Download example problems - Consolidated Electric Cooperative

END OF YEAR SUMMARY
8th Grade 2011
EXAMPLE PROBLEMS
(unedited student work)
What is a Linear Graph:
Equation : Mx+B
How to evaluate:
How to use Pathagous Theory:
A²+B²=C², 3²+4²=C²
9+16=C²
9+16=25
square root of 25= 5²
C²=5²
done!
What is a Nonlinear Graph:
Y = 2X + 8 for X = 4
Y = 2(4) + 8
Y=8+8
Y = 16
done!
Equation: AB²
What is a Histogram:
Shows the
history of
sales in a
certain time
period
What is a pie chart:
What is a Box and Whisker plot:
Can find Mean, Median, Mode, Range with a
box and whisker graph
What is exponential growth:
2x2 or 2 squared
Shows the percentages of data in a pie form
2x2x2
2x2x2x2
2x2x2x2x2x2
done!
Things to know--
How to evaluate:
Interval-- space between two things
Y = 2X + 8 for X = 4
Y = 2(4) + 8
Y=8+8
Y = 16
done!
use factors to find the percent
Linear data-- mx+b ( b= the y intercept
Linear-- constant adding of numbers
expanded & factored-difference= /
quotient= /
product= *
sum= +
growth factor (up)
decay factor (down)
Example of Linear.......
Examples of the Growth Factor.............
7
< growth factor 12
19
THEY GO UP AT A CONSTANT RATE
Examples of decay factor...............
19
< growth factor 12
7
Example of convenience sample..............
Ask students on your bus for data, this is
convenient to you and a easy way to get your
data!
How to evaluate:
Example of Systematic Sampling.................
Y = 2X + 8 for X = 4
Y = 2(4) + 8
Y=8+8
Y = 16
done!
If you see a line or a group of people then ask
every 4th person of whatever is convenient to
you for data, that way it is in a system and you
get your data for your sample!
Example of a parabola.............................
2
Data that goes with the equation X
Example of Factored equation................
(16x^2 - 12x) - (12x – 9) will become (4x-3)
(4x-3)
Example of a Interval........
19
Example of an Expanded equation.......
(4x-3)(4x-3) will become (16x^2 - 12x) - (12x –
9) this makes it expanded......
< Space between numbers
23
Example of Random Sampling.....................
Asking random people questions in order to
collect your data these can be random people
in your class, on the street, in town, in your
neighborhood, etc..........
Example of Dependent Variable..............
Y axis
Example of Distribution.................
Original equation : y= 3(x-2)=21
Distributed equation : 3x-6=21
Example of Independent Variable..............
Example of Voluntary Response Sampling......
Ask people if they would like to participate in
your sampling that way they are volunteering
and your getting your data for your sample!
X axis
Example of a equation......................
Example of Data.......................................
Y= MX+B is a example of the many equations
that exist
5,3,7,3,1,5,7,4,2,1,3,5,7,4,3,3,1,4,4,7,7,7,8,3,2,2,
Random Numbers that have a purpose.
Example of Y Intercept..............................
Example of Area.................................
The linear equation is y= MX+B
M is the Y intercept
The blue shading in this rectangle is the area
Example of Non Linear.............................
PARABOLAS AND EXPONENTIAL
GRAPHS ARE EXAMPLES OF NON
LINEAR EQUATIONS
How to use PEMDAS:
How to find slope:
rise over run
If rise is 4 and run is 2....
4/2= 2
answer = 2
done!
Parenthesis
Exponents
Multiply
Divide
Add
Subtract
Example: How do you work out 3 + 6 × 2 ?
Multiplication before Addition:
First 6 × 2 = 12, then 3 + 12 = 15
Finding the area of a circle:
Finding the area of a square:
‫*ח‬R²(3.14 times radius squared)
3.14*12², 12²=144
3.14*144= 452.16
answer= 452.16
Length X Width
done!
If length was 3 and width was 8.....
8 x 3= 24
area=24
done!
How to find the Mean:
Add up all the #'s and divide by how many #'s
there are...
4,4,2,5,2,5,2
4+4+2+5+2+5+2= 24
24/7= 3.43
done!
. How to find the Mode:
Find the most often #
3,5,6,4,7,4,8,6,4,5,6
the most often # is 6
answer = 6
done!
How to find Median:
Put the # data in order and find the # in the
middle
2,5,6,7,7,8,9,9,9
middle # is 7
answer= 7
done!
How to find the Range:
Lowest to Highest #
2,3,4,5,6,7,8,9
Minimum= 2
Maximum= 9
Range= 2-9
done!
How to evaluate:
How to Solve:
2(2+3x)=8x-12
Y = 2X + 8 for X = 4
Y = 2(4) + 8
Y=8+8
Y = 16
done!
4+6x=8x-12
-6x -6 x
4
= 2x-12
+12 =2x
16 = 2x
/2 =/2
Non-Linear Graph:
Linear Graph:
Inverse Relationship:
Pythagorean Theory:
Direct Relationship:
A2+B2=C2
42+82=C2
16+64=80
√80=9
14x+12=52
-12=-12
14x=40
14 =14
x=2.8
PEMDAS:
P: parenthesis
E: exponents
M: multiply
D: divide
A: addition
S: subtraction
x=8
How to evaluate:
How to find slope:
Y = 2X + 8 for X = 4
Y = 2(4) + 8
Y=8+8
Y = 16
done!
RISE / RUN = SLOPE
Rise = 4
Run = 2
SLOPE = 2
Pythagorean Theory:
2
2
2
Exponential relationships:
2
A +B =C
4/2=2
2
2
20 + 50 = C
400 + 2500 = 2900
√ 2900 = 54
C2 = 54
210=1,024
2*2*2*2*2*2*2*2*2*2= 1,024
How to find area:
7 * 4 = 28
How to find perimeter:
7
5
4
4
2
2
7
5
How to find area of triangle:
PEMDAS
5 * 10 = 50
5
50 / 2 = 25
10
5 + 5 + 2 + 2 = 14
Y-Intercept:
Y intercept = 2
Keys 2 Algebra:
2( 2 + 3x ) = 8x – 12
2*2=4
2 * 3x = 6x
4 + 6x = 8x – 12
- 6x - 6x
4 = 2x – 12
+12
+12
16 2x
2 = 2
8=X
16 / 2
=8
How to make a histogram:
Box and whiskers graph:
Linear Equations:
Y = Mx + B
Y= 5x +9
Slope = 5
Y intercept = 9
Exponential Equation
ABn
EXAMPLE PROBLEMS
How to evaluate:
How to solve:
How
Y = 2X
to +
Distribute:
8 for X = 4
2x(x+7)
Y = 2(4) + 8
2x
Y2=
+14x
8+8
Y = 16
2x
done!
times x equals 2x2 and 7 times 2x equals
14x.
Done!
How to find the perimeter:
10
10 + 5 + 10 + 5 = 30
5
5
Perimeter = 30
4x + 2 = 10
-2
-2
4x
=
8
8 / 4 = 2
X = 2
DONE!
How to find the area:
5
5
10
A = L*W
5
5 * 5 = 25
5
A = 25
How to find median:
How to find mode:
155629823789
Put numbers in order
1,2,2,3,5,5,6,7,8,8,9,9
Cross out till u get to the middle number
1,2,2,3,5,5,6,7,8,9,9
Get your group of numbers
1,5,5,5,6,2,9,2,3,7,8,9,8
look which number is most often
5,5,5,6,2,9,2,3,7,8,9,8
Mode = 5
Median = 5
How to find the range:
1,2,2,3,5,5,6,7,8,8,9,9
You would take the biggest number minus
smallest number.
9
- 1 to find Slope:
How
8
Range = 8
Rise
Run
9
3
Slope = 3
How to find Pythagoras theory :
A2 + B2 = C2
102 + 202 = C2
100 + 400 = 500
√500 = 22.5
How to find Y-intercept:
Use PEMDAS:
Independent & Dependent axis
(Dependent)
(Y)
(X)(Independent)
How to use box-n-whisker plot:
Linear equation:
Y=Mx+B
How to use P.I.E
How to find volume:
-You have an income of $700 but your
expenses cost $200, to find your profit you do:
700
-200
500
Income
-Expenses
Profit
4x4x4=64
Volume=64
Histogram:
Factored form equation:
Parabola Graph:
arched.
Parabola graph should be
Percent:
2
4 To find the percent you divide
numerator by denominator which would
be .500 then move the decimal over twice
to get 50%
Exponent Short Cut Rules:
How to combine an equation:
Ax * Ay = Ax+y
Ax / Ay = Ax-y
Ax * Bx = A * Bx
(Ax)y = Ax*y
A0 = 1
A1 = A
P = 2.50V – 500
V = 600 – 500R
Combined equation: P = 2.50(600 – 500R) 500
How to find the circumference of a circle:
How to find the area of a circle:
3.14 * Diameter
Example: 3.14 * 16 = 50.24
3.14 * radius2
Example: 3.14 * 82 = 200.96
How to find the volume of a cylinder:
3.14 * radius2 * height
2
Example: 3.14 * 8 * 12 = 2411.52
Equation meanings:
Y = Abx
A = Slope
B = Y-intercept
x
= Exponent
All exponential patterns follow this equation.
EXAMPLE
PROBLEMS
How to evaluate:
Foil Method:
Y = 2X + 8 for X = 4
Y = 2(4) + 8
Y=8+8
Y = 16
done!
(x+6)(x+10)
Median: Put all the numbers in order from
least to greatest.
Range: Whenever you want to find the range,
all you have to do is find the minimum
number and subtract that number from the
maximum number.
1, 5, 8, 12, 15, 36, 56
Cross each one off until you are at the center
number. Which would be 12. 12 is the
median .
First: x*x = x2
Outer: x*10 = 10x
Inner: 6*x = 6x
Last: 6*10 = 60
X2 +10x+ 6x+ 60
Example: 1, 5, 8, 12, 15, 36, 56
56 – 1 = 55
Mean: When you are trying to find the mean
Distribution:
you have to add up all the numbers and divide
that number by how many numbers there are. 30(x+10)
Example: 1 + 5 + 8 + 12 + 15 + 36 + 56 = 133
133 / 7 =
30 * x = 30x
Answer: 30x + 300
30 * 10 = 300
How to evaluate:
Y = 2X + 8 for X = 4
Y = 2(4) + 8
Y=8+8
Y = 16
done!
COPY THIS BOX AS MUCH AS NEEDED
y= 9x + 3
x=17
y= 9(17) +3
y= 153 + 3
y= 156
done!
3(71-2)
3(71-2)
what is the growth factor and table going to
look like?
what is the growth factor and table going to
look like?
210
Y= X2 = parabola
210 = 2*2*2*2*2*2*2*2*2*2
210 = 2*2*2*2*2*2*2*2*2*2= 1,024
done!
A2+B2=C2
2
2
7 +9 =C
AB2
2
what is the growth
factor for the
50(3d)
49+81=130
√130 =11.40
Side C = 11.40
How to evaluate:
Writing expressions in exponential form:
Y = 2X + 8 for X = 4
Y = 2(4) + 8
Y=8+8
Y = 16
done!
A. 2x2x2x2= 24
B. 10x10x10x10x10x10x10= 107
C. 4x4= 42 (or four-squared)
Writing equations for linear graphs.
Writing equations for exponential graphs.
If...
your slope is 5, and your y-intercept is (0,20)
If...
your starting value is 200, and your growth
factor is 2
Then...
your equation would be 5X+20 (MX+B)
Figuring out Pythagorean Theorem
1.
2.
3.
4.
5.
Follow: a2+b2=c2
62+22=c2
36+4=c
40=c
√40=6.32
Then...
your equation would be 200(2)x (ABx)
Figuring Profit
Profit=Income-Expenses or PIE
Income- $200
Expenses- $50
Profit- $150
Finding “X” in an equation.
500=2x+50
How to F.O.I.L.
1. First (x+5)(3+x)
2. Outer (x+5)(3+x)
3. Inner (x+5)(3+x)
4. Last (x+5)(3+x)
500=2x+50
-50
-50
450=2x
∕2 /2
225=x
How to Distribute
How to find area of a square and circle.
A=∏r2
Multiply everything inside the parenthesis
with the outside number.
A=l*w (square=l2)
Finding the area of a
triangle.
A= 1/2bh
4*7=28
28/2=14