Math State Test Study Sheet!! with Free Download

For each topic I'll have sample questions and formula on the bottom.These are the topics that will be on the Math State Exam:
Angle pairs
Pythagorean Theorem
Transformation
Measurement
Equations / Inequalities
Sum of Interior Angles
Exponents
Percent
Polynomial
Unit Price
Map Scale
Convert Money

Angle Pairs
Complementary Angles - Angles that add up to 90° or a right triangle.
Example Of Complementary Angles:


Supplementary Angles - Angles that add up to 180° or a straight angle.
Example Of Supplementary Angles:


Vertical angles – The angles that are opposite of one another when two lines are formed. NOTE two angles equal each other.
Example Of Vertical Angles:



Adjacent Angles – two angles with a common side and vertex.
Example Of Adjacent Angles:


Corresponding Angles – angels that are equal. The angles are on the same side of the transversal one exterior and one interior. a, e are corresponding angles. Angles c, g are corresponding angles. b, f are corresponding angles. d, h are corresponding angles.
Example Of Corresponding Angles:


Transversal – A line that intersects two or more other lines to form eight or more angles.
Example Of Transversal:


Interior Angles – Angles formed inside a polygon. To find the sum of interior angles use: Sum of interior angles = 180(n-2); n = number of sides

Exterior Angles – Angles formed outside of a polygon.

Alternate Interior Angles – Angles that are created on the opposite sides of the transversal inside the parallel lines. d, e, and c, f are alternate interior angles.
Example Of Alternate Interior Angles:


Alternate Exterior Angles – Angles on the outside of the parallel lines. a, h, and b, g are alternate exterior angles.
Example Of Alternate Exterior Angles:


Pythagorean Theorem
If a and b are the measures of the legs of a right triangle and c is the measure of the hypotenuse, then a2 + b2 = c2.
Example Of Pythagorean Theorem:



Transformation *NOTE* Notation is normally not used in Math State Exam.
The image of a point, P, being transformed. P’ is P prime.

Reflection – mirror image. The line acts like a mirror. Notation is raxis.
If the image reflect across the x-axis use (x,y) → (x, -y)
If the image reflect across the y-axis use (x,y) → (-x, y)

Rotation – turning the figure either 90o or 180o or 270o. Angles of rotation assume a figure is rotated counterclockwise. All formulas below are ONLY used when the figure is rotated counterclockwise. If the figure is rotated clockwise FIRST use 360o minus the rotated degree THEN follow the formula. Notation is Rdegree.
If the figure is rotated 90o counterclockwise use: (x, y) → (-y, x)
If the figure is rotated 180o counterclockwise use: (x, y) → (-x, -y)
If the figure is rotated 270o counterclockwise use: (x, y) → (y, -x)
If the figure is rotated 90o clockwise use: 360 – 90 = 270, then use the 270 degree counterclockwise formula: (x, y) → (y, -x).
If the figure is rotated 180o clockwise use: 360 – 180 = 180, then use the 180 degree counterclockwise formula: (x, y) → (-x, -y).
If the figure is rotated 270o clockwise use: 360 – 270 = 90, then use the 270 degree counterclockwise use: (x, y) → (y, -x).

Translation
Moving a figure a specific distance in a specific direction. After translating the figure will still have the same orientation. Notation is Ta,b
a is direction for left (negative) or right (positive); b is direction for up (positive) or down (negative).
Formula: Ta,b (x, y) → (x + a, y + b)
Example: The coordinates of the vertices of figure ABC are A (-3, 5), B (4, 6), C(0, 2). What would the coordinates of the vertices of figure ABC be under the translation T3,2 ?
We know a is 3, b is 2, and we know all the coordinates for figure ABC. So now we would plug everything into the formula, which is Ta,b (x, y) → (x + a, y + b).
A’ = (-3, 5) → (-3 + 3, 5 + 2) → (0, 7) that is the new coordinates for vertex A.
B’ = (4, 6) → (4 + 3, 6 + 2) → (7, 8) that is the new coordinates for vertex B.
C’ = (0, 2) → (0 + 3, 2 + 2) → (3, 4) that is the new coordinates for vertex C.

Dilation – When the figure gets larger or smaller. Dilation creates figures that are similar but nor necessarily congruent. Use a scale factor to dilate the figure. Notation is Dk.
Formula is: (x, y) → (xk, yk) k = the scale factor.
Example: Figure ABC has vertices whose coordinates are A (0, 4), B(-1, 1), and C(-3,2). Dilate figure ABC and find the new coordinates using the scale factor 2 (D2).
We know that the scale factor is 2, and we also know all the coordinates for figure ABC.
A’ = (0, 4) → (0*2, 4*2) → (0, 8)
B’ = (-1, 1) → (-1*2, 1*2) → (-2, 2)
C’ = (-3, 2) → (-3*2, 2*2) → (-6, 4)

Measurement
Geometry Formulas

Area (click the picture to get a better view) :

Area:
Square: A= s2
Circle: A= pi × r2
Rectangle: A= a × b
Triangle: Area = 1/2(b × h)
Parallelogram: A= b × h
Trapezoid: A= 1/2h(b1 + b2)

Volume (click the picture to get a better view) :

Volume
Cube: V= a3
Rectangular Prism: V= a × b × c
Pyramid: V= (1/3) × b × h
Cylinder: V= pi × r2 × h

Perimeter (click the picture to get a better view) :

Perimeter:
Square: P= 4a
Circle P= 2 × r × pi
Rectangle: P= 2 (a + b)
Parallelogram: P= 2a + 2b
Triangle: P= a + b + c
Trapezoid: P= a + b + c + d =2m + c + d

Equations / Inequalities

Practice for equations http://www.sosmath.com/algebra/solve/solve0/solve0.html

Practice for inequalities http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut18_ineq.htm

Exponents

Any number raised to the first power is that number itself.

Any number raised to the zero power is ALWAYS 1, EXCEPT zero to the zero power it is undefined.

Any number to the negative power the expression becomes a fraction with a numerator of 1 and a denominator if the positive power.

Adding and subtracting with exponents – like bases with unlike exponents CANNOT be added or subtracted unless they can be evaluated first.

Multiplying with exponents – to multiply powers of like bases, add the exponents.

Dividing with exponents – to divide powers of like bases, subtract the exponents of the divisor from the exponents of the dividend.

Raising a power to a power (power to the power rule) – to raise a term with an exponents to some power, multiply the exponents.

Raising a fraction to a power – to raise a fraction to a power, raise the numerator and the denominator to that power.

Raising a product to a power – to raise a product to a power, raise each factor to that power.

Percent

Percent increase/ decrease use the new price minus the old price and divided by the old price, and then multiply it by a 100 to get the percent increase/ decrease.

Percent increase/ decrease 100 (New – Old / Old )

Polynomial

Term – is an algebraic expression written with numbers, variables, or both and using multiplication, division, or both.

Constant – a term that has no variables

Coefficient- is the numerical part of the term. If no coefficient is written, then it is understood to be 1.

Like terms- terms that contain the SAME VARIABLE with corresponding variables having the SAME EXPONENTS. Terms are separated by plus (+) and minus (-) signs.

Monomial – an algebraic expression of exactly on term.

Add or Subtract Monomials With Like Terms – Use the distributive property and the rules of signed numbers to add or subtract the coefficients of each term. Write the sum with the variable part from the terms.

Polynomial – an algebraic expression of on or more unlike terms is a polynomial.

Binomials – polynomials with two unlike terms.

Trinomials – polynomials with three unlike terms.

Standard Form – a polynomial with one variable. When it has no like terms and is written from the largest exponents to the smallest.

Add polynomials – use the commutative property to rearrange the terms so like terms are beside each other. Combine like terms.

Unit Price

Unite Price is a rate: the rate of cost, or price, per 1 unit of measure, such as $1 per pound. To find the unit price, divide the total cost by the number of units.

Example: 4 pounds of grapes cost $7. How much does it cost to buy 1 pound?

So we use the total cost $ 7 divided by the number of units, which is 4, and we get an answer of $ 1.75 per pound of grape. 7/4 = 1.75.

Map Scale

If 1 unit on the map is equal to 15 mile real life, and you want to find out how many miles is 8 units on the map is in real life you would set up a proportion.

1 / 15 = 8 / x; where x is # of miles in real life. Then you cross multiply. You will get 120 = x

Convert Money

Use the conversions that the test give you and set it to a proportion.

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