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Summer work for Honors Calculus(349) This packet contains problems involving skills that you should already know. Please take your time with these problems and SHOW YOUR WORK. Do not use a calculator unless otherwise noted. The review should be time to practice things you’ve relearned (or learned) over the summer. Please use your resources wisely. There are many online resources available to guide you through any problems you may have. Ex. khanacademy.org, wolframalpha.com, mathisfun.com You may also contact me at [email protected] if you have questions. This packet is due August 29, 2016. A. Simplify. Show the work that leads to your answer. x4 1) 2 x 3x 4 3) 5 x x 2 25 x3 8 2) x2 4) x 2 4 x 32 x 2 16 B. Simplify each expression in order to obtain a single fraction. Show all work. 1) 1 1 xh x 2 x2 2) 10 x5 3) 2 1 1 a2 4) x 1 2 x 1 C. If f ( x) 1 x 2 and g ( x) 2 x 1 , find: 1) f (3) 2) g (2) 3) g ( f (4)) 4) f (g (0)) 5) f ( x h) 6) f ( g ( x)) 7) g ( x) f ( x) 8) f ( x) g ( x) 9) g ( x h) g ( x ) h D. Using point-slope form y y1 m x x1 , write an equation for the line… 1) with slope –2, containing the point (3, 4) _________________________________ 2) containing the points (1, -3) and (-5, 2) _________________________________ 3) with slope 0, containing the point (4, 2) _________________________________ 4) perpendicular to the line in #1, containing the point (3, 4) __________________________________ E. Find the equation of all vertical ( x ? ) and horizontal ( y ? ) asymptotes, if they exist. 1) y x x3 2) y x3 4 x2 1 3) y 2x 5 x2 1 F. For each of the following, sketch the function and then determine its domain and range. 1) y x4 2) y 3sin 2 x 2 3) y 9 x 4) y G. Complete the following identities. 2 2 1) sin x cos x _________ 2 2 3) csc x cot x _________ 2 2) 2 2 tan x _________ 1 x 1 H. Factor the following completely. 2) t 4 13t 2 36 1) 2 x 2 13x 15 5 2 3 2 3) x x 12x 1 2 4) ( x 3)2 (2 x 1)3 ( x 3)3 (2 x 1)2 I. Multiply and simplify your results. 1) 2x 9 y 3 y 8x 2) 2u v3 v 3u 3) 6s 2 10st 5t 3 6s 3 4) x2 4 2 x 4 6 x2 5) 3y 9 y3 2 14 y y 9 6) t 2 25 2s 3 4s 2 9 5 t J. Complete the missing sides and angles of the special right triangles. 1) 2) X 2X X X K. Determine the exact value of each expression. Remember NO CALCULATORS! 1) sin 0 ______ 2) sin 3 __________ 4 3) cos __________ 4) cos 7 _______ 6 5) tan 7 __________ 4 6) tan 0 __________ 7) csc 2 _______ 3 8) sec 3 __________ 2 9) cot ______ 3 11) cos 10) sin 13) tan 1 1 =____ __________ 2 14) arccos 1 =_____ 11 __________ 6 12) arcsin 3 =_________ 2 1 15) arcsin ________ 2 L. Simplify each radical/radical expression. 1) 56 2) 4) 64 121 5) 3 108 4 6 4 6 6) M. Solve the equation for x, where x is a real number. 1) x2 3x 4 14 3) x 5 2 9 125 80 3) 2) x4 1 0 x3 4) 2 x2 5x 8 11 2 2 5) 5 1 e 1 2x 7) 5 ln(2 x 1) 3 6 6) 8) x 1 5 0 x 1 4 1 5 x 1 6 x 3 Solve each equation on the interval [0,2 ) . 9) sin x 1 0 10) 2 cos x 3 0 11) 4 sin 2 x 1 12) 2 sin x cos x sin x 0 Solve for z. 13) 4 x 10 yz 0 14) h 3 2x4 z N. The number of elk after t years in a state park is modeled by the function P(t ) You may use a calculator for this problem. 1) What was the initial population? 2) When will the number of elk be 750? 3) What is the maximum number of elk possible in the park? 1216 1 73e 0.03t O. Limits x 2) lim sin x 5 6 1) lim 2 x 5 x 3 x 2 4 x 21 x 7 x 2 49 x2 x x 2 5 4) lim 5) lim 3) lim x 4 x4 x 5x 4 2 4 x2 5x 2 x 3 x 2 5 x 12 6) lim P. Geometry 1) Find the area of the trapezoid below. 12cm 45o 16cm 2) Find the volume and surface area of the sphere that has a radius of r 4 cm.