Section 1
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Fractional Exponents
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Section 1
(50 cards)
Fractional Exponents
The denominator becomes the value to which you take the root, and the numerator becomes the exponent to which you take the number under the root sign.
Domain
the set of all possible input values. he domain of a rational expression includes all real numbers except for those that make its denominator zero.
Difference of Two Squares
(a2 - b2) = (a+b) (a-b)
6. Even + Even =
6. Even
Rational Expressions
a quotient of two polynomials. Or in other words, it is a fraction whose numerator and denominator are polynomials.
2. Odd * Odd =
2. Odd
4. Even + Odd =
4. Odd
i =
square root of -1
x/0 =
undefined
Quadratic Functions
our output variable will always be squared. Parabola Two inputs make the same output (3^2 and -3^2)
x^a * y^a = (xy)^a
When multiplying different numbers but are raised to the SAME POWER, then just multiply the bases together.
Alternative to Completing the Square
In x(squared) + ax = y, move y over to the left hand side: x(squared) + ax + y = 0. Then complete the square.
Determining Prime Factors
To make sure you try every necessary potential factor, take the square root of the number you are trying to determine is prime. Any integer equal to or less than the square root will be a potential factor, but you do not have to try any numbers higher.
SAT Integer Strategies
1.Make sure the question requires an integer. 2. Use real numbers if you forget your integer rules. 3. Keep your work organized.
When solving a Special Topics problem,....
Treat the sin/cos/tan variables as a unit (as a whole)
Parabola Direction with C
C = y-intercept of the parabola (when b=0, the y-intercept will also be the vertex of the parabola)
Prime Numbers
1 is NOT a prime number 2 is the ONLY even prime number
Root Indicator
If there is a number on the outside of a square root symbol, that represents how many numbers should be multiplied to equal the number under the square root symbol.
x^a * x^b = x^[a+b]
When multiplying numbers WITH THE SAME BASE raised to a power, just add the powers together.
0/x =
0
Lines with slopes of 1 or -1
Make a 45-45 triangle on the xy-plane
Factoring Exponents -
Any even power of x is the square of another power x9 = (x3)2
No Solution (system of equations)
In order for a system of equations to have no solution, the "x"values must be equal and the "y" values must be set to 1 (both variables will be equal).
Pythagorean Identity
sin^2 x + cos^2 x = 1
Degrees to Radians Conversions
360 degrees (1 360) = 2π (1 2π) 270 degrees (3/4 360) = 3π/2 or 3/2 π (3/4 2π) 180 degrees (1/2 360) = π (1/2 2π) 90 degrees (1/4 360) = π/2 or 1/2 π (1/4 2π)
To Solve Absolute Value Equations
Break the absolute value apart into two equations, one with a positive solution and one with a negative solution.
Unknown Consecutive Numbers
You can write unknown consecutive numbers out algebraically by assigning the first in the series a variable, x, and then continuing the sequence of adding 1 to each additional number.
Parabola Direction with A
Positive a = parabola upwards Negative a = parabola downwards Large a = skinny parabola Small a = large parabola
Outliers
are a small group of values that are significantly smaller or larger than the other values in the data When there are outliers in the data, the mean will be pulled in their direction (either smaller or larger) while the median remains the same.
Unknown Consecutive Odd/Even Numbers
This is the same as consecutive integers, only they are going up every other number instead of every number. This means there is a difference of two units between each number in the sequence instead of 1.
Remainder Theorem
P (x) / x-K = remainder = P(x)
5. Odd + Odd =
5. Even
Arc Length of a Circle
X/2pir = central or inscribed angle/360. Cross-mulitiply
Perfect Square
In a polynomial expression, two numbers that add to equal the ax term and multiply to equal the b term. x(squared) + ax + b
Remainders
Now we also know that, when positive consecutive integers are divided by any number, the remainders increase by 1 until they hit their highest remainder possible. When that happens, the next integer remainder resets to 0. This is because our smaller number has gone into the larger number an even number of times (which means there is no remainder).
Solving Fraction, Ratio, or Proportion equations
1) Identify whether the problem involves fractions or ratios 2) If a ratio question asks you to change or identify values, first find the sum of your pieces (This sum will either be your complete whole or will be a factor of your whole, if your ratio has been reduced). 3) When in doubt try to use decimals 4) Remember your special fractions
Calculate Slope
Use the slope triangle if you can
1. Even * Even =
1. Even
Parabola Direction with B
Positive b = left of origin Negative b = right of origin
Turn a mixed fraction into an ordinary fraction
You can turn a mixed fraction into an ordinary fraction by multiplying the whole number by the denominator and then adding that product to the numerator. 7 3/4 => 7*4 = 28 => 28+3 = 31 => 31/4
Absolute Value
An absolute value is a representation of distance along a number line, forward or backwards. This means that an absolute value equation will always have two solutions. It also means that whatever is in the absolute value sign will be positive, as it represents distance along a number line and there is no such thing as a negative distance.
Completing the Square
In x (squared) + ax + b, where b is unknown, find b by taking half of a and squaring that answer. Add b to the opposite side of the equation so that it stays equivalent.
x ^ -y = 1/x^y
A base raised to a negative exponent equals 1 divided by the base raised to the positive exponent.
Imaginary Numbers will always simplify to...
1, -1, i, or -i
Quadratic Formula
Quadratic Formula:
Imaginary Numbers 1
i^n = 1 if and only if n is a multiple of 4
3. Even * Odd =
3. Even
Function
A given input, sent through the function, produces a given output. f(x) = y a -> f -> b Multiple inputs can ONLY produce ONE output
Linear Functions
if you have a variable on the output side of the function, it cannot be raised to a power higher than 1. Line
Infinite Solutions (system of equations)
Each system is identical (it is the same line)
Section 2
(19 cards)