Free Printable HPC Final Review Part II

1.

Has magnitude and direction

a)

Scalar

b)

Vector

c)

Initial Point

d)

Terminal Point

2.

A quantity described by magnitude and does not need direction

a)

Vector

b)

Scalar

3.

How do scalars and vectors differ?

a)

scalers have units

b)

scalers have direction

c)

vectors have units

d)

vectors have direction

4.

Another name for the "tail" of a vector

a)

Terminal Point

b)

Standard Position

c)

Initial Point

d)

Magnitude

5.

Another name for the "tip" of the vector

a)

Terminal point

b)

Initial point

c)

Standard position

d)

Direction

6.

Vector or scalar?

75 meters due East

a)

Scalar

b)

Vector

7.

Vector or scalar?

50 minutes

a)

Scalar

b)

Vector

8.

Vector or scalar?

82 Newtons to the left

a)

Scalar

b)

Vector

9.

Vector or scalar?

Wind blowing at 20 mph.

a)

Scalar

b)

Vector

10.

Vector or scalar?

A deer running 15 meters per second due west.

a)

Scalar

b)

Vector

11.

Find the magnitude of the vector <2, -3>.

a)

√11

b)

13

c)

√-4

d)

√13

12.

When the vector's initial point is at the origin, it is in ___.

a)

quadrant bearing

b)

true bearing

c)

resultant

d)

standard position.

13.

which of the following is a vector in standard position, if the coordinates of their tail and head are given?

a)

A(2,1) B(0,0)

b)

C(0,0) D(5-12)

c)

E(0,-1) F(9,-2)

d)

V(-1,-2) X(0,-1)

14.

Two vectors who have the same or opposite direction.

a)

Parallel vectors

b)

Equivalent vectors

c)

Opposite vectors

15.

Two vectors that have the same magnitude and direction

a)

Parallel vectors

b)

Equivalent vectors

c)

Opposite vectors

16.

Two vectors that have the same magnitude but opposite direction

a)

Parallel vectors

b)

Equivalent vectors

c)

Opposite vectors

17.

If c=<-5, 4> and d=<8, 0>, calculate 2c+d

a)

<-2, 8>

b)

<-2, 0>

c)

<6, 8>

d)

<6, 0>

18.

If v =〈a,b〉, then a is the ___________ component of v.

a)

vertical

b)

horizontal

c)

parallel

d)

slope

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.

If y = <2, 0> and
z = <-1, -4>, find 3y - 2z.

a)

<5, -8>

b)

<4, 8>

c)

<8, 8>

d)

<-8, -8>

21.

Find the component form of a vector whose magnitude is 10 and direction is 150°.

a)

<10, 150>

b)

<-8.66, 5>

c)

<6.99 , -7.14>

d)

10i + 150j

22.

u + v

a)

4i - j

b)

6i + j

c)

3j + 4j

d)

i + 6j

23.

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

a)

<21, 2>

b)

<-11, 26>

c)

<8, 3>

d)

23

24.

George Washington throws a baseball with an initial velocity of 20.2 feet per second at an angle of 69° with the horizontal. Find the initial vertical and horizontal velocity of the ball.

a)

Horizontal 18.9
Vertical 7.2

b)

Horizontal 7.2
Vertical 18.9

c)

Horizontal 15.2
Vertical 9.6

d)

Horizontal 9.6
Vertical 15.2

25.

If a turtle moves from coordinate
P = (3,2) to
Q = (5,6). Which vector models the turtle's motion?

a)

〈-2,-4〉

b)

〈2,4〉

c)

〈8,8〉

d)

none of these

26.

Given v = 〈3,-5〉 and w = 〈-2,3〉, what is v + w?

a)

〈6,-10〉

b)

〈1,-2〉

c)

〈0,-1〉

d)

none of these

27.

Find the components of a vector v such that
v + 〈-6,4〉 = 〈10,-3〉

a)

〈4,1〉

b)

〈16,4〉

c)

〈16,-7〉

d)

none of these

28.

Given
v = 〈3,-5〉 and
w = 〈-2,3〉, what is 2v + 3w?

a)

〈6,-10〉

b)

〈1,-2〉

c)

〈0,-1〉

d)

none of these

29.

Find the magnitude of the vector -5i + 12j

a)

13

b)

10.91

c)

7

d)

17

30.

Find the magnitude of the vector 10i -8j

a)

2

b)

2√41

c)

6

d)

18

31.

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

a)

<21, 2>

b)

<-11, 26>

c)

<8, 3>

d)

23

32.

Find the component form of the vector. Round to three decimals.

a)

<16.116, 7.798>

b)

<16.298, 7.335>

c)

<16.892, 7.530>

d)

<16.314, 7.607>

33.

Find the component form of the vector. Round to three decimals.

a)

<11.468, 8.030>

b)

<8.030, 11.468>

c)

<8.934, 11.873>

d)

<11.873, 8.934>

34.

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

a)

<-8, -3>

b)

<8, 11>

c)

<-2, 11>

d)

<2, 3>

35.

Let a = <-2, 0> and b = <-4, -8>.

Find a - b.

a)

<2, -8>

b)

<2, 8>

c)

<-6, -8>

d)

<-6, 8>

36.

Convert the rectangular coordinates to polar form

a)

(√2 , 7π/4)

b)

(2 , 3π/4)

c)

(4 , π/4)

d)

(4 , 5π/4)

37.

Convert the polar coordinates to rectangular form

a)

(1, 1)

b)

(1, -1)

c)

(-1, 0)

d)

(-1, -1)

38.

Convert the polar coordinates to rectangular form

a)

( -3, 3)

b)

(3, 3√3)

c)

(-3, 3√3)

d)

(3, -3√3)

39.

Which equation represents the polar graph?

a)

r = sin θ

b)

r = sin 4θ

c)

r = 4 sin θ

d)

r = 4 cos θ

40.

Which point represents the polar coordinate
(-4, -2π/3)

a)

B

b)

F

c)

D

d)

A

41.

How do you write an ordered pair?

a)

(X,X)

b)

(θ, r)

c)

(r,θ)

d)

(Y,Y)

42.

Convert the polar coordinates to rectangular form.
(6, 2π/3)

a)

( -3, 3)

b)

(3, 3√3)

c)

(-3, 3√3)

d)

(3, -3√3)

43.

Find the polar coordinates of the rectangular point. (-3,0)

a)

(3,π)

b)

(3,0)

c)

(3,π/2)

d)

(3,-3π/2)

44.

Find the polar coordinates of the rectangular point. (0,3)

a)

(3,π)

b)

(3,0)

c)

(3,π/2)

d)

(3,-3π/2)

45.

Which point represents (-4, 4π/3)

a)

F

b)

E

c)

B

d)

A

46.

Which point represents the polar coordinate
(-4, -2π/3)?

a)

B

b)

F

c)

D

d)

A

47.

Which point represents (5, π)

a)

F

b)

E

c)

B

d)

A

48.

Which point represents (-4, π/2)

a)

D

b)

C

c)

B

d)

A

49.

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

50.

What are the coordinates of the center and the radius of the circle with equation:

(x - 4)² + (y - 3)² = 25 ?

a)

Center (4,3)

Radius = 5 units

b)

Center (4,3)

Radius = 25 units

c)

Center (-4,-3)

Radius = 25 units

d)

Center (-4,-3)

Radius = 5 units

51.

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

52.

What is the center of the circle with this equation is (x+2)²+(y-4)²=41?

a)

(-2,41)

b)

(-2,4)

c)

(2,-4)

d)

(2,41)

53.

What is the radius of the circle

(x+7)²+(y-2)²=144?

a)

7

b)

12

c)

24

d)

144

54.

What is the equation for this circle?

a)

(x+1)²+(y+1)²=9

b)

x²+y²=9

c)

x²+y²=6

d)

x²+y²=3

55.

The diameter of a circle has length 12. The center is at (-5, 2). Give the equation of the circle.

a)

(x - 2)²+ (y + 5)²= 36

b)

(x - 5)² + (y + 2)² = 6

c)

(x + 5)²+ (y - 2)²= 36

d)

(x + 2)²+ (y - 5)²= 6

56.

In the circle represented by the equation (x-4)²+(y-3)²=25, the diameter is

a)

10

b)

3

c)

5

d)

25

57.

A circle has the equation
x² + y² - 12x + 8y + 3 = 0. Write the equation in standard form.

a)

(x - 6)² + (y + 4)² = 49

b)

(x + 4)² + (y - 6)² = 49

c)

(x - 6)² + (y + 4)² = 55

d)

x² + y² = 55

58.

Change the following equation to standard form
x²+y²-4x+12y-8=0

a)

(x+2)²+(y-6)²=48

b)

(x-2)²+(y+6)²=48

c)

(x-6)²+(y-2)²=48

d)

(x+2)²+(y-6)²=48

59.

What is the center of the ellipse?

a)

(0, 0)

b)

(1, 5)

c)

(1, 0)

d)

(0, 1)

60.

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

61.

Given the following, write the equation of the ellipse.

a)

A

b)

B

c)

C

d)

D

62.

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)

63.

See Picture

a)

A

b)

B

c)

C

d)

D

64.

See Picture

a)

A

b)

B

c)

C

d)

D

65.

What is the center of the shifted ellipse?

a)

(0,0)

b)

(-3,1)

c)

(1,-3)

d)

(3,-1)

66.

What is the center of the given equation?

a)

(h, k) = (4, 3)

b)

(h, k) = (-4, -3)

c)

(h, k) = (-4, 3)

d)

(h, k) = (4, -3)

67.

What are the vertices of the ellipse?

a)

(0, 0)

b)

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

c)

(3, -5) and (3, 7)

d)

(3, 1)

68.

What is the equation for the focus points on an ELLIPSE?

a)

c² = a² + b²

b)

c² = a² - b²

c)

1/4d

d)

(x-h)² + (y-k)² = r²

69.

The set of all points in a plane the sum of whose distances from two fixed points is a constant is a/an _____.

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

70.

Find the coordinates of foci of the ellipse (x/25)^2 + (y/16)^2 = 1

a)

(3, 0) (-3,0)

b)

(4, 0) (-4,0)

c)

(0, 3) (0, -3)

d)

(0, 4) (0, -4)

71.

What is the major axis length for ellipse (x/25)^2 + (y/16)^2 = 1

a)

5

b)

4

c)

8

d)

10

72.

What is the center of this ellipse? [(x-4)^2]/9 + [(y-5)^2]/16 = 1

a)

(4, 5)

b)

(4, -5)

c)

(-4, -5)

d)

(-4, 5)

73.

For the following ellipse, identify the value of a, b and c.

x^2/36 +[(y-4)^2]/25 = 1

a)

a=6 b=5 c=3.32

b)

a=6 b=5 c=11

c)

a=6 b=5 c=3

d)

a=36 b=25 c=11

74.

For the following ellipse, identify the orientation, its width and its height.

[(x+3)^2]/16 +[(y-1)^2]/49 = 1

a)

horizontal, width=8, height=14

b)

vertical, width=8, height=14

c)

vertical, width=14, height=8

d)

vertical, width=4, height=7

75.

For the following ellipse, how would you graph the two focus points or foci?

[(x-4)^2]/1 + [(y-5)^2]/10 = 1

a)

Move up and down by 3 units from a starting point of (5, 4) and plot two points

b)

Move left and right by 3 units from a starting point of (4, 5) and plot two points

c)

Move up and down by 3 units from a starting point of (4, 5) and plot two points

d)

Move up and down by 9 units from a starting point of (4, 5) and plot two points

76.

If the two points F and G are the foci of an ellipse, which of the following statements is true?

a)

The ellipse is the set of points, P, such that FP-GP is constant.

b)

The ellipse is the set of points, P, such that FP+GP is constant.

c)

The ellipse is the set of points, P, such that FP x GP is constant.

d)

The ellipse is the set o points, P, such that FP/GP is constant.

77.

The center of ellipse is same as a vertex.

a)

TRUE

b)

FALSE

c)

Probably

d)

Maybe

78.

If length of major axis is 10 and minor axis is 8, with major axis along x-axis then find the equation of the ellipse.

a)

(x/4)^2 + (y/5)^2 = 1

b)

(x/5)^2 + (y/4)^2 = 1

c)

(x/10)^2 + (y/8)^2= 1

d)

(x/8)^2 + (y/10)^2 =1

79.

An ellipse has ____ vertex/vertices and ____ focus/foci.

a)

two, one

b)

one, one

c)

one,two

d)

two, two

80.

In a hyperbola, which is the longest segment?

a)

a

b)

b

c)

c

81.

Determine the length of the transverse axis

a)

1.5

b)

2

c)

3

d)

4

82.

Determine the value of b

a)

1

b)

2

c)

3

d)

4

83.

What is the distance between the 2 foci?

a)

6

b)

8

c)

10

d)

12

84.

Determine the equation of the hyperbola.

a)

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

b)

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

c)

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

d)

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

85.

Determine the equation of the hyperbola.

a)

$\frac{\left(y-1\right)^2}{4}-\frac{\left(x-1\right)^2}{12}=1$

b)

$\frac{y^2}{9}-\frac{x^2}{16}=1$

c)

$\frac{x^2}{16}-\frac{y^2}{9}=1$

d)

$\frac{\left(x-1\right)^2}{16}-\frac{\left(y-1\right)^2}{4}=1$

86.

What is the orientation of the hyperbola?

\frac{x^2}{4}-\frac{y^2}{25}=1

a)

vertical

b)

horizontal

87.

Which of the following is a vertex?

$\frac{\left(y-1\right)^2}{4}-\frac{\left(x+2\right)^2}{9}=1$

a)

$\left(0,2\right)$

b)

$\left(3,0\right)$

c)

$\left(-2,\ 1\right)$

d)

$\left(1,1\right)$

88.

What is the distance between the two foci?

\frac{\left(x+4\right)^2}{36}-\frac{\left(y-5\right)^2}{4}=1

a)

$2\sqrt{10}$

b)

$4\sqrt{10}$

c)

$4\sqrt{2}$

d)

$8\sqrt{2}$

89.

Which is the graph of the hyperbola?

\left(x-1\right)^2-\frac{\left(y+2\right)^2}{9}=1

a)

b)

c)

d)

90.

What are the foci of the graph of $\frac{\left(y-1\right)^2}{16}-\frac{\left(x+1\right)^2}{4}=1$

a)

$\left(-1,\ 1\pm2\sqrt{5}\right)$

b)

$\left(1,\ 1\pm2\sqrt{5}\right)$

c)

$\left(1\pm2\sqrt{5},\ 1\right)$

d)

$\left(1,\ 1\pm2\sqrt{5}\right)$

91.

Which graph represents $\frac{\left(y-1\right)^2}{16}-\frac{\left(x+1\right)^2}{4}=1$

a)

b)

c)

d)

92.

Convert

16x^2-9y^2-64x+18y-89=0\

to standard form

a)

$\frac{\left(x-2\right)^2}{9}-\frac{\left(y-1\right)^2}{16}=1$

b)

$\frac{\left(x-2\right)^2}{9}-\frac{\left(y+1\right)^2}{16}=1$

c)

$\frac{\left(y-1\right)^2}{16}-\frac{\left(x-2\right)^2}{9}=1$

d)

$\frac{\left(y+1\right)^2}{16}-\frac{\left(x-2\right)^2}{9}=1$

93.

What is the standard form equation of the hyperbola that has vertices at $\left(1,\ -1\right)\ and\ \left(1,\ -5\right)$ and foci at $\left(1,\ -3\pm2\sqrt{37}\right)$ ?

a)

$\frac{\left(x-1\right)^2}{144}-\frac{\left(y+3\right)^2}{4}=1$

b)

$\frac{\left(y-1\right)^2}{4}-\frac{\left(x-3\right)^2}{144}=1$

c)

$\frac{\left(y+3\right)^2}{144}-\frac{\left(x-1\right)^2}{4}=1$

d)

$\frac{\left(y+3\right)^2}{4}-\frac{\left(x-1\right)^2}{144}=1$

94.

Write the standard form equation of the hyperbola that has vertices at (-2, -3) and (-8, -3) and an asymptote of $y+3=\frac{8}{3}\left(x+5\right)$ .

a)

$\frac{\left(x+5\right)^2}{64}-\frac{\left(y+3\right)^2}{9}=1$

b)

$\frac{\left(y+3\right)^2}{9}-\frac{\left(x+5\right)^2}{64}=1$

c)

$\frac{\left(y+3\right)^2}{64}-\frac{\left(x+5\right)^2}{9}=1$

d)

$\frac{\left(x+5\right)^2}{9}-\frac{\left(y+3\right)^2}{64}=1$

95.

Write the standard form equation of the hyperbola that has foci at $\left(-10,\ -8\pm\sqrt{157}\right)$ and asymptotes at $y+8=\pm\frac{11}{6}\left(x+10\right)$ .

a)

$\frac{\left(x+10\right)^2}{121}-\frac{\left(y+8\right)^2}{36}=1$

b)

$\frac{\left(y+8\right)^2}{121}-\frac{\left(x+10\right)^2}{36}=1$

c)

$\frac{\left(y+8\right)^2}{36}-\frac{\left(x+10\right)^2}{121}=1$

d)

$\frac{\left(x+10\right)^2}{36}-\frac{\left(y+8\right)^2}{121}=1$

96.

What are the asymptotes of the hyperbola in the picture?

a)

y = x and y = –x

b)

y = 2x and y = –2x

c)

y = ¹/₂x and y = –¹/₂x

d)

y = 2x and y = 4x

97.

The focus is always inside the parabola.

a)

true

b)

false

98.

All parabolas with a vertical directrix open the left or right.

a)

true

b)

false

99.

(x+3)² = 4(y+5)
What is the equation of the directrix?

a)

x = 4

b)

x = 2

c)

y = -4

d)

y = -6

100.

The focus is at (2,0) and the vertex is at (-4,0). What is the equation of the parabola?

a)

y² = 24(x+4)

b)

(y+4)² = -12x

c)

x² = 16(y+4)

d)

(x+4)² = -20y

101.

If given the equation 1/3(y + 4) = (x + 5)², what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

102.

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 )

103.

Given the equation of the parabola, where would the VERTEX be? (put in standard form)

a)

( 3 , 3)

b)

(24, 3)

c)

( - 24, 3)

d)

(-3, 3)

104.

What is the vertex of the parabola?

a)

(-3, -1)

b)

(3, 1)

c)

(1, 3)

d)

(-1, -3)

105.

Which way does the parabola open?

(y - 4)²= -8(x+1)

a)

up

b)

down

c)

left

d)

right

106.

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

a)

-8

b)

2

c)

4

d)

-32

107.

What is the equation of the directrix?

(y - 4)²= -8(x+1)

a)

x = -3

b)

x = 1

c)

y = 6

d)

y = 2

108.

Where is the line of symmetry?

(y - 4)²= -8(x+1)

a)

x = 1

b)

x = -1

c)

y = 4

d)

y = -4

109.

Write the equation of the parabola in standard form: $-2x^2-8x+4=12y$

a)

$\left(x+2\right)^2=-6\left(y-1\right)$

b)

$\left(x+2\right)^2=6\left(y-1\right)$

c)

$\left(y+2\right)^2=-6\left(x-1\right)$

d)

$\left(y+2\right)^2=6\left(x-1\right)$

110.

a)

0

b)

2

c)

3

d)

4

111.

a)

0

b)

2

c)

3

d)

4

112.

a)

0

b)

3

c)

4

d)

DNE

113.

a)

0

b)

1

c)

2

d)

DNE

114.

a)

0

b)

1

c)

2

d)

DNE

115.

a)

0

b)

1

c)

-1

d)

DNE

116.

a)

-1

b)

0

c)

1

d)

DNE

117.

a)

0

b)

∞

c)

- ∞

d)

DNE

118.

a)

3

b)

1

c)

Infinity

d)

Does not exist

119.

a)

Does not exist

b)

6

c)

4

d)

3

120.

a)

Infinity

b)

Negative Infinity

c)

2

d)

Does not exist

121.

Find the limit as x approaches 3 from the left

a)

4

b)

3

c)

2

d)

DNE

122.

What is the limit of the function as x approaches -4 from the left?

a)

2

b)

-4

c)

DNE

d)

-2

123.

What is the limit of the function as x approaches 1 from the left?

a)

DNE

b)

1

c)

4

d)

-2

124.

What is the limit of the function as x approaches 1 from the right?

a)

DNE

b)

1

c)

4

d)

-2

125.

Use interval notion to describe those intervals on which the function is positive.
y=-x(x+2)(x-1)

a)

(-2,0),(1,∞)

b)

(-2,0),(0,1)

c)

(-∞,-2),(0,1)

d)

(0,1),(1,∞)

126.

What is the limit of the function as x approaches a from the left?

(a)

127.

What is the limit of the function as x approaches a from the right?

(a)

128.

What is the limit of the function as x approaches a?

(a)

129.

What is f(a)?

(a)

130.

What is the limit of the function as x approaches b from the left?

(a)

131.

What is the limit of the function as x approaches b from the right?

(a)

132.

What is the limit of the function as x approaches b?

(a)

133.

What is f(b)?

(a)

134.

What is the limit of the function as x approaches c from the left?

(a)

135.

What is the limit of the function as x approaches c from the right?

(a)

136.

What is the limit of the function as x approaches c?

(a)

137.

What is f(c)?

(a)

138.

What is the limit of the function as x approaches e?

(a)

139.

What is f(e)?

(a)

140.

If this table represents the work to find the limit of f(x) as x approaches c. What is c?

(a)

141.

What is the limit of f(x) as x approaches c from the left?

(a)

142.

What is the limit of f(x) as x approaches c from the right?

(a)

143.

What is the limit of f(x) as x approaches c

(a)

144.

If this table represents the work to find the limit of f(x) as x approaches c. What is c?

(a)

145.

What is the limit of f(x) as x approaches c?

(a)

146.

If this table represents the work to find the limit of f(x) as x approaches c. What is c?

(a)

147.

What is the limit of f(x) as x approaches c?

(a)

148.

If this table represents the work to find the limit of f(x) as x approaches c. What is c?

(a)

149.

What is the limit of f(x) as x approaches c?

(a)

150.

a)

0/0

b)

DNE

c)

-1/4

d)

1/4

151.

What is the limit?

a)

DNE

b)

Infinity

c)

6

d)

12

152.

1

a)

4

b)

1/4

c)

0

d)

infinity

153.

a)

A

b)

B

c)

C

d)

D

154.

a)

A

b)

B

c)

C

d)

D

155.

a)

A

b)

B

c)

C

d)

D

156.

a)

-1/4

b)

8

c)

DNE

d)

∞

157.

Find $\lim_{x\rightarrow2}\frac{\text{}\frac{x}{x+2}-2}{x+4}$ .

a)

4

b)

-4

c)

$\frac{1}{4}$

d)

$-\frac{1}{4}$

158.

What is the limit?

a)

DNE

b)

2/3

c)

1/4

d)

Infinity

159.

a)

1/6

b)

0

c)

indeterminate form

d)

infinity

160.

f'(x)=

a)

$\lim_{h\rightarrow0}\left(\frac{f\left(x+h\right)-f\left(x\right)}{h}\right)$

b)

$\lim_{x\rightarrow c}\left(\frac{f\left(x\right)-f\left(c\right)}{x-c}\right)$

c)

$\frac{\text{d}y}{\text{d}x}$

d)

an equation for the slope of the tangent line

161.

Derivative means the same thing as

a)

slope of the tangent line

b)

slope of the normal line

c)

exponent

d)

potato

162.

The derivative of a function is its

a)

Slope

b)

Maximum/Minimum

c)

Instantaneous rate of change

d)

Common Denominator

163.

$\frac{\text{d}}{\text{d}x}\left[x^3\right]$

a)

$6x$

b)

3

c)

$3x^2$

d)

6

164.

$\lim_{x\rightarrow\infty}x^2+3x-5$

a)

$-\infty$

b)

2

c)

0

d)

$\infty$

165.

Derive y=3x²-4x+2

a)

6x-6

b)

6x-2

c)

4-6x

d)

6x-4

166.

Find the slope of y= 3x² - 5 using the point x=2

a)

10

b)

11

c)

12

d)

13

167.

This is the equation of the line tangent to the graph of y=x^2+3 at the point x = -1.

a)

y = -2x + 2

b)

y = 2x + 2

c)

-(1/2)x + (7/2)

d)

y = (1/2)x + (7/2)

168.

Find the value of the derivative at the indicated x-value.

a)

-4

b)

3

c)

0

d)

24

169.

Find the slope of the tangent line at x=2 for the function f(x) = 3x² - 5.

a)

10

b)

11

c)

12

d)

13

170.

Use the definition of the derivative to find the derivative of with f(x) respect to x.

f\left(x\right)=3x+1

(a)

171.

Use the definition of the derivative to find the derivative of h(x) with respect to x.

f\left(x\right)=-2x^2+7

(a)

172.

Use the definition of the derivative to find the derivative of f(x) with respect to x.

f\left(x\right)=x^2-4x

(a)

173.

Use the definition of the derivative to find the derivative of f(x) with respect to x.

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

a)

$2$

b)

$\sqrt{2x}$

c)

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

d)

$2\sqrt{2x}$

174.

Use the definition of the derivative to find the derivative of f(x) with respect to x.

f\left(x\right)=\frac{3}{5x}

a)

$-\frac{3}{5x^2}$

b)

$-\frac{3}{5}x^2$

c)

$\frac{3}{5x}$

d)

$\frac{3}{5}x$

175.

Use the definition of the derivative to find the derivative of f(x) with respect to x.

f\left(x\right)=-\frac{2}{x-4}

a)

$f'\left(x\right)=-\frac{2}{\left(x-4\right)^2}$

b)

$f'\left(x\right)=\frac{2}{\left(x-4\right)^2}$

c)

$f'\left(x\right)=2\left(x-4\right)^2$

d)

$f'\left(x\right)=2x-8$

HPC Final Review Part II - Chapters 6, 7, & 10

Total questions: 175

Worksheet time: 15hrs 35mins

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