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Grade 11 College Math Final Exam Review Trig Summary Rule Name Pythagorean Theorem Formula side12 + side22 = hyp2 sin SOHCAHTOA Sine Law opp hyp cos Alternate Form side12 = hyp2 – side22 side22 = hyp2 – side12 opp adj a b c sin A sin B sin C a b c 2bc cos A 2 Cosine Law 2 2 b 2 a 2 c 2 2ac cos B c 2 a 2 b 2 2ab cos C tan opp adj sin A sin B sin C a b c a2 b2 c2 2bc 2 b a2 c2 cos B 2ac 2 c a2 b2 cos C 2ab cos A Given 2 sides of a right angle triangle 2 sides of a rightangle triangle Use to find The remaining side 1 side and 1 angle of a right angle triangle A corresponding side-angle pair and one other side or angle SAS Any other side Any angle The opposite angle given a side; the opposite side given an angle The side opposite the given angle or SSS Any angle Grade 11 College Math Final Exam Review Summary of Quadratic Forms Expand & Simplify Vertex Form y = a(x – h)2 + k Standard Form y = ax2 + bx + c (Complete the Square) Factor Factored Form y = a(x – r)(x – s) FOIL a is vertical stretch/compression factor direction of opening Vertex Form Standard Form Vertex is (h, k) y-intercept is c Describing transformations Sketching the graph Read information from a graph Examples pp. 146 #1, 2, 4, 5, 6 Factored Form Roots / x-intercepts are r and s Grade 11 College Math Final Exam Review One-Variable Statistics Graph types – which one is best to show a set of data and why? Tally Chart / Frequency Table Histogram Pie Graph Pictograph Identify data as: Numerical / Quantitative Continuous (decimals) Histogram Discrete (whole numbers) Bar Graph, Pictogram, Pie Graph Categorical / Qualitative Bar graph Definitions: Population, Census, Sample, Biased sample Given a scenario, describe how to take a sample using: Random Sampling Methods Simple Random Sampling, Stratified Sampling, Cluster Sampling, Systematic Sampling Other Sampling Methods Convenience Sampling, Judgement Sampling, Voluntary Sampling Know how to calculate and interpret: Measures of Central Tendency: Mean Median Mode Measures of Spread Range = max – min Standard Deviation Probability Review Experimental # of times the desired outcome occurred total # of trials probability n( A) where; n(A) represents the number of n( S ) ways that event A can occur and n(S) represents the number of total outcomes possible for the experiment. Theoretical Probability P(A) = Tree diagrams e.g. Draw a tree diagram for flipping a quarter, loonie and toonie. What is the probability of getting less than 2 heads? Grade 11 College Math Final Exam Review Exponential Functions Review Standard Form of Equation y = a•bx where a = starting value, b = growth/decay factor Growth factor 1 + r Decay factor 1 – r Where r is % increase/decrease Doubling time – the time it takes for a quantity to double Half life - the time it takes for a quantity to be cut in half Exponent Rules Multiplication – keep the base, add the exponents Division – keep the base, subtract the exponents Power of a Power – keep the base, multiply the exponents Zero a0 = 0, 00 = undefined or ∞ 1 1 Negative Exponents 4-3 = 43 = 64 Linear Quadratic Exponential 1 𝑎5 = 𝑎−5 1st diff. are constant, 2nd diff. are 0. 1st diff. are not equal, 2nd diff are constant 1st and 2nd diff are not equal, ratio is constant (approximately) Investing Simple Interest I = Prt where I = Total interest P = Original principal r = annual interest rate t = time in years Compound Interest 𝑨 = 𝑷(𝟏 + 𝒊)𝒏 𝑨 𝑷 = (𝟏+𝒊)𝒏 where A = Total amount P = original principal i = interest rate per compounding period n = number of compounding periods Grade 11 College Math Final Exam Review NAME _________________________________ Grade 11 College Math – Final Exam Review Topic Questions Trigonometry Trigonometry pp. 208 – 210 #1-4 pp. 388 – 390 #1-2 Quadratics Quadratics pp. 208 – 210 #9-17 pp. 388 – 390 #6-9 One-Variable Statistics One-Variable Statistics Probability p. 344 #1-6 pp. 388 – 390 #24 pp. 388 – 390 #26 – 29 Exponential Functions Exponential Functions Personal Finance pp. 208 – 210 #18, 19ab, 20, 22-24 pp. 388 – 390 #10-13 pp. 388 – 390 #14-18 Geometry pp. 208 – 210 #6ab, 8