AB Calculus 2013 Summer Assignment. Theme 1: Linear Functions

Transcription

1 01 Summer Assignment Theme 1: Linear Functions 1. Write the equation for the line through the point P(, -1) that is perpendicular to the line 5y = 7. (A) + 5y = -1 (B) 5 y = 8 (C) 5 y = 1 (D) 5 + y = 7 (E) 5 + y = 8. Which of the following is an equation of the line through (-, 4) with slope 1? (A) y 4 = 1 ( + ) (B) y + = 1 ( 4) (C) y 4 = -( + ) (D) y 4 = ( + ) (E) y + = ( 4). Which of the following is an equation of the vertical line through (-, 4)? (A) y = 4 (B) = - (C) y = -4 (D) = 0 (E) = 4. A table of values is given for a linear function. Determine the slope and y-intercept f () (A) slope: (B) slope: - (C) slope: -0.5 y-intercept: -9 y-intercept: 1 y-intercept: -6 (D) slope: 0.5 (E) slope: 0.5 y-intercept: -6 y-intercept: 6

2 Theme : Function Simplification True or False Decide whether the given statement is true or false. If true, use specific numbers to show four different eamples and eplain why it s true. If false, use specific numbers to show a single countereample and eplain why it s false. [Hint: just one of these is true!] 5. If and y are numbers, then y = + y. 6. If and y are numbers, then ( + y) = + y. 7. If y is not zero, then y = y. 8. If is a number, then =. 9. If is not zero, then. 10. If is a number, then sin sin. 11. The length L of a rectangle is twice as long as its width W. Which of the following gives the area A of the rectangle as a function of its width? (A) A(W) = W (B) A(W) = 1 W (C) A(W) = W (D) A(W) = W + W (E) A(W) = W W 1. Epress the length d of a square s diagonal as a function of its side length. (A) d() = (B) d() = (C) d() = (D) d() = (E) d() =

3 Theme : Fractions and Eponents 1. What is the simplified form of 9 10? 6 (A) 5 (B) 5 (C) 5 (D) Which epression represents the simplified form of? 1 5 (A) (B) 5 (C) 5 (D) What is (are) the solution(s) of 4 4? (A) - (B) -, 4 (C) 4 (D), -4 Free Response 16. Epress the following epressions in the form n. (a) 1 (b) (c) 17. Add one to the power of given the epressions below. Write your final answer in two forms, eponential and radical. (a) 1 (b) 1 (c) 5

4 Theme 4: Logarithms Free Response 18. In a single word, what are logarithms? 19. Sketch y = ln() 0. Give the base for each epression: a) log 4 () b) log() c) ln() 1. Epress log 7 () in words, beginning with the words What power of Then determine the answer by hand.. Simplify the following epressions without using a calculator: a) e ln() b) ln e. Evaluate log 18 using a calculator. (A) 18 (B) 4.46 (C) (D) (E) None of these 4. Evaluate ln e without using a calculator. (A) ln (B) ln (C) (D) (E) None of these 5. Evaluate ln (.76) using a calculator. (A) 1.44 (B) (C) (D) (E) None of these 6. Evaluate log 4 7 using a calculator. (A) 0.40 (B) (C) (D) (E) None of these 7. Simplify: e ln() without using a calculator (A) 9 (B) 8 (C) 6 (D) 5 (E) None of these

5 Theme 5: Trigonometry Free Response 8. Draw the graph of y = sin () on the interval [0, π]. Label both aes, counting by on the -ais. 9. Determine the values of the following sine functions using your graph: a) sin 0 b) sin c) sin d) sin e) sin 0. Draw the graph of y = cos () on the interval [0, π]. Label both aes, counting by on the -ais. 1. Determine the values of the following cosine functions using your graph: a) cos 0 b) cos c) cos d) cos e) cos. Draw a unit circle. Identify the four quadrant positions (all 4 intercepts) in terms of π for one positively directed revolution. Give the values of sin (), cos () and tan () at each position.. Draw a 0 o -60 o -90 o triangle. Label the angles and sides numerically. Give the values of sin (), cos () and tan () for both 0 o and 60 o. 4. Repeat the problem directly above using a 45 o -45 o -90 o triangle. 5. Use a unit circle, the definition of sin () and cos () on a unit circle, and a right triangle to illustrate why sin () + cos () = 1. What famous theorem are you using? 6. Cite the Trig Cheer. Write complete equations, starting with sin (A + B) = and cos (A + B) =. Identify the two equations the cheer relates to by inserting angles A and B among the words. 7. State the matching pairs of reciprocal trig functions.

6 01 Summer Assignment Answer Key Name: Date: ALL solutions should be placed on this sheet. Work should be attached to this sheet. If you eperience difficulty, contact Mr. Weisner ( bdweisner@smcps.org ) at any time during the summer. Bring both this paper and your completed work to class on the first day of school, Wednesday August 5, 010. Theme 1: Linear Functions Theme : Function Simplification Theme : Fractions and Eponents a. 17a b. 17b c. 17c Theme 4: Logarithms 18. 0a b. 4. 0c. 5. 1a. 6. 1b. 7.. What power of log 7 () = Please continue to the other side for Theme 5

7 Theme 5: Trigonometry 8. 9a. 0. 1a. 9b. 1b. 9c. 1c. 9d. 1d. 9e. 1e. Use the space below to complete # s - 7