\infty}8\left(\frac{1}{5}\right)^{n-1}$

a)

8

b)

8/5

c)

10

d)

Does not exist

42.

Evaluate, if it exists:

1 + 1/5 + 1/25 + ...

a)

5/4

b)

9/5

c)

5/6

d)

65/27

43.

Choose the right Pascal's triangle

a)

b)

c)

d)

44.

Expand: $\left(a-b\right)^5$ using Pascal's Triangle

a)

$a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5$

b)

$a^5-5a^4b+10a^3b^2-10a^2b^3+5ab^4-b^5$

c)

$a^5-5a^4b+10a^2b^3-10a^3b^2+5ab^4-b^5$

d)

$a^5-5a^4b-10a^3b^2-10a^2b^3-5ab^4-b^5$

45.

Use the binomial theorem to expand $\left(4-2z\right)^3$

a)

$64-96z+48z^2+8z^3$

b)

$64-96z+48z^2-8z^3$

c)

$64+96z+48z^2+8z^3$

d)

$64-64z+144z^2-8z^3$

46.

Find the coefficient of the x³ term in (x-3)¹⁰

a)

3240x³

b)

3240

c)

262440x³

d)

262440

47.

What is the fifth term of the binomial expansion $\left(3x-4\right)^4$ .

a)

256

b)

-64

c)

42

d)

-12

48.

a)

Answer Choice A

b)

Answer Choice B

c)

Answer Choice C

d)

Answer Choice D

49.

How many outcomes are there with tossing a coin and rolling a dice?

a)

2

b)

6

c)

12

d)

24

50.

What is the probability of spinning green?

a)

0

b)

1/4

c)

1/2

d)

3/4

51.

The letters that form the word ALGEBRA are placed in a bowl. What is the probability of choosing a letter other than “A”?

a)

2/7

b)

5/49

c)

5/7

d)

10/49

52.

Ryan has 4 rap songs, 11 pop songs, 8 country songs, and 2 rock songs. What is the probability of Ryan picking a rock song or a pop song?

a)

2/25

b)

13/25

c)

11/25

d)

22/25

53.

If a dice is rolled 300 times, how many times would you predict a roll of a 1 or a 6?

a)

50

b)

100

c)

150

d)

75

54.

P(Red Card)?

a)

26/52, or 1/2

b)

1/4

c)

1/3

d)

1/5

55.

In a deck of 52 playing cards, what is the probability of getting a 5 of Hearts or 5 of Diamond?

a)

0

b)

$\frac{2}{13}$

c)

$\frac{1}{4}$

d)

$\frac{1}{26}$

56.

How many ways can a club select a president, vice president, and a secretary from a group of 5 people?

a)

12

b)

60

c)

15

57.

How many ways can you listen to 3 songs from a CD that has 12 selections?

a)

1320

b)

33

c)

36

58.

Which of the following is an example of combination?

a)

Form a passcode with 4 digits

b)

Students line up in a queue to assembly

c)

Choose 4 students in a class committee

d)

Choose the chairperson, secretary and treasurer in a club

59.

Choosing 3 toppings for your sundae out of a list of 15.

a)

Permutation

b)

Combination

c)

Neither

60.

How many ways can you make a 3-letter arrangements out of the letters in the word

TRAPEZOID.

a)

Permutation

b)

Combination

61.

How many outfits are possible with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

a)

15

b)

40

c)

80

d)

10

62.

How many 5-digit (numerical) passwords are possible for the school email system if the first digit cannot be 0?

a)

11,424,400

b)

10,967,424

c)

9000

d)

90,000

63.

How many distinct ways can the letters in the word OPPORTUNITIES be arranged?

a)

389,188,800

b)

2,028,377,600

c)

1,556,755,200

d)

16,227,020,800

64.

What is the center of the ellipse?

a)

(0, 0)

b)

(1, 5)

c)

(1, 0)

d)

(0, 1)

65.

What is the equation for the graph?

a)

b)

c)

d)

66.

Which way does the parabola open? (y - 4)²= -8(x+1)

a)

up

b)

down

c)

left

d)

right

67.

What is the value of p?
(y - 4)²= -8(x+1)

a)

-8

b)

2

c)

4

d)

1/2

68.

What is the focus of this parabola?

a)

(1/2,0)

b)

(0,1/2)

c)

(2,0)

d)

(0,2)

69.

Find the equation of the figure shown.

a)

(x-5)² + (y-3)²= 25

b)

(x+5)²/4 + (y+3)²/9= 1

c)

(x-5)²/2 + (y-3)²/3= 1

d)

(x-5)²/4 + (y-3)²/9= 1

70.

What is the focus of the following parabola?
(y + 5)²= -12 (x - 2)

a)

(2, - 5)

b)

( -5, 2)

c)

(1 , -5 )

d)

(-1, -5 )

71.

What are the foci of the ellipse?

a)

(-3,1 + √3) and (-3,1 - √3)

b)

(±√3,0)

c)

(0,1) and (-6,1)

d)

(-3 + √3,1) and (-3 - √3,1)

72.

Identify the center and the length of a and b.

a)

Center: (0, 0) a= 5, b = 2

b)

Center: (0, 0) a= 2, b = 5

c)

Center: (25, 4) a= 25, b = 4

d)

Center: (0, 0) a= 25, b = 4

e)

Center: (0, 0) a= 4, b = 25

73.

Determine the equation of the hyperbola.

a)

$\frac{x^2}{4}-\frac{y^2}{1}=1$

b)

$\frac{x^2}{2}-\frac{y^2}{1}=1$

c)

$\frac{x^2}{4}+y^2=1$

d)

$\frac{x^2}{2}+y^2=1$

74.

Identify the conic

a)

Parabola

b)

Circle

c)

Ellipse

d)

Hyperbola

75.

Identify the conic

a)

Parabola

b)

Circle

c)

Ellipse

d)

Hyperbola

76.

Identify the conic

a)

Parabola

b)

Circle

c)

Ellipse

d)

Hyperbola

77.

Identify the conic

a)

Parabola

b)

Circle

c)

Ellipse

d)

Hyperbola

78.

Identify the conic

a)

Vertical Hyperbola

b)

Vertical Ellipse

c)

Horizontal Hyperbola

d)

Horizontal Ellipse

79.

Which point represents (3, 3π/4)?

a)

F

b)

E

c)

B

d)

A

80.

Which point represents (-4, 4π/3)

a)

F

b)

E

c)

B

d)

A

81.

What are the polar coordinates of the point $\left(-1,\ \sqrt[]{3}\right)$ ?

a)

$\left(2,\ \frac{2\pi}{3}\right)$

b)

$\left(2,\ \frac{5\pi}{3}\right)$

c)

$\left(2\ ,\ \frac{5\pi}{6}\right)$

d)

$\left(2\ ,\ \frac{11\pi}{6}\right)$

82.

Convert the polar coordinates to rectangular form

a)

( -3, 3)

b)

(3, 3√3)

c)

(-3, 3√3)

d)

(3, -3√3)

83.

Give some other polar coordinate representations of the point, one with r > 0 and one with r < 0. Select all that apply.

a)

b)

c)

d)

e)

84.

Write the complex number in polar form

a)

√50 (cos π/2 + i sin π/2)

b)

50 (cos π/4 + i sin π/4)

c)

√50 (cos 5π/4 + i sin 5π/4)

d)

√50 (cos π/4 + i sin π/4)

85.

Express the point in polar form in rectangular form.
4 ( cos π /3 + i sin π /3)

a)

2 + 2√3 i

b)

2 + √3 i

c)

2 - 2√3 i

d)

-2 + 2√3 i

86.

Find the indicated power using DeMoivre's Theorem

a)

72 - 72√3i

b)

- 72√3 + 72i

c)

- 72√2 + 72√2i

d)

-72 + 72√3i

87.

Find

5(cos 2π /3 + i sin 2π /3)⋅2( cos π /3 + i sin π /3)

in trig form. Then express your final answer in rectangular form.

a)

-10

b)

10

c)

-10i

d)

10i

88.

Find the absolute value of the complex number. Also state what quadrant the point would land in.
2 + 3i

a)

√13, Quadrant 1

b)

√5, Quadrant 1

c)

√11, Quadrant 2

d)

√11, Quadrant 3

89.

Express the complex number in trigonometric (polar) form.

-2 + 5i

a)

$\sqrt{29}\left(\cos1.95+i\sin1.95\right)$

b)

$\sqrt{29}\left(\cos65.06+i\sin65.06\right)$

c)

$\sqrt{7}\left(\cos1.95-i\sin1.95\right)$

d)

$\sqrt{7}\left(\cos65.06-i\sin65.06\right)$

90.

Sketch the curve of x(t) = 2t + 1 and y(t) = t² + 2 by setting up a parametric table

a)

A

b)

B

c)

C

d)

D

91.

Which set of parametric equations satisfies the given data table?

a)

x(t) = t³ - 1
y(t) = 2t

b)

x(t) = t³ - 1
y(t) = t + 2

c)

x(t) = t + 8
y(t) = t + 2

d)

x(t) = t + 8
y(t) = 2t

92.

Write x = 2t and y = t² + 3 in rectangular form .

a)

y = 4x² + 3

b)

y = ¼ x² + 3

c)

y = 4t²+ 12

d)

y = (x - 2)² + 3

93.

Eliminate the parameter (aka rewrite in rectangular form)

x= 2+4t and y=-1+6t

a)

y=(3/2)x - 4

b)

t=(x-2)/4

c)

y=x - 4

d)

y= (2/3)x + 4

94.

Express this complex number in rectangular form.

4 ( cos π /3 + i sin π /3)

a)

2 + 2√3 i

b)

2 + √3 i

c)

2 - 2√3 i

d)

-2 + 2√3 i

95.

Find the product z₁z₂

a)

-7√3 - 7i

b)

-7√2 - 7√2i

c)

-7√2 + 7√2i

d)

-7 - 7√3i

96.

This particular equation generates what graph

a)

b)

c)

d)

97.

In a normal curve, what percentage of individuals lies between $\pm$ 1 standard deviation

a)

68%

b)

95%

c)

99.7%

d)

Not Enough Information

98.

What is the minimum value?

a)

64

b)

58

c)

66

d)

60

99.

What data value is the upper quartile (Q3)?

a)

64

b)

62

c)

66

d)

58

100.

Which has a higher median?

a)

Florida

b)

Texas

MA Sem 2 Final Review

Total questions: 100

Worksheet time: 6hrs 14mins

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