Do Now 1/24/12
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Copy HW in your planner.
– Mid-Term Review worksheet #1
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Take out Benchmark Tests #1-4.
– Be ready to correct.
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Count down to the mid-term – 1 school day!
Benchmark Test #3
#2-56 evens
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2) C
4) y = -2x + 2
6) y + 9 = -13/11(x – 5)
8a) p/q
b) –px + qy = qp
10) y = 3/4x – 15/4
12) y = -5/2x + 10
14) positive correlation
16) relatively no correlation
18) B. y = 2x + ½
20) on next slide
(b.) p = -12t + 1055
(c.) ≈ 910
22) on next slide
24) A
26) -3 < x ≤ 4
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28)
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on next slide
on next slide
x > -7
x > -3
f ≤ -19
no solution
2 > b ≥ -5
c < -11/2 or c ≤ -6
C
x = -13 or x = 13
m = -7/2 or m = 15/2
d = -6 or d = 0
-2 < z < 2
p > 1 or p < -3
B
Benchmark Test #3
#2-56 evens
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22)
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26)
Benchmark Test #4
#2-14 evens, 18-21 all
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2) a). 9j – 4m = 72
j – 12 = ½(m – 12)
b).
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19) B
20)
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21) B
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c). Mari will be 41
James will be 29.
4) A. none
6) infinitely many solutions
8) (5/4, -2)
10) (1, -1)
12) (-13/6, -10/3)
14) no solution
18)
Algebra Midterm Review
“No Calculator”
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1)
2)
3)
4)
No solution
4
x > -2 or x < -4
a. y = 4x – 11
b. 4x – y = 11
c. y – 1 = 4(x – 3) or
y + 3 = 4(x – 2)
5) m = -1/2, b = 4, shade
above the solid line
6) y > 3
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7) -3
8) y = -3/5x – 2
9) -1/2
10) p/2 – L
11) (5, 4)
12) all real numbers
13) 2
14) 8, 0
15) 12
Algebra Midterm Review
“Calculator”
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1) -5 < x ≤ 1
2) -2x + 10
3) y = mx – 2; slope can be anything
but -1/5
4) 1, -2
5) area = 3
6) x – 2y = 8
7) m = -3, b = 1, shade above the
dashed line
8) x > 8 or x < 2
9) -8 < x < 2
10) -3 < x < 3
11) y = 1/2x + 11/2
12) (K - πr²) / (πr)
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13) ???
14) m = -1/3, b = -2
15) horizontal line through 3
16) no solution
17) no solution
18) x + 2x + x + 20 = 180;
40°, 80°, 60°
19) y – 1 = -3/5(x – 2) or
y – 4 = -3/5(x + 3)
20) (2, -1)
21) 10
22) parallel
23) y = -3x + 13
24) a. any equation with m = -1/2
b. any equation with m = 2
Algebra Mid-Term Preview
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Wednesday, January 26th
Two hours from 8:21-10:29 (Periods 2 & 3).
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45 Total Questions
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– Part I: (No calculator)
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10 multiple choice
4 short constructed
1 open-ended
– Part II: (calculator)
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20 multiple choice
6 short constructed
4 open-ended
Objective
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SWBAT review Chapter 1-4 topics for
Mid-Term
Chapter 1
Expressions, Equations, &
Functions
Section 1.1- Evaluate Expressions
3 x  12
x
when x is equal to 5.
x
3
5
Section 1.2- Order of Operations
Section 1.3- Write Expressions
Twice a number d plus 8.
2d  8
Section 1.4- Write Inequalities and Equations
The sum of twice a number b and 3 is less than 12.
2b  3  12
Section 1.5- Problem Solving
What is the interest on an investment of $1000 at 8% over
5 years?
$400
Section 1.6- Represent Functions as Rules and Tables
What is the domain and range of the function? What is the
rule?
x
0
1
2
3
y
2.2
3.2
4.2
5.2
Domain is 0,1,2,3 and Range is 2.2,3.2,4.2,5.2
y = x + 2.2
Section 1.7- Represent Functions as Graphs
What is the rule of this function?
What is the domain and range?
y=x÷2
Domain is 0,2,4,6,8
Range is 0,1,2,3,4
Chapter 2
Properties of
Real Numbers
“Real Numbers”
Real Numbers
Rational Numbers
Integers
Integers
-3,-2,-1, 0,1,2,3…
Whole Numbers
0,1,2,3,4,5…
Whole
Numbers
Rational Numbers
numbers that can
represented as a
ratio or fraction
a
,b  0
b
Properties of
Real Numbers
1).
2).
3).
4).
5).
6).
Commutative Property
Associative Property
Identity Property
Inverse Property
Property of Zero
Property of -1
Chapter 3
Solving Linear
Equations
Section 3.1- Solve One-Step Equations
3x  12
x4
Section 3.2- Solve Two-Step Equations
Section 3.3- Solve Multi-Step Equations
2(d  8)  10
d  13
Section 3.4- Equations with Variables on Both Sides
w 7  w 4
No solution
Section 3.5- Ratios and Proportions
v 8

20 4
v  40
Section 3.6- Solve Proportions Using Cross Products
7 2x  5

3
x
x  15
Section 3.7- Solve Percent Problems
What number is 15% of 88?
a  15%  88
a  13.2
Section 3.8- Rewrite Equations and Formulas
Solve the equation so that y is a function of x.
12 = 9x + 3y
Solve the interest equation for P.
I  Pr t
I
P
rt
y = 4 – 3x
Chapter 4
Graphing Linear
Equations and Functions
Section 4.1 “Coordinate Plane”
y-axis
Quadrant II
(-,+)
Origin
(0,0)
Quadrant I
(+,+)
x-axis
Quadrant III
(-,-)
Quadrant IV
(+,-)
Section 4.2 “Graph Linear Equations”
Graph the equation
SOLUTION
STEP 1
Solve the equation for y.
y  2x  4
y  4  2x
y + 2x = 4.
STEP 2
Make a table by
choosing a few values
for x and then finding
values for y.
x -2 -1 0 1 2
y 8 6 4 2 0
STEP 3
Plot the points. Notice
the points appear on a
line. Connect the points
drawing a line through
them.
Section 4.3 “Graph Using Intercepts”
Graph the equation
Find the x-intercept
6x + 7y = 42.
Find the y-intercept
6x + 7y = 42
6x + 7y = 42
6x + 7(0)=42
6(0) + 7y = 42
x = 7  x-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.
y = 6  y-intercept
Section 4.4 “Find Slope and Rate of Change”
Find the slope of the line that passes through the
points (0, 6) and (5, –4)
Let (x1, y1) = (0, 6) and (x2, y2) = (5, – 4).
y2 – y1
Write formula for slope.
m=
x2 – x1
– 4– 6
Substitute.
=
5–0
10
=–
= – 2 Simplify.
5
Section 4.5 “Graph Using Slope-Intercept Form”
SLOPE-INTERCEPT FORMa linear equation written in the form
y-coordinate
x-coordinate
y = mx + b
slope
y-intercept
Graph Using Slope and the Y-Intercept
Graph the equation 3y – 2x = 3.
STEP 1
Rewrite the equation in slope-intercept form.
y =
Slope of 2/3 means:
2 rise

3 run
2 x
+1
3
STEP 2
Identify the slope and the y-intercept.
m = 2/3
and
b =1
STEP 3
Plot the point that corresponds to the
y-intercept,(0, 1).
STEP 4
Use the slope to locate a second point on the line. Draw a line
through the two points.
Determine which of the lines are parallel.
Find the slope
of each line.
Line a: m =
–1– 0
–1– 2
Line b: m = – 3 – (–1 )
0 – 5
– 5 – (–3)
Line c: m =
–2–4
–1
1
= –3 =
3
–2
2
= –5 =
5
–2
1
= –6 = 3
Line a and line c have the same slope, so they are parallel.
Section 4.7 “Graph Linear Functions”
Function Notationa linear function written in the form y =
mx + b where y is written as a function f.
x-coordinate
This is read
as ‘f of x’
f(x) = mx + b
slope
y-intercept
f(x) is another name for y.
It means “the value of f at x.”
g(x) or h(x) can also be used to name functions
Graph a Function
Graph the Function
SOLUTION
STEP 1
STEP 2
Make a table by
choosing a few values
for x and then finding
values for y.
1
-1
STEP 3
Plot the points. Notice
the points appear on a
line. Connect the points
drawing a line through
them.
f ( x)  2 x  3
x -2 -1 0
f(x) -7 -5 -3
f(x) = 2x – 3
2
1
f ( x)  2 x  3
The domain and
range are not
restricted
therefore, you do
not have to
identify.
Compare graphs with the graph f(x) = x.
Graph the function g(x) = x + 3, then compare it
to the parent function f(x) = x.
f(x) = x
x
f(x
)
-5 -5
-2 -2
0 0
1 1
3 3
g(x) = x + 3
g(x) = x + 3
f(x) = x
x
-5
-2
0
1
3
The graphs of g(x) and f(x) have the same slope of 1.
f(x
)
-2
1
3
4
6
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Mid-Term
Review
worksheet #1 all