Precalculus, IB Precalculus and Honors Precalculus

Transcription

1 NORTHEAST CONSORTIUM Precalculus, IB Precalculus and Honors Precalculus Summer Pre-View Packet DUE THE FIRST DAY OF SCHOOL The problems in this packet are designed to help ou review topics from previous mathematics courses that are important to our success in Precalculus, Honors Precalculus and IB PreCalculus DO ALL PROBLEMS WITHOUT A CALCULATOR. Show all work that leads ou to each solution on separate sheets of paper. You ma use our notes from previous mathematics courses to help ou. You must do all work without an help from another person. Additional copies of this packet ma be obtained from the Main Office in our school or printed from the school s website. Springbrook: Paintbranch: Blake: ALL work should be completed and read to turn in on the FIRST DAY of school. This packet will count as part of our first quarter grade. ENJOY YOUR SUMMER!! WE ARE LOOKING FORWARD TO SEEING YOU IN THE FALL. Student Name: School: Date:

2 Name USE A SEPARATE SHEET OF PAPER AND SHOW ALL WORK. PROBLEMS WITH AN ASTERISK * ARE FOR IB and HONORS ONLY. I. Polnomials and operations on real and imaginar numbers. A. Simplif these epressions ( i 7). 5. (3 + i) + (5 + 7i) 6. i (3 - i) 7. (3 + i) (3 - i) 8. r 0 5 r 9. 8 i 10. (3 + i 5) 5i ( Hint: Use the conjugate of denominator) 6 i B. Factor Completel 1. t - t * C. Simplif the following epressions (- c 3 ) 3. h k h+ k 8 5. t 3 t n - 3 * 6. ( m) n (n) n-m 1

3 * D. Divide and simplif these epressions. (for IB PreCalculus/Honors PreCalculus onl) * 1. * E. Solve each quadratic equation for 1. ( - 1)(5 + 3). (-)=3(1-) 3. + = = 0 F. Graph the functions using a table of values, smmetr, rational zero theorem, or other properties of polnomials to plot points. Verif the graph with the calculator. Describe the following characteristics for each function: a. domain and range b. zeros c. -intercept d. end behavior e. intervals where the function is increasing /... decreasing 1. f() = f() = f() = f ( ) = 5 5. f ( ) = 5 6. f ( ) = + 5 II. Function Operations A. If f() = and g() = +, determine 1. f(3). f() = 0 when =? 3. f(g()). f(g()) 5. Domain of f(g() ) 6. g(f(0)) * 7. g(f(a + )) 8. f -1 () 9. Is the inverse of f() a function? *If not, how could the domain of f be restricted to make its inverse a function? * B. Write the function h() = ( + ) 3 - as the composition of two functions f and g so that f(g()) = h(). Identif the functions f() and g().

4 III. Rational Epressions and Rational Functions A. Graph the following functions using a table of values. Identif: a. intercepts b. asmptotes 1. 3 f ( ) =. h( ) = k( ) = 9 B. Simplif. Write our answer as a single fraction IV. Rewriting and Solving Equations A. Solve each equation for = = 15 B. Find the solution(s) of the given sstems of equations. Write answers in the form (, ) = = 7 + = = 1 C. Solve for and =. + 9 = = 6 3

5 V. Pthagorean Theorem and Trigonometric Ratios A. Solve for the missing side of the triangle using the Pthagorean Theorem: a 1. a = 6 ft. b = 8 ft.. b = 17 ft. c = 19 ft. c b B. Solve for and using a (ratio of sides 1:1: ) or a triangle (ratio of sides 1: 3 : ) C. Given the right triangle, determine the trigonometric ratios. B 1. sin A. cos A 3. tan A C 15 A

6 D. Use trig ratios to solve for and in each right triangle. Round answers to three places after the decimal point *VI. Conic Sections (for IB and Honors PreCalculus onl) *A. Complete the square to write each equation in standard form. Then identif the tpe of conic figure represented b each equation. * = 5 * = 0 * = 0 * = 1 *B Write an equation in standard form for each of the following conic figures. 1. * An ellipse with center at the origin, one verte at (0, 5) and one focus at (0, ).. * A parabola with verte (1,) and directri = - 3. * A hperbola with foci (0, - 5) and (0, 5) and difference of focal radii 8.. * A circle with center (, 3) passing through ( - 3, 5) 5. * A parabola with focus ( -1, 0) and directri = 1. *C. Solve the sstem of equations. Write our solution(s) in the form (, ) * = 5 *. = + = 5 + = 0 5