1) Find the equations of lines (in point-slope form) passing through (-1,4) having the given characteristics:
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1 AP Calculus AB Summer Worksheet Name 10 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. any questions to: Be sure to round all decimal answers to 3 decimal places. 1) Find the equations of lines (in point-slope form) passing through (-1,4) having the given characteristics: a) Passing through (-4, -7) b) Perpendicular to x 3y = 5 ) The velocity of sound in dry air increases as the temperature increases. At 40 o C, sound travels at a rate of about 355 meters per second. At 49 o C, 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 60 o C.
2 -- 3) In 1998, the product was worth $0,600. 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 + y + 6 = 0 b) x = 4 5) An employee has two options for positions in a large corporation. One position pays $1.50 per hour plus an additional unit rate of $0.75 per unit produced. The other pays $9.0 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?
3 -3-6) Solve graphically. Draw a rough sketch of the graphs and give the solution(s). a) x = 15 4x b) y = 5 x y = x 3-3 c) y = 0.77x 1.3x 9.31 y = 500 7) Evaluate the following expressions, given that f(x) = -x - 5x 7. a) f(-4) b) f(x - 1) c) f(c) d) f(x + h) - f(x) h
4 -4-8) Solve for y. Determine whether y is a function of x. a) x + y = 4 b) x y x + 4y = 0 9) Given: A(-, 1) and B (3, 4) a) Find the distance between A and B. b) Find the midpoint of segment AB. 10) Solve for x: 5 = ln (7x + 18) 11) Solve for x: 14e 3x+ = 560 1) Solve for x: ln (x + 9) - = ln x
5 -5- Graph the following: 13) y = sin x 14) y = sec x ) y = [ x ] 16) y = x, x < 0 x - 3, 0 x 5 x, x > Simplify: 17) ) x 3 x x
6 -6- Write the equation of the lines with the following characteristics. Put answers in point-slope form: 19) Passing through (, -5) with slope = /3: 0) Passing through (6, -8) and (9,4): 1) The symbol is read and means. Complete the following Pythagorean triples: ) 7, 4, 3) 1, 35, 4), 60, 61 5) 9,, 41 6) 3,, 5 7), 15, 17 8) Solve for x if 0 x < π: a) sin x + 3 sin x = -1 b) csc x - = 0 c) sin x + cos x = -1
7 -7-9) Find the exact value of each without using a calculator: a) cot 45 o b) sec 180 o c) sin 10 o d) cos (7π/6) e) csc (-3π/4) f) tan (-7π) 30) Find all values of θ on the interval 0 θ < π: a) sin θ = -½ b) cot θ = -1 c) cos (3θ) = ½ 31) State the domain and range for each function: DOMAIN RANGE a) y = ln (x - 3) b) y = x 8x - 48 c) y = -x + 10x + 15 d) y = 5x - 70x x + 4x - 1
8 -8-3) Find the x-intercepts and y-intercepts algebraically: a) y = x + x - b) y = x 9 x c) y = x + 3x (3x + 1) 33) Find each of the following if f(x) = 3x 4 g(x) = x 5 h(x) = 5x - a) f(g(x)) b) g(f(x)) c) f(g(-3)) d) g(h(-4)) e) f -1 (x) f) h -1 (x) True or false?? 34) sin (30 o + 60 o ) = sin 30 o + sin 60 o 35) ln (x + 5) = ln x + ln 5
9 -9-36) Sketch the graph of f(x) without using technology, then provide the requested information: f(x) = 4x - x + a) domain: b) vertical asymptotes : c) horizontal asymptotes: d) holes: e) x-intercept(s): f) y-intercept: 37) Sketch the graph of f(x) without using technology, then provide the requested information: a) g(-1): b) lim g(x) x - c) g(): d) lim g(x) x
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