1-1 Name: Summer Worksheet for students entering AP Calculus AB This worksheet is due at the beginning of class on the first day of school. It will be graded on accuracy. You must show all work to earn credit. You may work together with other students but each must turn in his/her own sheet. Please refer to your old Honors Precalculus or Precalculus notes. Email any questions to me at [email protected] Be sure to round all decimal answers to 3 decimal places. 1. Find the equations of lines (in slope-intercept form) passing through (-1,4) and having the following characteristics a. Passing through the point ( -4, -7) b. Perpendicular to 2x – 3y = 5 c. With an undefined slope d. Parallel to the x-axis 2. The velocity of sound in dry air increases as the temperature increases. At 40oC, sound travels at a rate of about 355 meters per second. At 49oC it travels at a rate of about 360 meters per second. a. Write a linear equation, in slope-intercept form, for the velocity v of sound as a function of the temperature T. b. Use this equation to find the velocity of sound at 60oC. 3. In 1998, the product was worth $20,600. The value is expected to decrease in value $1500 per year during the next 5 years. Use this information to write a linear equation that gives the dollar value V of the product in terms of the year t. ( Let t = 8 represent 1998) 4. Graph the following lines a. x + 2y + 6 = 0 b. x = 4 5. An employee has two options for positions in a large corporation. One position pays $12.50 per hour plus an additional unit rate of $0.75 per unit produced. The other pays $9.20 per hour plus a unit rate of $1.30. a. Find linear equations for hourly wages W in terms of x, the number of units produced per hour, for each of the options. b. Algebraically, find the point of intersection. c. Interpret the meaning of the point of intersection. How would you use this information to select the correct option if the goal were to obtain the highest hourly wage? 6. Solve graphically. Draw a rough sketch of the graph and give the solution(s). a. 2x = 15 − 4x b. y = 5 – 2x c. y = .77 x2 –1.32x –9.31 y = x3 – 3 y = 500 7. Evaluate f(x) = -2x2 - 5x – 7 a. f(-4) b. f( 2x – 1) c. f(2c) d. f ( x + h) − f ( x ) h 8. Solve for y. Determine whether y is a function of x. a. x2 + y2 = 4 b. x2y – x2 + 4y = 0 9. Given: A(-2 , 1) and B (3 , 4) a. Find the distance between A and B. 10. Simplify a. ln e 4 b. Find the midpoint of segment AB. 11. a. Write 8 = ln (x+3) in exponential notation. b. ln 1 b. Write e x = 9 in log notation 12. Find each of the following in simplest radical form. a. cos (7π/6) b. csc ( -3π/4) c. tan (-7π ) 13. Find Θ , 0 ≤ Θ< 2π a. sin Θ = ½ c. cos (3Θ) = ½ b. cot Θ = -1 14. Find the domain a. y = 3 3x − 2 15. Solve algebraically. a. 14e 3x +2 = 560 b. y = -4x3 –5x –2 b. 4 ln 3x = 15 c. y = 2x − 5 7−x d. y = ln(2x − 3) c. ln(x + 5) − ln x = 2 16. Draw the graphs of each of the following: ( n is any positive integer) a. y = - x 2n b. y = x 2n+1 c. y2 + 3 = x d. y = x + 3 e. y = 3 x + 3 f. y = | x + 3 | g. y = e x h. y = ln x i. y = 9 − x 2 17. .Find x and y intercepts algebraically. a. y = x2 + x –2 b. y = x 2 9 − x 2 c. y = x2 + 3x (3x+1)2 18. Find each of the following if f (x) = 3x – 4 a. f o g (x) b. g o f (x) e. f –1(x) d. g ( h (-4)) 19. Graph a. Domain: f ( x) = g(x) = x2 – 5 h ( x ) = 5x + 2 c. f (g (-3)) f. h –1(x) 4x − 2 x+2 b. Vertical Asymptote: c. Horizontal Asymptote d. Holes e. Root f. y-intercept 20. Solve for x, 0 ≤ x < 2π a. 2 sin 2 x + 3 sin x = −1 21. Graph b. csc 2 x − 2 = 0 ⎧ x − 6, x < 2 ⎫ g ( x) = ⎨ 2 ⎬ ⎩ x + 2, x ≥ 2⎭ a. g(-1) c. lim+ g ( x ) b. g(2) d. lim g ( x) x→2 x→ 2 c. sin 2 x + cos x = −1