Are you Ready for Pre-AP PreCalculus? 2020-21

Welcome to Mrs. Dodds Pre-AP PreCalculus.

Email: dodds.k@monet.k12.ca.us Phone: (209) 574-1719

PLEASE, join my "2020 Summer Pre-AP PreCalculus" course on Schoology to receive additional help & resources during summer. You can join the course by logging into Schoology, click on “courses”, click on “join”, & type in the code: VCPW-RF79-B5R86. My plan is to offer a two-week Virtual Summer Boot Camp at the end of July. However I was told, that may not be possible. There will be a definite decision made by the district in mid-July. I will keep you posted via schoology as soon as I know. The purpose of the Boot Camp is to help you refresh your prerequisite Math skills for PreCalculus, & to teach the essential mathematical standards that were not taught due to the COVID-19 pandemic. If I can offer the Boot Camp, I will be using the above Schoology course to have virtual conferences for teaching and tutoring.

The summer assignment is designed to help you Review, Practice, & Deepen your understanding & Fluency of the Essential Mathematical Skills NECESSARY for Success in PreCalculus. It is imperative to know confidently: What, When, Why, & How you can Apply Each Rule. I strongly suggest that you take this assignment seriously. Study the given rules & examples before attempting the Assignment. The goal is Not to just get the assignment done, but for you to thoroughly Master the Required Skills or Re-Learn the Skills you Struggle with. If you have difficulty with a question, DO NOT SKIP IT – RESEARCH IT. That research can be in the form of a textbook, a parent, a friend, or an on-line resource. I will post a list of online resources on schoology that can be helpful to you during your research.

You must offer legible & legitimate work that supports your answer. Neatness is important in Math, so take your time. Calculators are NOT permitted, unless specified. Summer Assignment will be submitted/collected on the first day of school, August 10th. Points will be deducted if the packet is turned in late. This packet will be graded and will count as a 50 point Quiz. There will be a Test on the first week of school covering the mathematical concepts from the summer assignment. There will be NO RETAKES FOR A POOR TEST SCORE. The Test will assess your mastery and retention of the prerequisite math skills to succeed in the Pre-AP PreCalculus. Students who do not meet the standards will be reassigned to a lower level Math class where they can be successful.

How Can You Submit Your Summer Assignment? Option A (Preferred option): I will have the assignment broken into 3 - 4 smaller files and post them on schoology in the course listed above that you must join. You will complete the assignment neatly using Kami, and then you will submit the assignment on Schoology as soon as you are done and have double checked for accuracy. Using Kami is easy & very neat. I will post a video on schoology showing how to upload & use Kami. For graphs, use your Stylus to draw.

Option B (May be a problem): Print ONLY the assignment pages & not the examples. Do the work on the assignment page using pencil; then turn in ONLY the Assignment Pages in order of page # to me on the first day of school, August 10th. However, it will be very difficult to turn in those assignments to me on the first day of school--if we start the school year through distance learning!

DODDS 1

DODDS 2

Rules of Exponents Simplify without calculator. Answers MUST be in terms of Positive Exponents.

1]08x 2] 32 5 4 3] 214x y

4] 3

25x y 5]

36

3 5

4

3

x y

x y

6] 6

4

25

49

x

y

7]

1

2

1

3

x

x

8] 4 954x y 9]

2 3 2

31 2

3a b c

a b c

10]

1

481 11] 5

3

32 12] 2

1

4

6

25

9

x

x

13]

1

3125

64

14] 18 50y y 15] 3 2 3

4 9

8 15

9 12

x y x y

y x

Solve for x without using logs or calculator. “SHOW WORK LEADING TO YOUR ANSWER”

16] 3 12

8

x

x

17] 3 116

32

x 18] 6432 x

19] 4

27 25

125 9

x

20] 4 1

25 4

16 5

x

21] 3 232 8x x

DODDS 3

Add, Subtract, & Multiply Polynomials Write your answer in Standard Form, 2ax bx c .

1] 2 23 5 7 12x x x 2] 2 23 2 4 5x x x 3] 14 32 xx

4] 2 2 3 24 3 3 2 6 4y y y y y 5] 22 3 4x x x 6] 2 2x x

7] 2

5 4x y 8] 2

4 3x 9] 3 32 4 2 4k m k m

Factor Polynomials Apply various factoring techniques to Factor Completely.

10] 212 18x x 11] 3532 xxx 12] 169 2 y 13] 24 25

9 16m

14] 16249 2 kk 15] 156 2 yy 16] 22 5 3x x 17] 24 12 9x x

18] 22 246 xxx 19] 5 3 23 5 15x x x 20] xxx 14162 23 21]

2 23 2a ab b

DODDS 4

Solving Equations for x. Do Not use Calculator! “SHOW WORK LEADING TO YOUR ANSWER”

1] 4 3 5 2 8 6x x x 2] 1 1 1

3 4 6x x 3]

4 52 4

3

xx

4] 1 5 1

3 4 2

k k 5] 6 5 10 3x 6]

32 25 7 2

5x

7] 52 2 4 3 1x 8]

3

44 12 96x 9]

5

32 21 85x

Solving Absolute Value Equations for x. “SHOW WORK SUPPORTING YOUR ANSWER”

10] 2 6 4x 11] 4 2 5 9 3x 12] 1892

3x

13] 7 3 10 2x 14] 3 2 4 5x x 15] 4 3 6 2x

DODDS 5

1. Solve by Factoring: “SHOW WORK LEADING TO YOUR ANSWER.”

1] 063 2 xx 2] 372 2 xx

3] xx 12182 2 4] 24 9 3 2x x x

2. Solve using Quadratic Formula: Make sure your final answer is reduced.

5] 132 2 xx 6] 0423 2 xx

7] 24 12 9x x 8] 422 xx

3. Solve by Completing the Square: Make sure your final answer is reduced.

9] 216243 2 xx 10] xx 1033 2

Various Methods used to Solve Quadratic Equations

DODDS 6

4. Solve by taking the Square Root:

1] 15217322

x 2] 21

5 123

x 3] 2

5 7 6 141x

Solve Square Root Equations: Make sure to check for extraneous solutions!

4] xx 3230 5] 327 xx

6] 2 8 2 2 1x x 7] 2 8 3 2x x

Add, Subtract, & Multiply Complex Numbers a bi Write the result in Standard Form, a bi .

8] ii 4332 9] ii 932 10] 5 3 2 9i

11] 3 5 4 2i i 12] ii 31 4 13] 4 6 5i i

DODDS 7

Multiply each complex number by its conjugate & obtain the result.

1] i65 2] 1 2 i 3] 4 3i

We can’t have any complex number a bi in a denominator. We use Rationalizing to clear the issue.

Rationalize & write each complex number in Standard Form, a bi . Ex: 5 3

4 2i and NOT

5 6

4

i

4] 7

2i 5]

i

i

3

2

6] 6

3 i 7]

i

i

42

3

Solve using Quadratic Formula & write your answer in reduced standard form, a bi .

8] 1942 xx 9] 23 8 19 5x x

Solving Linear & Compound Inequalities Write the final answer in Interval Notations. Ex: ,5

10] 3 2 2 3

26 8

x xx

11] 2444625 xx 12] 7382 x

DODDS 8

A

B C

12

Right Triangle Trigonometry

Find the trigonometric ratios of the given triangle. Make sure to reduce your answers.

1] sin( )A 2] cos( )A 3] tan( )A

4] sin( )B 5] cos( )B 6] tan( )B

Solve each right triangle. (Meaning, find the measure of all missing sides & angles). You may use a calculator when

necessary & round your answers to the hundredth.

7] 8]

9] A 24-foot ladder forms a 65 angle with the ground. The top of the ladder rests against a building. Draw a

diagram to find how high up the building the ladder is to the nearest hundredth of a foot. (need to use a calculator.)

Radian & Degree Measure

Write the radian measure (in terms of 𝜋 ) for each given angle.

10] 135° 11] 60° 12] 270° 13] 120° 14] 30°

Write the degree measure of the angle given in radians.

15] 𝜋

2 16]

2𝜋

3 17] 𝜋 18]

3𝜋

4 19]

5𝜋

6

k

m 12

B

K

5

M N

c

DODDS 9

Graphing Functions & Analyzing their Details. Do NOT use a Graphing Calculator or Demos.

PLEASE, Graph neatly and make sure your graphs display the x- & y-intercepts of each graph.

Calculate x-intercept (x, 0) and y-intercept (0, y) algebraicaly and write them as points. Ex: (-3, 0) & (0, 5)

Write domain, range, increasing or decreasong intervals in Interval Notations. Ex: , 4

A graph may have Minimum, Maximum, & sometimes both. We identify & lable them as Min or Max due to

their y-values compared to the rest of the graph. So, when asked Max/Min Value, find the highest or lowest

y-value and label it Max or Min. Ex: Max value 7.

1] 12 xy 2] xxf4

3)(

3] 2x 4] 3y

Zero(s): .

y-intercept: .

Domain: .

Range: .

Increasing Intervals:

.

Decreasing Intervals:

.

Max/Min Values:

.

Zero(s): .

y-intercept: .

Domain: .

Range: .

Increasing Intervals:

.

Decreasing Intervals:

.

Max/Min Values:

.

Zero(s): .

y-intercept: .

Domain: .

Range: .

Increasing Intervals:

.

Decreasing Intervals:

.

Max/Min Values:

.

Zero(s): .

y-intercept: .

Domain: .

Range: .

Increasing Intervals:

.

Decreasing Intervals:

.

Max/Min Values:

.

DODDS 10

5] 24

3y x 6] 2 3 6y x

7] 412 xy 8] 12 xy

Zero(s): .

y-intercept: .

Domain: .

Range: .

Increasing Intervals:

.

Decreasing Intervals:

.

Max/Min Values:

.

.

Zero(s): .

y-intercept: .

Domain: .

Range: .

Increasing Intervals:

.

Decreasing Intervals:

.

Max/Min Values:

.

.

Zero(s): .

y-intercept: .

Domain: .

Range: .

.

Increasing Intervals: .

Decreasing Intervals: .

Max/Min Values: .

9] 35 xy

Zero(s): .

y-intercept: .

Domain: .

Range: .

Increasing Intervals:

.

Decreasing Intervals:

.

Max/Min Values:

.

Zero(s): .

y-intercept: .

Domain: .

Range: .

Increasing Intervals:

.

Decreasing Intervals:

.

Max/Min Values:

.

DODDS 11

10] 542 xxy 11] 642 2 xxy

12] 2

2 1 6y x 13] 2 2 9x y

14] 2 2

19 25

x y

Zero(s): .

y-intercept: .

Domain: .

Range: .

Increasing Intervals:

.

Decreasing Intervals:

.

Max/Min Values:

.

.

Zero(s): .

y-intercept: .

Domain: .

Range: .

.

Zero(s): .

y-intercept: .

Domain: .

Range: .

Increasing Intervals:

.

Decreasing Intervals:

.

Max/Min Values:

.

.

Zero(s): .

y-intercept: .

Domain: .

Range: .

Increasing Intervals:

.

Decreasing Intervals:

.

Max/Min Values:

.

.

Zero(s): .

y-intercept: .

Domain: .

Range: .

.

DODDS 12

15] 16)1()3( 22 yx 16]

2 22 3

116 4

x y

17]

1 32

1 12)(

2 xxx

xxxf 18]

4 , 138

3 , 1

2 , 51

)(2 xxx

x

xx

xf

Zero(s): .

y-intercept: .

Domain: .

Range: .

Increasing Intervals:

.

Decreasing Intervals:

.

.

Zero(s): .

y-intercept: .

Domain: .

Range: .

Increasing Intervals:

.

Decreasing Intervals:

.

.

Zero(s): .

y-intercept: .

Domain: .

Range: .

.

Zero(s): .

y-intercept: .

Domain: .

Range: .

.