1. Distance Formulas: Number Line:  b-a  for a and b the coordinates of the points Plane: Exercises: 1.Find the distance AB if a = -3 and b=7 2.Find the distance MN if M(2,-1) and N(-2, 4)

2. Slopes Exercises: 1.Find the slope of the line that passes through points (2,-5) and (0, -3) 2.Find the slope of the line perpendicular to y = ¾ x – 6 If m > 0, line rises from left to right If m < 0, line falls from left to right If m = 0, horizontal line If no slope (undefined), vertical line

3. Midpoint: Exercises: 1.Find the midpoint of a segment whose endpoints have coordinates (6, 7) and (-5, -5). 2.If the midpoint of a segment is (2, -4), and one of the endpoints is (0, 8), find the other endpoint.

4. Pairs of Angles:  Complementary and supplementary angles  Linear pair  Vertical angles Exercises: Complete each statement. 1. If two angles are vertical angles, then they are ______________. 2. If two angles are a linear pair of angles, then they are ______________. 3. If two angles are both equal in measure and ________________, then each angle measures 90°.

5. Parallel Lines CongruentSupplementary Alternate Interior Alternate Exterior Corresponding Vertical Consecutive Interior Unrelated Linear Pair

6. More Parallel Lines Exercises Find the measure of each angle indicated in the figure below.

7. Quadrilaterals: Quadrilaterals ParallelogramsKitesTrapezoids RectangleRhombus Square Isosceles Trapezoids

8. Parallelograms Opposite sides are parallel Opposite sides are congruent Opposite angles are congruent Consecutive angles are supplementary Diagonals bisect each other

9. Rectangles Opposite sides are parallel Opposite sides are congruent Opposite angles are congruent Consecutive angles are supplementary Diagonals bisect each other Right angles Congruent diagonals

10. Rhombus Opposite sides are parallel Opposite sides are congruent Opposite angles are congruent Consecutive angles are supplementary Diagonals bisect each other Congruent sides Perpendicular diagonals Diagonals bisect both pairs of opposite angles

11. Squares Opposite sides are parallel Opposite sides are congruent Opposite angles are congruent Consecutive angles are supplementary Diagonals bisect each other Right angles Congruent diagonals Congruent sides Perpendicular diagonals Diagonals bisect both pairs of opposite angles

12. Trapezoids  Exactly one pair of opposite sides are parallel — bases  Non parallel sides are the legs  Median: half of the sum of the bases  Isosceles Trapezoid:  Congruent legs  Base angles are congruent  Congruent diagonals

13. Kites o No parallel sides o Consecutive sides are congruent o Diagonals are perpendicular o Non vertex angles are congruent o One diagonal splits the kite in congruent halves

14. More quadrilaterals: Match each statement: a. Rhombusi. Parallel b. Rectanglej. Supplementary c. Trapezoidk. Complementary d. Parallelogram 1._______Two angles whose measures add up to 180° 2._______Two lines in the same plane that do not intersect 3._______An equiangular parallelogram 4._______A quadrilateral with exactly one pair of parallel sides 5._______An equilateral quadrilateral

15. More Exercises Fill in the blanks 1. ___?____ An equiangular parallelogram 2. ___?____ A quadrilateral with exactly one pair of parallel sides 3. ___?____ An equilateral quadrilateral True or False 4. _____ A trapezoid is a quadrilateral having exactly one pair of equal length sides. 5. _____ A parallelogram is a quadrilateral with all the angles equal in measure.

16. Triangles AnglesSides AcuteObtuseRightEquilateralIsoscelesScalene

17. Congruent vs. Similar CongruentSimilar  Same shape  Same size  Congruent angles  Congruent sides  Shortcuts: SSS SAS AAS or ASA  Same shape  Different size  Congruent angles  Proportional sides  Shortcuts: SSS SAS AA

18. Right Triangles Pythagorean Theorem (and its converse): a c b Special right triangles: 45°-45°-90° 1 30°-60°-90° 1 2

19. Exercises 1. What is the length of the hypotenuse of a right triangle with legs that measure 80 feet and 150 feet? 2. What is the length of the larger leg of a 30-60 right triangle with a hypotenuse of length 24 m? 3. If the area of a square is 225 cm2, what is the length of the diagonal? 4. In an isosceles right triangle, if the hypotenuse has length x then each leg has length —?—. 5. In a 30-60 right triangle, if the hypotenuse has length y, then the shorter leg has length —?— and the longer leg has length —?—.

20. Trigonometric Ratios      

21. Exercises using trig ratios: Calculate each distance or angle: 1.The angle of elevation from a ship to the top of a 40 meter lighthouse on the shore is 18°. To the nearest meter, how far is the ship from the shore? 2.Igor is flying a kite with 300 m of kite string out. His kite string makes an angle of 64° with the level ground. To the nearest meter, how high is his kite? Use a calculator to find the values accurate to four decimal places: 1.sin 57° » –?– 2.cos 9° » –?– Find the measure of each angle to the nearest degree: 3. sin A = 0.5447 4.cos B = 0.0696

22. Polygons Facts:  Exterior angle sum: 360°  Interior angle sum: 180°(n – 2)  Exterior and interior angles are supplementary  Concave vs. convex  Classification according to the number of sides

23. Exercises Complete each statement: 1.The sum of the measures of the interior angles of an 15-gon is ________. 2. The sum of the measures of the exterior angles of a 25-gon is __________________. 3.The measure of one interior angle in a regular octagon is _____________. 4.If the measure of one exterior angle of a regular polygon is 24°, then the polygon has ______ sides.

24. Independent VS. Dependent Events Two events are said to be independent if the result of the second event is not affected by the result of the first event. If A and B are independent events, the probability of both events occurring is the product of the probabilities of the individual events

25. Mutually Exclusive/Inclusive Events

26. The Counting Principle Examples

27. Permutations and Combinations

29. Systems of Linear Equations The solution of a system of linear equations in two variables is any ordered pair that solves both of the linear equations. The solution to the system is the point that satisfies ALL of the equations. This point will be an ordered pair.

30. N UMBER OF S OLUTIONS OF A L INEAR S YSTEM I DENTIFYING T HE N UMBER OF S OLUTIONS y x y x Lines intersect one solution Lines are parallel no solution y x Lines coincide infinitely many solutions

31. Transformations Image – is the new figure. Image after the transformations. Pre-image – is the original figure. Image before the transformations. Transformation – In a plane, a mapping for which each point has exactly one image point and each image point has exactly one pre-image point.

32. To transform something is to change it. In geometry, there are specific ways to describe how a figure is changed. The transformations you will learn include: Translation Rotation Reflection Dilation

33. Given (x, y) is the pre-image, then…

34. Vertex Form y = a(x-h) 2 +k Standard Form y = ax 2 +bx+c Parabolas

35. Exponential Functions

36. Examples of Exponential Graphs When b > 1 the graph increases and decreases when 0 < b < 1

37. The Equality Property for Exponential Functions Basically, this states that if the bases are the same, then we can simply set the exponents equal. This property is quite useful when we are trying to solve equations involving exponential functions. Basically, this states that if the bases are the same, then we can simply set the exponents equal. This property is quite useful when we are trying to solve equations involving exponential functions.

38. Original relationInverse relation y420– 2– 2– 4– 4 x210– 1– 1– 2– 2 RANGE F INDING I NVERSES OF L INEAR F UNCTIONS x420– 2– 2– 4– 4 y210– 1– 1– 2– 2 An inverse relation maps the output values back to their original input values. This means that the domain of the inverse relation is the range of the original relation and that the range of the inverse relation is the domain of the original relation. RANGE DOMAIN

39. Logarithms 10 2 = 100 “10 raised to the power 2 gives 100” Base Index Power Exponent Logarithm “The power to which the base 10 must be raised to give 100 is 2” “The logarithm to the base 10 of 100 is 2” Log 10 100 = 2 Number

40. Logarithms 10 2 = 100 Base Logarithm Log 10 100 = 2 Number Logarithm Number Base y = b x Log b y = x 2 3 = 8Log 2 8 = 3 3 4 = 81Log 3 81 = 4 Log 5 25 =25 2 = 25 Log 9 3 = 1 / 2 9 1/2 = 3 log b y = x is the inverse of y = b x

41. Graphs of Trig Functions