Free Printable Precalculus Semester 2 Final Study

1.

Which of these is not a conic section?

a)

Ellipse

b)

Hyperbola

c)

Rectangle

d)

Parabola

2.

Why are Conic Sections given this name?

a)

They are the cross-sections given when a cone is sliced.

b)

Because it's part of 'da rules'

c)

They are the cross-sections given when any 3D image is sliced.

3.

In the equation (x-3)²+(y+4)²=121, the radius of the circle is

a)

242

b)

11

c)

121

d)

22

4.

x + 3 = (y - 1)²

a)

Parabola Opens Up

b)

Parabola Opens Down

c)

Parabola Opens Right

d)

Parabola Opens Left

5.

What direction does the parabola open?
(y-9)²= -40(x+4)

a)

Up

b)

Down

c)

Left

d)

Right

6.

What are the vertices of the shifted ellipse?

a)

(1, 5) and (1, -5)

b)

(0, 5) and (0, -5)

c)

(1, 1) and (1, -1)

d)

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

7.

What is the center of the shifted ellipse?

a)

(0,0)

b)

(-3,1)

c)

(1,-3)

d)

(3,-1)

8.

What are the foci of the shifted ellipse?

a)

(-5,1) and (-1,1)

b)

(±√3,0)

c)

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

d)

(√3 - 3,1) and (-√3 - 3,1)

9.

The foci of an ellipse are located at (-2, 3) & (2, 3), where is the center?

a)

(0, 3)

b)

(3, 0)

c)

(-2, 0)

d)

(2, 0)

10.

Write the equation of a circle with center (7, 0) with radius 3.

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

11.

Classify the conic section.

a)

Circle

b)

Ellipse

c)

Line

d)

None of these

12.

Classify this conic:
36x² – 5y² + 8x + 2y + 12 = 0

a)

Hyperbola

b)

Parabola

c)

Ellipse

d)

Circle

13.

Classify this conic:
6x² + 6y² – 3x + 4y = 0

a)

Circle

b)

Parabola

c)

Hyperbola

d)

Ellipse

14.

Classify this conic:
x²+5xy+8y²−10x+3y+10=0

a)

Ellipse

b)

Circle

c)

Hyperbola

d)

Parabola

15.

Identify the conic: 2x² + 6y – 9 = 0

a)

Parabola

b)

Hyperbola

c)

Ellipse

d)

Circle

16.

Classify this conic:

a)

Hyperbola

b)

Ellipse

c)

Parabola

d)

Circle

17.

Classify this conic:

a)

Ellipse

b)

Hyperbola

c)

Degenerate Conic Section

d)

Circle

18.

Which conic do you get from slicing a double cone on a slant (not through the base)?

a)

circle

b)

ellipse

c)

ellipse (except at the apex)

d)

hyperbola

19.

Which conic do you get from slicing a double cone vertically?

a)

circle

b)

ellipse

c)

hyperbola (except at the apex)

d)

parabola

20.

What equation is used to find the foci points on an ellipse?

a)

c² = a² + b²

b)

c² = a² - b²

c)

1/4d

d)

(x-h)² + (y-k)² = r²

21.

Identify the center and the length of a and b.

a)

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

b)

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

c)

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

d)

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

22.

For the ellipse with the following characteristics:
Vertices ( 4, 3), (4, - 9)
Length of minor axis is 8
What is the center of this ellipse?

a)

(4, 6)

b)

( - 4, 3)

c)

(6, 4)

d)

(4, -3)

23.

What is the equation of the circle?

a)

(x+1)² + (y +1)² = 3

b)

(x+1)² + (y -1)² = 3

c)

(x+1)² + (y +1)² = 9

d)

(x-1)² + (y -1)² = 9

24.

Given the equation of the ellipse and the C value, write the foci ordered pair

a)

(4 ± 7.42, -2)

b)

(4, - 2 ± 7.42)

c)

(- 4 ± 7.42, 2)

d)

( - 4, 2 ± 7.42)

25.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

26.

A vector is a ray with both ____________ and _____________.

a)

Wings and halos

b)

Space and time

c)

Direction and magnitude

d)

Radicals and exponents

27.

Which of the following quantities are vectors?

a)

speed, velocity, acceleration

b)

velocity, acceleration, force

c)

force, acceleration, mass

d)

length, mass, time

28.

Which are equivalent vectors?

a)

u and -u

b)

u and a

c)

u and v

d)

u and b

29.

Two vectors that have the same magnitude but opposite direction

a)

Parallel vectors

b)

Equivalent vectors

c)

Opposite vectors

30.

Two or more vectors with sum that is vector r.

a)

Zero vector

b)

Resultant

c)

Direction

d)

Components

31.

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

32.

What is the horizontal component of < 5, 2>

a)

5

b)

2

c)

7

33.

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

34.

What is the x component of the vector?

a)

14cos(30)

b)

14sin(30)

c)

-14cos(30)

d)

-14sin(30)

35.

$p=<3,\ -9>$

Find the magnitude to the nearest tenth.

(a)

36.

Find the magnitude of a vector using ...

a)

Sine & Cosine

b)

Inverse Tangent

c)

Pythagorean Theorem

d)

Multiplication

37.

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

38.

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

a)

7.211

b)

52

c)

3.162

d)

4.472

39.

a)

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

b)

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

c)

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

d)

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

40.

a)

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

b)

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

c)

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

d)

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

41.

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)

42.

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

43.

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)

44.

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

a)

<-10, 2>

b)

<4, -5>

c)

<-6, 10>

d)

<6, -10>

45.

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

46.

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

47.

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

48.

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

a)

<21, 2>

b)

<6, 26>

c)

<6, 14>

d)

23

49.

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

50.

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

51.

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 )

52.

What is the entry at r₃₁?

a)

3

b)

1

c)

4

d)

7

53.

What are the dimensions of matrix B?

a)

2 x 3

b)

3 x 2

c)

-8 x 10

d)

3 x 3

54.

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

a)

8

b)

6

c)

-5

d)

5

55.

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

a)

b)

c)

d)

56.

Subtract

a)

-5
-8
3
10

b)

-9
8
3
2

c)

5
-8
3
10

d)

-5
8
3
2

57.

Add

a)

11 8
-4 2

b)

3 2
-6 -6

c)

-3 2
-4 -6

d)

10 8
-6 2

58.

Given matrices A and B find B+A

a)

b)

c)

d)

59.

Find X - Y

a)

b)

c)

d)

60.

Perform the following operation

a)

b)

c)

d)

e)

not possible

61.

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 )

62.

Perform the matrix multiplication, if possible.

a)

b)

c)

d)

Cannot be multiplied, dimensions not compatible.

63.

Perform the matrix multiplication, if possible.

a)

b)

c)

d)

Cannot be multiplied, dimensions not compatible.

64.

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

65.

Solve the system of equations:

a)

( -2, 3, -3)

b)

None of these

c)

( -2, -3, 3)

d)

( -3, 3, -2)

66.

Solve the system of equations:

a)

( 5, 1, -4)

b)

(-5, 3, -1)

c)

None of these

d)

( -1, 5, -4)

67.

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)

68.

Write the following system of equations as an augmented matrix.

a)

b)

69.

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)

70.

Will this matrix have an inverse?

a)

Yes

b)

No

c)

Unable to Determine

71.

Are these matrices inverses of each other?

a)

Yes

b)

No

c)

Unable to Determine

72.

What is the determinant of this matrix?

a)

5

b)

-5

c)

0

d)

-12

73.

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

74.

Solve the system of equations:

a)

( -2, 4, 3)

b)

( 2, 1, 6)

c)

No solution

d)

None of these

75.

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

76.

There are seven kinds of fruit sold at a fruitstand in the market. Kate buys here three kinds of fruit, 1 kg of each. How many ways are there for Kate to make her choice?

a)

7!

b)

210

c)

3!

d)

24

77.

How many three-digit natural numbers can be assembled from the digits 2, 3, 4, 5, 6, 7, if the digits are not repeated?

a)

120

b)

720

c)

7!

d)

3!

78.

The number of permutations of the letters in the word MICHIGAN is _____.

a)

40320

b)

5040

c)

7!

d)

20160

79.

Evaluate

a)

A

b)

B

c)

C

d)

D

80.

Evaluate

a)

A

b)

B

c)

C

d)

D

81.

How many different teams of 8 can be chosen from 12 players?

a)

₁₂C₈ = 495

b)

12×8 = 96

c)

12⁸

d)

8¹²

82.

8 girls need to be arranged around a table. Two among them always sit together. In how many ways can they be arranged?

a)

8!

b)

7! × 2

c)

6!

d)

6! × 2

83.

Amy, Ben, Claudia and Dan are sitting down randomly on a bench, next to one another. In how many different ways can it happen that neither the two boys (Ben and Dan), nor the two girls (Amy and Claudia) are sitting next to each other?

a)

24

b)

8

c)

12

d)

6

84.

There are 6 routes from City A to City B, 11 routes from City B to City C. Find the number of different ways for a person to travel from City A to City C via City B.

a)

66

b)

17

c)

5

d)

6! × 11!

85.

A fair coin is flipped eight times. What is the probability that all of the flips come up tails?

a)

0.39%

b)

6.25%

c)

12.5%

d)

1.56%

86.

There are 11 runners in a race. If the first three runners all receive a different prize, in how many ways can these prizes be awarded?

[There are no ties, and at least three runners finish the race.]

a)

33

b)

1,331

c)

990

d)

177,147

87.

How many hands of 5 playing cards can be dealt using a standard deck of 52 cards?

a)

311,875,200

b)

133,784,560

c)

5,197,920

d)

2,598,960

88.

A jar contains 2 pink, 6 red, and 4 blue marbles. If you pick one marble without looking, what is the probability that the marble you pick will be red or blue?

a)

5/6

b)

1/2

c)

1/3

d)

1/6

89.

The chart below represents the number of marbles in a jar.
P(green) =

a)

5/19

b)

10/28

c)

5/14

90.

Experimental Probability is:

a)

What Will happen

b)

What actually happens

c)

What should happen

d)

What I think Happens

91.

A bag contains 30 pieces of candy. There are 15 grape, 7 cherry, 3 lemon, 5 strawberry. What is the probability of drawing a lemon?

a)

3

b)

1/10

c)

3/10

d)

30%

92.

P(not A) =
*Remember to simplify.*

a)

6/8

b)

3/4

c)

2/8

d)

1/4

93.

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

a)

Dependent

b)

Independent

94.

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

95.

A store sells shirts that are either small, medium, or large. The colors are either red, blue, green, or white. What is the probability someone will select a large green shirt?

a)

1/3

b)

1/7

c)

1/9

d)

1/12

96.

What is the probability of flipping a coin

3 times and getting 3 heads?

a)

1/8

b)

1/4

c)

1/2

d)

3/4

97.

What is Theoretical Probability?

a)

The ratio of favorable outcomes to the total number of possible outcomes

b)

The ratio of favorable outcomes to the total number of trials in an experiment

c)

In probability, a controlled, repeated process (such as repeatedly tossing a coin).

d)

A single possible result.

98.

Yummy-Yum has prepared cupcakes with five different toppings: sprinkles, coconut, chocolate chip, oreo crumbles, and M&M’s. In how many ways can they arrange three of the cupcakes in a display case?

a)

60

b)

125

c)

15

d)

12

99.

Permutation, combination, or neither?

The batting order for seven players on a 12 person team.

a)

combination

b)

permutation

c)

neither

d)

arithmetic

100.

A supervisor will choose a shift of four workers from a seven person crew. How many different shifts of four workers can the supervisor choose?

a)

5040

b)

144

c)

840

d)

35

Precalculus Semester 2 Final Study

Total questions: 100

Worksheet time: 5hrs 41mins

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