Honors Pre-Calculus Summer Work

Transcription

1 Honors Pre-Calculus Summer Work Attached you will find a variety of review work based on the prerequisites needed for the Honors Pre-Calculus curriculum. The problems assigned should be the minimum you do to be successful in your net course. It is epected that you understand and can do all the attached. If you don t understand any topic I advise you to go on line to Khan Academy for help.. Quadratic Review. Polynomial Review. Logarithmic Review 4. Standards Review. Trig Review (A-F) The Quadratic Review Factor: State the discriminate and describe the nature of the roots: Solve by completing the square. 6 0 Solve by Factoring Solve using the quadratic formula Place the following quadratic function into verte form and state the verte: 4. y 8. y 4 Graph the following parabolas 6. y ( 4)( ) 7. y 6 8. y

2 The Polynomial and Quadratic Review Add/subtract,and or multiply the following 9 (6 0) 4( ) 0. ( 7) ( ). ( )( 7 ) Divide the following. (6 0) ( ). 4 ( ) ( ) Solve. Find all answers, real and imaginary Logarithmic Review Simplify: 0.. /. 6 / 4 6. / 49. / / 7. / 9 8. / 7 4. / / / Epand and/or Condense simplify when necessary: 40. log 4. log log log 7 4. ln ln 4ln y ln y Evaluate without a calculator: 4. 4 ln e 44. log 6 4. log log 9 Solve. No calculator. Check for etraneous solutions. 47. log 48. log log log () log ( ). log 4( ) log 4( 8)

3 Pre-Calculus SAMPLE MASTERY QUIZ ***Drawings are not to scale. The graded mastery quiz will only include one of each type of question, additional problems are provided to give a sense of the variations each question might contain.***. (Geo. St. 7) Calculate the midpoint of and distance between points A(4, ) and B(7, -9).. (Alg. St. ) Evaluate the following for the given functions. a. f 4, find f a+4 b. f 4, find f -w.. (Geo. St. 0) Use special right triangles to find the eact value of and y for the given triangles. a. 60 o 60 b. o 8 0 o 0 o y 4º y 4º 4. (Alg. St. 7&8) Find the equation of the line which passes through the point (, -) and is perpendicular to the line determined by y 7. Write your answer in both point-slope form and slope-intercept form. 4. (Alg. St. 9) Solve the following systems of equations algebraically. c6d 4 y a) c4d 6 y 9 6. (Alg. St. ) Write the Absolute Value Inequality that represents the given graphical solution. a) (Alg. St. 7) Answer the following for the given graphs: a) Type of function/relation Domain. c) Range.

4 8. (Alg. St. 8) Find the roots of the following equations over the comple numbers. a) c) (Alg. St. 6) Simplify each epression a) 7 4 i 7 7i 0. (Alg. St. 4) Given f 7 and g, find f g and g f.. (Alg. St. 4) Find the inverse of each function listed below. a) f 7 g 8 c) h 8. (Alg. St. 7) Simplify the following epressions, recall there are to be no negative eponents in final answer. 4 a) y y y 6y 4 7 Problems - are Graphing Calculator Problems. (Alg. St. ) For the following find the zeros, ma/min, the regions where f() is increasing and decreasing, and the regions where f() is positive and negative a) 4 y (Alg. St. ) Solve for algebraically or graphically. a) 6 y 4 4 y. (Alg. St. 8) Complete the square and answer the following for the given quadratic. a. Write in verte form. b. ma/min c. find zeros in eact form a) y 6 y 8

5 Answers to Review problems The Quadratic Review State the discriminant and describe the nature of the roots:. D 0, real roots 6. D 0, imaginary roots 7. Solve by completing the square. i Solve by Factoring 8., , Solve using the quadratic formula.. i Place the following quadratic function into verte form and state the verte: 4. y 4, V:(4,-). y 6, V:(-,-6) Graph the following parabolas 6. y ( 4)( ) 7. y y 9 y y The Polynomial and Quadratic Review Add/subtract,and or multiply the following Divide the following Solve. Find all answers, real and imaginary. i 4.,. 0, 6. i, 4 7. i, 8. i,, 0 9.,

6 Logarithmic Review log log log log y 4. 8 log ln y Pre-Calculus SAMPLE MASTERY QUIZ.,. a. a 6 b. w 4w 9. a. 9 y=9 b. y=6 4. y+=4 -, y=4-. a. 4,- b. 69 -, 6. a. + b i) a) Radical ii) a)quadratic iii) a) Absolute Value,,, c) y0, c) y,8 c) y-6, 8. a) i, 9. a) 46, - c) 9 7 i 4 f g 0. = -+ and g f a) f g 8 c) h 9 y. a)

7 Honors Precalculus Trigonometry Review: A to F Name Date Per.. Sketch the following in standard position and find their complimentary and supplementary angles: a. 87 b. c. 8. Sketch the following in standard position and find a positive and negative co-terminal angle: a. 9 b. 4 c. 8. Sketch the following in standard position and find their reference angles: a. 0 b. c. d. For each of the given trigonometric functions: draw the angle, list the reference angle, and find the desired ratio. 4. sin 40 ref. angle:. cos0 ref. angle: 80 0 (60 ) 80 0 (60 ) tan ref. angle: 7. tan 600 ref. angle: 80 0 (60 ) 80 0 (60 ) cos ref. angle: 9. sin 40 ref. angle: 80 0 (60 ) 80 0 (60 ) 70 70

8 0. csc0 ref. angle:. cot 40 ref. angle: 80 0 (60 ) 80 0 (60 ) sec( 0) ref. angle:. cot( ) ref. angle: 80 0 (60 ) 80 0 (60 ) sin ref. angle:. cos 6 4 ref. angle: tan ref. angle: 7. tan 4 ref. angle: 8. cot ref. angle: 9. sec 4 ref. angle:

9 0. sin( ) ref. angle:. 6 cos 4 ref. angle:. 7 tan ref. angle:. csc 6 4 ref. angle: Given the following information, determine the quadrantal angle in both radians and degrees. 4. cos 0 and sin. tan 0 and cos or or 6. tan is undefined, and sin 7. sin 0 and cos 0 or or 8. cos 0 and csc 9. tan 0 and sec or or Find the values of the si trigonometric function of cos in QIII. tan and sin 0 8. csc 4 and cot 0. sec and csc 0 4. sin in QI

10 For each of the following trigonometric ratios and quadrants determine the reference angle (in radians) that would give that ratio and the actual value of (in radians).. sin in QII. 6. cos in QI 7. tan in QIII. 8. cos in QII 9. tan in QIV. 40. cot in QIV. 4. cos in QIII 4. csc in QI For each of the following trigonometric ratios and quadrants determine the reference angle (in degrees) that would give that ratio and the actual value of (in degrees). 4. cos in QIII 44. cos in QI 4. tan in QIII. 46. cos in QII 47. tan in QIV. 48. sin in QIV 49. csc in QI. 0. cot in QIV.