-4x2

Algebra I

Chapter 1 – Connections to Algebra 1.1 Variables in Algebra

Warm-up: Ken-Ken problem Variables – letters that represent 1 or more #s Expression – letters & #s for a meaningful purpose; tells us

what we are doing i.e. adding, multiplying Term pieces – “Evaluate” the expression – find the #s that expression Pg. 4-5 ex.

Practice: Pg. 6 #11,17,23,27,31,33 Ken-Ken #2

1.2 Exponents and Powers Warm-up: ACT #34,17 46 is a power base raised to an exponent Exponents tell us “how many are you multiplying” (remember

how multiplication tells us how many groups we are adding) 46 = 4•4•4•4•4•4 Order of operations is important Pg. 10 ex. 3,4,5,6 Pg. 12 4-7

Practice: Pg. 12 #11,21,31,35,43,57,61,67,69 1.3 Order of Operation

Warm-up: Number Enigmas #31 & ACT #460 Grouping symbols first, then “Please expect my dear aunt sally” “left to right rule” – if all the same operation **Division sign can act like a grouping symbol – Pg. 17 Groups: do Pg. 18 ex 5 if calculators

Practice: Pg. 19 #7,21,29,31,39,41,51,53,56

1.4 Equations and Inequalities Warm-up: Number Enigmas #58 Equation – an expression with an “=” Solution – value that makes both sides of “=” equal. This is

“checking a possible solution Solve – find all the solutions Mental math – figuring it out in your head, estimating Inequality – read from the variable out Group: Pg. 27 #10-13

Practice: Pg. 27 #9,21,25,35,49,55,59,67,69,75 Start Review Pg. 54 1.1 – 1.4

1.5 A Problem Solving Plan Using Models Warm-up: ACT example #1 Make “Secret Math Code” – on index card Paper clip pg. 29 for formulas Modeling – real life that translates into algebraic expression or

equation

-103

-103

Algebra I

Pg. 33 ex 2,3 pg. 35 1-12Practice: Pg. 35 #23,27,33,37,43,47,51,61

1.6 Tables and Graphs Warm-up: Math logic –“20?” Pg. ex 1-3 show different graphs. ACT #12

Practice: Pg. 43 9,11,13,17,19 Logic “You’re Busted”

1.7 An Introduction to Functions Warm-up: C=5/9 x (F0 – 32) what are the following

temperatures in C0 ? 0, 212, 70, 90 F0 Wouldn’t it be nice to have a machine that would calculate the temps?

Function – rule that establishes a relationship between 2 quantities (input, output)

For each input, there is exactly one output Group: Pg. 49 #4-6, 10-12 Input/output table shows the relationships Domain – input values Range – output values Pg. 47 ex. 1-3

Practice: Pg. 49 #17,21,25,37 Puzzle math “Identify Function”Review Pg. 54 1.5 – 1.7

X Y0 -11 32 6

Algebra I

Chapter 2 – Properties of Real Numbers2.1 The Real Number Line

Warm-up: What are all the types of numbers included in Real numbers and what is not?

Number systems chart Number line – neg, 0, pos integers, fractions, decimals Plotting the point – putting a value where it should go on the

number line <> plotting - 〇 ≤≥ plotting Pg. 64 ex. 4 Opposite #s – equidistance from the center 0. Absolute value – always returns a positive value Pg. 66 ex. 8 Although velocity might be in a downward motion,

speed is always + (doesn’t care about direction) Counter example – only need to find one example to prove

something false. (a true statement must withstand all examples)Practice: Pg. 67 #11,23,31,39,49,53,63,75,77,79

2.2 Addition of Real Numbers Warm-up: 5 ? 19 ? 6 ? 1 = 4 (+ ÷÷∨×) Properties of addition – Commutative (order), Associative

(groups), identity (0), Zero property (opposite) Pg. 74 ex. 4 Practice: Pg. 75 #11,29,31 don’t use calculator #39,47,51,53,57

2.3 Subtraction of Real Number Warm-up: Why is 5-(-3) = 8? Subtraction of a negative #: 7-(-2) = 7+2 Subtraction of a term: -9 – 2x when x=2: -9 – (2)(2) = -9-4 = -

13 Use parenthesis!!

o Difference between highest and lowest: 2.26 – (-1.35) = 3.61 why? Show on a number line.

Practice: Pg. 82 #9,19,35,39,49,61,71 & 73 but use the chart below:

2.4 Adding and Subtracting Matrices Warm-up: Group – decide on a #code for 4 colors (assign them

each a unique #) Get the cubes in order – 1 color per side Matrix – rectangular arrangement of numbers into rows and

columns. A table that organizes data. Work with the color cubes Entry or element – each # in the matrix Size of matrix is "rows by columns” or – “3 by 4”

#73 was written in 2000.

(1) What is the change in gold prices since then?

(2) Find the year with the greatest change overall in the gold price. Estimate the change.

Index card

Algebra I

Equal Matrices – entries in same position are equal Add/subtract Matrices - +/- corresponding entries (can only

combine if they are the same size matrix) Pg. 87 ex. 2,3,4Practice: Pg. 89 #9,15,19,21,23,25,29a Review Pg. 122 2.5 – 2.8

2.5 Multiplication of Real Numbers Warm-up: Solve 12 •6

12 as many different ways as you can

Multiplication – repeated addition + • + = + - • - = + Odd # of negative signs – answer will be negative Even # of negative signs – answer will be positive You can determine the sign before or after you multiply the #s Displacement - change in position of an object (+ or -) Pg. 95 ex. 4,5

Practice: Pg. 96 #21,29,33,41,43,47,57,61,65,69

2.6 The Distributive Property Warm-up: Distributive property – distribute the work so 3•68 = 3(60+8) **Make sure you watch the signs! 4(x-3) = 4•x + 4•(-3) = 4x-12 Pg. 101 ex. 2-4 “Like terms” – same base and exponent “Constant terms” – 4x0 or just 4 Simplifying equations – combining all like terms and distributing

everything possiblePractice: Pg. 103 #9,17,23,35,43,65,73,75,79,92

2.7 Division of Real Numbers Warm-up: Reciprocal – x and 1x Inverse prop of mult. - for every #x (≠ 0), there is a number 1x

that when multiplied together = 1 Division rule – a ÷ b = a • 1b Pg. 109 ex. 2

Group: Pg. 109 ex. 3 a-c work: 10 ÷ (-15) and 16−29

and −2b7 ÷ 79

Pg. 110 ex. 4 d= rate displacementtime

Algebra I

Domain changes with division – we have to worry about what is in the denominator of a fraction ( denominator ≠0)

Practice: Pg. 111 #25,27,37,43,51,57,61,63 (d = rt ), 69

2.8 Probability and Odds Warm-up: Probability of an event – measure of the likelihood the event will

occur Outcomes – different possible results

o For N equally likely outcomes, probability = 1N that one

will occur - a 5 coming up on a dice, P= 16 Event – One action – roll a dice – and it’s collection of outcomes P = number of favorableoutcomestotalnumber of outcomes even # on a dice = 36 = 12 Experimental Probability – starts with a survey or experiment.

Based on the results, predictions are made as to another event. Odds – equally likely outcomes, odds = ¿ of favorableoutcomes

¿of unfavorableoutcomes

o If you know the P of that event, odds = Pevent occurs1−Pevent occurs

All examplesPractice: Pg. 117 #7,11,15,17,19,21,23,31 Review Pg. 122 2.5 – 2.8

Algebra I

Chapter 3 – Solving Linear Equations3.1 Solving Equations Using Addition & Subtraction REVERSE THE + or – to get x alone

Same steps we used to evaluate -5 + (-4) – x 1. Simplify the expression using PEMDAS -5 – 4 – x2. Combine like terms -9 – x

Equations have the added “=”-8 = n – (-4)-8 = n + 4-4 -8 = n +4 -4-12 = n actually find what n equals

Try it: t – (-4) = 4

¿2| - (-b) = 6

What is the equation for: The temperature rose 15 degrees to 70 F. What was the original temperature?

Practice: Pg. 135 #25,29,31,33,35,41,43,49,51 Make sure you are writing the steps you are using for the first problem and any problems that use new or different steps!

3.2 Solving Equations Using Multiplication & Division REVERSE the x or ÷ (after you handle the + or - )

Sometimes x is not by itself: 2x = 4 or x2 = -42x = 4 (reverse 2•x by dividing

x2 = -4 (reverse x ÷ 2 by multiplying)

2x = -4 (first rewrite 2x = -41 ) Flip both fractions x2 = -14 Multiply by 2 to reverse the division

Similar Triangles & Ratios – ways we solve real life problems.

Practice: Pg. 141 #7,11,13,21,33,35,41,51,59 Make sure you are writing the steps you are using!

3.3 Solving Multi-Step Equations ALWAYS take care of the + or – before the x or ÷ to get x alone

These are COMBINATION equations:13x+6=−8 7x – 3x – 8 = 24

Algebra I

Practice: Pg. 148 #7,11,17,23,27,33,35,43,51,53

3.4 Solving Equations with Variables on Both Sides GET VARIABLES on one side and CONSTANTS on the other

3(x + 2) = 3x + 6

Don’t forget: Simplify by using PEMDAS, get x’s on one side (+ - ) then get x’s alone.

Practice: Pg. 157 #13,15,17,23,31,37,41,43,45

3.5 Linear Equations and Problem Solving 1. Change the problem into algebra 2. Draw it! 3. Check it!

Package size: Pg. 163 #6-8Total Girth = 108 = L + 4s (P of the square end)

L = 36 inches

Practice: Pg. 163 #9,11,13,23-26

3.6 Solving Decimal Equations Rounding – sometimes common sense: $34.23 uses 2 decimal places

(always check the next decimal place in line and see if you need to round - $34.236 would round to $34.24)

EASY way to solve 7.2 x−3.5=2.6−3.4 x since each term has one decimal place, multiply whole equation by 10.

72x – 35 = 26 – 34x

Every time you round, you put in a little bit of error. ≈ is the symbol for “approximately”

Practice: Pg. 169 3,4,11,15,27,35,39,41,53

3.7 Formulas and Functions Common formulas: A =LW, A = ½ bh, P=Irt, d=rt, S=L-rL, C=2πr,

A = πr2

Function form: replace y with f(x) where x is the variable in the equation. If y = 2x+1, rewrite __________________

If b = 2a +1 rewrite _________________If a=-1 what would the equation look like?

Algebra I

Practice: Pg. 177 #3,5,11,15,23,25,29,35

3.8 Rates, Ratios and Percents Rates – comparison of 2 quantities with different units.

d= rt example If we solve for r (the rate) we get r = dt

Rates are also used for conversions 3 ft per yard = 3 ft1 yd

30 miles per gallon = 30miles1gal Average rates – we are generalizing or estimating “per

person” or “per day”

***When you say the rate, you will know how to write it! Pg. 180 Example 1: you want to find “money spent per person”

so $ spent∈US totalpeople∈UStotal=avg .$ / person

Ratio – comparison of 2 numbers (rates are ratios) Looks like 412 or 41:2 (said “41 to 2)

How many boys vs. girls in class? 14boys3 girls or 14:3

How many boys in class? 14 boys17 s tudents or 14 boys:17 students

Proportions: comparison of 2 ratios Always has “=” sign in the middle Pg. 181 example 3: exchange $180 US for pesos. $1 = 9,990

pesos (that’s a rate of exchange). Set up 2 ratios with matching units: $1US

9,990 pesos=$180US

x pesos or “if $1 = 9,990 pesos how many pesos for $180?

***Any time you have a proportion (2 fractions with an “=”), you can cross multiply to solve.

Write the cross multiplication here

Percents – always think “parts of 100” or “parts of the total” Pg. 182 example 5: what percentage of 15-17 year olds said

they are dating? So, 15−17 year olds datingtotal¿15−17 surveyed ¿

***Remember! When you see the word “percent” the decimal needs to be moved sometime during the problem. If I were to model this problem: “what percentage” = x%

“of” = “times”

Algebra I

“15-17 year olds” = 482“are” or “is” = “=”“total” or “out of” is implied by percent

x% • 482 = 992 or x% = 992482 or x% = .48588… ***if in doubt what to do replace % with “over 100”

x% = x100 so x

100 = .48588… or x=.48588 •100

x= ________%

***ALWAYS include UNITS with these problems!!Practice: Pg. 183 #5,9 (write the algebra!), 13,17,21,23,27,29,33,39

x

yIII

III IV

y + 2 = 3x Get in the habit of putting your equation into y=mx+b form

What are the easiest #s to plug in for x?

x y

Algebra I

Chapter 4 – Graphing Linear Equations & Functions4.1 Coordinates & Scatter Plots

Graphing – done on a coordinate plane Ordered Pair – tells us where the point should go

(x,y) (2,3)x axis – shows horizontal movementy axis – shows vertical movement

Origin – point (0,0) – where the x,y axis meetQuadrants – x,y axis cuts the graph into 4 pieces, we label those with

Roman numeralsScatter Plots – taking data & plotting the individual points on a graph

- sometimes we can see trends or patterns in the graph

Practice: Pg. 206 #7,11,15,19,25,27,29,31,35

4.2 Graphing Linear EquationsGraph – visual solution to an equation in two variables (x,y). It show

the set of all answers that are solutions of the equation.Linear equation – looks like y=mx+b (mslope or slant, bwhere

the line hits the y-axis). It’s graph is always a line.How many points do you need before you can draw a line??

y=3 Line that hits the y-axis at 3x=4 Line that hits the x-axis at 4Function form – just write the y=mx+b like this: f(x) = mx+b

**Match the graphs on Pg. 215 #52-55

Practice: Pg. 214 #7,13,17,18,21,31,41,43,63

4.3 Quick Graphs Using InterceptsEasiest way to graph – plug in x=0 and y=0 gives you the x,y

intercepts**Pg. 220 Example 4 – Zoo tickets – how to graph something with

many solutions.**Pg. 222 #41-43 match the graphs**Groups: Pg.222 School play, Marathon and Movie tickets problems

Practice: Pg. 221 #4,9,15,21,31,35,47,57

4.4 The Slope of a Line

-1

0

3

-1

0

3

Algebra I

Lines are not always flat or straight up/down.Slanted lines have a “slope” – how far the line rises off “flat”NEVER MESS UP THE SLOPE – if you move up/down first (with the

sign) then right.−23 slope would be down 2, right 3

Slope - riserun or up/down¿

or change∈ ychange∈x or ∆ y

∆x or y2− y1x2−x1

Slope is the “rate of change” for your graphWhat is the slope of a horizontal line?What is the slope of a vertical line?

Practice: Pg. 230 #5,11,13,25,35,39,47,51,53

4.5 Direct VariationDirect Variation – means that x & y are multiples of each other

y=2x or y= ½ x or y=7x or y=kxWhat point will this line always go through?**Pg. 236 Example 4 – Animal studies

Practice: Pg. 237 #3,7,13,27,34-35,36-37

4.6 Quick Graphs Using Slope-Intercept FormSlope-intercept form – y=mx+b (m=slope, b=intercept)Parallel lines – have the same slope, but different y-interceptPerpendicular lines – have the negative reciprocal slope

y=2x+4 y= - ½ x -4**Pg. 245 #52-55

Practice: Pg. 244 #15,23,37,45,47,51,59,65,674.7 Solving Linear Equations Using Graphs

Graphing a line shows us the “answer” or solution. The x-intercept is the solution to the equation, i.e. x=?

Graph y=mx+b and find the x-intercept Graph both sides of the equation, i.e. 2.5 = .055t + 1.26

would produce 2 graphs: y=2.5 and y=.055t + 1.26. The intersection would be the answer.

**Pg. 253 #11-13

Practice: Pg.253 15,23,25,33,37,47

4.8 Functions and RelationsA relation is an equation where an input can have more than one output value associated with it, i.e. x=y2 If x=4 then y=2 or -2A function is a relation between inputs and outputs where each x has

only one y output value#1 RULE – a function is predictable! If you put a value in for x, you

better only have one path that it will follow (output possibility) Which one is a function: (2,3) (3,3) (2,4) (4,5)

Algebra I

(2,1) (3,2) (4,1) (5,2)(1,1) (2,1) (3,4) (4,2)

Which is a function? Do the vertical line test.

Function notation substitutes F(x) for y f(x) = 2x + 3 or g(a) = 4a + 1 When we plug a value in for the variable it becomes:

g(2) = 4(2) + 1 f(2) = 9 or (2,9) is a point on the graphf(2) = 2(2) + 3 f(2) = 7 or (2,7) is a point on the graph

Graph with slope and y-intercept (y=mx+b)** Pg. 260 #29-31 in class

Practice: Pg. 259 9,13,15,16,18,21,35,37,45

Algebra I

Chapter 5 – Writing Linear Equations5.1 Writing Linear Equations In Slope-Intercept Form

Slope-intercept form – y=mx + b gives us slope (m) and intercept (b)

Slope - ∆ y∆x - the slant of the line

“Model” is a function that is used to model real life situations

Practice: Pg. 276 9-11,15,20,23,28-29,31Extra Credit (on separate paper): #40 a,b,c

5.2 Writing Linear Equations Given the Slope & a PointWhat are the 2 things we need to write the equation of a line?? ____________________________ ____________________________y = mx + b (when we find m & b) will work for every point on the

lineIf we don’t know m or b, but we know a point on the line, we can find

the missing piece: (1,4) is a point on the line, m=3

y = mx + b (b is the only unknown)Find b:

Check by graphing it!Find the equation of the line: x-intercept = 2, m = - 2/3

(don’t be tricked!)

“rate”, “miles per hour”, “change in”, “increase”, “decrease” – clues that we are talking about the “slope” or rate of change between 2 #s.

Practice: Pg. 282 2,4,9,13,23,25,29,31,33Extra Credit: #50 a,b,c

Company T – initial charge of ______After that, they charge a constant rate of _________

Company S – initial charge of ______After that, they charge a constant rate of _________

What does the slope represent? _______________________What does the y-intercept represent? ___________________Who would benefit from each phone company’s service? Why?

Algebra I

5.3 Writing Linear Equations Given Two PointsSlope - ∆ y

∆x All we need is 2 points to find a lineWe can find more than just the equations of lines, we can draw

shapes and tell whether or not they are parallelograms, squares, rectangles, etc.

Find the equations of the 4 lines hereWhat can you tell about this shape??

Practice: Pg. 288 1 (list the steps for each process) 2,3,4,7,11,19,27,2,39,47,49

5.4 Fitting a Line to Data“Line of best fit” – a line that is close to representing graphed dataTRICK: plot the points and then move your ruler around until you

have as many points above the ruler as you do below it. Correlation – how well a line represents the data graphed.

Positive – points follow closely a line with positive slope Negative – points follow a negative slope No correlation – points don’t follow a straight line pattern

Groups: try Pg. 296 10-12 and 17-22 then worksheet

Practice: Pg. 296 13,17-22, worksheet(s)

5.5 Point-Slope Form of a Linear EquationPoint slope formula comes from m= ∆ y

∆x Rework:y1 – y2 = _______________

Group activity: Pg. 301 Practice: Pg. 303 3,5,6,15,19,25,33,43 Extra Credit #57-59

5.6 The Standard Form of a Linear EquationStandard form – ax + by = c

useful when equations have fractions y = 15 x−

75 becomes ________________________in standard form

Practice: Pg. 311 3,9,13,16-17,27,29,35,63

5.7 Predicting With Linear ModelsSome data can be represented by a linear graph.

Plot data on a graph Can the data be approximated with a line of fit? Draw the line (original points don’t have to be on the line) Pick two points on the line and determine the slope Find the y-intercept and build the y=mx + b equation

Algebra I

You now have a linear model for predicting points that are not given originally

Linear interpolation – estimating a point between 2 given points

Linear extrapolation – estimating a point that lies to the right or left of all the points given originally

Practice: Pg. 319 6-10,17-22

Algebra I

Chapter 6 – Solving & Graphing Linear Inequalities6.1 Solving One-Step Linear Inequalities

Linear inequalities – have more than one answer or more points than fit on a straight line. They have a set of numbers that do not work, also.

Number line is used to graph simple problems Arrow points at the small # & opens its mouth to eat the large one Start from the variable and read out: x > 2 is “x is greater than 2” x < 2 & 2 > x are both “x is less than 2” when you graph, <> get 〇; ≤≥ get •

Rules for inequalities like 2x + 4 > 20 Math rules are the same except for one thing: if you • or ÷ by a

negative #, then the <> flips -2x + 4 > -20 works out to: -2x > -24 x < 12

As a group: Pg. 338 match the graphs 55-60

Practice: Pg. 337 7,15,19,20-21,29,41,45,53,61

6.2 Solving Multi-Step Linear Inequalities- still want the linear equations in y=mx+b format- arrange what’s given and then solve for y

Practice: Pg. 343 3,5,11,15,19,27,32,37,43,44

6.3 Solving Compound Inequalities“and” inequalities look like −2<3 x−8<10

solve as 2 separate equations or solve all pieces at once

“or” inequalities look like x←1∨x>4

Practice: Pg. 349 2,3,9,15,21,25,29,33,37

6.4 Solving Absolute-Value Equations & Inequalities|x| = 8 x=±8 (inside expression can be positive or negative) |x-2| =5 break into 2 equations x-2 =5 and x-2 = -5 solve bothAbsolute value <> - are split into 2 equations also: < “or” / > “and”

Practice: Pg. 356 3,10,13,17,27,31,38,44,53,636.5 Graphing Linear Inequalities in Two Variable

Linear equations like 2x – 3y ≤ -2 has many (x,y) solutions - graph just like a line and then test to find the side to shade

- <> will have a dotted line- ≤≥ will have a solid line (includes the points of the line)

Groups: Pg. 364 43-48,61-63 Practice: Pg. 363 3,9,13-14,19,23,27,63

6.6 Stem-and-Leaf Plots & Mean, Median, Mode

Algebra I

Like a plant – branches of data that help organize

Central tendency – “most typical” value for a given set of data Mean – average (sum of #s / #of items) Median – in a set of ordered #s, it’s the center Mode – most frequent # (or n1-n2/2 if no center)

Bell Curve – distribution of data in the shape of a bell

Practice: Pg. 371 1,4,7,9,11,21,33

6.7 Box-and-Whisker Plots- all about medians

Practice: Pg. 378 7,9, draw both the leaf/stem and the box/whisker for these: 11,17,19,25-29

Algebra I

Chapter 7 – Systems of Linear Equations & Inequalities7.1 Solving Linear Systems by Graphing

Linear systems – is there a point that works in more than one linear equation or model? Two linear equations can intersect at one (x,y) point System can have no answers (line are parallel and never

intersect) Systems can have all points that work in both equations

Practice: Pg. 401 2,3-6,11,15,17,19,23,31,35,43

7.2 Solving Linear Systems by SubstitutionSolve the easiest equation for one variable. Substitute what the

variable equals into the second equation.- if y = 2x+1 then 2x + 3y = 7 would be 2x +3(2x+1) =

7

Practice: Pg. 408 1-5,17,21,27,31,33 (day 1) 9,19,25,33,35,43,44 (day 2)

7.3 Solving Linear Systems by Linear CombinationPerform addition horizontally on equations

Practice: Pg. 414 3,5,7,9,11,13,15,17,19,21 (day 1) 23,25,27,29,31,33,35,44,48 (day 2)

7.4 Applications of Linear Systems1. Graphing2. Substitution3. Combination

Decide which is easiest for each problem.

Practice: Pg. 421 3-9,11,17,19,25,31,33 (day 1) 35-45 odds, 47,49-50, 52-54 (day 2)

7.5 Special Types of Linear SystemsPractice: Pg. 429 1-5,7,11,12-17 all (day 1)

19,21,23,31,32,33,39,41 (day 2)

7.6 Solving Systems of Linear InequalitiesPractice: Pg. 435 1-5, 7, 9-14 (day 1)

15-21 odds, 31, Quiz 2 odds

-x + 3y = 18 x – y = 4 add down 2y = 14 y = 7Mixed

Review & Quiz 1 Pg. 416

Algebra I

Chapter 8 – Exponents & Exponential Functions8.1 Multiplication Properties of Exponents

ADDing bases and exponents – only if they are the same animal!! 2x5 + x5 = 3x5 - x5 is a group of 5 x’s all multiplied (like groups

can be added). x5 + x4 are NOT like groups – both the exponent and base must

match to add or subtract groupsOther math operations are done for like bases

x5 • a5 x and a are the bases, but are not alike so they don’t multiply together!

3c4 only c is the base (3c)4 everything inside ( ) is the base 2x4 • 3x2 = 6 (multiply constants first) x4+2 or 6x6

Practice: Pg. 453 1-21 all (day 1) 23-59 odds (day 2)

8.2 Zero & Negative Exponentsa0 is always 1 anything to the zero power is 1a-n says “flip me!” and becomes 1

an

Practice: Pg. 459 3-10 all, 15-21 odds, 31-37 odds, 53

8.3 Division Properties of ExponentsRemember – like bases only!! 6

5

63=65−3=62=36

( 3y)3

= 33

y3=27

y3

Practice: Pg. 466 19-47 odds

8.4 Scientific NotationUsed for very large or very small numbers

Always 1 decimal place when you are done 276.3 = 2.763 x 102 (moved the decimal 2 left - # will get

bigger) .000458 = 4.58 x 10-4 (moved 4 right - # will get smaller)

***easy to use exponent rules when using scientific notation (handle constant part normally and then the 10n part like all like bases

Practice: Pg. 473 3-11 odds, 14, 15, 37-47 odds

Algebra I

8.5 Exponential Growth FunctionRabbit populations, bacteria, our savings account – all things that can

grow exponentially fast. y = C(1+r)t y=future amount C=starting amount r=rate

t=time rate usually a %, so change to a decimal rate will be > 1 if rate “triples” then (1+r) = 3 or r=2 or 200%

Practice: Pg. 480 4-5, 7-21 odds

8.6 Exponential Decay FunctionDepreciation of a car, devaluation of the dollar, sports tournament

bracket, declining enrollment are examples of decay. y = C(1-r)t y=future amount C=starting amount r=rate

t=time rate will be < 1

Practice: pg. 488 5,8,9,13,17-21 odds, 27-30 all

Algebra I

Chapter 9 – Quadratic Equations & Functions9.1 Solving Quadratic Equations by Finding Square Roots

Quadratics always have an x2 term – which means that we have to √ x2 to get it back to x = ___. Only √ x2 positive #s Each √ x2 yields a positive and a negative answer √9=±3

Perfect squares have integer answers with no remainderIrrational Numbers – numbers written with the √a (not the quotient of 2

integers)√50=√25√2=√5√5√2=5√2 2 of the same √a one “comes out of jail”Standard form for quadratic: ax2+bx+c = 0 (a,b,c are constants)

a is the “leading coefficient” – in front of the highest exponent term

Practice: Pg. 507 4-22 all (day 1) (day 2) 23-41 odds, 51-61 odds

9.2 Simplifying RadicalsSimplest form – all perfect squares have been factored outRULES – not many for adding/subtracting

Only add/subtract “like” terms, apples/oranges: √3+√3 RULES – multiplication is in 2 steps

Outside √ x - constants outside can be multiplied together Inside √ x - numbers can be multiplied or factored apart Ex: 2√3 •4 √5=2• 4 •√3 •5=8√15

RULES – division can be all together or in parts √ 455 =√9=√3√3=3 or

√ 455 =√45√5

=√5√9√5

=√9=3

Practice: Pg. 514 4-7 all, 9, 11-17 odds, 23-29 odds(day 2) 31-49 odds, 50-54 all

9.3 Graphing Quadratic FunctionsParabola – an x2 graph y = x2 Vertex – lowest or highest point of the curve - −b

2a Axis of symmetry – “fold” or line that divides the parabola in ½

Practice: Pg. 521 1-4 all, 5-19 odds, 20(day 2) 21-35 odds, 45-49 odds (day 3) 65-71 all, 76

9.4 Solving Quadratic Equations by Graphing“Solutions” or “roots” or “zeros” are what x equals when you solve for

x (can be 2 answers) Where the graph crosses the x-axis

Algebra I

1. If there is an x2 and an x term – get everything in standard form, find the vertex and some points on the graph

2. If there is only an x or x2 term – solve for x and find the vertex

Practice: Pg. 529 3-5 all, 7-17 odds, 18-20 all(day 2) 21-43 every other odd

9.5 Solving Quadratic Equations by the Quadratic FormulaIf a quadratic isn’t easily factored, use the big nasty x=−b±√b2−4ac

2a

Practice: Pg. 536 5,9,11,13,23,27,33,37,53

Factoring – another method to try to find the zerosExtra worksheets on factoring

9.6 Application of the Discriminantb2 – 4ac is the discriminant – it tells how many real zeros there will be

+ means 2 solutions, - means no solutions, 0 means 1 solution Perfect square means zeros are integers Negative means there are 2 imaginary roots (not seen on graph)

Practice: Pg. 544 1-11 all, 15-17 all(day 2) 18-20 all, 21,23,25-26,31

9.7 Graphing Quadratic InequalitiesSame rules as graphing linear inequalitiesTest points to find out where the graph is shaded

Practice: Pg. 4-6, 7-11 odds, 17-22 all

9.8 Comparing Linear, Exponential & Quadratic Models

Practice: Pg. 557 3-8 all, 9, 15, 17, 23-26 all

Algebra I

Chapter 10 – Polynomials & Factoring10.1 Adding & Subtracting Polynomials

Polynomials – “many terms” – we group terms by what variable/exponent mix they have. Group all x3 and all x2 separately, for instance.

Classify terms by: Degree – if x3 is the highest term, it is a degree 3 or quartic Terms – how many terms there are (binomial = 2 terms)

Always put in standard form (highest degree variable first and then step down as the equation goes to the right)

Leading coefficient – variable in front of the highest term (includes sign)

Practice: Pg. 579 1-6 all, 7-17 odds (day 1)31-35 odds vertical, 39-45 odds horizontal, 47-53 odds

(day 2)

10.2 Multiplying PolynomialsDistributive way: (x+2)(x-3) = x(x-3) + 2(x-3) = x2 -3x +2x – 6 = x2 –x -6 FOIL – multiply first terms, add rainbow multiplication, multiply last termsVertical way: used less, but just like multiplying 121 x 12Horizontal way: a lot like distributing, then combine

Practice: Pg. 587 1-8 all, 9-17 odds (day 1)19-43 odds, 52,53 (day 2)

10.3 Special Products of Polynomials“Special” cases that can make solving easier

(a+b)(a-b) the middle term always drops out! (a+b)2 and (a-b)2 have a pattern

“Box” multiplication – organizes the multiplication

Practice: Pg. 593 1-3 all, 7-35 odds (day 1)39-47 odds, 49-52 all (day 2)

10.4 Solving Polynomial Equations in Factored FormFactoring is the hard part!! Once you factor, you can find the solutions

easily by setting each one = 0 (this gives you where the polynomial crosses the x-axis – or where y=o) Called factors, roots, zeros, x-intercepts or solutions

Zero-Product Property – in a product, if one of the terms = zero, then the entire answer is zero. Zero times anything = zero. So, find what values would make y=o.

Practice: Pg. 600 1-17 all (day 1)19-29 odds, 35-47 odds (day 2)

10.5 Factoring x2 + bx + cAlready learned easy factoring – now how do we do a little harder

problems?

Algebra I

1. Pull out GCF – greatest common factor2x3 +4x2 -6x = 2x(x2 +2x - 3) = 2x (x+3)(x-1) zeros o,-3,1

2. Factor remaining quadratic3. Find all zeros4. Use x-box, discriminant or quadratic formula for harder ones (10.6)

Practice will be on worksheets

10.6 Factoring ax2 + bx + c = 0Quadratics where a > 1

1. Find the factors of c and a2. Trial and error as you put together the factors3. Or…use x-box

Practice: Pg. 614 5-17 all (day 1)19 – 47 every other odd (day 2) Good review: 48-63 all

10.7 Factoring Special ProductsUse the special products (a+b)(a-b), (a+b)2 and (a-b)2

Practice: Pg. 622 4-17 all (day 1)19 – 59 every other odd (day 2)

10.8 Factoring Using the Distributive PropertyPolynomials are easier to factor if you pull out all the common pieces

(GCF)Each factor that has a variable will give you a zero – or a place where the

graph crosses the x-axis

Practice: Pg. 629 15-49 every other odd, 55-57 (graph 2 problems) Graph 3x(x-7)(x+4)

Chapter 11 – Rational Equations & Functions11.1 Ratio & Proportion11.2 Percents11.3 Direct & Inverse Variation11.4 Simplifying Rational Expressions11.5 Multiplying & Dividing Rational Expression11.6 Adding & Subtracting Rational Expressions11.7 Dividing Polynomials11.8 Rational Equations & Functions

Chapter 12 – Radicals & Connections to Geometry12.1 Functions Involving Square Roots12.2 Operations with Radical Expressions12.3 Solving Radical Expressions

Algebra I

12.4 Completing the Square12.5 The Pythagorean Theorem & Its Converse12.6 The Distance & Midpoint Formulas12.7 Trigonometric Ratios12.8 Logical Reasoning: Proof