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Final Exam Review Foundations 20 Know all these concepts for the final exam. All formulas and the z-score table will be provided on the exam. The assignment questions are at the end of this document. Chapter 1 Making conjectures, inductive reasoning, deductive reasoning, number tricks, counter examples, invalid proofs Chapter 2 Definitions – transversal, converse, corresponding angles, same-side interior angles, alternate exterior angles, alternate interior angles When a transversal intersects 2 parallel lines… the alternate interior angles are equal the corresponding angles are equal the same-side interior angles are supplementary the alternate exterior angles are equal The sum of the measures of the interior angles of any triangle is 180° The measure of an exterior angle of a triangle is equal to the sum of the measures of the 2 non-adjacent interior angles. The sum of the measures of the interior angles of any n-sided convex polygon is ( n 2)180 The measure of each interior angle of a regular polygon is (n 2)180 n The sum of the measures of the exterior angles of any convex polygon is 360° Chapter 3 Sine Law: a b sin A sin B Cosine Law: a2 = b2 + c2 – 2bc CosA SOH CAH TOA (right triangles only) Pythagorean Theorem: a2 + b2 = c2 (right triangles only) Angle of Elevation, Angle of Depression, Compass Directions (N30⁰E, S48⁰W) Word Problems – Be sure to write a final sentence which includes units. Chapter 4 For any angle θ: sin θ = sin (180 – θ) cos θ = - cos (180 – θ) tan θ = - tan (180 – θ) The Sine Law and the Cosine Law can be used to solve acute and obtuse triangles. Note: When using Sine Law, you must decide if you are solving for an acute or an obtuse angle. (Your calculator will only give the acute angle measurement). Ambiguous Case – only occurs when given ASS (two sides and a non-included angle) A. Acute Triangles – 3 cases B. Obtuse Triangles – 2 cases Solving Word Problems Chapter 5 Measures of Central Tendency – Mean, Median, Mode Range – the difference between the maximum value and the minimum value in a data set. Frequency distribution chart, Histogram (bar graph) and Frequency Polygon (line graph) Standard Deviation : ( x x) n 2 z-scores: z xx or z x Normal Distribution Definitions - Confidence level, Confidence Interval, Margin of Error Chapter 6 Graphing linear inequalities with 2 variables – example: 2x + 3y > 8 Solid line / Dotted line / Dashed Lines Shading – use a point like (0, 0) to check where to shade/ dot Graphing Systems of Linear Inequalities – example: x + 3y < 6 and 2x – y >1 Graph 2 (or more) inequalities on the same set of axes. Shade each appropriately Find points of intersection (overlapping shaded regions) Optimization Problems – finding the maximum or minimum solutions Chapter 7 Quadratic Function (y = ax2 + bx + c) – has a degree of 2 and graph is a parabola If y = ax2 + bx + c, then: a) y-intercept = c b) graph opens up if a > 0, graph opens down if a < 0 c) x-intercept: set y = 0 and solve (factor or use quadratic formula) Solving, finding roots/zeroes, determining x-intercepts – factor or use quadratic formula Finding vertex: fully factor equation (this gives x-intercepts, then find axis of symmetry), then use the axis of symmetry to find the vertex and then draw the graph Assignment: Chapter 1 – 2 Cumulative Review: Page 110 #1 – 6, 10 – 12 Chapter 3 – 5 Cumulative Review: Page 287 #1 – 7, 9 – 14 Chapter 6 – 8 Cumulative Review: Page 520 #1, 2, 4, 6 – 11