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Algebra 1: Regents Review
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Gravity
Terms in this set (63)
Linear Regression
Stat- Edit- L1 and L2
Stat- Calc- LinReg (#4)
Exponential Regression
Stat- Edit- L1 and L2
Stat- Calc- ExpReg (#0)
Standard Deviation
small- data close together
large- data spread out
Shape: Symmetric
The data on the graph is evenly spaced out.
Shape: Skewed Right
The data on the graph starts large from the left and gets smaller as it goes to the right.
Shape: Skewed Left
The data on the graph starts small from the left and gets larger as it goes to the right.
Shape: Uniform
The data on the graph is the same amount at each interval.
Mean
Only a good measure of center for symmetric data
Median
(middle) Better measure of center for skewed data or data with an outlier
"R"
Correlation Coefficient. It tells how good of a fit your scatter plot is to your line of best fit. -1 < r <1
Strong Negative
R is closer to -1
Strong Positive
R is close to 1
Weak Correlation
R is close to 0
Residual
Actual-Predicted
Residual Plots: Scattered means data is a good fit. Pattern means data is a bad fit.
Function
A relation where each x-value has only one y-value.
Domain
X-values (input)
Range
Y-values (output)
Positive
Interval(s) of x where graph is above the x-axis
Negative
Interval(s) of x where graph is below the x-axis
Increasing
Interval(s) of x where graph is going from left to right
Decreasing
Interval(s) of x where graph is going down from left to right
End Behavior
When x increases, what does y approach?
When x decreases, what does y approach?
Relative Max
Highest y-value in a specific part of a graph
Sequences
A list of numbers whose domain is all positive integers (make sure to say this when you are asked to write any rule for a sequence!)
Arithmetic
Has an adding pattern.
Arithmetic: Explicit Rule
An = a1 + (n-1)d
Arithmetic: Recursive Rule
An+1 = An + d, a1 = first term
Geometric
Has a multiplying pattern
Geometric: Explicit Rule
An = a1(r)n-1
Geometric: Recursive Rule
An+1 = An x r, a1 = first term
Linear Functions
Constant rate of change. Model arithmetic sequences (adding).
Slope-Intercept Form
y=mx+b
m= slope
b= y-intercept
Point-Slope Form
y-y1 = m(x-x1)
m= slope
(x1, y1) is a point on the line
Standard Form
Ax+By = C
Parallel Lines
Equal Slopes
Perpendicular Lines
Slope are opposite reciprocals. Ex: m = (-3/4) and m = (4/3)
Systems: Solving Graphically
-Get into y = form
-Graph and find points of intersection
-2nd-TRACE-INTERSECT
Systems: Solving by Substitution
Solve for x or y and plug in
Systems: Solving by Elimination
Get opposite coefficients and add, OR get same coefficients and subtract
Example: 2x+3y=12
x+5y= -7 (multiply this equation by -2, then eliminate x's)
Compound Inequalities
-5 < 2x+1 < 4
-Split into two different inequalities
-5 < 2x+1 AND 2x+1 < 4
-Solve each separate inequality
*
HAVE TO FLIP INEQUALITY WHEN MULTIPLYING OR DIVIDING BY A NEGATIVE
*
Graphing Inequalities
-Get into "y=" form
Greater than/less than = Dashed line
Greater than/less than or equal to = Solid Line
System of Inequalities
-Graph both inequalities
-Solution set is where shading overlaps
Shading
Plug in (0,0) or use calculator:
Upper triangle = greater than
Lower triangle = less than
Exponential Functions
-Increase at an increasing rate or decreasing at a decreasing rate
-Models a geometric sequence (multiplying by a common ratio)
Exponential Equation
y = a x bx
a = y-intercept
b = common ratio
when b >1, the function increases
when 0 < b < 1, the function decreases
Simple Interest
I = prt
P = total you start off with
R= rate you go up/down by
T = time
Compound Interest
A = P(1 + r)t
Quadratic Functions: Factoring
-Always look for a GCF first
Ex: 2x2 + 4x = 2x(x+2)
-All other factoring... use the box method!
Hint: y1 = ac/X in calculator if you need to!
Quadratic Graphs
Roots: (Zeros) x-intercepts and the solution to the equation when function = 0
Vertex: turning point (min or max)
Quadratic Tables
There is a constant 2nd difference
Factored Form
Ex: y = (x+3) (2x+1)
-helps find zeros
-set each factor equal to 0
(Quadratic) Standard Form
y = ax2 + bx+ c
-if a > 0 parabola opens up
-if a < 0 parabola opens down
-c (the constant) is the y-intercept
Vertex Form
Y = (x-h)2 + k
-vertex (h,k)
-axis of symmetry at x = h
Solving Quadratic Equations
Option 1- Can you solve by using square roots?
Ex 1: 4x2 + 2 = 10
4x2 = 8
x2 = 2
x = (plus/minus) square root of 2
Ex 2: (x-2)2 = 10
x-2 = (plus/minus) square root of 10
x = (plus/minus) square root of 10 + 2
Solving Quadratic Equations 2
Option 2- Set equal to 0 and factor
Ex: x2 + 2x = 8
x2 + 2x - 8 = 0
(x+4) (x-2) = 0
x = -4, x = 2
Solving Quadratic Equations 3a
Complete the square.
Ex: x2 + 6x + 7 = 0
x2 + 6x + _ = 7 + _
x2 + 6x + 9 = 7 + 9
(x+3) (x+3) = 2
(x+3)2 = 2
x +3 = (plus/minus) square root of 2
x = (plus/minus) square root of 2 - 3
Solving Quadratic Equations 3b
Quadratic Formula.
-On formula sheet
-Get in standard form (ax2 + bx + c = 0)
-Find a, b, and c and plug into your formula!
Discriminant
-b2-4ac
-Positive discriminant: 2 real solutions
-Negative discriminant: no real solutions
-Discriminant equal to 0: one real solution
Free Falling Motion: Feet
H(t) = -16t2 + vot + ho
Free Falling Motion: Meters
H(t) = -4.9t2 + vot + ho
Revenue
R = (linear function for price) (linear function for quantity)
*
when there are no productions costs, revenue = profit!
*
Transformations
Parent function: y = f(x)
y = f(x) + b shifts up "b" units
y = f(x) - b shifts down "b" units
y = f(x-c) shifts left "c" units
y = f(x+c) shifts right "c" units
Step Functions
y = [x]
-greatest integer less than or equal to x
Ex: y = [3.7] = 3 (since 3 is the greatest integer less than 3.7)
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