Advanced Algebra
A line contains the points (5, -4) and (4, -6). What is the slope of the line perpendicular to it?
(-1/2)
The slope of the line is 6. The slope of the line perpendicular to the aforementioned line is
(-1/6)
Factor 4t^2 + 4t + 1 completely
(2t+1)^2
The slope parallel to that of the line 6x-4y=12
(3/2)
Factor 3x^2 - 4x - 4 completely
(3x+2)(x-2)
Square of a sum rule
(A+B)^2 = a^2+2AB+B^2
Conjugate Binomials
(A-3) (A+3) =A^2 - 9 (A+B) and (A-B)
Power of a power rule
(X^A)^B=X^(AxB)
Product of Powers Rule
(X^a)x(X^b)=X^(a+b)
Formula for finding slope
(Y2-Y1)/(X2-X1)
Reciprocal (https://www.google.com/search?q=reciprocal&oq=reciprocal&aqs=chrome..69i57j0l5.4023j0j7&sourceid=chrome&ie=UTF-8)
(of a function) related to one another such that their product is 1 (X/1)x(1/X)=(X/X)=(1/1)=1
Algebraic Definition of Absolute Value
- If x is greater than or equal to zero, then the absolute value of x=x -If x is less than zero, then the absolute value of x=-x
Coefficient (https://www.mathsisfun.com/definitions/coefficient.html)
A numerical constant quantity placed before (and multiplying) the variable in an algebraic expression or equation (4 IN 4xy^2)
Variable (http://mathinsight.org/definition/variable) (https://www.mathsisfun.com/definitions/variable.html)
A quantity that may change within the context of a mathematical equation or experiment; a symbol for a number that we do not yet know the value of.
Point-slope form
For this one, they give you a point (x1, y1) and a slope m, and have you plug it into this formula: y - y1 = m(x - x1)
Zero product property
If the product of two quantities is zero, then a least one of the quantities must be zero.
Integers
Natural numbers (positive integers), zero, and negative integers. Negative integer is the opposite, or additive inverse, of a positive number.
Whole numbers
Natural numbers and zero (0, 1, 2, 3, 4)
What is the y-intercept of a line whose equation is y+9=2(x-3)?
Negative 15
Linear: --(A/B)
Slope (Negates the numerator and the denominator)
Y=Mx+B
Slope-intercept equation of a line
Ax+By=C
Standard form
Natural numbers
The numbers used for counting: 1, 2, 3, 4
Sample space (http://www.regentsprep.org/regents/math/algebra/apr4/Lsample.htm)
The set of all possible outcomes for an activity or experiment (Roll a die: 1, 2, 3, 4, 5, 6). (Flip a coin: 1, 2).
Absolute value (http://www.purplemath.com/modules/absolute.htm)
distance of a number from zero, without regard to its sign
the slope of a line perpendicular to another line is
negative reciprocal of the first slope
Additive inverse (https://en.wikipedia.org/wiki/Additive_inverse)
opposite of a number that, when added to a given number, yields zero
Simplify p(p-2q) + 3(pq - q^2)
p^2+pq-3q^2
If a quadratic (Ax^2 +/- By +/- C) is difficult to factor, you can use the...
quadratic formula
The slope of a line parallel to another line is
the same
Which equation is equivalent to 15x+3y=10?
y=-5x+(10/3)
Find the prime factorization of 1350
2x3^3x5^2
Factor 3x^3-27x completely
3x(x+3)(x-3)
Express (3t-4)(2t+3) as a simplified polynomial
6t^2+t-12
Algebraic expression (http://home.avvanta.com/~math/def2.cgi?t=expression)
A mathematical phrase that can contain ordinary numbers, variables (like x and y), and operations (add, subtract, multiply, or divide).
Multiplicative inverse (https://en.wikipedia.org/wiki/Multiplicative_inverse)
A number X, denoted by 1/X or X^-1 (which are the same thing), is a number which, when multiplied by X, is equal to one. (1/X)x(X/1)=(X/X)=1
Solution of an equation (https://www.google.com/search?q=solution+of+an+equation+definition&oq=solution+of+an+equation&gs_l=serp.1.1.0i71l8.0.0.0.4283.0.0.0.0.0.0.0.0..0.0....0...1c..64.serp..0.0.0.PmE0TvR1ROY)
A value or values which, when substituted for a variable in an equation, make the equation true
Square of a difference rule
A-B)^2=A^2-2ab+B^2
Difference of two squares rule
A^2-B^2=(A-B)(A+B)
Rational numbers
All the numbers can be written as quotients as integers. Must have a nonzero denominator. Some rational numbers can be written as terminating numbers. All other numbers can be written as repeating decimals
QUADRATICS
B^2-4(A)(C) >0 two solutions =0 one solution <0 no real solutions, 2 imaginary solutions
Irrational numbers
Cannot be written as quotients of integers Decimal representations neither terminate nor repeat If a positive number is not a perfect square, its square root is irrational
Properties of Natural Numbers
Chart #1
Properties for Simplifying Algebraic Expressions
Chart #2
Properties of Equality
Chart #3
Properties of Inequality
Chart #4
Proof of the quadratic formula
Chart #5
Term (https://simple.wikipedia.org/wiki/Term_(mathematics))
Either a number or variable, or the product of several numbers or variables, separated by a sign, + or - in an overall expression or equation
This is the process used to multiply two binomials
F.O.I.L.
Evaluate (algebra) (https://www.google.com/search?q=evaluate&oq=evaluate&aqs=chrome..69i57j0l5.3599j0j7&sourceid=chrome&ie=UTF-8)
Find a numerical expression, solution, or equivalent for
Opposite (http://www.mathgoodies.com/glossary/term.asp?term=opposites)
Two integers are opposite of they are the same distance away from zero, but one is negative and one is positive
Slope of a vertical line
Undefined
Linear: (C/A, 0)
X-Intercept
For the equation of the line 4x-5y=-20 find The x-intercept The y-intercept The slope
X-Intercept (-5,0) Y-intercept (0,4) Slope (4/5)
Simplify (-X^3)^2(X^4)
X^10
Simplify (X^3 - 3x^2 - 2x + 5) - (X^2 - 2x + 2)
X^3 - 4x^2 + 3
Quotient of powers rule
X^a/X^b=X^(a-b)
Linear: (0, C/B)
Y-Intercept
Slope of a horizontal line
Zero
Solve the equation 6x^2=5x-1
[(1/2), (1/3)]
Express ax(x-a)(x+a) as a simplified polynomial
ax^3-a^3x
If you want to determine whether or not a quadratic (Ax^2 +/- By +/- C) is factorable...
determine whether or not descriminant of a quadratic equation is a perfect square (B^2 -4(A)(C)). If so, factorable; if not, not factorable.