Free Printable HPC Practice Final 2nd Semester 23

1.

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

a)

<-2, 8>

b)

<-2, 0>

c)

<6, 8>

d)

<6, 0>

2.

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

a)

<5, -8>

b)

<4, 8>

c)

<8, 8>

d)

<-8, -8>

3.

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

4.

Write in component form.

a)

<0, 4>

b)

<8, 2>

c)

<2, 8>

d)

<0, 2>

5.

Find the component form of vector AB with initial point A(0, 8) and terminal point B(-9, -3)

a)

<-9, 5>

b)

<-9, 11>

c)

<-9, -11>

d)

<-9, 5>

6.

Find the magnitude of the vector <10, -8>

a)

2

b)

12.81

c)

6

d)

18

7.

Choose the correct true bearing

a)

$62\degree$

b)

$062\degree$

c)

$332\degree$

d)

$152\degree$

8.

What is the bearings of the direction NW?

a)

300 degrees

b)

315 degrees

c)

345 degrees

d)

295 degrees

9.

What is the bearings of the direction S?

a)

100 degrees

b)

200 degrees

c)

180 degrees

d)

360 degrees

10.

The air vector of an airplane is flying on a bearing of 340^o at 355 mph. A wind is blowing with the bearing of 115^o at 40 mph. Find the terminal point of the vector.

a)

<-85.17, 316.69>

b)

<316.69, -85.17>

c)

<-316.69, -85.17>

d)

<-89.54, 309.29>

e)

Did you remember to do 90- the bearing first???

11.

The air vector of an airplane is flying on a bearing of 340^o at 355 mph (air vector). A wind is blowing with the bearing of 115^o at 40 mph. What is the ground speed?

a)

The correct answer is 327.94 mph.

b)

Recall, bearings you have to subtract 90 first, then find the component form

12.

Find the point based on the parametric equations. t = 3

x = 1 - 2t

y =4t + 1

a)

(-5, 13)

b)

(13, -5)

c)

(5, 13)

d)

(13, 5)

13.

Eliminate the parameter from x(t) = t² + 5 and y(t) = t² - 4. Which of the following sketches results?

a)

Linear

b)

Quadratic

c)

Quartic

d)

Square Root

14.

Find the ordered pair based on the parametric equations.

t = -2

x = t² - 2

y = -t + 2

a)

(2, 4)

b)

(4, 2)

c)

(-6, 0)

d)

(0,-6)

15.

Write the rectangular equation for the following parametric equations.

x = 4cosθ

y = 3sinθ

a)

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

b)

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

c)

$\cos^2\theta+\sin^2\theta=1$

d)

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

16.

What is the center and radius of the curve:
x=1+3cost
y=-2+3sint

a)

(-1,2) , r=3

b)

(-1,2) , r=9

c)

(1,-2) , r=3

d)

(1,-2) , r=9

17.

Eliminate the parameter.

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

18.

Eliminate the parameter.

x= √t and y=5t

a)

y=5x²

b)

y=5x

c)

y= x - 5

d)

y=x²

19.

Convert the polar coordinates to rectangular form $\left(\sqrt{2},\ -\frac{\pi}{4}\right)$

a)

(1, 1)

b)

(1, -1)

c)

(-1, 0)

d)

(-1, -1)

20.

Convert the polar coordinates to rectangular form $\left(6,\ \frac{2\pi}{3}\right)$

a)

( -3, 3)

b)

(3, 3√3)

c)

(-3, 3√3)

d)

(3, -3√3)

21.

Which point represents (5, π)

a)

F

b)

E

c)

B

d)

A

22.

Converting between rectangular and polar coordinates:

x = ?

a)

rcosθ

b)

rsinθ

c)

x² + y²

d)

y/x, x ≠ 0

23.

Converting between rectangular and polar coordinates:

y = ?

a)

rcosθ

b)

rsinθ

c)

x² + y²

d)

y/x, x ≠ 0

24.

Converting between rectangular and polar coordinates:

tan θ = ?

a)

rcosθ

b)

rsinθ

c)

x² + y²

d)

y/x, x ≠ 0

25.

Convert from polar coordinates, (6, 5π/4) to rectangular coordinates.

a)

(-3√2, -3√2)

b)

(3√2, 3√2)

c)

(6.0, 0.4)

d)

(-6.0, -0.4)

26.

What is it about the equation y = 2(9/7)^x that indicates that it is a model for exponential growth?

a)

The equation is growth because 2 is positive.

b)

The equation is growth because the b-value is positive.

c)

The equation is growth because the b value is greater than one.

d)

The equation is growth because the exponent is positive.

27.

Using 20th-century U.S. census data, the population of New York can be modeled by $P\left(t\right)=\frac{19.875}{1+57.993e^{\left(-0.035005t\right)}}$ where P is the population in millions and t is the number of years since 1800. Based on this model, what was the population of New York in 1850?

a)

0.337 million

b)

1.7946 million

c)

17946 million

d)

19.875 million

28.

Which of the following functions is logistic?

a)

$f\left(x\right)=-2\log_ex$

b)

$f\left(x\right)=\ln\left(x+2\right)$

c)

$f\left(x\right)=\frac{1}{1+e^{-.1x}}$

d)

$f\left(x\right)=4e^{\left(x-1\right)}$

29.

Find the upper asymptote for the logistic function $f\left(x\right)=\frac{60}{1+4e^{-2x}}$ .

a)

$y=60$

b)

$y=120$

c)

$y=15$

d)

$y=12$

30.

The maximum number of students allowed at East High School since 2005 is given by the function $f\left(x\right)=\frac{1800}{1+0.8e^{-0.693x}}$ . What was the maximum number of students allowed at EHS in 2010?

a)

1756

b)

1799

c)

1800

d)

1778

31.

The function $P\left(x\right)=\frac{5000}{1+6e^{-0.125x}}$ represents the number of people in Indian Trail who are projected to regularly frequent Mr. H's new restaurant each week after his grand opening, where x is the number of weeks after the grand opening. Approximately how many people are expected to regularly frequent Mr. H's restaurant 8 weeks after his grand opening?

a)

1,559

b)

5,002

c)

1,153

d)

3,281

32.

What type of function is f(x)=2(1/7)^x ?

a)

Exponential Growth

b)

Linear

c)

Exponential Decay

d)

None of the Abovee

33.

A new savings account is opened with $400 and gains 3% every year. What is the exponential function?

a)

f(x)=400(1+3)^x

b)

f(x)=400(1-0.03)^x

c)

f(x)=400(1+0.03)^x

d)

f(x)=400(0.03)^x

34.

A flea medicine breaks down at a rate of 20% per hour. This is the rate of decay of the medicine. The initial dose is 60 milligrams. Which of the following represent the equation the models the amount of flea medicine left in an animal?

a)

$y=60\left(.2\right)^x$

b)

$y=20\left(60\right)^x$

c)

$y=60\left(.8\right)^x$

d)

$y=60\left(1.2\right)^x$

35.

Use the function, N = 14,000(.96)^t. Where N is the number of employees and t is the number of years.

How many employees will there be after 3 years?

a)

14,000 employees

b)

12,386 employees

c)

40,360 employees

d)

15,748 employees

36.

A new savings account is opened with $400 and gains 3% every yr. What's the amount after 5 years?

a)

$415

b)

$463.71

c)

$343.49

d)

$460.12

37.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

a)

y=8(15,000)^x

b)

y=15,000(1.08)^x

c)

y=15,000(0.92)^x

d)

y=15,000(0.08)^x

38.

Rewrite log₂8 = 3 in exponential form.

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

39.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

40.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

41.

Solve for x:
log₄ x = 3

a)

4

b)

12

c)

32

d)

64

42.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

43.

log₉(x)+log₉(x+2)=log₉(35)

a)

5

b)

-7

c)

5, -7

d)

-7, -13

44.

2log₅7 = 3x+1 log₅49

a)

1

b)

-1

c)

5

d)

0

45.

Solve the equation for x.

a)

7.389

b)

0.693

c)

0.0183

d)

6.581

46.

Log with a base "e" (log_e) is the same thing as...

a)

"e"

b)

Natural Logarithm (LN)

c)

Common Logarithm (Log)

d)

Natural Log, base "e"
LN_e

47.

Select the coefficients of the 5th Row in Pascal's Triangle

a)

1;3;3;1

b)

1;4;6;4;1

c)

1;5;10;10;5;1

d)

1;6;15;20;15;6;1

48.

What is the Binomial expansion of (x + 1)⁵ ?

a)

x⁵ + 5x⁴ + 10x³ + 10x² + 5x + 1

b)

x⁵ + 5x⁴ + 15x³ + 15x² + 5x + 1

c)

x⁵ + 6x⁴ + 15x³ + 15x² + 6x + 1

d)

x⁵ + 1

49.

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

a)

3240x³

b)

3240

c)

262440x³

d)

262440

50.

Use Pascal's Triangle to expand the expression.

(2x+5)⁴

a)

2x⁴ + 40x³+ 300x² + 1000x +625

b)

16x⁴+ 160x³ +600x² +1000x + 625

c)

16x⁴ + 1000x³ + 600x²+ 160x +625

51.

Find the 4th term in the expansion of (4x-3)⁵.

a)

5760

b)

-4320x²

c)

5760x³

d)

-4320

52.

Find the sum of the infinite geometric series, 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

53.

Which of the series below is CONVERGENT?

a)

a₁=4, 1.5a_n-1, n≥2

b)

a_n=-n²- 8n +106

c)

a_n = 5/10ⁿ

d)

a_n = 5n + 6

54.

Which of the following is DIVERGENT?

a)

2+4+8+16+...

b)

25+5+1+0.2+...

c)

100+50+25+5+...

d)

3(.25)ⁿ = A_n

55.

Is the sequence convergent or divergent?

a)

Convergent

b)

56.

Evaluate the infinite geometric series:

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

a)

5/4

b)

9/5

c)

5/6

d)

65/27

57.

Find the sum of the infinite geometric series, if it exists. $\frac{1}{2}-\frac{5}{3}+\frac{50}{9}-\frac{500}{27}+...$

a)

205

b)

19.5

c)

108.75

d)

Does Not Exist

58.

$\sum_{k=1}^{\infty}\left(\frac{4}{5}\right)^{k-1}$ Find the sum of the series if it exists.

a)

4/5

b)

5

c)

6.5

d)

Does not exist

59.

What is the limit?

a)

DNE

b)

Infinity

c)

6

d)

12

60.

What is the limit?

a)

DNE

b)

2/3

c)

1/4

d)

Infinity

61.

a)

0

b)

-1

c)

infinity

d)

-infinity

62.

a)

Does not exist

b)

2

c)

0

d)

1

63.

a)

Does not exist

b)

0

c)

-1

d)

1

64.

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

a)

2

b)

-4

c)

DNE

d)

-2

65.

a)

-7

b)

0

c)

1

d)

DNE

66.

a)

A

b)

B

c)

C

d)

D

67.

Find $\lim_{x\rightarrow2^-\ }f\left(x\right)$

a)

-1

b)

5

c)

0

d)

DNE

68.

Find $\lim_{x\rightarrow2^+\ }f\left(x\right)$

a)

-1

b)

5

c)

0

d)

DNE

69.

Find $\lim_{x\rightarrow2\ }f\left(x\right)$

a)

-1

b)

5

c)

0

d)

DNE

70.

Find $\lim_{x\rightarrow-1^-\ }f\left(x\right)$

a)

4

b)

0

c)

-1

d)

DNE

71.

Find $\lim_{x\rightarrow-1^+\ }f\left(x\right)$

a)

4

b)

0

c)

-1

d)

DNE

72.

Find $\lim_{x\rightarrow-1\ }f\left(x\right)$

a)

4

b)

0

c)

-1

d)

DNE

73.

Find $\lim_{x\rightarrow-4\ }f\left(x\right)$

a)

-2

b)

3

c)

-4

d)

DNE

74.

Average Rate of Change is also known as...

a)

y-intercept

b)

x-intercept

c)

linear

d)

slope

75.

What is Mrs. Gordon'S average rate of change from 0 to 2 seconds?

a)

2.5 feet per second

b)

.4 feet per second

c)

5 feet per second

d)

.2 feet per second

76.

Calculate the average rate of change from 20 to 40 minutes.

a)

-2 minutes per gallon

b)

-20 minutes per gallon

c)

-2 gallons per minute

d)

-20 gallons per minute

77.

What is the average rate of change from x=0 to x=1

a)

-3

b)

3

c)

0

d)

2

78.

A line that touches a given function at one point is called a _______ ____. The slope of the line is the same as the instantaneous rate of change on the interval [a, b].

a)

Infinite

b)

Jump

c)

removable

d)

Tangent

79.

Which of the following is true?

a)

b)

c)

d)

80.

The following limit is used to find the value(s) of what?

(select all that apply) $\lim_{h\rightarrow0}\ \frac{f\left(a+h\right)-f\left(a\right)}{h}$

a)

Average Rate of Change

b)

Instantaneous Rate of Change

c)

Slope of the Secant Line

d)

Slope of the Tangent Line

81.

Find the average rate of change on the interval $\left[a,a+h\right]$

a)

$\left(\frac{f\left(a+h\right)-f\left(a\right)}{a}\right)$

b)

$\left(\frac{f\left(a+h\right)-f\left(a\right)}{h}\right)$

c)

$\left(\frac{f\left(a\right)-f\left(a+h\right)}{h}\right)$

d)

$\frac{f\left(a+h\right)}{f\left(a\right)}$

82.

Approximate the instantaneous rate of change of the function at x = -1.

f\left(x\right)=3x^2+2x-1

a)

-4

b)

-1/4

c)

3

d)

-2

83.

Find the limit
$\lim_{h\rightarrow0}\frac{\left(3+h\right)^2-\left(3\right)^2}{h}$

a)

3

b)

4

c)

6

d)

8

84.

Find the instantaneous rate of change for f(x) at x = 8 for $f\left(x\right)\ =-\frac{3}{4}x+2$

a)

-8

b)

- $\frac{3}{2}$

c)

8

d)

- $\frac{3}{4}$

85.

What is the approximate area under the curve, using 4 intervals with heights using left values?

a)

20

b)

14

c)

10

d)

8

86.

What is the approximate area under the parabola using 4 intervals with heights using right values?

a)

6

b)

10

c)

11

d)

20

87.

a)

1.5

b)

1.1418

c)

1.1

d)

1.4914

88.

a)

35

b)

40.625

c)

32.1

d)

41

89.

Estimate the area of the region using two intervals and heights using right values. Then estimate the area using four intervals and heights using right values.

What is the difference between the two estimates?

a)

0

b)

2.5

c)

5.75

d)

8

90.

Based on the table, use a left Riemann sum and 4 sub-intervals to estimate the Area under the curve. (Choose the correct set-up.)

a)

5(3) + 1(4) + 2(5) + 1(7)

b)

5(4) + 1(5) + 2(7) + 1(6)

c)

5(3) + 6(4) + 8(5) + 9(7)

d)

0(3) + 5(4) + 6(5) + 8(7)

HPC Practice Final 2nd Semester 23

Total questions: 90

Worksheet time: 5hrs 44mins

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