Pre-Calculus

Have pre-calculus questions? Ask a pre-calculus tutor

Connect one-on-one with {0} who will answer your question

Record your answers and work...

Record your answers and work on the separate answer sheet provided.

There are 28 problems.

Problems #1–6 are Multiple Choice.

Problems #7–17 are Short Answer. (Work not required to be shown)

Problems #18–28 are Short Answer with work required to be shown.

MULTIPLE CHOICE

1. Solve, and express the answer in interval notation: | 9 – 3x | ³ 6. 1. _______

A. (–¥, 5] È [1, ¥)

B. [1, ¥)

C. [1, 5]

D. (–¥, 1] È [5, ¥)

2. Which of the following polynomials has a graph which exhibits the end behavior of upward to

the left and upward to the right? 2. _______

A. f (x) = 5x6 – x3 – x2 – 5

B. f (x) = –2x3 + 8x2 – x + 3

C. f (x) = –7x4 + 3x2 + x

D. f (x) = 6x3 + 2x2 – x – 1

3. Express in equivalent form: log (x2 + 3) – 4 log z + log 1 3. ______

A. log

B.

C. log

D. log + 4 − 4

vvvv

MATH 115 Precalculus Spring, 2015, V4.1

Page 2 of 7

4. Determine the interval(s) on which the function is increasing. 4. ______

A. (−4 / 3, 1)

B. (−¥,−5/ 3) , (0, 2) , and (11/ 3,¥)

C. (−1,1) and (3,¥)

D. (−¥,0) and (2,¥)

5. Which of the functions corresponds to the graph? 5. ______

A. ( ) 2 x f x e− =

B. ( ) 2x f x e− =

C. ( ) 1 x f x e− = +

D. ( ) 2 x f x e− = +

MATH 115 Precalculus Spring, 2015, V4.1

Page 3 of 7

6. Which of the functions corresponds to the graph? 6. ______

A. f (x) = cos(2x) + 2

B. f (x) = 2 cos x + 1

C. f (x) = sin x + 3

D. f (x) = 3 – sin x

SHORT ANSWER:

7. Points (3, –1) and (9, 1) are endpoints of the diameter of a circle.

(a) What is the exact length of the diameter? (Simplify as much as possible) Answer: ________

(b) What is the center of the circle? Answer: ____________

(c) What is the equation of the circle? Answer: ___________________________

8. Find the value of the logarithm:log

. Answer: ____________

9. A salesperson earns a base salary of $1,900 per month and a commission of 7.3% on the

amount of sales made. If the salesperson has a paycheck of $3,768.80 for one month, what was

the amount of sales for the month? Answer: _____________

MATH 115 Precalculus Spring, 2015, V4.1

Page 4 of 7

10. A can of soda at 78° F. is placed in a refrigerator that maintains a constant temperature of 35°

F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by

T(t) = 35 + 43e

– 0.058 t

Find the temperature of the soda 12 minutes after it is placed in the refrigerator. (Round to the

nearest tenth of a degree.) Answer: ________

11. Given the function =56

−12

, find a formula for the inverse function.

Answer: __________________

12. (a) State the reference angle associated with 168°. Answer: ________

(b) Convert 168° to radians. Leave the answer in terms of p. Answer: ________

13. Given y = 3 sin(8x – p), state the

(a) period Answer: ________

(b) phase shift Answer: ________

14. Solve the trigonometric equation (cos x)(2sin x + 1) = 0 in the interval [0, 360°).

Answer: _________________

15. (a) Find the exact value of cos# tan '

Answer: ________

(b) Find the exact value of sin# sin '

Answer: ________

16. For the parabola given by (y – 7)2 = 8(x + 6), find the following:

(a) direction parabola opens (to the left, right, up, or down) Answer: ___________

(b) vertex Answer: ___________

(c) focus Answer: ___________

MATH 115 Precalculus Spring, 2015, V4.1

Page 5 of 7

17. Let

2

2

5 5

( )

9

x

f x

x

+

=

−

.

(a) State the domain. Answer: _________________

(b) State the horizontal asymptote. Answer: _________________

(c) State the vertical asymptote(s). Answer: _________________

(d) Which of the following represents the graph of

2

2

5 5

( )

9

x

f x

x

+

=

−

? Answer: ______________

GRAPH A. GRAPH B.

GRAPH C. GRAPH D.

MATH 115 Precalculus Spring, 2015, V4.1

Page 6 of 7

SHORT ANSWER, with work required to be shown, as indicated.

18. Find the equation for a line which passes through the points (1, 3) and (–8, 6). Write the

equation in slope-intercept form. Show work.

19. Find the exact solutions and simplify as much as possible: 9x2 + 29 = 30x. Show work.

20. Let f (x) = 3x2 – 7 and g(x) = x – 2.

(a) Find the composite function ( f o g)(x) and simplify. Show work.

(b) Find ( f o g) (−1) . Show work.

21. A projectile is launched from a platform 20 feet high with an initial velocity of 104 feet per second,

The height h of the projectile at t seconds after launch is given by h = –16t2 + 104t + 20 feet.

(a) How many seconds after launch does the projectile attain maximum height? Show work.

(b) What is the maximum height? Show work.

22. Solve:

+ )

#* = 0. Show work.

23. Suppose that cos q = 12/13 and that q is a Quadrant IV angle.

(a) Find the exact value of sin q. Show work.

(b) Find the exact value of sin 2q. Show work.

24. Prove the identity (sin x + cos x)2 – 1= sin 2x

MATH 115 Precalculus Spring, 2015, V4.1

Page 7 of 7

25. From a point 63 feet from the base of a redwood tree, the angle of elevation to the top of the

tree is 51.8°. Find the height of the tree to the nearest foot. Show work.

(sketch is not to scale)

26. For the triangle ABC, we are given that A = 44°, B = 62°, and c = 30.0.

Find the length of side a, rounded to the nearest hundredth. Show work.

27. Let u = 4, 3 and v = 9, –12.

(b) Calculate the dot product u • v. Show work.

(c) Determine the angle between u and v. Round the result to the nearest degree. Show work.

28. An ellipse has the equation

#,

+ -

= 1

(a) Is the major axis horizontal or vertical?

(b) Find the exact values of the foci of the ellipse. Show work.

There are 28 problems.

Problems #1–6 are Multiple Choice.

Problems #7–17 are Short Answer. (Work not required to be shown)

Problems #18–28 are Short Answer with work required to be shown.

MULTIPLE CHOICE

1. Solve, and express the answer in interval notation: | 9 – 3x | ³ 6. 1. _______

A. (–¥, 5] È [1, ¥)

B. [1, ¥)

C. [1, 5]

D. (–¥, 1] È [5, ¥)

2. Which of the following polynomials has a graph which exhibits the end behavior of upward to

the left and upward to the right? 2. _______

A. f (x) = 5x6 – x3 – x2 – 5

B. f (x) = –2x3 + 8x2 – x + 3

C. f (x) = –7x4 + 3x2 + x

D. f (x) = 6x3 + 2x2 – x – 1

3. Express in equivalent form: log (x2 + 3) – 4 log z + log 1 3. ______

A. log

B.

C. log

D. log + 4 − 4

vvvv

MATH 115 Precalculus Spring, 2015, V4.1

Page 2 of 7

4. Determine the interval(s) on which the function is increasing. 4. ______

A. (−4 / 3, 1)

B. (−¥,−5/ 3) , (0, 2) , and (11/ 3,¥)

C. (−1,1) and (3,¥)

D. (−¥,0) and (2,¥)

5. Which of the functions corresponds to the graph? 5. ______

A. ( ) 2 x f x e− =

B. ( ) 2x f x e− =

C. ( ) 1 x f x e− = +

D. ( ) 2 x f x e− = +

MATH 115 Precalculus Spring, 2015, V4.1

Page 3 of 7

6. Which of the functions corresponds to the graph? 6. ______

A. f (x) = cos(2x) + 2

B. f (x) = 2 cos x + 1

C. f (x) = sin x + 3

D. f (x) = 3 – sin x

SHORT ANSWER:

7. Points (3, –1) and (9, 1) are endpoints of the diameter of a circle.

(a) What is the exact length of the diameter? (Simplify as much as possible) Answer: ________

(b) What is the center of the circle? Answer: ____________

(c) What is the equation of the circle? Answer: ___________________________

8. Find the value of the logarithm:log

. Answer: ____________

9. A salesperson earns a base salary of $1,900 per month and a commission of 7.3% on the

amount of sales made. If the salesperson has a paycheck of $3,768.80 for one month, what was

the amount of sales for the month? Answer: _____________

MATH 115 Precalculus Spring, 2015, V4.1

Page 4 of 7

10. A can of soda at 78° F. is placed in a refrigerator that maintains a constant temperature of 35°

F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by

T(t) = 35 + 43e

– 0.058 t

Find the temperature of the soda 12 minutes after it is placed in the refrigerator. (Round to the

nearest tenth of a degree.) Answer: ________

11. Given the function =56

−12

, find a formula for the inverse function.

Answer: __________________

12. (a) State the reference angle associated with 168°. Answer: ________

(b) Convert 168° to radians. Leave the answer in terms of p. Answer: ________

13. Given y = 3 sin(8x – p), state the

(a) period Answer: ________

(b) phase shift Answer: ________

14. Solve the trigonometric equation (cos x)(2sin x + 1) = 0 in the interval [0, 360°).

Answer: _________________

15. (a) Find the exact value of cos# tan '

Answer: ________

(b) Find the exact value of sin# sin '

Answer: ________

16. For the parabola given by (y – 7)2 = 8(x + 6), find the following:

(a) direction parabola opens (to the left, right, up, or down) Answer: ___________

(b) vertex Answer: ___________

(c) focus Answer: ___________

MATH 115 Precalculus Spring, 2015, V4.1

Page 5 of 7

17. Let

2

2

5 5

( )

9

x

f x

x

+

=

−

.

(a) State the domain. Answer: _________________

(b) State the horizontal asymptote. Answer: _________________

(c) State the vertical asymptote(s). Answer: _________________

(d) Which of the following represents the graph of

2

2

5 5

( )

9

x

f x

x

+

=

−

? Answer: ______________

GRAPH A. GRAPH B.

GRAPH C. GRAPH D.

MATH 115 Precalculus Spring, 2015, V4.1

Page 6 of 7

SHORT ANSWER, with work required to be shown, as indicated.

18. Find the equation for a line which passes through the points (1, 3) and (–8, 6). Write the

equation in slope-intercept form. Show work.

19. Find the exact solutions and simplify as much as possible: 9x2 + 29 = 30x. Show work.

20. Let f (x) = 3x2 – 7 and g(x) = x – 2.

(a) Find the composite function ( f o g)(x) and simplify. Show work.

(b) Find ( f o g) (−1) . Show work.

21. A projectile is launched from a platform 20 feet high with an initial velocity of 104 feet per second,

The height h of the projectile at t seconds after launch is given by h = –16t2 + 104t + 20 feet.

(a) How many seconds after launch does the projectile attain maximum height? Show work.

(b) What is the maximum height? Show work.

22. Solve:

+ )

#* = 0. Show work.

23. Suppose that cos q = 12/13 and that q is a Quadrant IV angle.

(a) Find the exact value of sin q. Show work.

(b) Find the exact value of sin 2q. Show work.

24. Prove the identity (sin x + cos x)2 – 1= sin 2x

MATH 115 Precalculus Spring, 2015, V4.1

Page 7 of 7

25. From a point 63 feet from the base of a redwood tree, the angle of elevation to the top of the

tree is 51.8°. Find the height of the tree to the nearest foot. Show work.

(sketch is not to scale)

26. For the triangle ABC, we are given that A = 44°, B = 62°, and c = 30.0.

Find the length of side a, rounded to the nearest hundredth. Show work.

27. Let u = 4, 3 and v = 9, –12.

(b) Calculate the dot product u • v. Show work.

(c) Determine the angle between u and v. Round the result to the nearest degree. Show work.

28. An ellipse has the equation

#,

+ -

= 1

(a) Is the major axis horizontal or vertical?

(b) Find the exact values of the foci of the ellipse. Show work.

Show More

Show Less

Was this answer helpful?

Describe your issueThe assistant will guide you

Chat 1:1 with a tutorLicensed Experts are available 24/7

100% satisfaction guaranteeGet all the answers you need

Related Pre-Calculus Questions

1. Use the polynomial approximations to the function sin x

1. Use the polynomial approximations to the function sin x derived in class to find a polynomial approximation to sin x on the interval [-1, 1] so that the error at any point is less than 0:01. (a) Wr… read more

I just need an answer for some questions. Just need answers

Just need answers for my homework as I've missed some work. … read more

I need someone to help me with this. I need to compare my

HI, I need someone to help me with this. I need to compare my answers before I turn this in. Thank you. Exam: 250311RR - Trigonometric Functions 1. Find a positive angle less than 360° that's cotermin… read more

I have 28 precalculus questions as part of a review

I have 28 precalculus questions as part of a review for an exam. If someone could work them, I can send them to you via upload or email.… read more

1. Convert 2π/3 radians into degrees. 2. Determine the

1. Convert 2π/3 radians into degrees. 2. Determine the length of a shadow cast by a flagpole that is 15 feet high when the sun has an angle of elevation of 28˚ Round your answer to the nearest foot. 3… read more

Precalculus Problems. (big bonus for great solutions) 1. Solve

Precalculus Problems. (big bonus for great solutions) 1. Solve the following equation for x: log2(x + 7) + log2(x + 8) = 1 Note: Be sure to plug any solutions back into the original equation; if they … read more

1. Find the complete exact solution of sin x = −√3/2. 2. Solve

1. Find the complete exact solution of sin x = −√3/2. 2. Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to two decimal places. 3. Solve tan² x + tan x – 1 = 0 for the principal value(s) t… read more

1. Simplify the following expression: sin 4x cos 3x + sin 3x

1. Simplify the following expression: sin 4x cos 3x + sin 3x cos 4x 2. Use half-angle formulas to solve the given problem. Find tanx if sin (x/2)=24/26 *x represents the angle sign-looks like a 0 with… read more

1- what is the frequency of y=(pie/3 x)? a. pie/3 b. 1/3

1- what is the frequency of y=(pie/3 x)? a. pie/3 b. 1/3 c. 1/6 d. 3 2- how many soltions does the system x=10y y=sin x have? a. 4 b. 10 c. 6 d. 7 3. what is tan the power of -1 root3/3 ? a. pie/4 b. … read more

MATH 115 FINAL EXAMINATION This is an open-book exam. You

MATH 115 FINAL EXAMINATION This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. You must complete the exam individual… read more

1. calculate the anti derivative of x cube dx a. x square

1. calculate the anti derivative of x cube dx a. x square + c b. 3x square + c c. x the power of 4 + c d. x the power of 4/4 + c 2. calculate the anti derivative of x the power of 2/3 dx. a. 2/3x the … read more

Hey Steve its Eva can you help me show all work1.Given f(x)

Hey Steve its Eva can you help me show all work 1.Given f(x) = 3(x^2) + x, find ( f(2+h) - f(2) )/h 2.Find the domain of the radical of (4 – x) and explain your answer. 3.Graph each function (reminder… read more

1. Calculate the length of side X given that sin = 0.82.

1. Calculate the length of side X given that sin = 0.8 2. Calculate the value of cos 3. Use the law of sines to determine the measure of an angle b in the figure below… read more

"for ryan" 1.fill in the table shown below for the function

"for ryan" 1.fill in the table shown below for the function an plot the graph from these points. x -pi/2 -pi/3 -pi/4 -pi/6 0 pi/6 pi/4 pi/3 pi/2 2pi/3 3pi/4 5pi/6 pi y y=5 sec x (round to one decimal … read more

"for ryan" 1.find tan 2x if sin x = 0.5(in sec quad0 tan2x=? 2.simplify

"for ryan" 1.find tan 2x if sin x = 0.5(in sec quad0 tan2x=? 2.simplify the given expression by giving the results in terms of one half of the given angle.then use the calculator to verify the result.… read more

I would be extremely grateful if you can provide an answer

I would be extremely grateful if you can provide an answer for the following integration questions. Thank you very much for your help. 1 i) Explain why the graph of the function f(x) = (3x – pie) cos(… read more

1. Verify that the functions f and g are inverse of each other

1. Verify that the functions f and g are inverse of each other by showing that f(g (x) ) = x and g (f (x) ) = x. Give any values of x that need to be excluded. f(x) = x – 5 / 2x + 3; g(x) = 3x + 5 / 1… read more

Disclaimer: Information in questions, answers, and other posts on this site ("Posts") comes from individual users, not JustAnswer; JustAnswer is not responsible for Posts. Posts are for general information, are not intended to substitute for informed professional advice (medical, legal, veterinary, financial, etc.), or to establish a professional-client relationship. The site and services are provided "as is" with no warranty or representations by JustAnswer regarding the qualifications of Experts. To see what credentials have been verified by a third-party service, please click on the "Verified" symbol in some Experts' profiles. JustAnswer is not intended or designed for EMERGENCY questions which should be directed immediately by telephone or in-person to qualified professionals.

Ask-a-doc Web sites: If you've got a quick question, you can try to get an answer from sites that say they have various specialists on hand to give quick answers... Justanswer.com.

JustAnswer.com...has seen a spike since October in legal questions from readers about layoffs, unemployment and severance.

Web sites like justanswer.com/legal

...leave nothing to chance.

...leave nothing to chance.

Traffic on JustAnswer rose 14 percent...and had nearly 400,000 page views in 30 days...inquiries related to stress, high blood pressure, drinking and heart pain jumped 33 percent.

Tory Johnson, GMA Workplace Contributor, discusses work-from-home jobs, such as JustAnswer in which verified Experts answer people’s questions.

I will tell you that...the things you have to go through to be an Expert are quite rigorous.

Wonderful service, prompt, efficient, and accurate. Couldn't have asked for more. I cannot thank you enough for your help.

Freshfield, Liverpool, UK

This expert is wonderful. They truly know what they are talking about, and they actually care about you. They really helped put my nerves at ease. Thank you so much!!!!

Los Angeles, CA

Thank you for all your help. It is nice to know that this service is here for people like myself, who need answers fast and are not sure who to consult.

Hesperia, CA

I couldn't be more satisfied! This is the site I will always come to when I need a second opinion.

Kernersville, NC

Just let me say that this encounter has been entirely professional and most helpful. I liked that I could ask additional questions and get answered in a very short turn around.

Woodstock, NY

Thank you so much for taking your time and knowledge to support my concerns. Not only did you answer my questions, you even took it a step further with replying with more pertinent information I needed to know.

Elkton, Maryland

He answered my question promptly and gave me accurate, detailed information. If all of your experts are half as good, you have a great thing going here.

Dallas, TX

< Previous | Next >

Mr. Gregory White

Master's Degree

167 satisfied customers

M.A., M.S. Education / Educational Administration

rajeevanpillai

Master's Degree

149 satisfied customers

B.Sc in Mathematics and M.Sc, M Phil in Statistics

mhasan420

Master's Degree

37 satisfied customers

BA Maths, Oxford

JACUSTOMER-yrynbdjl-

Master's Degree

13 satisfied customers

I have taught college Mathematics for the past 10 years.

Dr. Arthur Rubin

Doctoral Degree

12 satisfied customers

Ph.D. in Mathematics, 1978, from the California Institute of Technology, over 20 published papers

Sandhya_sharma

Master's Degree

1,085 satisfied customers

I hold M.Sc and M.Phil degrees in math and have several years of teaching experience.

Kofi

PhD in Statistics

765 satisfied customers

Masters in Mathematics and Statistics

< Previous | Next >

Disclaimer: Information in questions, answers, and other posts on this site ("Posts") comes from individual users, not JustAnswer; JustAnswer is not responsible for Posts. Posts are for general information, are not intended to substitute for informed professional advice (medical, legal, veterinary, financial, etc.), or to establish a professional-client relationship. The site and services are provided "as is" with no warranty or representations by JustAnswer regarding the qualifications of Experts. To see what credentials have been verified by a third-party service, please click on the "Verified" symbol in some Experts' profiles. JustAnswer is not intended or designed for EMERGENCY questions which should be directed immediately by telephone or in-person to qualified professionals.