An arithmetic sequence is created by adding or subtracting a common difference.

Back

Arc functions

Front

Back

Converting radians to degrees and minutes

Front

Multiply by 180 and then divide by pi.
The part before the decimal is the degrees. Multiply the decimal by 60 to find the minutes.

Back

Inverse variation

Front

The inverse variation formula is x one times x two equals y one times y two.
Inverse variation creates a corner hyperbola.

Back

Conterminal Angles

Front

Coterminal angles are just different ways of naming the same angle.

Back

Cosecant

Front

Cosecant equals 1 divided by sine.

Back

Secant

Front

Secant equals 1 divided by cosine.

Back

Complex fractions

Front

Back

Equations with fractions

Front

To solve equations with fraction, find a common denominator.
Drop the denominators
Solve the resulting equation.
Check the answer(s) in the denominators for extraneous roots.

Back

Law of Sines

Front

The law of sines is a divided by sine of A equals b divided by sine of B equals c divided by sine of C.

Back

Trigonometric identity

Front

Cosine squared plus sine squared equals 1.

Back

Absolute value inequalities

Front

To solve absolute value inequalities
Isolate the absolute value on one side of the equation.
Change the inequality sign and the sign(s) of the terms on the right to the opposite signs.
If the original inequality has a greater than or greater than or equal to (≥ or >) sign use or between your solutions.
Solution is <(≤) x or x >(≥) solution.
If the original inequality has a less than or less than or equal to (≤ or <) write as an interval.
Solution <(≤) x <(≤) solution.
You have to divide by a negative, do not forget to flip the inequality sign.

Back

Binomial Expansion

Front

Back

Arc length - radius formula

Front

In a circle the central angle in radians equals the arc length divided by radius.

Back

Function

Front

To be a function
It must pass the vertical line test.
No x coordinate can repeat.
An equation must have a y, but the y cannot be squared.

Back

Quadratic formula (Find the Roots)

Front

the quadratic formula is x equals negative b plus or minus the square root of b squared minus 4 times a times c all over 2 times a.

Back

Geometric sequence

Front

A geometric sequence is created by multiplying or dividing a common ratio.
If the terms alternate between positive and negative, the common ratio is negative.

Back

Absolute value equations

Front

To solve an absolute value equation
Isolate the absolute value on one side of the equation.
Change the sign(s) of the terms on the right to the opposite sign(s).
check your answer(s) for extraneous roots.

Back

Factoring by grouping

Front

Back

Law of cosines given (S.S.S.)

Front

The law of cosines a squared(the side across from the angle) equals b squared plus c squared minus 2 times b times c times the cosine of x (A). Use numerical solve to find the measure of angle A.

Back

Law of cosines given (S.A.S.)

Front

The law of cosines is b squared plus c squared minus 2 times b times c times the cosine of A.
Take the square root of the answer to find the missing side.

Back

Sum and product of roots

Front

The sum of the roots is negative b divided by a.
The product of the roots is c divided by a.
The equation for sum and product of the roots is x squared minus the sum times x plus the product equals 0.

Back

Area of a triangle (need S.A.S.)

Front

Need side angle side (S.A.S) to find area.
The area of a triangle equals ½ times a times b times sine of C.

Back

Factoring out a -1

Front

To factor out a -1, remove the negative and change the signs of the terms

Back

Discriminant (describe the roots)

Front

if the discriminant is 0, the roots are real, rational and equal.
if the discriminant is negative, the roots are complex or imaginary.
if the discriminant is a perfect square, the roots are real, rational, and unequal.
if the discriminant is not a perfect square, the roots are real, irrational, and unequal

Back

Quadrants

Front

All students take classes.
Sine and cosecant are positive in quadrants 1 and 2.
Cosine and secant are positive in quadrants 1 and 4.
Tangent and cotangent are positive in quadrants 1 and 3.

Back

Completing the square

Front

Back

Conjugate

Front

To find the conjugate
The first term stays the same.
Change the sign of the second term.

Back

Permutations with repetition

Front

Back

Circle formula

Front

The circle formula is x minus h squared plus y minus k squared equals the radius squared.

Back

Tangent

Front

Tangent equals sine divided by cosine.

Back

Canceling out opposites

Front

If both terms are opposite signs they can be crossed out and replaced by a negative 1.

Back

Rationalizing the denominator

Front

To rationalize a denominator multiply the numerator (top) and denominator (bottom)
by the conjugate of the denominator (bottom).

Back

Raising a negative number to a power

Front

When raising a negative number to a power always put the negative number in a parenthesis.

Back

Operations with fractions

Front

Back

Convert radians to degrees

Front

To convert from radians to degrees, multiply the radians by 180 and divide by pi.

Back

Degrees and radians

Front

Once around a circle is 2 pi radians or 360 degrees.
½ of the way around a circle is pi radians or 180 degrees.
¼ of the way around a circle is pi divided by 2 or 90 degrees.

Back

Ambiguous Case (0,1,2 triangles?

Front

Back

Sine, Cosine, Tangent on the unit circle

Front

Back

Area of a parallelogram

Front

A parallelogram is made up of 2 congruent triangles.

Back

One to one function

Front

A one to one function must pass the vertical and horizontal line test.
No x or y coordinate can repeat.

Back

Recursive sequences

Front

a to the n minus 1 - look to the term behind.
a to the n plus 1 - loot to the term in front.

Back

Domain, range, inverse

Front

The domain is the x coordinates.
The range is the y coordinates.
To find the inverse switch the x and y coordinates.

Back

Logarithms

Front

Back

Convert degrees to radians

Front

To convert from degrees to radians multiply the degrees by pi and divide by 180.

Back

Cotangent

Front

cotangent equals 1 divided by tangent or
cosine divided by sine.

Back

Factoring ax²+bx+c

Front

Back

Exact values of trigonometric functions

Front

Back

Survey, observational study, experiment

Front

Survey - ask
Observation study - watch
Experiment - change

Back

Vector problems

Front

To solve vector problems remember that
The opposite sides in a parallelogram are congruent.
The consecutive angles in a parallelogram are supplemental (add up to 180 degrees).
Use law of Cosines to find the resultant and the angle between the 2 forces.
Use law of Sines to find the angle between a force and the resultant.

Back

Section 2

(6 cards)

Inverses of exponential and logarithmic equations

Front

...

Back

Converting between logarithm and exponent form

Front

To convert from logarithmic form to exponent form the base remains the base and the rest of the stuff crosses.
the b and the n can never be negative.

Back

Natural Logarithms

Front

Back

Common Logarithms

Front

Back

Square root equations

Front

To solve square root equations
Isolate the square root on one side of the equation.
Square both sides of the equation
Check the answer(s) in the original equation for extraneous roots.