Common Core Algebra Review Sheet June 2016

COMMON CORE ALGEBRA REVIEW SHEET JUNE 2016

QUALITATIVE/QUANTITATIVE:
Quantitative: #’s (ex.age, height, weight)
Qualitative: not #’s (ex.groupings, categories)
Bias: unfair
Unbiased: fair
Bivariate: 2 variables correlate
(ex.ice cream sales & hot weather) / UNDEFINED:
“under” (denominator ONLY)
Discriminant domain means solve for x, set to zero
Ex: 2x – 5
10x – 20 *10x -20 = 0
x = 2
GRAPHING:
Dotted Line/ Open Circle: < or >
Solid Line/ Closed Circle: or
Absolute Value: V shaped (math, num, abs) y=l5xl
Parabola/Quadratic: U or ∩ y=x2=4x -2
Exponential: gentle curve up or down y=5x
Linear: y=mx+b (m=slope, b = y-intercept)
(positive, negative, undefined, zero slope)
Square root function:√x
Vertical Line: x = 5 Horizontal Line: y = 5 / PROPERTIES:
Additive Identity Property: 7+0=7
Associative Property: (Always Stays Same)
(a+b)+c = a+(b+c)
Distributive Prop. of Multiplication over Addition:
9 (4a +2) = 36a + 18
Commutative Property: (Change Order)
(7)(4)= (4)(7)
SCIENTIFIC NOTATION:
2.4 x 10-5 = .000035 (move →/negative exponent)
(move ←/positive exponent) / INVERSE RULES:
Multiplicative Inverse (Reciprocal): 1 / 4 = - 4/1
(Flip and change sign)
Additive Inverse: 2/3 = - 2/3
(Change sign only)
EXPONENTS:
No NEGATIVE exponents!
EX: 3-3 = 3-3 = 1
1 33
Multiplying: add exponents
(4x2 y) (-2xy2) = -8x3y3
Power to Power: multiply exponents/terms
(2x3y5)2 = 4x6y10 / EXPONENTS:
Adding: combine like terms/keep exponents same
4x2 + 2x -5
+ X2 -3x + 2
5x2 - 1x -3
Dividing: Subtract exponents.
RATIOS:
The ratio to boys to girls is 2:8. The total is 400. How many girls?
2x + 8x = 400
10x = 400
10 10 x=40 *plug in 40 → 8x=8(40)=320 girls / FORMULAS: (Use reference sheet/end of test)
Volume of a Cylinder: V = 2h
Slope: m = y2 – y1
X2 – x1
Volume of a cube: V=s3 (not of reference sheet)
y = mx+b = m is the slope, b is the y-intercept
A = P(1+r)n
*A=value/investment r= decimal interest rate
n=# of years
MEASUREMENTS:
12 inches per foot 1 inch = 2.54 cm
12x5=60 inches How much is 60 inches in cm?
1__ = 60 = x = 152.4 cm
2.54 x
*cross multiply / FUNCTIONS:
X’s cannot repeat to be a function
Y’s can repeat
YES FUNCTION: (1,2), (2,5), (5,2)
NOT A FUNCTION: (2,1), (5,3), (5,0)
Use VERTICAL LINE TEST with a pencil, touches more than once NOT a function.
LINEAR/EXPONENTIAL:
Linear: line (add or subtract)
Exponential: curve (multiply or divide)
Arithmetic: (adding/subtracting)
Geometric: (multiply/divide) / VARIES DIRECTLY:
X x=2 when y = 4
Y What is the value of x when y = 20?
2 = x
2 5 *Cross multiply x = 5
NEED TO KNOW!
* ( ) distribute # or negative sign to everything
* “8 less than twice the given number” = 2x – 8
*Perpendicular Slope:
1.) Put in y=mx+b
2.)Flip & Change sign of slope / FIND POINTS THAT PASS THROUGH A LINE
1.)Put in y=mx+b
2.)Use calculator buttons 2nd, graph
3.)Look on table for x and y coordinates
SUBTRACTION → ADD THE OPPOSITE
When 3x2 – 5x + 2 is subtracted from 4x2 -3x + 6
4x2 -3x + 6 – (3x2 – 5x + 2) *Distribute negative
4x2 -3x + 6 -3x2 + 5x – 2 *Combine like terms
X2 + 2x + 4 / FORMULA:
A = p (1 + r)n
A= value/investment
r = rate (percent)
n= time (years)
AXIS OF SYMMETRY:
“Symmetrical” draw line down the middle of parabola, find where in crosses the X-axis
*AXis = X(where it crosses)
x = -b
2a y =3x2 + 5x + 2 a=3 b=5 / TURNING POINT/VERTEX:
The vertex of a parabola is the highest or lowest point, also known as the maximum or minimum of a parabola. (X,Y) point

Causal:
Between two events exists if the occurrence of the first causes the other.
Ex: Snow is falling and stores run out of snow shovels
NOT an ex: Alarm goes off and the sun rises / Dividing:
Do not divide multiply by the reciprocal
(flip the signs, only 2nd term)
Correlation:
Positive: most of dots in positive slope
Negative: most of dots in negative slope
No correlation: when scattered all over / Slope: (rise ↑↓over run ←→)
m = y2 – y1 *use when given 2 points
X2 – x1
Positive, Negative,
Zero (horizontal), Undefined (vertical)
Binomial Distribution: (FOIL)
/ Interval Notation:
( or ) < or > * number NOT included
[ or ] or *number included because of line
Box & Whisker Plot or Box Plot:
Numbers must be in numerical order
*Minimum *Q3 (Upper Quartile, 75th percentile)
*Maximum *Median (Q2, 50th percentile)
*Q1 (Lower Quartile, 25th percentile)
Systems of Equations:
Graphically: Set to y=, graph both lines using calculator or by using slope and intercept.
Elimination (Addition): Add equations by canceling, must have one + and one – number to eliminate. Solve for remaining variable. Plug in the equation to other and solve for the other letter (variable).
Substitution: Look for a letter (variable) by itself and plug it in to the other, solve for both letters (variables). / Inequalities:
Is at most, Is less than or equal to
Is at least, Is greater than or equal to
< Is less than
>Is greater to
Perfect Squares:
√4 = 2
√9 = 3
√16 = 4
√25 = 5
√36 = 6
√49 = 7
√81 = 9
√100 = 10
√121 = 11
Quadratic Equation:
F(x)= ax2 + bx + c
*know how to complete a square
*Use quadratic formula (on reference sheet) / Factors:
Change the signs of the ROOTS to find the factors.
Use calculator: y= plug in equation, 2nd graph, find zeros in y column, change the signs of the x’s
Roots:
Cross X axis
*Also known as solutions or answers, zeros
Line of Regression: (Best Fit Line)
Use calculator:
*Stats, Edit, enter data, stats, calc, enter, enter
y=ax+b, use r1 (for best fit)
*If this does not work go to
2nd, hit zero, go to diagnostic on, hit enter twice / Absolute Value:
Use calculator:
*Math, Num, Abs
Remember: V shape

NOTES:

Calculator: hit y=, 2nd, 0 to get to ALL commands (alphabetical list)

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COMMON CORE EXAM JUNE 16th at 8:00am