do now 1/24/11 copy hw in your planner. copy hw in your planner. –mid-term review worksheet #2,...
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Do Now 1/24/11Do Now 1/24/11
Copy HW in your planner.Copy HW in your planner.– Mid-Term Review worksheet #2, #1-13Mid-Term Review worksheet #2, #1-13
Take out Benchmark Tests #1-4.Take out Benchmark Tests #1-4.– Be ready to correct.Be ready to correct.
Count down to the mid-term – 1 school day!Count down to the mid-term – 1 school day!
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] = 17) 50p – [100(0.60) + 50] =
100; you should sell each 100; you should sell each magnet for $4.20magnet for $4.20
18a) 7r + 5c b) 7r + 5c ≤ 35 18a) 7r + 5c b) 7r + 5c ≤ 35 c) Yes; 7(2) + 5(3) = 29 c) Yes; 7(2) + 5(3) = 29 which is ≤ 35which is ≤ 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) 24) a) on board b) p = 2n c)
140140 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 24a) 2 ¼ cups b) 3 3/8
cupscups 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)
Benchmark Test #4Benchmark Test #4#2-14 evens, 18-21 all#2-14 evens, 18-21 all
2) a). 9j – 4m = 722) a). 9j – 4m = 72 j – 12 = ½(m – 12) j – 12 = ½(m – 12)
b). b).
c). Mari will be 41 c). Mari will be 41 James will be 29.James will be 29. 4) A. none4) A. none 6) infinitely many 6) infinitely many
solutionssolutions 8) (5/4, -2)8) (5/4, -2) 10) (1, -1)10) (1, -1) 12) (-13/6, -10/3)12) (-13/6, -10/3) 14) no solution14) no solution
18) 18)
19) B 19) B 20) 20)
21) B 21) B
Algebra Mid-Term Algebra Mid-Term PreviewPreview
Wednesday, January 26Wednesday, January 26thth Two hours from 8:21-10:29 (Periods 2 & 3).Two hours from 8:21-10:29 (Periods 2 & 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
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
x
x 123 when x is equal to 5.when x is equal to 5.
5
3x
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 33
yy 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 NumbersNumbers
Whole 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, bb
a
Properties of Properties of Real NumbersReal Numbers
1). 1). Commutative PropertyCommutative Property
2). 2). Associative PropertyAssociative Property
3). 3). Identity PropertyIdentity Property
4). Inverse Property4). Inverse Property
5). 5). Property of ZeroProperty of Zero
6). 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
4
8
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 a
Section 3.8- Rewrite Equations and FormulasSection 3.8- Rewrite Equations and Formulas
x
x 52
3
7 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 Prrt
IP
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 11
SOLUTION
Graph the equation Graph the equation y + 2x = 4y + 2x = 4..
STEPSTEP 22
Make a table by choosing a few values for x and then finding values for y.
STEPSTEP 33
Plot 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 + b
slope y-intercept
y-coordinate x-coordinate
Graph Using Slope and the Y-InterceptGraph Using Slope and the Y-Intercept
Graph 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 33
Plot the point that corresponds to the Plot the point that corresponds to the y-y-intercept,intercept,(0, 1).(0, 1).
STEPSTEP 44
Use 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:
run
rise
3
2
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 22
f(x)f(x) -7-7 -5-5 -3-3 -1-1 11
STEPSTEP 11
SOLUTION
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 33
Plot 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 11
00 33
11 44
33 66
f(x) = xf(x) = xf(x) = x
xx f(xf(x))
-5-5 -5-5
-2-2 -2-2
00 00
11 11
33 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.
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Review worksheet
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