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Percent formula

Part = Percent X Whole

Counting the Possibilities

m ways one even can happen and n ways a second event happen, so there are m X n ways.

Multiplying powers

x^3 X x^4 = x^3+4 = x^7 (add the powers)

Dividing Powers

y^13/y^8 = y^13-8 = y^5 (Subtract the powers

Raising Power to Power

(x^3)^4 = x^3X4 = x^12 (Multiply the powers)

Adding and Subtracting Monomials

To combine like terms, keep the variable part unchanged while adding or subtracting the coefficients: 2a + 3a = (2+3)a = 5a (add the coefficients)

Multiplying Monomials

To multiply monomials, multiply the coefficients and the variables separately: 2a X 3a = (2X3)(aXa) = 6a^2

Multiplying Binomials

product is found by FOIL (First Outer Inner Last)

Multiplying other Polynomials

product is found by multiplying each term in the first polynomial by each term in the second.

Possibilities

mCn= m!/n! (m-n)!----!=4X3X2X1...etc

Factoring Squares of Binomials

(a+b)^2 = a^2+2ab+b^2--------(a-b)^2 = a^2-2ab+b^2

Direct Variation

a linear function defined by an equation of the form y = kx, where k cannot equal 0

Domain

the set of values of the independent variable for which a function is defined

Range

the set of all output values

Inverse Variation

y varies inversely as x; as increases y decreases; as x decreases y increases; xy=k or y=k/x;

Triangles sides

3:4:5, 5:12:13,

Triangles angles

30-60-9=x-x root 3-2x

Interior Angles of Polygons

(n-2)(180)-----n=# of sides

Length of Arcs

(n/360)(2 pie r)----n=angle measure

Area of sectors

(n/360)(pie r^2

Surface Area

2lw + 2wh + 2lh

Volume

lwh

Volume of Cylinders

pie r^3h

Distance formula

root (x1-x2)^2 + (y1-y2)^2

Midpoint

(x1+x2/2, y1+y2/2)

Slopes

change in y/change in x = rise/run

fractional exponents

x^y/z=z-root(x^y)

domain & range

the domain of a function is the set of values for which the function is defined. The range of a function is the set of outputs or results of the function.

inverse variation

xy=k

direct variation

y=kx

average of consecutive numbers

average the smallest & the largest.

converting eights

when converting, remember that 1/8=0.125=12^1/2%.37^1/2%is 3 times ,so it equals 3/8.*

average rates

avg. Aper B=total A/total B........avg. speed=total distance/total time.

sum of exterior angles

the 3 exterior angles of any triangle add up to 360 degree.*

triangle inequality theorem

z=third side...Ix-yI<z....x+y>z

negative exponents

1/a^b

slopes

slope=change in y/change in x=rise/run

qualitative behavior

some quations will ask you to identify parts of the graph of a function. They may ask for the value of the function, or, as here, the maximum or minimum valuies of the function....q(x)is represented by the y- value.

distance between points

distance=root(x2-x1)^2+(y2-y1)^2.

union & intersection of sets

is the set of elements that are in either or both.....set of elements common to both

finding midpoints

x1+x2/2,y1+y2/2*

symbols

is plug in the given values of

powers of negatives

a negative number raised to an even power yields a positive result.A negative number raised to an odd power yields a negative result.

powers of fractions

raising a fraction between 0 & 1 to a power yields a number smaller than the original.

exterior angles of triangles

An exterior angle of a triangle is equal to the sum of the remote interior angles.

parallelograms

a parallelogram has 2 pairs of parallel sides.opposite sides are equal. opposite angles are equal.consecutive angles add up to 180 degree.

addiong & subtracting polynomials

combine loke terms

factoring products of binomials

Foil,first,Last,Outer & Inner

parallel lines & transversals

A transversal across parallel lines forms 4 equal acute angles & 4 equal obtus angles.

pemdas

Parentheses,Exponents,Multiplication/Division(left to right)Addition/Subtraction(left to right)

percent increase

one way is to re- express them with a common denominator.Another way is to convert them both to decimals.