HOW TO NOT LOSE POINTS...

Transcription

1 Math Analysis B Final Review

2 GROUP MATERIALS

3 INSTRUCTIONS 1) Ms. Lee picks a student randomly. 2) Selected student chooses a question. 3) Group discusses question and writes FINAL WORK & SOLUTION on whiteboard. 4) When Ms. Lee calls TIME, all groups raise their whiteboards. 5) Groups with the correct answer earn points.

4 HOW TO NOT LOSE POINTS... - Students take turns writing on the whiteboard. After each question, whiteboard must be rotated CLOCKWISE. - Follow instructions! - Ask for hints ONLY when your group absolutely needs one. Hints cost $50. - Don t write/draw anything unnecessary. Don t use the markers on anything other than the whiteboards.

5 JEOPARDY BOARD Exponential Functions Logarithmic Functions Log & Exp Expressions Transform ations Unit Circle $100 $100 $100 $100 $100 $200 $200 $200 $200 $200 $300 $300 $300 $300 $300 $400 $400 $400 $400 $400 $500 $500 $500 $500 $500

6 Exponential Functions - $100 Repeated addition Repeated multiplication Click to see answer

7 Exponential Functions - $100 Repeated addition multiplication Repeated multiplication power Click to return to Jeopardy Board

8 Exponential Functions - $200 Which equation represents an exponential function? A. f(x) = 2(x-4) + 1 B. h(x) = 2^(x-4) + 1 C. t(x) = (x-4)^2 + 1 D. m(x) = e^(x-4) + 1 Click to see answer

9 Exponential Functions - $200 Which equation represents an exponential function? B. h(x) = 2^(x-4) + 1 D. m(x) = e^(x-4) + 1 Click to return to Jeopardy Board

10 Exponential Functions - $300 Which graph represents an exponential function? A. B. C. D. Click to see answer

11 Exponential Functions - $300 A. Which graph represents an exponential function? Click to return to Jeopardy Board

12 Exponential Functions - $400 Which table represents an exponential function? A. x y B x y - 1 1/ C. x y D. x y Click to see answer

13 Exponential Functions - $400 Which table represents an exponential function? B. x y - 1 1/ C. x y Click to return to Jeopardy Board

14 Exponential Functions - $500 Which of the following does not represent an exponential function? A. n(x) = 5-4^x B. b(x) = 5-4x C. D. x y Click to see answer

15 Exponential Functions - $500 Which of the following does not represent an exponential function? B. r(x) = 5-4x C. Click to return to Jeopardy Board

16 Logarithmic Functions - $100 What is the inverse function of logarithmic functions? Click to see answer

17 Logarithmic Functions - $100 What is the inverse function of logarithmic functions? Exponential functions Click to return to Jeopardy Board

18 Logarithmic Functions - $200 Which equation represents a logarithmic function? A. f(a) = 5 - ln(a+3) B. h(a) = 5 - sin (a+3) C. t(a) = 5 - log(a+3) D. m(a) = 5 - e^(a+3) Click to see answer

19 Logarithmic Functions - $200 Which equation represents a logarithmic function? A. f(a) = 5 - ln(a+3) C. t(a) = 5 - log(a+3) Click to return to Jeopardy Board

20 Logarithmic Functions - $300 Why are common logarithms and natural logarithms important? Click to see answer

21 Logarithmic Functions - $300 Common logs - base of 10 Natural logs - base of e *These are the only logs that are available on the calculator. Click to return to Jeopardy Board

22 Logarithmic Functions - $400 Which graph represents a logarithmic function? A. B. C. D. Click to see answer

23 Logarithmic Functions - $400 B. Which graph represents a logarithmic function? Click to return to Jeopardy Board

24 Logarithmic Functions - $500 Which of the following does not represent a logarithmic function? A. r(x) = -log5 (x+3) B. q(x) = -ln(x+3) C. D. x y Click to see answer

25 Logarithmic Functions - $500 Which of the following does not represent a logarithmic function? D. x y Click to return to Jeopardy Board

26 Log & Exp Expressions - $100 Which are equivalents of ln 1? A. log 1 B. 1 C. 0 D. 10 E. log41 Click to see answer

27 Log & Exp Expressions - $100 Which are equivalents of ln 1? A. log 1 C. 0 E. log41 Click to return to Jeopardy Board

28 Log & Exp Expressions - $200 Simplify each expression. a) ln e 4 b) 7 log Click to see answer

29 Log & Exp Expressions - $200 Simplify each expression. a) ln e = 4 4 log b) 7 = Click to return to Jeopardy Board

30 Log & Exp Expressions - $300 8 Simplify log 10 Click to see answer

31 Log & Exp Expressions - $300 Simplify log /8 Click to return to Jeopardy Board

32 Log & Exp Expressions - $400 When the bases in an exponential equation are the same, you can solve the equation by Click to see answer

33 Log & Exp Expressions - $400 When the bases in an exponential equation are the same, you can solve the equation by Writing a separate equation for the exponents and solving the equation. Click to return to Jeopardy Board

34 Log & Exp Expressions - $500 When the bases in an exponential equation cannot be manipulated to be the same, you can solve the equation by... Click to see answer

35 Log & Exp Expressions - $500 When the bases in an exponential equation cannot be manipulated to be the same, you can solve the equation by... Rewriting the exponential equation as a logarithmic equaiton. Click to return to Jeopardy Board

36 Transformations - $100 How do you identify a translation in an equation? Click to see answer

37 Transformations - $100 How do you identify a translation in an equation? addition/subtraction of a number Click to return to Jeopardy Board

38 Transformations - $200 How do you identify a stretch/shrink in an equation? Click to see answer

39 Transformations - $200 How do you identify a stretch/shrink in an equation? multiplication/division of a number Click to return to Jeopardy Board

40 Transformations - $300 How do you identify a reflection in an equation? Click to see answer

41 Transformations - $300 How do you identify a reflection in an equation? Taking the opposite or Making it negative Click to return to Jeopardy Board

42 Transformations - $400 How do you distinguish a vertical translation/stretch/shrink from a horizontal translation/stretch/shrink? Click to see answer

43 Transformations - $400 How do you distinguish a vertical translation/stretch/shrink from a horizontal translation/stretch/shrink? vertical +/-/ / to whole function horizontal +/-/ / to input only Click to return to Jeopardy Board

44 Transformations - $500 Describe how to transform f (x) = log x to obtain m(x) = -4 - log (3x - ½). Click to see answer

45 Transformations - $500 Describe how to transform f(x) = log x to obtain m(x) = -4 - log (3x - ½). m(x) = -4 - log (3(x - ⅙)) Translate right ⅙ units Horizontally shrink by ⅓ Reflect across the x-axis Translate down 4 units Click to return to Jeopardy Board

46 Trigonometry - $100 What is the unit circle created with a hypotenuse of Click to see answer

47 Trigonometry - $100 The unit circle is created with right triangles with a hypotenuse of 1. The hypotenuses are represented by the radii of the unit circle. Click to return to Jeopardy Board

48 Trigonometry - $200 Identify the quadrant of the terminal side and reference angle of 31 /3. Click to see answer

49 Trigonometry - $200 Identify the quadrant of the terminal side and reference angle of 31 /3. terminal side is in QI reference angle is /3 Click to return to Jeopardy Board

50 Trigonometry - $300 Which of the following trig functions have a domain of all real numbers? Click to see answer

51 Trigonometry - $300 Which of the following trig functions have a domain of all real numbers? SINE & COSINE (sinusoid functions) Click to return to Jeopardy Board

52 Trigonometry - $400 Which key feature does each transformation affect? Transformation V Translation H Translation V Stretch/Shrink H Stretch/Shrink Key Feature Domain Range Zeros Asymptotes Amplitude Period Click to see answer

53 Trigonometry - $400 Which key feature does each transformation affect? Transformation V Translation H Translation V Stretch/Shrink H Stretch/Shrink Key Feature Range, Zeros Domain, Zeros, Asymptotes Range, Amplitude Domain, Zeros, Asymptotes, Period Click to return to Jeopardy Board

54 Trigonometry - $500 Evaluate the following trigonometric values WITHOUT the unit circle. a) sin 3 /2 = -1 b) cos /2 = 0 c) tan /4 = 1 d) cot - /4 = -1 e) sec /2 = undefined Click to see answer

55 Trigonometry - $500 Evaluate the following trigonometric values WITHOUT the unit circle. a) sin /2 b) cos /2 c) tan /4 d) cot - /4 e) sec /2 Click to return to Jeopardy Board