RSGC 2014 MCR3U Exam Outline

Transcription

1 RSGC 2014 MCR3U Exam Outline Course code and name: MCR3U/E Teachers: Mr. Tam and Mr. Doerksen Date and Time of Examination: Monday, June 2 nd, 12:30pm Duration of Exam: 2 hours Value on June report card: 30% Materials students are permitted to bring into the exam room: graphing calculator, ruler, pens or pencils, sharpener, eraser Format of Exam: short answer, long answer Recommended study resources: Corrected tests, mini-tests and assignments Notes from class/ssd/haiku Cumulative and Review sections from your text (see below) Recommended study tasks: Make sure your notebook is complete. Review your corrected tests, quizzes and assignments; re-do questions. From your textbook: Cumulative Review Chapters 1-3 pg. 206 Cumulative Review Chapters 4-6 pg. 408 Cumulative Review Chapters 7-8 pg. 538 Chapter 1 Review pg. 74 Review Test pg. 78 Chapter 2 Review pg. 131 Review Test pg. 134 Chapter 3 Review pg. 200 Review Test pg. 205 Chapter 4 Review pg. 265 Review Test pg. 270 Chapter 5 Review pg. 336 Review Test pg. 340 Chapter 6 Review pg. 403 Review Test pg. 406 Chapter 7 Review pg. 467 Review Test pg. 470 Chapter 8 Review pg. 532 Review Test pg. 536

2 SOME SUGGESTED REVIEW QUESTIONS Rational expressions p132 #4a, 9bc, 10bcdef, 12bc, 13bd, 14; p134 #7 Functions p40 #1-6, 8 p76 #1, 2, 4, 5, 8, 11 13, 14, 15, 16, 17 Trigonometry p338 #1, 2, 3, 4, 5, 7, 8, 10 p340 #1, 2, 6, 7 Sinusoids p404 #1, 3-6, 8-13 also p406 #1, 2, 4, 5 Sequences and Series p468 #2, 3ab, 4, 5, 6, 7adf, 9abd, 10, 14ab, 15abf, 18ad p470 #3, 5, 7 Financial Math and Exponential functions p267 #3, 4, 5, 8, 11, 13, 14, 15, 17 p534 #4, 5, 8, 9, 10, 11, 12, 13, 14, 19 also p536 #1bc, 3, 4, 6 Quadratics p202 #1, 2, 4, 9, 12; p204 #1, 2, 5, 6, 7

3 TOPICS COVERED Chapter 1 Functions Functions, relations and function notation Properties of parent functions Domain and range of a function The inverse function and its properties Transformations of functions Horizontal stretches, compressions and reflections of functions Graph functions in the form y = af[k(x-d)] + c Chapter 2 Algebraic Expressions Adding, subtracting, multiplying and factoring polynomials Simplifying rational functions Adding, subtracting, multiplying and dividing rational expressions Chapter 3 Quadratic Functions Properties of quadratic functions Determining the max and min of a quadratic function Inverse of a quadratic function Operations with radicals Solving quadratic equations The zeros of a quadratic function Evaluating trigonometric ratios for special angles Evaluating trigonometric ratios for any angle between 0 and 360 degrees Trigonometric identities The Sine and Cosine Laws Solve 3-D problems using trigonometry Chapter 6 Sinusoidal Functions Periodic functions and their properties Interpreting sinusoidal functions Transformations of sinusoidal functions Solving problems with sinusoidal models Chapter 7 Sequences and Series Arithmetic sequences Geometric sequences Recursion formulas Arithmetic series Geometric series Chapter 8 Financial Applications Compound interest future value and present value Future value of an ordinary annuity Present value of an ordinary annuity Chapter 4 Exponential Functions Exploring growth and decay Integer and rational exponents Simplifying algebraic expressions with exponents Properties of exponential functions Transformations and applications of exponential functions Chapter 5 Trigonometric Ratios Trigonometric ratios of acute angles

4 Some Key Skills You Should Know: Rational Expressions - add, subtract polynomials e.g., ( ) (m 3 6m 2 7) 3 m 2 4 ( ) 2 - multiply polynomials, e.g., 4(2m 2 m + 3) 3m 4 - factor polynomials, i.e., common factoring, decomposition, difference of squares, grouping - simplify rational expressions, by factoring and canceling common factors, identifying restrictions, e.g., 5x 3 5x 2 4x 3 6x 2 + 2x = 5x 2 (x 1) 2x(2x 2 3x +1) = 5x 2 (x 1) 2x(2x 1)(x 1) = 5x 2(2x 1) ; x 0, 1 2, 1 - multiply and divide rational expressions - add and subtract rational expressions, including identifying lowest common denominator Trigonometry - apply secondary trig ratios, secant, cosecant, and cotangent to solve for missing angles and sides in right angle triangles, e.g., secθ = hyp, secθ = 1, adj cosθ cosθ = 1 secθ - use special triangles, 30 o -60 o -90 o, and 45 o -45 o -90 o to determine exact values for trig ratios and trig expressions - represent angles from 0 o to 360 o on a grid, identify negative angles, principal angle, related acute angle, coordinate (x, y) and predict the sign of trig ratios using CAST - solve trigonometric equations e.g., tanθ = 1.7, and use the CAST rule to identify two possible answers between 0 o to 360 o - solve triangles using cosine law a 2 = b 2 + c 2 2bccosA, and sine law a (including ambiguous case - acute angle, side, side) sin A = b sin B = c sinc Sinusoids and Trigonometric Identities - identifying periodic functions - describing graphs of sinusoids, f(x)=sin x, f(x) = cos x, equation of axis, max, min, peak, trough, period, cycle, amplitude - applying transformations f(x) = a sin k(x - d) + c and f(x) = a cos k(x - d) + c - modelling periodic behaviour from table of values or description of periodic behaviour, and determining an equation f(x) = a sin k(x - d) + c or f(x) = a cos k(x - d) + c - using Pythagorean identities, definitions of secondary trig ratios to prove trig identities

5 Functions and Transformations - define a function as a mapping of each element in a domain to an element in range - define domain and range using set notation, e.g., { 4 x < 8; x } - interpret functions as equations, arrow mapping diagrams, function notation, and graphs - distinguish between relations and functions from equations, arrow mapping diagrams, and graphs (using vertical line test) - use function notation to solve for unknown output, e.g., find f(3), and unknown input, e.g., solve for x if f(x)=20 - graph parent functions f (x) = x, f (x) = x 2, f (x) = x, f (x) = 1, f (x) = x 3, f (x) = x x and discuss key points or aspects of graphs, e.g., vertex, asymptote, domain, range - apply transformations y = af (k(x d)) + c in systematic order to functions, graphs, and coordinates of points as vertical translation, horizontal translation, vertical stretch/compression/reflection, horizontal stretch/compression/reflection from function notation f (x 3) + 5, equation f (x) = 2(x + 5) and graph - determine the inverse of a function from its equation algebraically, i.e., find f 1 (x) given f (x), interchange x and y, solve, etc. - determine the graph of the inverse of a function, as a reflection across the line y=x, or as a switch of x and y coordinates Quadratics - find the coordinates of the vertex of a quadratic function by completing the square - finding the zero(s) of a quadratic function by factoring, when appropriate, and using the quadratic formula - solving quadratic equations by factoring and quadratic formula - understanding the role of the discriminant in predicting the number of real solutions Rational Exponents and Exponential Functions - working with exponents, e.g., b 0 = 1, b n = 1 n a 1,, b and a not zero b n b = ( a b ) = b n n a m m n - working with roots in radical form and exponent form, e.g., b = b n - simplifying expressions involving exponents and radicals - graph exponential functions, e.g., f (x) = ab k(x d) + c and identify the vertical and horizontal translations, equation of horizontal asymptote, y-intercept - applying exponential functions to describe, exponential growth, decay, population growth, depreciation, cooling, etc.

6 Sequences and Series - work with arithmetic and geometric sequences, e.g., general term, first term, common difference/ratio, number of terms, t n = a + (n 1)d, t n = ar n 1 - work with arithmetic and geometric series, e.g., sum of terms in a sequence, first term, ( ) common difference/ratio, number of terms, S n = n a + t n = n [2a + (n 1)d], 2 2 S n = a(rn 1) = t n+1 t 1 r 1 r 1 - apply recursive notation to describe sequences, e.g., t 1 = 3, t n+1 = 4t n solve problems involving sequences and series, e.g., seats in a theatre Financial Math A - compound interest (future and present value), e.g, A = P(1+ i) n and, GICs, (1+ i) = P n investments, depreciation - annuities (future and present value), e.g., FV = R (1+ i)n 1 and i 1 (1+ i) n PV = R, e.g., mortgages, trust funds, RRSPs i - using TVM-Solver to solve problems involving annuities - using graphing technology to solve for unknown time, e.g, how long will it take...

7 FORMULAS PROVIDED ON EXAM