Free Printable Precalculus Semester 2 Final Study

1.

A vector is a ray with both ____________ and _____________.

a)

Wings and halos

b)

Space and time

c)

Direction and magnitude

d)

Radicals and exponents

2.

Which of the following quantities are vectors?

a)

speed, velocity, acceleration

b)

velocity, acceleration, force

c)

force, acceleration, mass

d)

length, mass, time

3.

Which are equivalent vectors?

a)

u and -u

b)

u and a

c)

u and v

d)

u and b

4.

Two vectors that have the same magnitude but opposite direction

a)

Parallel vectors

b)

Equivalent vectors

c)

Opposite vectors

5.

Two or more vectors with sum that is vector r.

a)

Zero vector

b)

Resultant

c)

Direction

d)

Components

6.

The component form of a vector describes:

a)

the horizontal and vertical change of the vector

b)

the slope of a vector

c)

where it starts on your graph

7.

What is the horizontal component of < 5, 2>

a)

5

b)

2

c)

7

8.

If a vector has direction 40 degrees West of North, what quadrant would it lie in?

a)

Quadrant 1

b)

Quadrant 2

c)

Quadrant 3

9.

What is the x component of the vector?

a)

14cos(30)

b)

14sin(30)

c)

-14cos(30)

d)

-14sin(30)

10.

$p=<3,\ -9>$

Find the magnitude to the nearest tenth.

(a)

11.

Find the magnitude of a vector using ...

a)

Sine & Cosine

b)

Inverse Tangent

c)

Pythagorean Theorem

d)

Multiplication

12.

Find the magnitude of AB if the initial point is (-3, 1) and the terminal point is (3, 9).

a)

6

b)

8.2

c)

10

d)

10.4

13.

Find the magnitude of the vector <-4, -6>.

a)

7.211

b)

52

c)

3.162

d)

4.472

14.

a)

2(1,2)=(2,4)

b)

3(1,2)=(3,6)

c)

2(1,-2)=(2, -4)

d)

3(1,-2)=(3,-6)

15.

a)

2(1,2)=(2,4)

b)

3(1,2)=(3,6)

c)

2(1,-2)=(2, -4)

d)

3(1,-2)=(3,-6)

16.

If vector a= (4, -5) and vector b= (-7, 4) Find a-b

a)

(-11, -9)

b)

(11, 9)

c)

(11, -9)

d)

(-3, -1)

17.

Which vector equation matches the vector operation shown in the diagram below?

a)

u-v=w

b)

u-v=-w

c)

u+v=w

d)

v+u=-w

18.

Let vector a= (5, -7) and vector b= (-12, 2) Find 2b-4a

a)

(44, -32)

b)

(-4, 24)

c)

(-44, 32)

d)

(4, -24)

19.

If w = <2, -5> and y = <2, 0>, find 2w + y.

a)

<-10, 2>

b)

<4, -5>

c)

<-6, 10>

d)

<6, -10>

20.

Find the direction and magnitude of the resultant vector for the drawing of two forces.

a)

Direction 75.0°

Magnitude 221.8mph

b)

Direction 41.9°

Magnitude 233.3mph

c)

Direction 48.1°

Magnitude 233.3mph

d)

Direction 57.2°

Magnitude 238.6mph

21.

An airplane flying due south (270°) 485 mph against a 25 mph wind blowing due west(180°). Determine the new speed and direction of the plane.

a)

Direction 267.0°
Magnitude 485.6mph

b)

Direction 93.0°
Magnitude 485.6mph

c)

Direction 237.0°
Magnitude 485.6mph

d)

Direction 87.0°
Magnitude 510.0mph

22.

A plane is flying at a speed of 320 mph on a bearing N 70° E. Its resultant speed is 370 mph and resultant direction is 60°. Find the speed and direction of the wind.

a)

687.3 mph, N 64.6° E

b)

78.1 mph, N 14.6° E

c)

78.1 mph, N 75.4° E

d)

687.3 mph, N 25.4° E

23.

Given u = <3, 7>, find 2u

a)

<21, 2>

b)

<6, 26>

c)

<6, 14>

d)

23

24.

Add (27 m/s, 21 degrees N of W) + (12 m/s, 38 degrees N of E)

*pay attention to sign and direction!

a)

37 m/s, 59 degrees W of N

b)

23 m/s, 43 degrees W of N

c)

23 m/s, 37 degrees N of E

d)

37 m/s, 46 degrees N of W

25.

Two dogs pull a sledge along an icy track, as shown. Dog X pulls with a force of 200N at an angle of 65° to the front edge of the sledge. Dog Y pulls with a force of 120N at an angle of 45° to the front edge of the sledge.

What is the resultant forward force on the sledge exerted by the two dogs?

a)

80 N

b)

170 N

c)

270 N

d)

320 N

26.

What is the dimension (order) of the matrix shown?

a)

( 2 x 2 )

b)

( 1 x 2 )

c)

( 2 x 1 )

d)

( 2 x 4 )

27.

What is the entry at r₃₁?

a)

3

b)

1

c)

4

d)

7

28.

What are the dimensions of matrix B?

a)

2 x 3

b)

3 x 2

c)

-8 x 10

d)

3 x 3

29.

Using matrix A find the element $a_{2,3}$

a)

8

b)

6

c)

-5

d)

5

30.

Matrix C is a 3 x 2 matrix with $c_{1,2}=6$
Which could be matrix C?

a)

b)

c)

d)

31.

Subtract

a)

-5
-8
3
10

b)

-9
8
3
2

c)

5
-8
3
10

d)

-5
8
3
2

32.

Add

a)

11 8
-4 2

b)

3 2
-6 -6

c)

-3 2
-4 -6

d)

10 8
-6 2

33.

Find X - Y

a)

b)

c)

d)

34.

Perform the following operation

a)

b)

c)

d)

e)

not possible

35.

If the matrices can be multiplied, what dimension is the product? If not, write undefined.

a)

( 2 x 2 )

b)

( 6 x 2)

c)

( 2 x 6 ) )

d)

( 3 x 2 )

36.

Perform the matrix multiplication, if possible.

a)

b)

c)

d)

Cannot be multiplied, dimensions not compatible.

37.

Perform the matrix multiplication, if possible.

a)

b)

c)

d)

Cannot be multiplied, dimensions not compatible.

38.

Multiply

a)

20 15 -10
30 -5 0

b)

-20 15 -10
30 -5 0

c)

1 8 3
11 4 5

d)

20 -15 10
-30 5 0

39.

Solve the system of equations:

a)

( -2, 3, -3)

b)

None of these

c)

( -2, -3, 3)

d)

( -3, 3, -2)

40.

Solve the system of equations:

a)

( 5, 1, -4)

b)

(-5, 3, -1)

c)

None of these

d)

( -1, 5, -4)

41.

Solve the system of equations:
x + y + z = 4
x = -2y
z = -3y

a)

(2, -1, 3)

b)

(2, 3, 1)

c)

None of these

d)

(4, 1, -1)

42.

Write the following system of equations as an augmented matrix.

a)

b)

43.

What is the formula for the determinant of a 2x2 matrix?

a)

ad-bc

b)

ab-cd

c)

ad+bc

d)

(a+d)(b+c)

44.

Will this matrix have an inverse?

a)

Yes

b)

No

c)

Unable to Determine

45.

Are these matrices inverses of each other?

a)

Yes

b)

No

c)

Unable to Determine

46.

What is the determinant of this matrix?

a)

5

b)

-5

c)

0

d)

-12

47.

Solve the system of equations:
$2x-3y=3z-7$
$4z-2x+3y=12$
$4y+2z-3x=0$

a)

(2, 4, 5)

b)

(-2,-4, 5)

c)

(-2, 4, -4)

d)

None of these

48.

Solve the system of equations:

a)

( -2, 4, 3)

b)

( 2, 1, 6)

c)

No solution

d)

None of these

49.

Multiply

a)

20 15 -10
30 -5 0

b)

-20 15 -10
30 -5 0

c)

1 8 3
11 4 5

d)

20 -15 10
-30 5 0

50.

Find the exact value of $\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)$

a)

$-\frac{\pi}{3}$

b)

$\frac{\pi}{3}$

c)

$-\frac{\pi}{6}$

d)

$\frac{\pi}{6}$

51.

Which equation is true?

a)

sin (x) = 6/8

b)

cos (x) = 8/6

c)

cos (x) = 6/8

d)

tan (x) = 6/8

52.

Which equation would you use to solve for the unknown angle?

a)

x = sin^–1(4/5)

b)

x = cos^–1(4/5)

c)

x = cos^–1(5/4)

d)

x = tan^–1(4/5)

53.

Solve for x.

a)

x = 90º

b)

x = 60º

c)

x = 45º

d)

x = 30º

54.

You are standing 10 feet away from a tree. There is a cat up in the tree. Your eyes make a 48 degree angle to look up at the cat. How high is the cat?

a)

11.1 ft.

b)

9 ft.

c)

7.4 ft.

d)

13.8 ft.

55.

Simplify √-4

a)

2i

b)

-2i

c)

2

d)

4i

56.

Simplify √-23

a)

-√23

b)

23i

c)

23

d)

i√23

57.

Simplify √-25

a)

i√25

b)

5i

c)

-5i

d)

25i

58.

Simplify 2√-32

a)

2i√32

b)

4i√2

c)

8i√2

d)

-16i√2

59.

$i^2=?$

a)

i

b)

-1

c)

-i

d)

1

60.

$i^{63}\ =?$

a)

i

b)

-1

c)

-i

d)

1

61.

What is the real portion of the number

3+5i

a)

3

b)

5

c)

-3

d)

-5

62.

What is the imaginary portion of the number $-7-12i$

a)

7

b)

12

c)

$-7$

d)

$-12$

63.

Two complex numbers are added. How do we do this?

a)

We add up all 4 numbers you see.

b)

We add up all the big numbers.

c)

We add only the real parts. Because we cannot see the imaginary parts.

d)

We add the real parts together, and then separately add the imaginary parts together. Your final answer is in the form. $a+bi$

64.

What complex number is represented by the graph?

a)

-3-i

b)

-3+i

c)

1+3i

d)

1-3i

65.

What is the radius of a unit circle?

a)

1

b)

2

c)

1/2

d)

0

66.

The hypotenuse of any right triangle from the center of the unit circle to an edge is always

a)

1

b)

sqt2/2

c)

sqt3/2

d)

1/2

67.

Based on your unit circle cos(0^o)=

a)

1

b)

0

c)

-1

d)

1/2

68.

Based on your unit circle sin(90^o)=

a)

1/2

b)

0

c)

-1

d)

1

69.

sin(7π/4)

a)

1/2

b)

-√2/2

c)

√2/2

d)

-1/2

70.

sin(3π/2)

a)

0

b)

1

c)

-1

d)

1/2

71.

Simplify the expression:
$\left(1\ +\ 5i\right)\ +\ \left(1\ -\ 5i\right)$

a)

$2\ +\ 10i$

b)

$2\ +\ 10i^2$

c)

$2$

d)

$-8$

72.

Simplify the expression:
$\left(8\ +\ 9i\right)\ +\ \left(4\ -\ 6i\right)$

a)

$17\ +\ 3i$

b)

$12\ +\ 3i^2$

c)

$17\ -2i$

d)

$12\ +\ 3i$

73.

Simplify the expression:
$\left(5\ +\ 14i\right)\ -\ \left(10\ +\ 2i\right)$

a)

$5\ -16i$

b)

$-5\ +\ 16i$

c)

$5\ -\ 12i$

d)

$-5\ +\ 12i$

74.

$2\left(3\ +\ 4i\right)-\left(4\ -\ 6i\right)$

a)

$2\ +\ 14i$

b)

$10\ +\ 2i$

c)

$-1\ -2i$

d)

$-2\ -2i$

75.

What is the total number of roots for the following equation?
y = 4x⁶ - 12x⁵ - x⁴ + 2x³ - 6x² - 5x + 10

a)

4

b)

5

c)

6

d)

7

76.

Clare picks a marble at random, puts it back, and then picks another marble at random.

a)

Dependent

b)

Independent

77.

Pablo chooses a colored marble from a mixed bag and writes down the color. Pablo leaves it out and then draws another.

a)

Independent

b)

Dependent

78.

A jar contains 4 white chips, 5 purple chips, and 1 black chip. Chips are selected randomly one at a time, and are not replaced.
P(white, then purple, then black)

a)

1/36

b)

2/39

c)

5/41

d)

6/43

79.

Probability can be written as ...

a)

a fraction

b)

a decimal

c)

a percent

d)

all of the above

80.

P(Pizza|Senior): (simplify)

a)

10/15

b)

4/5

c)

2/3

d)

10/5

81.

You pick a marble from this bag.
What is the probability you will choose either a black or white marble?

a)

3/5

b)

9/100

c)

1/10

d)

2/5

82.

The tree diagram shows the outcomes of rolling a die and flipping a coin.
What is the probability of rolling a number higher than 3 and flipping a tails?

a)

¹/₁₂

b)

²/₁₂

c)

³/₁₂

d)

⁴/₁₂

83.

P(B or E) =
*Remember to simplify.*

a)

1/2

b)

1/4

c)

1/8

d)

4/8

84.

For Titanic Passengers, Find P(Survived|First Class)

a)

0.092

b)

0.286

c)

0.625

d)

0.675

85.

A die is rolled. What is the probability of rolling a 5 or a number greater than 3?

a)

2/3

b)

1/2

c)

5/6

d)

1

86.

Which term is 12,288 in the sequence given by: 3, 6, 12, 24, ...

a)

11

b)

12

c)

13

d)

14

87.

Which of the following expresses 1+3+5+...+39

a)

$\sum_{k=1}^{20}2k-1$

b)

$\sum_{k=2}^{40}k-1$

c)

$\sum_{k=-1}^{37}k+2$

d)

$\sum_{k=1}^{39}2k-1$

88.

Evaluate the arithmetic series described. (Find the sum):

a₁=0, a_n = 28, n = 8

a)

112

b)

252

c)

125

d)

119

89.

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

a)

2450

b)

4888

c)

2444

d)

4900

90.

Evaluate: $\sum_{n=1}^{15}2m+4$

a)

296

b)

299

c)

300

d)

309

91.

Evaluate the arithmetic series described. (Find the sum):

a₁= 14, a_n = 54, n = 11

a)

748

b)

374

c)

1504

d)

752

92.

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

Find a₃₄

a)

-3285

b)

-3585

c)

-3185

d)

-3385

93.

-20, -24, -28, -32, ...

Find a₂₄

a)

-116

b)

-120

c)

-118

d)

-112

94.

Find the rule or formula:

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

a)

a_n = -15 + 9n

b)

a_n = -24 + 9n

c)

a_n = -7 + 9n

d)

a_n = -6 + 9n

95.

Find the three terms in the sequence after the last one given.

-16, -23, -30, -37, ...

a)

-61, -70, -79

b)

-52, -61, -70

c)

-44, -51, -58

d)

-42, -49, -56

96.

Find the 22nd term of the following sequence:
5, 8, 11, ...

a)

14

b)

68

c)

63

d)

71

97.

Is the sequence arithmetic: 17, 9, 1, -7, ...

a)

Yes

b)

No

98.

Find the common difference: -34, -29, -24, -19, ...

a)

d = -5

b)

d = 5

c)

d = -6

d)

d = 6

99.

Given the recursive formula, find the first four terms:
a_n = a_n-1 + 5
a₁ = -16

a)

-16, -21, -26, -31

b)

5, -11, -27, -43

c)

-16, -80, -500, -200

d)

-16, -11, -6, -1

100.

What is the 5th term in the given sequence?
$a_n=5n-4$

a)

21

b)

16

c)

11

d)

6

Precalculus Semester 2 Final Study

Total questions: 100

Worksheet time: 5hrs 8mins

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