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Algebra 1 SOL Review
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Gravity
Vocabulary and Concept Reviews for the VA SOL test in Algebra 1
Key Concepts:
Terms in this set (43)
Commutative Property
Think: MOVE - when the terms have their order changed (get moved around), but they all keep their same sign (positive or negative)
Associative Property
Think: REGROUP - When the groupings (parentheses) are changed but the terms and the order stay the same
Distributive Property
Think: ARROWS - When a value is distributed (multiplied) by every term inside a group
Identity Property of Addition
Think: SELF - Any value added to zero automatically equals itself
Identity Property of Multiplication
Think: SELF - Any value multiplied or divided by one is automatically equal to itself
Zero Property
Think: ZERO - Any value multiplied by zero automatically equals zero
Additive Inverse Property
Think: OPPOSITES - Any value added to a negative version of itself [like 3 + (-3)] automatically equals zero
Multiplicative Inverse Property
Think: FRACTION - Any value multiplied by its inverse fraction [like 5 multiplied by 1/5] is automatically equal to one
Absolute Value
Any sign inside the absolute value symbols | | is kept or changed to a positive value. |-2| = 2 just like |2| = 2.
Use MATH -> NUM -> 1: abs( in your TI-83 calculator
Multiplying or Dividing an Inequality by a negative number
FLIP THE INEQUALITY SYMBOL!!!!
"Intercept"
Crossing Point. X-intercept is where a graph crosses the X-axis. Y-intercept is where a graph crosses the Y-Axis.
On your TI-83 Calculator, 2nd -> TRACE -> 5: intercept is used to find the point where two lines cross in a system of equations.
Function
1) NO SHARED X VALUES EVER!!!!!
2) Its graph must pass the Vertical Line Test
Domain
All possible X values. [Same as the inputs, independent variables]
Range
All possible Y values [Same as the outputs, dependent variables]
Direct Variation
Model equation: Y = KX
**
The Graph MUST be a straight line through (0, 0) the origin!!!
***
The K value might be a positive, negative, decimal, or fraction, they are all okay for Direct Variation.
Direct Variation NEVER adds or subtracts
Inverse Variation
Model Equation: Could be
Y = K / X or
XY = K. They both work.
**
The Graph is a mirror image that runs away from the axes
**
Y = MX + B
is the model equation for linear functions
**
Graph is always a straight line
**
M = the slope of the line
B = The Y - intercept
Slope
AKA Rate of Change. Letter M in Y = MX + B
(subtract Y values) / (subtract X values)
A simplified fraction is best. Use 1/2 instead of 0.5
Systems of Equations
Look like:
5x + 6y = 30
3x - y = 12
**
Make sure Y is by itself for both equations
**
TI-83 Calculator: Y= -> GRAPH -> 2nd -> TRACE -> 5: intersect
Systems of Inequalities
Very similar to systems of equations, but have shaded regions for their solutions. Also, they may have dotted or solid lines.
**
Any point in the darkest shaded region is automatically a solution to the system!!!
**
Quadratic Equations
ANY equation where X squared is the biggest exponent. Its graph is a parabola (curve)
Most of the time they look like:
**
Ax^2 + Bx + C = 0
**
You might have to rearrange to get Y = ; f(x) = ; or 0 = so you can use your calculator
Zero Product Property
When you factor a quadratic equation, it will probably look like
(x - n)(x + n)
You can set each parentheses equal to zero
Subtraction of Perfect Squares
If you see X^2 minus a perfect square, they all follow the same pattern to factor. Example:
X^2 - 49 factors to
(X + 7)(X - 7)
Synonyms for "Solutions"
X - intercepts
Roots
Zeros
Solutions
**
All mean same thing: where the graph touches the X - Axis!
**
Exponents "Side by Side" with same base
Multiply any regular numbers.
ADD the exponents
X^4 times X^7 = X^11
Exponents "Power to Power"
Distribute the exponent outside the parentheses times EVERY exponent inside
(2x^3)^4 = 16x^12
Exponent: Zero
ANY term to the zero power automatically gets crossed out of expressions, or just changed to (1)
Exponents: same base "Above and Below"
Divide regular numbers
SUBTRACT exponents
Negative Exponents
Negative exponents always have to SWITCH positions in their fractions. [If you don't see a fraction, make one by drawing a bar over 1, then switch]
X^-8 = 1 / X^8
Square root of a non-perfect number
Put it in your calculator as an inverse variation equation. Look for the largest perfect square factor. Write the pair as two square roots, then simplify.
Sq. Root of 448 = 8Sq.Rt.7
Square root of a variable (letter)
Divide its exponent by two.
If there is a decimal, "kick out" a variable and then divide by two.
Sq.Rt. X^5 = X^2 SqRtX
"Best Fit"
Is it LINE or CURVE of best fit?
Line of best fit = STAT-> Calc-> 4: LinReg
Curve of best fit = STAT-> Calc-> 5: QuadReg
"Evaluate"
Find out the value being "plugged in"
Type the equation in your TI-83 calculator, but replace the letters with ( ) and the substituted value
Mean, Standard Deviation, Median or Quartiles
Plug data into L1 and L2 using STAT-> Edit
Then hit STAT-> Calc-> 1: 1 Var Stats
Z - Score Problems
Use this model equation:
Mean + Z(SD) = Point
Plug in what you know, then solve using SADMEG
What Range is between ___ Standard Deviations away from the mean?
To find the range in between, ADD and SUBTRACT using the model equation:
Mean + Z(SD) = Upper Point
also Mean - Z(SD) = Lower Point
Interquartile Range
Distance between the First Quartile (Q1) and the Third Quartile (Q3)
It represents the size of the "Box" in the Box and Whisker Plot
Cube Roots
Simplify just like square roots, only look for perfect CUBES and use
MATH-> Math-> 4: in your TI-83 calculator
Quotient
Means DIVISION
It could also mean FACTORing
Factor
Any values capable of dividing without decimals
"Solve"
Maybe - ( 1. Can you distribute? )
Maybe - ( 2. Can you combine like terms? )
Definitely - Use **
SADMEG
** to do opposite operations.
f(x) or g(x) or h(x) or v(t)........
SAME AS LETTER Y!!!!
USE Y= BUTTON !!!!
"Per" or "Each" or ".... a day"
These are all terms meaning multiplication.
If the problem says "You earn $14 a day," then it gets written as 14d in the expression
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