Do Now 1/26/10Do Now 1/26/10 Copy HW in your planner.Copy HW in your planner.

– Benchmark Test 4 review worksheet 2-14 evens, Benchmark Test 4 review worksheet 2-14 evens, 18-21 all18-21 all

Be ready to finish Chapter 7 Test.Be ready to finish Chapter 7 Test.

Count down to the mid-term – 3 school days!!Count down to the mid-term – 3 school days!!

Algebra Mid-Term Algebra Mid-Term PreviewPreview

Friday, January 29Friday, January 29thth Two hours from 8:00-10:00. (Periods 1 – 3).Two hours from 8:00-10:00. (Periods 1 – 3).

45 Total Questions 45 Total Questions – Part I: (No calculator) Part I: (No calculator)

10 multiple choice10 multiple choice 4 short constructed4 short constructed 1 open-ended1 open-ended

– Part II: (calculator)Part II: (calculator) 20 multiple choice 20 multiple choice 6 short constructed6 short constructed 4 open-ended4 open-ended

Tuesday – Chapters 1-4 reviewTuesday – Chapters 1-4 review Wednesday– Chapters 5, 6, & 7 Wednesday– Chapters 5, 6, & 7

reviewreview Thursday– Mid-Term practiceThursday– Mid-Term practice Friday – MID-TERMFriday – MID-TERM

Algebra Mid-Term Algebra Mid-Term ScheduleSchedule

ObjectiveObjective SWBAT review Chapter 1-4 topics SWBAT review Chapter 1-4 topics

for Mid-Termfor Mid-Term

Chapter 1Chapter 1Expressions, Equations, Expressions, Equations,

& Functions& Functions

Section 1.1- Evaluate ExpressionsSection 1.1- Evaluate Expressions

xx 123

when x is equal to 5.when x is equal to 5.53

x

Section 1.2- Order of OperationsSection 1.2- Order of Operations

Section 1.3- Write ExpressionsSection 1.3- Write Expressions Twice a number d plus 8.Twice a number d plus 8. 82 d

Section 1.4- Write Inequalities and EquationsSection 1.4- Write Inequalities and Equations The sum of twice a number b and 3 is less than 12.The sum of twice a number b and 3 is less than 12.

1232 bSection 1.5- Problem SolvingSection 1.5- Problem Solving

What is the interest on an investment of $1000 at 8% over 5 What is the interest on an investment of $1000 at 8% over 5 years?years?

$400$400

Section 1.7- Represent Functions as GraphsSection 1.7- Represent Functions as Graphs What is the rule of this function? What is the rule of this function? What is the domain and range?What is the domain and range?

Domain is 0,1,2,3 and Range is 2.2,3.2,4.2,5.2Domain is 0,1,2,3 and Range is 2.2,3.2,4.2,5.2y = x + 2.2y = x + 2.2

Section 1.6- Represent Functions as Rules and TablesSection 1.6- Represent Functions as Rules and Tables What is the domain and range of the function? What is the What is the domain and range of the function? What is the rule?rule?

xx 00 11 22 33yy 2.22.2 3.23.2 4.24.2 5.25.2

y = x ÷ 2y = x ÷ 2Domain is 0,2,4,6,8Domain is 0,2,4,6,8Range is 0,1,2,3,4Range is 0,1,2,3,4

Chapter 2Chapter 2Properties of Properties of Real NumbersReal Numbers

““Real Numbers”Real Numbers”

Real NumbersReal Numbers

Rational NumbersRational Numbers

IntegersIntegers

Whole Whole NumbersNumbersWhole NumbersWhole Numbers

0,1,2,3,4,5…0,1,2,3,4,5…

IntegersIntegers-3,-2,-1, 0,1,2,3…-3,-2,-1, 0,1,2,3…

Rational NumbersRational Numbers numbers that cannumbers that canrepresented as a represented as a ratio or fractionratio or fraction

0, bba

Properties of Properties of Real NumbersReal Numbers

1). 1). Commutative PropertyCommutative Property2). 2). Associative PropertyAssociative Property3). 3). Identity PropertyIdentity Property4). Inverse Property4). Inverse Property5). 5). Property of ZeroProperty of Zero6). 6). Property of -1Property of -1

Chapter 3Chapter 3Solving Linear Solving Linear

EquationsEquations

Section 3.1- Solve One-Step EquationsSection 3.1- Solve One-Step Equations

123 x 4xSection 3.2- Solve Two-Step EquationsSection 3.2- Solve Two-Step Equations

Section 3.3- Solve Multi-Step EquationsSection 3.3- Solve Multi-Step Equations

10)8(2 d

Section 3.4- Equations with Variables on Both SidesSection 3.4- Equations with Variables on Both Sides

47 ww

Section 3.5- Ratios and ProportionsSection 3.5- Ratios and Proportions

13d

48

20

v40v

No solution

Section 3.7- Solve Percent ProblemsSection 3.7- Solve Percent Problems What number is 15% of 88?What number is 15% of 88?

Section 3.6- Solve Proportions Using Cross ProductsSection 3.6- Solve Proportions Using Cross Products

88%15 aSection 3.8- Rewrite Equations and FormulasSection 3.8- Rewrite Equations and Formulas

xx 52

37

15x

2.13a

Solve the equation so that y is a function of x.Solve the equation so that y is a function of x.

12 = 9x + 3y12 = 9x + 3y y = 4 – 3x

tI PrrtIP

Solve the interest equation for P.Solve the interest equation for P.

Chapter 4Chapter 4Graphing Linear Graphing Linear

Equations and FunctionsEquations and Functions

Section 4.1 “Coordinate Plane”Section 4.1 “Coordinate Plane”

y-axisy-axis

x-axisx-axis

OriginOrigin (0,0)(0,0)

Quadrant IQuadrant I(+,+)(+,+)

Quadrant IIQuadrant II(-,+)(-,+)

Quadrant IIIQuadrant III(-,-)(-,-)

Quadrant IVQuadrant IV(+,-)(+,-)

Section 4.2 “Graph Linear Equations”Section 4.2 “Graph Linear Equations”

42 xy

xy 24

Solve the equation for y. STEPSTEP 11SOLUTION

Graph the equation Graph the equation y + 2x = 4y + 2x = 4..

STEPSTEP 22Make a table by choosing a few values for x and then finding values for y.

STEPSTEP 33Plot the points. Notice the points appear on a line. Connect the points drawing a line through them.

xx --22

--11

00 11 22

yy 88 66 44 22 00

Section 4.3 “Graph Using Intercepts”Section 4.3 “Graph Using Intercepts”Graph the equation Graph the equation 6x + 7y = 42 6x + 7y = 42..

6x + 7y = 42

x = x-intercept7

Find the x-intercept

6x + 7(0)=42 6(0) + 7y = 42

y = y-intercept6

6x + 7y = 42

Find the y-intercept

Plot points. The x-intercept is 7, so plot the point (7, 0). The y- intercept is 6, so plot the point (0, 6). Draw a line through the points.

(0, 6) and (5, –4)

m =y2 – y1

x2 – x1

Let (x1, y1) = (0, 6) and (x2, y2) = (5, – 4).

– 4 – 6 5 – 0=

Write formula for slope.

Substitute.

Simplify. 10 5= – = – 2

Find the slope of the line that passes through the points

Section 4.4 “Find Slope and Rate of Change”Section 4.4 “Find Slope and Rate of Change”

Section 4.5 “Section 4.5 “Graph Using Slope-Intercept FormGraph Using Slope-Intercept Form””

SLOPE-INTERCEPT FORM-SLOPE-INTERCEPT FORM-a linear equation written in the a linear equation written in the formform

y = mx + by = mx + bslope y-intercept

y-coordinate x-coordinate

Graph Using Slope and the Y-InterceptGraph Using Slope and the Y-InterceptGraph the equationGraph the equation 3y – 2x =3y – 2x = 3. 3.

STEPSTEP 11Rewrite the equation in slope-intercept form.Rewrite the equation in slope-intercept form.

Identify the slope and the Identify the slope and the yy--intercept.intercept.STEPSTEP 22

STEPSTEP 33Plot the point that corresponds to the Plot the point that corresponds to the y-y-intercept,intercept,(0, 1).(0, 1).

STEPSTEP 44Use the slope to locate a second point on the line. Draw a line Use the slope to locate a second point on the line. Draw a line through the two points.through the two points.

= = 2/32/3mm andand = 1= 1bb

y = + y = + 112233

xx

Slope of 2/3 means: Slope of 2/3 means:

runrise

32

Determine which of the lines are parallelDetermine which of the lines are parallel..

Find the slope Find the slope of each lineof each line.. Line Line aa:: mm == – – 11 – – 00

– – 11 – – 22

– – 33 – – ((––11 ))00 – – 55

== –– 11–– 33

1133==

Line Line b:b: m m == –– 22–– 55== 22

55==

Line Line c:c: m m == – – 55 – – ((––3)3) – – 2 – 2 – 44

–– 22–– 66== 11

33==

Line Line aa and line and line cc have the same slope, so they are parallelhave the same slope, so they are parallel..

Section 4.7 “Section 4.7 “Graph Linear FunctionsGraph Linear Functions””

Function Notation-Function Notation-a linear function written in the form a linear function written in the form y = y = mx + bmx + b where y is written as a function where y is written as a function f.f.

f(x) = mx + bf(x) = mx + bslopeslope y-intercepty-intercept

x-coordinatex-coordinate

f(x) is another name for y.f(x) is another name for y.It means “the value of f at x.”It means “the value of f at x.”g(x) or h(x) can also be used to name functions g(x) or h(x) can also be used to name functions

This is read This is read as ‘f of x’as ‘f of x’

Graph a FunctionGraph a Function

32)( xxf

xx -2-2 -1-1 00 11 22f(x)f(x) -7-7 -5-5 -3-3 -1-1 11

STEPSTEP 11SOLUTION

Graph the Function Graph the Function f(x) = 2x – 3 f(x) = 2x – 3

STEPSTEP 22

Make a table by choosing a few values for x and then finding values for y.

STEPSTEP 33Plot the points. Notice the points appear on a line. Connect the points drawing a line through them.

32)( xxf

The domain and range are not restricted therefore, you do not have to identify.

Compare graphs with the graph f(x) = x.Compare graphs with the graph f(x) = x. Graph the function g(x) = x + 3, then Graph the function g(x) = x + 3, then

compare it to the parent function f(x) = x. compare it to the parent function f(x) = x.

xx f(xf(x))

-5-5 -2-2-2-2 1100 3311 4433 66

f(x) = xf(x) = xf(x) = x

xx f(xf(x))

-5-5 -5-5-2-2 -2-200 0011 1133 33

g(x) = x + 3g(x) = x + 3g(x) = x + 3

The graphs of g(x) and f(x) have the same slope of 1.

HomeworkHomework

– Benchmark Test 4 review Benchmark Test 4 review worksheet 2-14 evens, 18-21 allworksheet 2-14 evens, 18-21 all

Benchmark Test 1 review worksheet Benchmark Test 1 review worksheet evens evens

32) -5/2432) -5/24 34) -1734) -17 36) 1236) 12 38) ab38) ab 40) 1240) 12 42) 2 / 7542) 2 / 75 44) 1144) 11 46) ±846) ±8 48) A48) A 50) 650) 6 52) Yes; any whole # can be 52) Yes; any whole # can be

expressed as the quotient of expressed as the quotient of itself divided by 1.itself divided by 1.

54) -6.9, -21/4, |-7|, √5054) -6.9, -21/4, |-7|, √50 56) D56) D 58) C58) C 60) 8x³ - 10x²60) 8x³ - 10x² 62) 2x + x² - 2xy 62) 2x + x² - 2xy

2) 152) 15 4) 494) 49 6) -296) -29 8) B8) B 10) A10) A 12) No12) No 14) Yes14) Yes 17) 50p – [100(0.60) + 50] = 100; 17) 50p – [100(0.60) + 50] = 100;

you should sell each magnet for you should sell each magnet for $4.20$4.20

18a) 7r + 5c b) 7r + 5c ≤ 35 18a) 7r + 5c b) 7r + 5c ≤ 35 c) Yes; 7(2) + 5(3) = 29 which c) Yes; 7(2) + 5(3) = 29 which is ≤ 35is ≤ 35

20) y = 4x20) y = 4x 22) (-2,-5), (0,-1), (2,3), (4,7)22) (-2,-5), (0,-1), (2,3), (4,7) 24) a) on board b) p = 2n c) 14024) a) on board b) p = 2n c) 140 26) Domain: 1,2,3,4,5; Range: 26) Domain: 1,2,3,4,5; Range:

1,2,3,41,2,3,4 28) a) s = 2.5w b) on board28) a) s = 2.5w b) on board 30) –a = -0.2; |a| = 0.230) –a = -0.2; |a| = 0.2

Benchmark Test 2 review worksheet Benchmark Test 2 review worksheet evens evens

32a) x = (a+d)/(c-b) 32a) x = (a+d)/(c-b) b) x = 7b) x = 7 34) B34) B 36) y = -x + 136) y = -x + 1 38) y = -2x – 338) y = -2x – 3 40) on board40) on board 42) on board42) on board 44) (0,13), (3,9), (6,5), (9,1)44) (0,13), (3,9), (6,5), (9,1) 46) on board46) on board 48) on board48) on board 50) x-int: -10; y-int: 650) x-int: -10; y-int: 6 52) C52) C

56a) y = -1/3x + 256a) y = -1/3x + 2 58) C58) C

2) h = 82) h = 8 4) b = -94) b = -9 6) m = 126) m = 12 8) a = 3.38) a = 3.3 10) d = 53/410) d = 53/4 12) v = 1/512) v = 1/5 14) D14) D 16a) 3/2 b) 2/516a) 3/2 b) 2/5 18) w = 8/518) w = 8/5 20) x = 1220) x = 12 22) v = 1/222) v = 1/2 24a) 2 ¼ cups b) 3 3/8 cups24a) 2 ¼ cups b) 3 3/8 cups 26) A26) A 28) B28) B 30) $30 30) $30

Benchmark Test #3Benchmark Test #3#2-56 evens#2-56 evens

2) C2) C 4) y = -2x + 24) y = -2x + 2 6) y + 9 = -13/11(x – 5)6) y + 9 = -13/11(x – 5) 8a) p/q b) –px + qy = 8a) p/q b) –px + qy =

qpqp 10) y = 3/4x – 15/410) y = 3/4x – 15/4 12) y = -5/2x + 1012) y = -5/2x + 10 14) positive correlation14) positive correlation 16) relatively no correlation16) relatively no correlation 18) B. y = 2x + ½18) B. y = 2x + ½ 20) on next slide 20) on next slide

(b.) p = -12t + 1055(b.) p = -12t + 1055 (c.) ≈ 910(c.) ≈ 910

22) on next slide22) on next slide 24) A24) A 26) -3 < x ≤ 426) -3 < x ≤ 4

28) on next slide28) on next slide 30) on next slide30) on next slide 32) x > -732) x > -7 34) x > -334) x > -3 36) f ≤ -1936) f ≤ -19 38) no solution38) no solution 40) 2 > b ≥ -540) 2 > b ≥ -5 42) c < -11/2 or c ≤ -642) c < -11/2 or c ≤ -6 44) C44) C 46) x = -13 or x = 1346) x = -13 or x = 13 48) m = -7/2 or m = 15/248) m = -7/2 or m = 15/2 50) d = -6 or d = 050) d = -6 or d = 0 52) -2 < z < 252) -2 < z < 2 54) p > 1 or p < -354) p > 1 or p < -3 56) B 56) B

Benchmark Test #3Benchmark Test #3#2-56 evens#2-56 evens

20)20)

22)22)

26) 26)

28) 28)

30)30)