Pre-Calc. Final Review

May-June 2013

Assignments will be checked every day

Typed answers will be given at the beginning of the

hour so you can check your work. They will be

returned by the end of the hour.

No late work will be accepted

Review Packet is DUE the day of your final exam

Day/Date Assignment Completed

Thursday 5/23 Chapter 5 #1-26 all Chapter 6 #1-19 all

Friday 5/24 Chapter 7 #1-26 all Chapter 8 #1-30 all

Tuesday 5/28 Chapter 11 #1-30 all Wednesday 5/29 Chapter 12 #1-14 all

FINAL EXAM SCHEDULE: All exams begin promptly at 8:00 a.m.

Thursday, May 30th 6th & 7th hour exams [90 min each]

Friday, May 31st 4th & 5th hour exams [90 min each]

Monday, June 3rd 2nd & 3rd hour exams [90 min each]

Tuesday, June 4th 1st hour exam [90 min]

Semester 2 Final Exam REVIEW Name:_______________________________________

Pre-Calculus

Find the missing coordinate of P, using the fact that P lies on the unit circle in the given quadrant.

1.

; Quad III 2.

; Quad II 3.

; Quad IV

Find a) the reference angle and b) the terminal point P(x, y) determined by the angle.

4.

5.

6.

7. 960º

Find the exact value of the trigonometric function.

8.

9. 10.

11.

12. 13.

The terminal point P(x, y) determined by an angle is given. Find and .

14.

15.

Chapter 5 – Trigonometric Functions of Real Numbers

Find the value of the trigonometric functions of given the quadrant in which the terminal point lies.

16.

; Quad II 17.

; Quad III

Write the first trigonometric function in terms of the second for in the given quadrant.

18. Quad III 19. Quad I

Find the amplitude, period, vertical shift, and phase shift of the function. Then graph the function.

20.

Amplitude:______________

Period:__________________

Phase Shift:______________

Vertical Shift:____________

Use the graph to find the amplitude, period, and phase shift of the curve. Then write an equation that

represents the curve.

21. 22.

Amplitude:__________________ Amplitude:__________________

Period:______________________ Period:______________________

Phase Shift:__________________ Phase Shift:__________________

Equation:____________________ Equation:____________________

0

-2

2

0

-3

3

Identify whether the graph represents .

23. 24.

25. 26.

1

-1

--1

1

1

-1

1

-1

1. Convert to radians. 2. Convert

to degrees.

3. Find the length of an arc that subtends 4. Find the area of a sector with central angle

a central angle of in a circle with in a circle with radius 3 mi.

radius 10 m.

5. A woman is riding a bicycle whose wheels are 28 in. in diameter. If the wheels rotate at 130

revolutions per minute (rpm), find the speed at which she is traveling in mi/h.

6. A boy rotates a stone in a 3 ft. long sling at the rate of 15 revolutions every 10 seconds. Find the

linear and angular velocities of the stone.

Find the value of x in the triangle.

7. 8. 9.

10. 11.

Chapter 6 – Trigonometric Functions of Angles

12

x

36º

53º 25

x 68º

1000

x

60º

65º

50

x

60º x

85

30º

12. From the top of a 200 ft. lighthouse, the angle of depression to a ship in the ocean is 23º. How far

is the ship from the base of the lighthouse?

13. To estimate the height of a mountain above a level plain, the angle of elevation to the top of the

mountain is measured to be 32º. One thousand feet closer to the mountain along the plain, it is

found that the angle of elevation is 35º. Estimate the height of the mountain.

Solve the triangle with the given information.

14. A = 23º, B = 110º, c = 50 15. a = 3, b = 4, C = 53º

16. a = 28, b = 15, A = 110º 17. a = 20, b = 25, c = 22

18. In triangle ABC, a = 26, c = 15, C = 29º. Find angle A.

19. Two tugboats that are 120 ft. apart are pulling a barge behind them. Each tugboat is connected

to the barge by a cable. If the length of one cable is 212 ft. and the length of the other is 230 ft.,

find the angle formed by the two cables.

Simplify the expression.

1.

2.

3.

4. 5. 6.

Use an addition or subtraction formula to find the EXACT value of the expression.

7. 8. 9.

Find and from the given information.

10.

; 11. x in quadrant II

Chapter 7 – Analytic Trigonometry

Use a half-angle formula to find the EXACT value of the expression.

12. 13. 14.

Find the EXACT value of each expression, if it is defined.

15.

16.

17.

18.

19.

20.

Find all solutions of the equation. Work and answers must be in radians.

21. 22.

23. 24.

Find all solutions of the equation in the interval . 25. 26.

2

2

3

3

3

2

3

5 3

4

6

6

5

6

7 6

11

0

Graph each point and label them accordingly. Then find the rectangular coordinates of each point.

1.

2.

3.

4.

A point P(r, θ) is given in polar coordinates. Give two other polar representations of the point, one with

r < 0 and one with r > 0.

5.

6.

Convert the rectangular coordinates to polar coordinates with r > 0 and .

7. 8.

Chapter 8 – Polar Coordinates & Vectors

Match the equation with its graph (do this WITHOUT your calculator!). Name each shape.

9.

10. 11.

12. 13. 14.

A. B. C.

D. E. F.

A complex number is given. (a) Graph the number in the complex plane below. (b) Find the

modulus. (c) Write the number in polar form.

15. 16.

Find the product and the quotient

. Express your answer in polar form.

17.

Find the indicated power using DeMoivre’s Theorem. Write your answer in complex number form.

18.

Express the vector with initial point P and terminal point Q in component form.

19. 20.

Find u + v, -3u + 5v, , and .

21. 22.

23. Find the vector with and .

24. Find the magnitude and direction of the vector .

Find (a) and (b) the angle between u and v to the nearest degree.

25. 26.

27. Determine whether and are orthogonal.

28. Given , find .

29. Find the work done by the force in moving an object from P(0, 10) to Q(5, 25).

30. A constant force moves an object along a straight line from point (2, 5) to the point (11,

13). Find the work done if the distance is measured in feet and the force is measured in pounds.

Find the first five terms of the sequence.

1. 2.

3. Find the sum: 4. Write the sum of without sigma notation.

Write the sum using sigma notation.

5. 3 +6 + 9 + + 99 6.

Determine whether the sequence is arithmetic or geometric, then find the nth term of the sequence.

7. 3, 6, 9, 12, … 8. 27, -9, 3, -1, …

9. The 6th term of an arithmetic sequence is 17 and the fourth term is 11. Find the 2nd term.

10. Which term of the arithmetic sequence 1, 5, 9, … is 401?

Chapter 11 – Sequences & Series

11. The common ratio in a geometric sequence is

, and the third term is 9. Find the 5th term.

12. Find the partial sum of the arithmetic sequence with the given conditions: a = 1, d = 2, n = 10.

13. Find the sum of the arithmetic sequence: 1 + 5 + 9 + + 401

14. The first term of an arithmetic sequence is 1 and the fourth term is 16. How many terms of this

sequence must be added to get 2356?

15. Find the partial sum of the geometric sequence with the given conditions: a =5, r = 2, n = 6.

16. Find the sum of the geometric sequence: 1+ 3 + 9 + …. + 2187

17. Find the sum of the infinite geometric series:

18. Express as a fraction. YOU MUST SHOW WORK FOR THIS!!!!

Use Mathematical Induction to prove the following formulas. Show all four steps!

19.

20.

Expand the expression (you can use EITHER Pascal’s Triangle or the Binomial Theorem).

21. 22.

23. 24.

25. Find the 24th term of the expansion .

26. Find the 28th term of the expansion .

27. Find the first three terms in the expansion of .

28. Find the last three terms in the expansion of 5232 yx .

29. Find the term containing in the expansion of .

30. Find the term containing 6y in the expansion of 5222 yx .

1. For the function g whose graph is given, state the value of the given quantity, if it exists.

a) b) c)

d) e) f)

g) g(2) h) i) g(0)

Find the limit algebraically.

2. 3. 4.

5. 6. 7.

8. Evaluate the limits using the function below.

a) b) c) d) e)

Chapter 12 – Limits

Find an equation of the tangent line to the curve at the given point.

9. at (1, 1) 10.

at (-1, 1)

11. at (4, 2)

Find the derivative of the function at the given number.

12. at 3 13.

at 2

14. at 1