Tuesday, July 19, 2011

July 19th

Homework
  • pg pg 558 #'s 30-37 all, 38, 39, 42, 43, 47, 48, 50
  • pg 564 #'s 10, 11, 12, 14
  • Study for ch 10 Exponential and Logarithmic Relations test: Do practice test pg 571 #'s 1-27. ( Don't do the inequalities problems)





Example: Solve Base e and natural logarithms Equations




10. 6 Exponential Growth and Decay

Exponential growth and decay
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Monday, July 18, 2011

July 18th: Review and homework

Chapter 10 Exponential and Logarithmic Relations
  • 10.3 Properties of Logarithms-Hw: pg 544 #'s 13-17 odd, 21-31 odd
  • 10. 4 Common Logarithms-hw: pg 550 #'s 27-41 odd, 45, 46, 47

10.3 Properties of Logarithms

What you'll learn...
  • Simplify and evaluate expressions using the properties of logarithms
  • Solve logarithmic equations using the properties of logarithms
Properties of logarithms
View more presentations from Jessica Garcia


10.4 Common natural logarithms
What you'll learn...
  • Solve exponential equations using common logs
  • Evaluate logarithms expressions using the Change of Base Formula
Common natural logarithms
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Friday, July 15, 2011

Gaelic Football Match:

Location: Gaelic Park in the Bronx
Time: 12:30 pm
Bring your student I.D so you don't have to pay.

Take the 1 Train to 238th street. Walk north on Broadway to 240th street. Turn left on 240th street . Gaelic park is on 24oth on the right side of the street. If you come, stay after the match so I can say hi.

Hope to see a few of you. If not, no worries see you Monday.


Have a wonderful weekend.

NOTE: Homework quiz on Monday


Chapter 10 Exponential and Logarithmic Relations
  • 10.1 Exponential Functions-Hw: pg 528 #'s 21, 24, 27-32 all, 40, 41, 45-48 all, and 52
  • 10.2 Logarithms & logarithmic Functions-Hw:pg 536 #'s 21-31 odd, 33, 34, 35, 37, 47-59 all
Exponential functions
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Wednesday, July 13, 2011

Day: July 13th: Homework and review

Homework:
  • pg 803 #'s 15, 20, 21, 24, 27, 36
  • Do review sheet at bottom of page.
  • I would put all the useful notes on the unit circle sheet tonight. You never know, I might let you use it...



Solving Trig Equations
What you'll learn...

T0 solve trig equations you can use trig identities to solve trig equations, which are true for only certain values of the variable.









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Tuesday, July 12, 2011

Day: July 12 Homework and Review

Homework

  • pg 774-775 #'s 12, 15, 33, 34, 37, 39
  • pg 780 #'s 25-34 all.

14.1 and 14.2 Trig Graphs

What you'll learn...
  • Graph trig functions
  • Find the amplitude and period
  • Graph horizontal translations
  • Find phase shifts
  • Graph vertical translations




14.3 Trig Identities

What you'll learn...
  • Use identities to find trig values.
  • Use trig identities to simplify expressions.

Example 1:
Find a value of a trigonometric function


Example 2
Simplify Expressions

Trigonometric identities can also be used to simplify expressions containing trigonometric functions. Simplifying an expression that contains trig functions means that the expression is written a s a numerical value or in terms of a single trig function, if possible.


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Monday, July 11, 2011

Day: July 11th

HOMEWORK

-pg736 #'s 11-19 odds
-pg 738 practice quiz 2



What you'll learn...
  • Solve problems by using the Law of Sines
  • Determine whether a triangle has one, two, or no solutions








Law of sines-1






Law of cosines


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Friday, July 8, 2011

Day 14: July 10th review and homework

Homework:
  • 13.2 Angles and Angle measurements-HW: pg 713 #'s 27-41 odd, 43, 49, 53
  • 13.3 Trigonometric Functions of General Angles-HW: pg 722 #'s 17-21, 25-31, 33-39 ODDS!!
  • Also, watch the video on Inverse Trig Functions and try problems pg 749 #'s 6-13 all.
HAVE A WONDERFUL WEEKEND!


13.2 Angles and Angle Measure

What you'll learn...
  • Change radian measure to degree measure and vise versa
  • Identify coterminal Angles
Most of you are used to thinking of a circle in terms of degrees: 360° is the whole circle. 180° is half the circle etc... Well, radian measure is just a different way of talking about the circle. Radian measure is just different unit of measure.

Just as we can measure a football field in yards or feet--we can measure a circle in degrees (like the good old days) or in radians (welcome to the big leagues!)

Think about what the word radian sounds like...well, it sounds like 'radius', right? It turns out that a radian has a close relationship to the radius of a circle

Definition of radian(we'll break this down more on this page): a radian is the measure of an angle that, when drawn a central angle of a circle, intercepts an arc whose length is equal to the length of the radius of the circle.

Degrees to radians
The general formula for converting from degrees to radians is to simply multiply the number of degree by Π /180°
  • Example 1:
    Convert 200° into radian measure:
    200° (Π/180°) = 200/180Π radians or 3.49 radians
  • Example 2:
    Convert 120° into radian measure:
    120° (Π/180°) = (2/3)Π radians = 2.09 radians

Radians to degrees

The general formula for converting from degrees to radians is to simply multiply the number of degree by 180°/(Π)
  • Convert 1.4 radians into degrees: 1.4 (180°/Π) = 80.2 °
Example 1: Click on link






13.3 Trigonometric Functions of General Angles







Example 2: Use a Reference Angle to find a Trigonometric Value


13.7 Inverse Trigonometric Functions
What you'll learn...

* Solve Equations using Inverse Trigonometric Functions
* Find values of trigonometric expressions








Practice Quiz
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Tuesday, July 5, 2011

Day 12: Review and homework

HOMEWORK
  • Study for ch 9 test by finish the review sheet.
  • 13.1 Right Triangle Trig HW: pg 706-707 #'s 15, 17, 21, 23, 25, 31, 35

What you'll learn...

  • How to solve rational equations













Ch 9 Test Review



Chapter 13 Trigonometric Functions

What you'll learn...
  • Find values of trigonometric functions for acute angles
  • Solve problems involving right triangles.
*****Chapter 13 Trigonometric Functions
Right triangle trigonometry


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Day 11: Review and Homework

Chapter 9 Rational Expressions and Equations
  • 9.1 Multiplying and Dividing Rational Expressions
  • 9.2 Adding and Subtracting Rational Expressions
  • 9.3 Graphing Rational Functions
  • 9.4 Solving Rational Equations
Homework:
  • pg 483 #' 41, 42
  • pg 489 #'s 17, 19, 21, 23, 26, 29, 35
  • pg 510-511 #'s 13-16 all, 20-27 all
NOTE: There will be an exam on Thursday.


Chapter 9 Rational Expressions and Equations


Rational expressions and equations






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Wednesday, June 29, 2011

Day 9: Review and Homework

NOTE: Tomorrow we will have a factoring test and ch 7 quiz/review

Chapter 7 Polynomial Functions:

Homework:
  • 7.3 Solving Equations Using Quadratic Techniques- HW: pg 363 #'s 11-17, 25, 26, 27
  • 7.7 Operations on Functions-Hw: pg 387 #'s 17, 19, 21, 31, 33
  • 7.8 Inverse Functions and Relations-HW: pg 393 #'s 21, 24, 27, 30, 33, 35


Practice Questions for the quest.

7.3 Solving Equations Using Quadratic Techniques
7.7 Operations of Functions
7.8 Inverse Functions and Relations

What you'll learn...
  • Write expressions in quadratic form.
  • Use quadratic techniques to solve equations
7.3 quadratic techniques



What you'll learn...
  • Find the sum, difference, product, and quotient of functions
  • Find the compositions of functions. F(g(x)) and G(f(x))




Inverse functions
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Day 8: Homework and Review

Chapter 7 Polynomial Functions: Part 1

Homework:
  • 7.1 Polynomial functions Hw: pg 350-351 #'s 16-21 all, 23, 27, 30, 31, 39-44 all.
  • 7.2 Graphing Polynomial functions HW: pg 356 #'s 13, 15, 19, 23, 25
Examples of different polynomial graphs
View more presentations from Jessica Garcia.

Turning points- where the graph of a function changes from increasing to decreasing or vice versa

Local maximum point – highest point or “peak” in an interval
function values at these points are called local maxima

Local minimum point – lowest point or “valley” in an interval
function values at these points are called local minima

Extrema – plural of extremum, includes all local maxima and local minima









video on finding max and min

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Tuesday, June 28, 2011

Day 7: Homework and Review

NOTE:


  1. Quiz on Wednesday over solving Quadratic Functions ( Graphing, Factoring, Completing the square, and Quadratic Formula.
  2. Quiz on Thursday over ch 7 lessons
  3. Test on Friday over factoring.
Homework
  • 6.3 Solving Quadratic Equations by Factoring- Hw: pg 304's 23, 31, 35, 39
  • 6.4 Solving Quadratic Equations by Completing the Square -Hw: pg 311 #'s 33, 35, 37
  • 6.5 Quadratic Formula-HW: pg 318 #'s 15, 17, 19, 20

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Monday, June 27, 2011

Day 6: Review and homework

Chapter 6 Quadratic Functions and Inequalities

  • 6.1 Graphing Quadratic Functions-Hw: pg 291 #'s 15, 19, 25, 33, 35
  • 6.2 Solving Quadratic Equations by Graphing - HW: pg 297 #'s 14-19 all 21, 23, 27

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Week 2 Notes

Chapter 6 Quadratic Functions and Inequalities

Part 1

6. 1 graphing quadratics
6.2 solve quadratic equations by graphing
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Friday, June 24, 2011

Day 5: Homework and Review

Note: There will be a Quiz on Monday over:
NOTE: Click on link to find practice Quizzes.







Vocab:

Factoring a polynomial means to find its completely factored form.

What you'll learn...
  • Factor polynomials
  • Simplify polynomial quotients by factoring




Click for videos

Example 1: GCF
Example 2: Grouping
Example 3: Two or Three Term
  1. Factoring Trinomials: x2 + bx + c
  2. Factoring Trinomials: ax2 + bx + c
  3. Trinomials with a GCF
  4. Perfect Square Trinomials
  5. Difference of two squares
  6. Sum and Difference of two cubes
Example 4: Quotient of Two Trinomials


Factoring with higher powers




Practice Factoring Polynomials Expressions

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Thursday, June 23, 2011

Day 4: Homework and Review

Homework:
  • 5.7 pg 261 #'s 21-28, 29, 31, 32, 35, 36, 37, 39, 41, 44, 45, 47, 50, 53, 56, 59
  • 5.8 pg266 #'s 13-31 0dd (check your solutions)
  • 5.9 pg 274 #'s 18, 21, 24, 27, 30, 33, 36, 37, 49, 51, 53
Helpful song for Imaginary numbers:

"I won... I won... plus, minus, minus, plus" (i, -1, -i, 1)


NOTE: Quiz tomorrow over sections
  • 5.5 Roots of Real Numbers
  • 5.6 Radical Expressions


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Wednesday, June 22, 2011

Day 3: Review and Homework

NOTE: Test Friday



Chapter 5 part 2:

5.5 Roots of Real Numbers
Vocab
  • square root
  • nth root
  • principal root
5.6 Radical Expressions
Vocab
  • rationalizing the denominator
  • like radical expressions
  • conjugates
RECALL:

Steps to simplify a square root.
  1. Factor the radicand into as many squares as possible.
  2. Use the product property to isolate the perfect squares.
  3. Simplify each radical
To eliminate radicals from a denominator or fractions from a radicand, you can use a process called rationalizing the denominator. To rationalize a denominator, multiply the numerator and denominator by a quantity so that the radicand has an exact root.

Homework

Finish 5.5 worksheets pg 61 #'s 1-24 odds and 5.5 worksheet pg 62 #'s 1-17 odd

Finish 5.6 worksheet pg 32 #'s 2-24 even and 5.6 worksheet pg 64 #'s 2-12 evens



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Tuesday, June 21, 2011

Day 2: Review and Homework

Chapter 5 Part1: sections 5.1-5.4

NOTE:Quiz Wednesday

Homework:

pg 226-227 #'s 29, 30, 35, 40

pg 236 #'s 15, 17, 19

pg 237 #'s 37, 39, 41 (use long division and synthetic division for each)

pg 242 #'s 15-39 odd. Factoring is important for your current and future math career....focus!!

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Monday, June 20, 2011

Day 1: Review and Homework

Quiz: Wednesday
Test: Friday


By the way, if you want to access the online test book go to

www.algebra2.com
Username: ALG205
passwork: ThU9echa




Review questions from chapters 1-3.

NOTE: If you understand chapters 1-3 then do not waste your time on the review problems. Focus on the new material from today.

Happy studying.


pg 39 #'s 1-4

pg 50 #'s 49, 50

pg 74 #'s 1, 2, 4, 5

pg 105 #'s 52, 53, 54


Homework question from today's lesson.

pg 143 #'s 18, 19, 21, 29, 30
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Week 1: In class notes

a.) Review ch 1-3
- Solving Equations and Inequalities
- Linear Relations and Functions
- Systems of Equations

b.) Solve systems of Linear Equations in three Variables
Solving systems of equations in 3 variables


c.) Multiply Matrices/ show calculator use (click worksheet)

d.) Add, Subtract, multiply, divide, and factor polynomials (5.1-5.4)
Polynomials part 1
Long and synthetic division



e.) Simplify and solve equations involving roots, radicals, and rational exponents (5.5-5.8)

Roots of real numbers and radical expressions
View more presentations from Jessica Garcia


Simplifying radical expressions, rational exponents, radical equations
View more presentations from Jessica Garcia


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Thursday, June 16, 2011

Getting Started: Assignment1

It’s not too early to begin thinking about your success in Algebra 2 this summer! Since many of you have spent the past year in geometry class, it will be a good idea to refresh your algebra skills. Below are the prerequisite skills from algebra 1 along with some practice problems. This assignment will not be checked or graded. However, there will be a test on these skills the first or second day we return to school.

If you have trouble with any of these problems, solutions will be posted by Sunday.
(Feel free to email me or leave a comment if you have questions.)


Before you begin Algebra 2, you should be able to:

I. Solving Equations and Inequalities (ch 1 in text book)
  • Solve any one variable equation
  • Solve absolute value equation
  • Solve Inequalities
  • Solving Compound and Absolute Value Inequalities
II. Linear Relations and Functions (ch 2 in text book)
  • Identify a function, domain and range
  • Use function notation to evaluate a function
  • Find slope of a line given two points or a graph.
  • Write the equation of a line given slope and y-intercept, slope and a point, two points, or a graph.
  • Graph any line: Including vertical & horizontal, linear inequalities and absolute inequalities
II. Systems of Equation (ch 3 in text book)
  • Solve Systems of Equations by Graphing
  • Solve Systems of Equations Algebraically (substitution and Elimination)

Practice Problems( When downloading choose PDF or HTML)

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Ms. Garcia Daily Information

EMAIL: garciaj@xavierhs.org

Extra Help: Before class and after class.

Words from Ms. Garcia:

Come to class everyday with notebook, and something to write with and a good attitude.

Keep in mind students that our summer course is usually taught in a year. That being the case, we must move fast and smile everyday. If you have questions, please ask!! If not, we will move right past you.

Good Luck
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Algebra 2 Summer Outline

COURSE DESCRIPTION:

The Algebra II discipline complements and expands the mathematical content and concepts of Algebra I and Geometry. It emphasizes finding solutions for and graphing, polynomial functions, inequalities, systems of equations, exponential and logarithmic functions, rational functions, trigonometric functions, and conic sections. We will also explore matrices, the complex number system and trigonometric relationships. Class activities will incorporate problem solving competencies in algebraic operations, communicating mathematical thinking, and modeling algebraic reasoning in real-life situations. Successful completion of Algebra II will prepare the student to take Pre-Calculus or Advanced Topics, determined by teacher recommendation.


Week 1 June 20- June 24

a.) Review ch 1-3
- Solving Equations and Inequalities
- Linear Relations and Functions
- Systems of Equations
b.) Solve systems of Linear Equations in three Variables
c.) Perform Basic Matrix Operations
d.) Multiply Matrices/ show calculator use
e.) Add, Subtract, multiply, divide, and factor polynomials (5.1-5.4)
f.) Simplify and solve equations involving roots, radicals, and rational exponents (5.5-5.8)

Week 2 June 27- July 1

a.) Perform operations with complex number (5.9)
b.) Quadratic Functions and Inequalities (ch 6)
- Graphing quadratic functions and inequalities
- Solving Quadratic equations graphing and algebraically (factor, CTS, QF)

c.) Polynomial Functions (ch 7)
- Graphing polynomial functions
- Solving Polynomial Functions using quadratic techniques, find zeros
-Basic Operations on Functions
-Square Root functions and Inequalities


Week 3 July 4- July 8 (note: No class on Monday July 4 )

a.) Rational Expressions and Equations (ch9)
- Rational expressions basic operations
- Graphing Rational Functions
- Solving Rational Equations and Inequalities
b.) Trigonometry Functions (ch 13)
- Right Triangle Trig
- Angle Measurements: ref/terminal angles, radian/degree
- 6 Trig Functions


Week 4 July 11- July 15

a.) Trigonometry Functions (ch 13)
- Law of Sines, Cosines
- Circular Functions
- Inverse Trig Functions (no graphing)
b.) Trig Graphs and Identities (ch 14)
- Graphing Functions/Translations
- Trig Identities
- Solving Trig Equations

Week 5 July 18- July 22

a.) Exponential and Logarithmic Relations (ch10)
- Exponential and Logarithmic Functions
- Properties of Logs
- Base e and Natural Logs
- Exponential Grows and Decay
b.) Review for final test
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