Exam Review By: John Misiewicz Jeremiah Johnson. 1 st Power Equations -Has no exponents -Make the...
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![Page 1: Exam Review By: John Misiewicz Jeremiah Johnson. 1 st Power Equations -Has no exponents -Make the equation equal the variable.](https://reader030.fdocuments.net/reader030/viewer/2022032805/56649ef15503460f94c0265d/html5/thumbnails/1.jpg)
Exam ReviewBy: John Misiewicz
Jeremiah Johnson
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1st Power Equations
-Has no exponents
-Make the equation equal the variable
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1st Power Examples
Answer=x so the answer is All real numbers
Answer: x= 5
Ex2: x+12=x+12
Ex1: x-2=3
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1st power Examples cont.Ex3: Answer: x=
20
525
2x
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Properties Addition/ Subtraction property of Equality- If the
same number is added/ subtracted to equal numbers the sums/ differences are equal
a+c=b+c; a-c=b-c Multiplication/ Division property of Equality- If
equal number are multiplied/ divided by the same [(non zero) in the case of division] number the products/ quotients are equal
ca=cb; a b
c c
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Properties Reflexive property- all numbers equal
themselves. a=a Symmetric Property- If one number equals
another than the other number equals the first number. a=b, b=a
Transitive Property- If a=b and b=c than, a=c
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Properties Associative Property of Addition- (a+b)
+c=a+(b+c) Associative Property of Multiplication-
(ab)c=a(bc) Commutative property of Addition-
a+b=b+a Commutative Property of Multiplication-
ab=ba
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Properties Distributive Property-a(b+c)=ab+ac Property of Opposites- a+(-a)=0; -a+a=0 Property of Reciprocals- Identity Property of Addition- a+0=a; 0+a=a Identity Property of Multiplication- Multiplicative property of zero- Closure property of addition-a+b Closure property of multiplication- ab
11a
a
1a a 0 0a
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Properties Power of a product property-(2t)2 = 22 x t2
Product of a power property- 84 x 46
Power of a power property- (84)5
Quotient of powers property- Power of a quotient property- Zero power property-(x+5)(x-8)=0
6
2
x
x2
3
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Properties Negative power property- -3-3=1/27 Zero product property-(x+10)(x-15)=0 x=-10
or x=+15 Product of roots property-√9 x√5 = √45 Quotient of roots property-√225=√9x25
=3x5 = 15
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Inequalities in one variable x-8<15 solve and graph 3x-5>1 solve and graph 13-7n<8 solve and graph 4y+3>7 solve and graph 2x+7>3 solve and graph
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Conjunctions
2m<4 and 12+2m<0 solve and graph 2d-5>-8 and -2d-5<d-3 solve and graph -3+2<x-2+2<4+2 solve and graph 5-2p>-8 and -2d-5<d-3 solve and graph
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Disjunction 2w-1<3 or 3w>w+10 solve and graph 5-2p>11 or 5-2p<-1 solve and graph -6>18 or 12+3r>0 solve and graph H+5<-2 or h+5>2 solve and graph
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IMPORTANT!!!!!!!!!!!!!!!!!!!!!! When solving these equations conjunctions
join the sentences together using the word and (just like in a sentence in english class). In a conjunctions you will find that both of the sentences are true. In a disjunction the word or is used. This means that at least ONE sentence is true and it cancels out the other sentence.
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Linear Equations in Two Variables 4x+3y=10 here are a list of ordered pairs
(4,-2) (-2,6) (2,3) (8,5) plug these in to see which one fits the equation.
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All Equations For All Lines Standard/General- ax+by=c Point slope form- y-y1=m(x-x1) Slope intercept form- y=mx+b equation of a horizontal line-y=b Equation of a vertical line- x=a
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Slopes for all lines
The slope for a rising line is positive.
The slope of a falling line is negative.
A line that is parallel with the bottom of the graph has a slope of zero because it never rises.
A verticle line has a slop that is undefined because it it has no run.
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How to Graph Using the equation y=mx+b y= the equation of the line mx= the rise over the run or the slope of the
line And b is the where the line crosses the y-
axis
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Linear System Substitution Method- 2x+y=25
4x+3y=32
Solution- y=25-2x (plug this equation into your second one)
4x+3(25-2x)=32
X=21 y=67
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Linear Systems cont. Addition/Subtraction Method- 5-y=12
3x+y=4
solution is- 8x=16
Final solution is: x=2 y=-2
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4
2
-2
-4
4
2
-2
-4
4
2
-2
-4
Solution- Null set
Inconsistent System
Solution- Intercept point
Consistent System
Solution- A.R.N.
Dependent System
Linear Solution Commonalities
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Factoring Polynomials 5a3+b3 Solution is : 5(a3+b3) ax+bx-bx-by solution is: a(x+y)-b(x-y) 5a3-5a2+10a-10 solution is: (a-1) (5a2+10)
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Quadratic Equations Factoring- 20x2-49x+30 (5x-6) (4x-5) Quadratic Equation-ax2+bx+c=0
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Functions Quadratic Functions-Graphing the Parabola y = ax2 + bx + c 1. Determine whether the parabola opens upward or downward. a. If a > 0, it opens upward. b. If a < 0, it opens downward. 2. Determine the vertex. a. The x-coordinate is . b. The y-coordinate is found by substituting the x-coordinate, from
Step 2a, in the equation y = ax2 + bx + c. 3. Determine the y-intercept by setting x = 0. 4. Determine the x-intercepts (if any) by setting y = 0, i.e., solving the
equation ax2 + bx + c = 0.
5. Determine two or three other points if there are no x-intercepts. Remember point slope form and domains and ranges
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Simplifying expressions with exponents
(2r3s2)(-5r5s) Solutions is – 10r8s3
Important to note that the powers add together not multiply only the numbers multiply together
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Simplifying Expression with Radicals
2 2 2 2* 2
22 2
Rationalizing Denominators-
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Now Onto the Word Problems
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One rectangle’s length is five more (ft.) than
twice as long as the width. If the area of the rectangle is 35ft what is the width
2w+5
w
2w2+5=35So your equation is
And your solution is
W=the square root of 15
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The sum of two numbers is 100. Five times the smaller is 8 more than the larger. Find the number(s)
The numbers are 18 and 82
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A $200 coat is on sale for $166. What is the percent of discount.
17%
.
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You put $1000 into an investment yielding 6% annual interest; you left the money in for two years. How much interest do you get at the end of those two years?
I=Prt
$120I=Prt I=Prt
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The sum of two numbers is 100. Five times the smaller is 8 more than the larger. Find the number(s)
The numbers are 18 and 82
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Line of Best Fit Use this when- you have a linear
regression and you need to find a general estimate of the best line.
Your Calculator helps by having the technology to find the exact estimate and pick any one of the x or y axis’s.
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For extra help try these websites-
http://www.mathtv.com/
http://www.coolmath.com/
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