Saxon Algebra 2 Formulas
Sine, Cosine, and Tangent
SOH CAH TOA. Sine is the opposite angle divided by the hypotenuse, cosine is the adjacent angle divided by the hypotenuse, and tangent is the opposite angle divided by the adjacent angle (or sine divided by cosine).
Surface Area of a Cube
Six times the sides squared.
Pythagorean Theorem
The Pythagorean theorem is a² + b² = c², where c is the length of the hypotenuse and a and b represent the lengths of the other two sides (legs).
Denominator Numerator Rule
The denominator and the numerator of a fraction may be multiplied by the same nonzero quantity without changing the value of a fraction.
Discriminant of Quadratic Formula
The discriminant is written as: b^2 - 4ac
Distance Formula
The distance formula is written as: d = √[( x₂ - x₁)² + (y₂ - y₁)²]
First-degree polynomial equation graphed
The graph of a first-degree polynomial equation looks like a straight line.
Quadratic Formula
The quadratic formula is written as: x = -b ± √(b² - 4ac)/2a
Quotient Theorem for Square Roots
The quotient theorem of square roots is √x/y = √x/√y.
Addition rule for Equations
The same quantity can be added to both sides of an equation without changing the solution set of the equation.
Slope Intercept Form
The slope intercept form equation is written in the form y=mx+b, where m is the slope and b is the y-intercept.
The Sum of Adjacent Angles in Parallelograms
The sum of any 2 angles adjacent in a parallelogram is 180°.
Negative exponents a^-n=
When you have a^-n, you flip the base and the exponent so that the exponent is positive: 1/a^n.
Commutative Property of Multiplication
a*(b) = b*(a) or 4*(5) = 5*(4)
Commutative Property of Addition
a+b = b+a or 4+5 = 5+4.
Distributive Property
For any real numbers a, b, c: a(b+c) = ab + ac.
Monomials
Have only one term, like 4x or 6g.
Trinomials
Have three terms, like 8y+4x+2 or 2g+5t+7.
Binomials
Have two terms, like 4x +2 or 9g + 5.
PRODUCT Theorem for Exponents
If m and n and a are real numbers and x is not equal to 0, then x^m * x^n = x^m+n.
Product of Square Roots Theorem
If m and n are nonnegative real numbers, then √m√n = √mn and √mn = √m√n.
POWER Theorem for Exponents
If m and n are real numbers, and x is not equal to zero, then (x^m)^n = x^mn.
Uniform Motion
Motion at a constant speed in a straight line
Fractional Form of the Percent Equation
Part/Whole = Percent/100
Volume of a Cylinder
Pi times the radius squared times the height.
Multiplication/Division rule for Equations
Every term on both sides of an equation can be multiplied (or divided) by the same nonzero quantity without changing the solution set of the equation.
Volume of a Cone
1/3 times pi times the radius squared times the height.
Volume of a Pyramid
1/3 times the base times the height.
Degree of the polynomial 2x+3y=6
2x+3y=6 is 1st degree. 2x+3y=6 is a 1st degree polynomial because the exponent of x and y is 1.
Inverse Variations
A = k / B (A is inversely proportional to B)
Direct Variations
A = kB (A varies directly as B)
Complex Numbers
A complex number is written as a + bi, where a is the real part and bi is the imaginary part.
Scientific Notation
A method of expressing a quantity as a number multiplied by 10 to the appropriate power
Imaginary Number
An imaginary number is when i represents the square root of a negative real number.
Change sides
Change signs
Uniform Motion problems:
D1=D2 and D1 +D2 = k and D1+k = D2 where D=RT
Sum of the Angles Inside any Triangle...
Equals 180°
Area of a Circle
π×radius squared