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Final Exam Study Guide
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Geometry:
Triangles:
Right triangle: A triangle whose largest angle is 90˚.
Obtuse triangle: A triangle whose largest angle is more than 90˚.
Acute triangle: A triangle whose largest angle is less than 90˚. (All angles are less than 90˚.)
Equilateral triangle: A triangle with three congruent sides. (All sides equal.)
Isosceles triangle: A triangle with two congruent sides.
Scalene: A triangle with no congruent sides.
The sum of the angles of a triangle is 180˚.
Quadrilaterals:
Parallelogram: A quadrilateral with 2 pair of parallel sides, opposite sides congruent.
Rectangle: A quadrilateral with 2 pair of parallel sides, opposite sides congruent and
four 90 degree angles.
Square: A quadrilateral with 2 pair of parallel sides, all sides congruent and
four 90 degree angles.
Rhombus:
A quadrilateral with four congruent sides, opposite sides parallel.
Trapezoid: A quadrilateral with 1 pair of parallel sides.
The sum of the angles of a quadrilateral is 360˚.
Polygons:
Pentagon: 5 sides
Heptagon: 7 sides
Nonagon: 9 sides
Hexagon: 6 sides
Octagon: 8 sides
Decagon: 10 sides
Interior angles: To find the sum of the interior angles of any polygon, use the formula
(n-2)180˚, where n is the number of sides.
Circles:
Circle: A set of all points in a plane that are an equal distance from the center point.
Radius: A segment from the center of the circle to any point on the circle. ( 2r = d)
Diameter: A segment from one side of the circle to other, passing through the center. (1/2 d = r)
Chord: A segment connecting any two points on the circle.
Arc: Part of the circle.
Semicircle: Half of the circle.
Minor arc: An arc that is less than 180˚.
Major arc: An arc that is more than 180˚, but less than 360˚.
Central Angle: An angle whose vertex is at the center of the circle.
There are 360˚ in a circle.
Formulas:
Area (triangle) = ½bh
Area (parallelogram, rectangle, square) = bh or lw
Area (trapezoid) = ½(b1 + b2)h
Area (circle) = πr2
Circumference (circle) = πd or 2πr
Surface Area of a prism: 2lw + 2lh + 2wh
Surface Area of a cylinder: 2πr2 + 2πrh
Volume of a prism: lwh
Volume of cylinder: πr2h
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Final Exam Study Guide
Reference – Final Exam Review – Pg. 1
Final Exam Study Guide
Period_______
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Statistics:
Mean: (Average) The sum of the data divided by the number of data items.
Median: The middle number is a set of data that is written in order from least to greatest. If there
is no middle number, find the mean of the two middle numbers.
Mode: The data item that appears most often. There may be more than one mode. There is no
mode if all data items occur the same number of times.
Range: The difference between the greatest and the least values in a set of data.
Outlier: A data item that is far apart from the rest of the data items. An outlier affects the mean
more than the median or mode.
Line Plot: A line plot uses a number line to display data. Each x represents a data item.
Probability:
Probability: The likelihood that an event will occur.
Event: One or more results of an experiment.
Compound Event: The combination of two or more single events.
Certain Event: An event with a probability of 1. (It must happen.)
Impossible Event: An event with a probability of 0. (It can not happen.)
Theoretical Probability: The probability that is calculated by using the ratio:
P = Number of favorable outcomes
Number of possible outcomes
Experimental Probability: The probability found by repeating an experiment,
using the ratio: P= Number of times an event happens
Number of times the experiment is done
Complement: The complement for an event is all of the other possible events for a situation.
The probability of an event plus the probability of its complement equals 1.
Sample space: The set of all possible outcomes. Ex. The sample space for a coin is H, T.
The sample space for a die is 1, 2, 3, 4, 5, 6.
Counting Principle: The number of possible outcomes of a compound event equals the product
of the number of outcomes of the individual event.
Independent events: Two events are independent if the outcome of the first does not affect the outcome
of a second.
Probability of Independent Events: P(A and B) = P(A) x P(B)
Dependent events: Two events are dependent if the outcome of the first event affects the outcome of the
second event.
Probability of Dependent Events: P(A, then B) = P(A) x P(B after A)
Cavallaro 16
Final Exam Study Guide
Reference – Final Exam Review – Pg. 2
Final Exam Study Guide
Period_______
Name_________________________________
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Ratio/Proportion/Percent
Ratios: A comparison of two numbers.
Ex.
3/5
Written three ways:
3 to 5
1) - as a fraction
2) - with the word “to”
3) - with a “ : “
3:5
Rate: Comparison of two quantities. (Different units) 56 miles/ hour
Unit Rate: A rate with a denominator of 1.
Constant of Proportionality: Another name for the unit rate.
Proportion: A statement that two ratios are equal.
To determine if two ratios are a proportion:
1) Cross multiply.
 If the cross products are equal, it is a proportion.
 If the cross products are not equal, it is not a proportion.
To find the missing value in a proportion:
1) Cross multiply the two numbers.
2) Divide the cross product by the remaining number.
3) The quotient is the answer. Be sure to label.
Ex.
x = 7
4 • 7 = 9 • x
4
9
28 = 9x
9
9
3.11… = x
x = 3.11…
Percent: Per one-hundred. PERCENTS ARE ALWAYS OVER 100
 To solve any percent question use the equation: % = is
100 of






To change a percent to a fraction: drop the % and place it over 100. REDUCE
To change a percent to a decimal: move the decimal two places to the left. (Divide by 100)
To change from a decimal to a percent: Move the decimal two places to the right. (Mult. by 100)
To change from a decimal to a fraction: place the decimal (with-out the point) over the correct
power of ten.
To change from a fraction to a percent. Use the numerator as the percent if it is over
100 or set up a proportion to find its equivalent fraction with a denominator of 100.
To change from a fraction to a decimal: Divide the numerator by the denominator.
Fraction
Decimal
Percent
1/2
.5
50%
7/8
.875
87.5%
Cavallaro 16
Final Exam Study Guide
Reference – Final Exam Review – Pg. 3
Final Exam Study Guide
Period_______
Name_________________________________
Date__________________________________
Angle Relationships:
Adjacent angles: Angles that have a common side and a common vertex. There is no degree
measurement for adjacent angles.
Complementary angles: Two angles whose sum is 90°. The angles do not have to be adjacent.
 1 and  2 are complementary angles. Figure A.
Supplementary angles: Two angles whose sum is 180°. The angles do not have to be adjacent.
 3 and  4 are supplementary angles. Figure B.
1
3
2
4
Figure B
Figure A
Vertical angles: Opposite angles. Vertical angles are formed by the intersection of two straight lines.
Vertical angles must share a vertex, but do not share a side.  1 and  3 are vertical angels.
 2 and  4 are also vertical angles. Vertical angles have equal measures.
1
4
3
l1
2
l2
Transversal: The line that intersects two lines at separate places.
Corresponding angles: Angles that hold the same position with respect to the transversal.
 1 and 5 are corresponding angles. They are both above the lines and to the left of the
transversal.  2 and  6,  3 and  7, and  4 and  8 are also corresponding angles.
Corresponding angles have equal measures.
Alternate interior angles: Angles that are between the lines and on opposite sides of the transversal.
 3 and  5 are alternate interior angles.  4 and  6 are also alternate interior angles.
Alternate interior angles have the same measure.
Alternate exterior angles: Angles that are on the outsides of the lines and on opposite sides of the
transversal.
 1 and  7 are alternate exterior angles.  2 and  8 are also alternate exterior
angles.
Alternate exterior angles have the same measure.
t
1 2
l1
4 3
5
8
6
l2
7
Given that l1 and l2 are parallel.
Cavallaro 16
Final Exam Study Guide
Reference – Final Exam Review – Pg. 4