Pre- Calculus, Summer Packet 2015

Transcription

1 Name Pre- Calculus, Summer Packet 01 This summer packet is intended for you to brush up and possibly relearn the topics in pre- Calculus. Answer all questions without a calculator!! Spread out your work during the whole summer, since you need these skills to be relatively fresh in your mind in the fall. Also, don t fake your way through these problems; instead, visit the websites suggested below. The whole packet will take you about 10 hours to complete textbook=19 1

2 You will be responsible for the following questions It is crucial that you do not use a calculator for any of these questions. Solve the equation. x 1 = x ( ) ( ) 1. ( x 6) = x Write the equation of the quadratic function y = a( x h) + k the vertex is (,1) and passes through the point (,)., given. Graph the following quadratic equation: a) Determine whether it opens up or down f(x) = -x + 8x - 7 b) Find the vertex & determine if it is a maximum or minimum value c) Find x & y intercepts d) Domain & Range 4. If gx ( ) x 1 = + then find: a. g(-6) b. x if g(x) = 16 c. g -1 (x) Simplify the following expressions x x 1 4

3 Use the laws of exponents to simplify the following expressions ( x )( x ) m m 10. x 6y ( x y ) y 0 Simplify the following expressions completely Word Problems 16. A full mile is 4 ½ laps around the outside of the track. If you want to run of a mile, how many laps should you run? 17. The diameter of a tree varies directly as its age. A 0-year-old tree is 6 inches in diameter. How old will the tree be when it is 4 inches in diameter? a. What is the constant of variation? b. How old is the tree? 18. Assume that the rate at which a cricket chirps varies linearly with the temperature. Crickets make 70 chirps per minute at 60 F and 100 chirps per minute at 80 F. a. State what the independent and dependent variables are. b. Write the particular equation that expresses this relationship. c. What is the temperature-intercept? What does this tell you about the real world? d. What is the slope? What does it represent in terms of this problem?

4 19. The Brick Oven Bakery sells more loaves of bread when it reduces its price, but then its profits change. The function y = -100(x - 1.7) + 00 models the bakery s profits, in dollars, where x is the price of a loaf of bread in dollars. The bakery wants to maximize its profits. a. What is the domain of the function? Can x ever be negative? Explain. b. Find the daily profit for selling the bread at $.00 per loaf. c. What price should the bakery charge to maximize its profits? d. What is the maximum profit? 0. Given the right triangle, determine the trigonometric ratios. B sin A 48. cos A 49. tan A 0. sin B 1. cos B. tan B C 1 A 1. Use trig ratios to solve for x and y (to the nearest thousandth) in each right triangle. a. b. x 0 y 1 18 x 8 y Find an equation in slope intercept form for the line described.. The line through (, - ) with slope m = 4/. The line through the points ( -1, -4 ) and (, ) 4. The line through ( -, 4 ) with a slope m = 0. The line through (, - ) and parallel to the line x + y = 6. The line through (, - ) and perpendicular to the line x + y = 4

5 Simplify each and write your answer as a single fraction. State any restrictions on the variable. x x x + 6 x + x x + 7x+ 10 x 4 x x 9. x 6x x+ x x x x x+ 1. Given the following functions, ( x) = ( x ) 1 f and a. f (g()) b. g(f()) x g ( x) =, find: x +. Express as a single logarithm 4. log a 4 + log a n. log x log 6. log w 7. lnv (ln4 + lnu). Students should be familiar with trigonometric functions, special right triangles and the unit circle. 90 < ϑ < 180 Find the exact value of the 6 trigonometric functions for each angle. a. θ = 4 b. tanϑ = c. π d. θ = 10 e. θ = π f. θ = 40 4

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