enochs pre-ap sm3 summer assignment sm3 summer hw 18-19.pdfpage 2 enochs pre-ap sm3 summer...

Enochs Pre-AP SM3 Summer Assignment 2018-19

Mrs. Christina Rubalcava

Email: [email protected]

Phone: (209) 492-6300

Mrs. Rubalcava’s Class Material:

- Graph-ruled notebook (at least 2),

- Math binder or section of a binder,

- Colored pencils, pencils/erasers, pens,

- Highlighters & Pen tip whiteboard marker

- Graphing or scientific calculator.

All notes, which include important definitions,

formulas, & examples shown in class should be

done in your notebook. The teacher has the

discretion to perform random notebook checks

for a grade.

Mrs. Dodds & Mrs. Rubalcava will teach Pre-AP SM3 classes during 2018-19 school year. Both teachers

require the same Summer Assignment. You can find additional resources for the summer assignment

by logging into Schoology, clicking “courses”, clicking “join”, & then typing in the code: ZVXS2-JFW6P.

Mrs. Karolin Dodds

Email: [email protected]

Phone: (209) 574-1719

Mrs. Dodds’s Class Material:

- 2 inch 3-ring Binder for Math ONLY.

- Pen, Pencil, Eraser, & color pens or highlighters.

- TI-83 Plus Graphing or scientific calculator.

- Date & name all your notes & assignments.

- File related notes, assignments, handouts, &

returned quizzes together by date they were done.

- Have enough graph & lined paper in your binder.

- Your best resource for studying & preparing for any

Quiz or Test is your Math Binder.

In fairness to all, calculators with a computer algebraic system (CAS) will NOT be used on Quizzes or Tests.

Be noted that you will be taught to do calculations in this class with & without a calculator;

thus, you will be Quizzed and Tested in both ways.

SUMMER ASSIGNMENT: We strongly suggest that you take this assignment seriously. 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,

free on-line help, or your old math notebook. You may also refer to the websites below as a resource.

In addition, you can study the examples offered at the last few pages of this summer assignment.

Virtual Math Lab http://www.wtamu.edu/academic/anns/mps/math/mathlab/

Algebra Help https://www.wyzant.com/resources/lessons/math/algebra

Purple Math http://www.purplemath.com/

Khan Academy https://www.khanacademy.org/

MathBits.com http://mathbits.com/

The Math Page http://www.themathpage.com/

Math Open Reference http://www.mathopenref.com/

You must offer legible & legitimate work that supports your answer. The Summer Assignment will be

collected & graded based on completion & correctness on the 1st day of school, August 14th.

Points will be deducted if the packet is turned in late. You will be tested on the topics from the Summer

Assignment on Friday, August 17th. There will be NO RETAKES for a Poor Test Score, so seek out all

the help that you require prior to this test. The test will assess mastery & retention of the prerequisite

math skills needed to succeed in Pre-AP SM3.

mailto:[email protected]

mailto:[email protected]

http://www.wtamu.edu/academic/anns/mps/math/mathlab/

https://www.wyzant.com/resources/lessons/math/algebra

http://www.purplemath.com/

https://www.khanacademy.org/

http://mathbits.com/

http://www.themathpage.com/

http://www.mathopenref.com/


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

1] 08x 2]

25 3] yx 214

4] 3

25x 5] 4

5 23x y 6] 7

3

x

x

7]

3

1

2

1

x

x 8]

3

2

6

5

xy

x y 9]

321

2323

cba

cba

10]

1

481 11] 5

3

32 12] 32 5 4

13] 2

1

4

6

25

9

x

x 14]

1

3125

64

15] 8 216x y

16] 9454 yx 17] 6

4

25

49

x

y 18]

36

3 5

4

3

x y

x y

19] yy 5018 20] 9

3

4

23

12

15

9

8

x

yx

y

yx

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

21] 3 12

8

x

x

22] 3 116

32

x 23] 6432 x 24] 4

27 25

125 9

x

25] 3 3 1125

25

x 26] 4 1

25 4

16 5

x

27] 927 x 28] 3 232 8x x


Add, Subtract, & Multiply Polynomials Write your answer in standard form,2ax bx c .

1] 45363 22 xxxx 2] 12753 22 xxx 3] 2 23 2 4 5x x x

4] 2 2 3 24 3 3 2 6 4y y y y y 5] 14 32 xx 6] 43 2 2 xxx

7] 2

5x 8] 2

7x 9] 2

3 5x

10] 245 yx 11] 2

4 3x 12] 8 8x x

13] 2 2x x 14] 3 32 4 2 4k m k m 15] 2

k m

Factor Polynomials Do not stop factoring, unless completely factored.

16] 212 18x x 17] 3532 xxx 18] 169 2 y 19] 24 25

9 16m

20] 16249 2 kk 21] 156 2 yy 22] 210 2 12m m 23] 22 32 yxyx

24] 22 5 3x x 25] yyy 25204 23 26] 22 246 xxx 27] 5 3 23 5 15x x x

28] xxx 14162 23 29] 24 12 9x x 30]

22 7 3x x 31] 2 23 2a ab b


Solving Equations Do Not use Calculator! “SHOW WORK SUPPORTING YOUR ANSWER”

1] xxx 682534 2] 25124353 kkk 3] 5

4

3

2x

4] 6

1

4

1

3

1 xx 5]

4 52 4

3

xx

6]

2

1

4

5

3

1

kk

7] 31056 x 8] 272525

3x 9] 52 2 4 3 1x

10] 33 40 2 17x 11] 96124 4

3

x 12]

5

32 21 85x

Solving Absolute Value Equations “SHOW WORK SUPPORTING YOUR ANSWER”

13] 2 6 4x 14] 4 2 5 9 3x 15] 1892

3x

16] 7 3 10 2x 17] 3 2 4 5x x 18] 4 3 6 2x


1. Solve by Factoring: “SHOW WORK SUPPORTING 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:

5] 132 2 xx 6] 0423 2 xx

7] 24 12 9x x 8] 422 xx

3. Solve by Completing the Square:

9] 03102 xx 10] xx 1033 2

11] 216243 2 xx 12] 0232 xx

Various Methods used to Solve Quadratic Equations


4. Solve by Square Root:

1] 15217322

x 2] 21

5 123

x 3] 2

5 7 6 141x

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

4] xx 3230 5] 327 xx 6] 1462 xx

7] 2 8 2 2 1x x 8] 3 30 2x x 9] 2 8 3 2x x

Add, Subtract, & Multiply Complex Numbers a bi Write the result in standard form, a bi .

10] ii 4332 11] ii 932 12] 5 3 2 9i

13] 8157 2 i 14] 33 25 8 9 15] ii 31 4

16] 3 5 4 2i i 17] 4 6 5i i


Multiply each complex number by its conjugate.

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

Rationalize & write each complex number in standard form, a bi . Meaning 5 3

4 2i and NOT

5 6

4

i

4] 7

2i 5]

i

i

3

2

6] i

i

2 7]

6

3 i

8] i

i

42

3

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

9] 1942 xx 10] 23 8 19 5x x

Solving Linear & Compound Inequalities

11] 3 2 2 3

26 8

x xx

12] 2444625 xx 13] 7382 x 14] 7 23 5 x


A

B C

12

Right Triangle Trigonometry Find the trigonometric ratios of the given triangle. If possible, reduce your answers.

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

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

Solve the given right triangles (list all side & angle measures for each triangle). You may use a calculator when

necessary & round your answers to the underneath.

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.

Radian & Degree Measure

Write the radian measure of the angle given in degrees.

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

For problems 11 & 12, find the arc length and sector area in degrees. No calculator, give EXACT answers.

20] 21]

x y

12

B

z

5


Graphing Functions & Analyzing their Details. Follow these instructions.

Do not use a calculator. Graph neatly & show all the important details of each specific graph.

“x-intercepts” are also known as, “zeros” or “roots”.

Calculate x-intercept & y-intercept Algebraicaly & make sure they agree with what your graph displays.

Write x & y-intercepts as points (x, 0) and (0, y).

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

Min/Max value refer to the Highest or Lowest y-value on the entire graph.

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: .


.


.

Max/Min Values:

.

Zero(s): .

y-intercept: .

Domain: .

Range: .


.


.

Max/Min Values:

.

Zero(s): .

y-intercept: .

Domain: .

Range: .


.


.

Max/Min Values:

.


5] 24

3y x 6] 2 3 6y x

7] 412 xy 8] 12 xy

Zero(s): .

y-intercept: .

Domain: .

Range: .


.


.

Max/Min Values:

.

Zero(s): .

y-intercept: .

Domain: .

Range: .


.


.

Max/Min Values:

.

Zero(s): .

y-intercept: .

Domain: .

Range: .


.


.

Max/Min Values:

.

.

Zero(s): .

y-intercept: .

Domain: .

Range: .


.


.

Max/Min Values:

.

.

Zero(s): .

y-intercept: .

Domain: .

Range: .

.

Increasing Intervals: .

Decreasing Intervals: .

Max/Min Values: .

9] 35 xy


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: .


.


.

Max/Min Values:

.

.

Zero(s): .

y-intercept: .

Domain: .

Range: .

.

Zero(s): .

y-intercept: .

Domain: .

Range: .


.


.

Max/Min Values:

.

.

Zero(s): .

y-intercept: .

Domain: .

Range: .


.


.

Max/Min Values:

.

.

Zero(s): .

y-intercept: .

Domain: .

Range: .

.


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: .


.


.

.

Zero(s): .

y-intercept: .

Domain: .

Range: .


.


.

.

Zero(s): .

y-intercept: .

Domain: .

Range: .

.

Zero(s): .

y-intercept: .

Domain: .

Range: .

.


You DO NOT need to print these pages; they are for your reference only!

You are advised to use the next few pages of examples to help refresh your memory or relearn the

essential mathematical skills that you may have forgotten or not fully mastered.

Simplifying Radicals

Solving Absolute Value Equations

Law of Exponents

Multiplying Monomials


Factoring

Multiplying Polynomials

Dividing Monomials


Graphing a Piecewise Function

Solution graph

Solving Equations by Factoring


Quadratic Function (Polynomial of degree 2): Shape of the graph of a quadratic function is a Parabola. Three parabolas are shown below with important points labeld.

The graph of a quadratic funciton: - can open either upward or downward

- always has a vertex which is either the maximum or minimum

- always has exactly one y-intercept

- can have 0, 1, 2 x-intercepts

* A parabola is symmetric about a line through the vertex called the axis of symmetry.

* A quadratic function can be written in Transformation Form which is 2

f x y a bx h k

* In Transformation Form, the vertex is ,h

kb

and line of symmetry is h

xb

.

* A quadratic function can be written in Polynomial Form which is 2 f x y ax bx c

* In Polynomial Form, the vertex is , 2 2

b bf

a a

and line of symmetry is 2

bx

a

.

Greatest Integer Funtion


Changing from Polynomial Form to Transformation Form.

Nine Basic Funcitons of Algebra


Complex Numbers: The complex number system contains a number, denoted i , such that 2 1i .

Every complex number can be written in standard form a bi .


Logarithmic Rules

Composition of Fucntions:

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