Enochs Pre-AP SM3 Summer Assignment - James … Pre-AP SM3 Summer... · Enochs Pre-AP SM3 Summer...

Enochs Pre-AP SM3 Summer Assignment 2017-18

Mrs. Christina Rubalcava

Enochs High School

Email: [email protected]

Phone: (209) 492-6300

Schoology Classroom Code: JCFN7-TFMNB

(login to your schoology account, click courses,

click join and type in the code)

Mrs. Rubalcava’s class materials:

- 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.

In 2017-18 school year, Pre-AP SM3 classes will be taught by Mrs. Dodds & Mrs. Rubalcava.

Both teachers require the same Summer Assignment. However, in order to acquire more

information specific to each teacher, please see below.

Mrs. Karolin Dodds

Enochs High School

Email: [email protected]

Phone: (209) 574-1719

Website: http://calccore.blogspot.com/

Mrs. Dodds’s Class Material:

- 2” Math Only Binder with Graph & Regular Paper,

- Pen, Pencil, eraser, highlighter,

- TI-83 Plus Graphing or scientific calculator.

Notes, assignments, & handouts will be organized

& saved in the Math Binder. Your binder will be your

best resource for studying & preparing for any Quiz

or Test.

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:

TAKE THE SUMMER ASSIGNMENT VERY SERIOUSLY!

The first Test in this class is at the end of The First Week of School, and it will cover the content standards assigned

in the “Summer Assignment Packet.” and there are NO RETAKES! This Test contains Free Response Questions

without a calculator; this means you are required to show the mastery of essential skills covered in this packet.

mailto:[email protected]

mailto:[email protected]

http://calccore.blogspot.com/

http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=8MT787ry3DJs9M&tbnid=CxK2yAf31j5tEM:&ved=0CAgQjRwwAA&url=http://teensrunmodesto.org/schools/enochs-high-school/&ei=GFP8UcmAG4mciQLDloHoAw&psig=AFQjCNHyQzDRqhB3Gg6jTdEmKzQCbXZstw&ust=1375577240507951


Pre-AP Secondary Math III (SM3) Summer Assignment

Mrs. Karolin Dodds & Mrs. Christina Rubalcava

These problems must be completed on binder paper & be Ready to Turn in on the First Day of School.

Note: you must offer legible & legitimate work that supports your answer.

Use the offered resources to refresh your memory & re-learn the required skills.

Positive, Negative, & Rational Exponents

Simplify without using a calculator!

1] 08x 2]

25 3] yx 214 4]

325x 5]

7

3

x

x 6]

3

1

2

1

x

x 7]

3

2

6

5

xy

x y 8]

321

2323

cba

cba

9] 2

1

9 10] 5

3

32 11]

36

3 5

4

3

x y

x y

12] 2

1

4

6

25

9

x

x 13]

1

3125

64

14] 32 5 4

15] 8 216x y

16] 9454 yx 17]

9

3

4

23

12

15

9

8

x

yx

y

yx

18] 2841752 19] yy 5018

Solve for x without using logarithm.

20] 1000

110 x

21] 322 x 22] 6432 x

23] 162

1

x

24] 927 x 25]

4 125 4

16 5

x

Add, Subtract, & Multiply Polynomials

Perform the given operations and write the answer in standard form.

1] 45363 22 xxxx 2] 12753 22 xxx 3] 2 2 3 24 3 3 2 6 4y y y y y

4] 14 32 xx 5] mkmk 32 32 33 6] 245 yx 7] 22 35 x 8] 3

2x

9] 332 mk 10] 2 2x x 11] 43 2 2 xxx 12] 2

4 3x 13] 2

5x


Factor Polynomials

Factor each polynomial expression completely.

1] xx 205 3 2] 3532 xxx 3] 169 2 y 4] 2216 x

5] 643 y 6] 16249 2 kk 7] 278 3 m 8] 156 2 yy

9] 210 2 12m m 10]

22 32 yxyx 11] 2 23 2a ab b 12] 22 246 xxx

13] yyy 25204 23 14] xxx 14162 23 15] xx 243 4 16] 203252x

17] 5 3 23 2 6x x x 18]

22 5 3x x 19] 24 25

3 3x

Solving Equations Algebraically

Solve each equation. Do Not use Calculator!

1] xxx 682534 2] 25124353 kkk 3] 5

4

3

2x 4]

6

1

4

1

3

1 xx

5] 4 5

2 43

xx

6]

2

1

4

5

3

1

kk 7] 31056 x 8] 27252

5

3x

9] 52 2 4 3 1x 10] 33 40 2 17x 11] 96124 4

3

x 12] 5

32 21 85x

Solving Equations by Variety of Methods

Solve each Equation using the Recommended Method. Do Not use Calculator!

Factoring: 1] 063 2 xx 2] 372 2 xx 3] xx 12182 2 4] 2 1 7 2x x x

Quadratic Formula: 5] 23 10 5x x 6] 0423 2 xx 7] 132 2 xx 8] 422 xx

Completing The Square: 9] 03102 xx 10] xx 1033 2 11] 216243 2 xx 12] 0232 xx

Extracting The Root: 13] 15217322

x 14] 21

5 123

x 15] 2

5 7 6 141x

Solve each equation using your method of choice. Should you check for extraneous solutions!

16] xx 3230 17] 327 xx 18] 1462 xx 19] 2 8 2 2 1x x

20] 3 30 2x x 21] 2 8 3 2x x


Solving Absolute Value Equations

Solve each absolute value equation. Do Not use Calculator!

1] 4 2 5 9 3x 2] 1892

3x 3] 7 3 10 2x 4] 3 2 4 5x x

Operations with Complex Numbers

Write the sum or difference in standard form. 1] ii 4332 2] ii 932

3] 5 3 2 9i 4] 8157 2 i 5] 33 25 8 9

Write the product in standard from. 6] ii 31 4 7] 3 5 4 2i i 8] 4 6 5i i

Multiply each complex number with its conjugate & write the result in standard form.

9] i65 10] 1 2 i 11] 4 3i

Write each complex number in standard form.

12] 7

2i 13]

i

i

3

2 14]

i

i

2 15]

i

i

42

3

16]

6

3 i

Solve using quadratic Formula. 17] 1942 xx 18] 23 8 19 5x x

The examples below show how to write the solution to an inequality in interval notations.

Also, interval notations are used to express the domain, range, increasing, & decreasing intervals of a function.

Interval Notation Inequality

1,2 Set of all real #s x such that 1 2x

1,2 Set of all real #s x such that 1 2x

1, 2 Set of all real #s x such that 1 2x

1, 2 Set of all real #s x such that 1 2x

1, Set of all real #s x such that 1x

1, Set of all real #s x such that 1x

Set of all real #s x such that

Real Number Line Graphs

−∞ ∞

-5 -4 -3 -2 -1 0 1 2 3

−∞ ∞

, 3 1,

-5 -4 -3 -2 -1 0 1 2 3 −∞ ∞

, 3 1


Solving Linear Inequalities

Solve each Inequality algebraically & write the solution in Interval Notation.

1] 86 13 xx 2] 7 23 5 x 3] 3 1

1 14

x 4] 2444625 xx

5] 3 2 2 3

26 8

x xx

6] 7382 x 7]

7 12 2

2 2x 8] 1

3

25

2

3

xx

Graphing Functions and Analyzing their Details.

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]

11 4

2y x 6] 2 xy

7] 412 xy 8] 12 xy

9] 35 xy 10] 542 xxy

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: .


.


.

Max/Min Values:

.

Zero(s): .

y-intercept: .

Domain: .

Range: .


.


.

Max/Min Values:

.


11] 642 2 xxy 12] 2

3 6 6y x

13] 16)1()3( 22 yx

14]

1 32

1 12)(

2 xxx

xxxf 15]

4 , 138

3 , 1

2 , 51

)(2 xxx

x

xx

xf

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: .


.


.

Max/Min Values:

.

.


DayTwo

DayOne

At thebeginning

For 7-8, write as a single fraction.

Sequences/Functions

Determine if the pattern given is linear, exponential, quadratic, or neither. Next, give the recursive & explicit equations.

1.

Type of Sequence: ___________________ Recursive Rule: __________________ Explicit Rule:___________________

2.

Type of Sequence: ___________________ Recursive Rule: __________________ Explicit Rule: ____________________

3. Describe the pattern of change or rate of change for a linear, exponential, and a quadratic function.

Linear-

Exponential-

Quadratic-

4. Which type of function grows the fastest?

Fraction Operations (Answers in Reduced Form)

1. 2x5

6x∙5

8 2.

7

9n∙5n

8n 3.

4x2

10÷

3𝑥2

4x 4.

8x3

3x÷

6

7𝑥3

5. 5

6+

4

9 6.

7

15−

3

10 7.

5

6x+

3

10x2 8.

5

14𝑥2−

4

6x

Figure 1 Figure 2 Figure 3 Figure 4


vertex:________________

x-intercepts:___________

y-intercepts:___________

stretch or compress:_______

vertex:________________




Quadratic Functions

Use each function to identify the vertex, intercepts, vertical stretch, and graph it.

1. 2 10 24y x x 2. 3 3y x x 3. 22

3 63

y x

vertex:________________




Write the equation in vertex form.

5. 2 6 9y x x 6. 2 7 1y x x 7. 22 12 9y x x

Inverse Functions

Find the inverse of the function, graph both the original function and its inverse on the graph provided.

1. 1

( ) 32

f x x

Find the inverse of the given function.

2. 2 2f x x 3. 5 1f x x


A

B C

1

3

Absolute Value Functions

Graph the absolute value function and write it as a piecewise function.

1. Absolute Value: 1 2f x x 2. Absolute Value: ( ) 4f x x

Piece-Wise: ( )f x { Piece-Wise: ( )f x {

Right Triangle Trigonometry

Use the figure to write the following trigonometric ratios.

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

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

Solve the right triangles (list all side and angle measures for the triangle).

7. 8.

8. 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 to how high up the building the ladder is to the nearest hundredth of a foot.

X Y

12


Radian & Degree Measure

Write the radian measure of the angle given in degrees.

1. 122° 2. 50° 3. 270° 4. 0° 5. 1°

Write the degree measure of the angle given in radians.

6. 𝜋

2 7.

2𝜋

3 8. π 9.

3𝜋

4 10.

9𝜋

4

For problems 11 & 12, find the arc length and sector area in degrees. Give EXACT answers.

11. 12.


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

essential mathematical skill that you may have not fully mastered.

Simplifying Radicals

Solving Absolute Value Equations

Factoring


Solving Equations by Factoring

Multiplying Rational Expressions


Dividing Rational Expressions

Adding & Subtracting Rational Expressions


Multiplying Monomials

Dividing Monomials

Law of Exponents

Multiplying Polynomials


Graphing a Piecewise Function

Greatest Integer Funtion

Solution graph


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

.

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:

Enochs Pre-AP SM3 Summer Assignment - James … Pre-AP SM3 Summer... · Enochs Pre-AP SM3 Summer...

Documents

Transcript of Enochs Pre-AP SM3 Summer Assignment - James … Pre-AP SM3 Summer... · Enochs Pre-AP SM3 Summer...