Do Now 1/24/12 Do Now 1/24/12 Copy HW in your planner. Copy HW in your planner. – Mid-Term Review worksheet #1 Mid-Term Review worksheet #1 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 Count down to the mid-term – 1 school day! day!
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Do Now 1/24/12 Copy HW in your planner. Copy HW in your planner. –Mid-Term Review worksheet #1 Take out Benchmark Tests #1-4. Take out Benchmark Tests.
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Do Now 1/24/12Do Now 1/24/12
Copy HW in your planner.Copy HW in your planner.– Mid-Term Review worksheet #1Mid-Term Review worksheet #1
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 #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
1) No solution1) No solution 2) 4 2) 4 3) x > -2 or x < -43) x > -2 or x < -4 4) a. y = 4x – 114) a. y = 4x – 11 b. 4x – y = 11b. 4x – y = 11 c. y – 1 = 4(x – 3) orc. y – 1 = 4(x – 3) or y + 3 = 4(x – 2)y + 3 = 4(x – 2) 5) m = -1/2, b = 4, shade 5) m = -1/2, b = 4, shade
above the solid lineabove the solid line 6) y > 36) y > 3
7) -3 7) -3 8) y = -3/5x – 28) y = -3/5x – 2 9) -1/29) -1/2 10) p/2 – L10) p/2 – L 11) (5, 4)11) (5, 4) 12) all real numbers12) all real numbers 13) 213) 2 14) 8, 014) 8, 0 15) 1215) 12
Algebra Midterm Algebra Midterm Review Review
“Calculator”“Calculator” 1) -5 < x ≤ 11) -5 < x ≤ 1 2) -2x + 102) -2x + 10 3) y = mx – 2; slope can be 3) y = mx – 2; slope can be
anything but -1/5 anything but -1/5 4) 1, -24) 1, -2 5) area = 35) area = 3 6) x – 2y = 86) x – 2y = 8 7) m = -3, b = 1, shade above the 7) m = -3, b = 1, shade above the
dashed linedashed line 8) x > 8 or x < 28) x > 8 or x < 2 9) -8 < x < 29) -8 < x < 2 10) -3 < x < 310) -3 < x < 3 11) y = 1/2x + 11/211) y = 1/2x + 11/2 12) (K - 12) (K - ππr²) / (r²) / (ππr)r)
13) ???13) ??? 14) m = -1/3, b = -214) m = -1/3, b = -2 15) horizontal line through 315) horizontal line through 3 16) no solution16) no solution 17) no solution17) no solution 18) x + 2x + x + 20 = 180; 18) x + 2x + x + 20 = 180; 4040°, 80°, 60°°, 80°, 60° 19) y – 1 = -3/5(x – 2) or19) y – 1 = -3/5(x – 2) or y – 4 = -3/5(x + 3)y – 4 = -3/5(x + 3) 20) (2, -1)20) (2, -1) 21) 1021) 10 22) parallel22) parallel 23) y = -3x + 1323) y = -3x + 13 24) a. any equation with m = -24) a. any equation with m = -
1/21/2 b. any equation with m = 2b. any equation with m = 2
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
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
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) 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.