June Dear Future Functions/Analytic Geometry Students,

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1 June 016 Dear Future Functions/Analytic Geometry Students, Welcome to pre-calculus! Since we have so very many topics to cover during our school year, it is important that each one of you is able to complete these Algebra II/Trigonometry problems. I will assume that you know how to use the algebraic and graphing skills necessary to complete these problems as we build on these topics throughout the year. Remember these simple policies (that will also apply to each and every homework, quiz, test, and classwork assignment) in Func/An: Show all work IN THE PACKET. Yes, even for multiple choice questions. Do the problem completely, as if there were no choices to look at, then select the choice you arrive at on your own. When I say show your work, I mean every step of your algebraic work or sketch of a graph necessary. Simplify all answers completely. Reduce all fractions, rationalize denominators, do not leave negative exponents (unless otherwise stated), etc. Ask/search for help! Ask your friends, parents, teachers, tutors and use books and the internet to find help if you can t remember a skill. Just make sure that in the end, you can complete the work independently, without the help, for next time. Complete all work yourself, even if you are seeking the help of others. Feel free to me directly during the summer at wilsonla@pwcs.edu if you have any questions. I will be checking my periodically, so be patient I will get back to you! Do not wait until the last week (or night) of the summer to complete these. By then, it will be too late to get help (certainly from me!) Here are a few internet sites that may be of some help: This assignment is optional. However, I strongly suggest that you complete this assignment. If completed and turned in by Tuesday September 6, 016, you will receive up to extra points towards your 1 st quarter grade. Also, your life this year in Funct/An will be much better if you have mastered these skills prior to September. I am looking forward to working with you! Mrs. Wilson

2 Functions/Analytic Geometry Name Summer Assignment Be sure to show your work on EVERY SINGLE PROBLEM! Yes, even the multiple choice ones! Determine which value(s), if any, must be excluded from the domain of the variable in the expression. x - 6 1) x - 6 A) x = B) x = 8 C) x = 6 D) x = 8, x = -8 Determine the domain of the variable x in the expression. ) x + x - 1 A) {x x 0} B) {x x 1} C) {x x 0, -1} D) all real numbers Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. x-y ) 1x-y-1 A) x y B) x 8y6 9 C) x6y9 7 D) x 6y9 ) (xy 7)(xy) (xy) ) -1x7 6) 7( - ) 7) ( 1+ z)( 1 - z) 8) ( 11 + ) A) B) C) D) ) z-/ z/ A) z/6 B) z1/ C) z-1/ D) z6/ 10) 8x + 6x A) 6 x B) 7x C) x D) x Simplify the expression. 11) 81-/ 1) (-6)/ 1

3 Factor the expression. 1) x/ + x/ A) x/(x-1/ + ) B) x1/(x/ + ) C) x1/(x1/ + ) D) x/(x1/ + ) Rationalize the denominator of the expression. Assume that all variables are positive when they appear. 9 1) A) 81 B) 9 C) 9 D) 9 1) A) B) C) D) Solve the problem by WRITING ONE OR MORE EQUATIONS and showing your steps to solve it. 16) Find the area of the shaded region. A) 6-9 square units B) 9-9 square units C) 9-9 square units D) square units 17) A circular swimming pool, feet in diameter, is enclosed by a circular deck that is. feet wide. What is the area of the deck? Perform the indicated operations. Express the answer as a polynomial written in standard form. 18) (x - ) 19) (x + 7) - (x - 7) Factor completely. If the polynomial cannot be factored, say it is prime. 0) x ) x - x - 6

4 ) 1x - 6x - 0 ) x - 7x - 1 A) (x + )(x - )(x + 9) B) (x + )(x - )(x + )(x - ) C) (x - )(x + 9) D) (x - 16)(x + 9) ) x + 6x + 1x + 70 A) (x + 6)(x - )(x + x + ) B) (x + 6)(x + )(x - x + ) C) (x + 6)(x + 1) D) prime Perform the indicated operations and simplify the result. Leave the answer in factored form. 6x ) 1x x + 6) 9x - 7x x - 1 x + x - x + 8x +16x A) (x - 1) B) x(x - 1)(x - ) (x + ) C) x(x - 1) D) x(x + 1) 7) x + 6 x - A) 8x - 10 x( - x) B) 10x - 8 x( - x) C) 10x - 8 x(x - ) D) 8x - 10 x(x - ) 8) x + x + x x + x - 9 Solve the equation. 9) 8 x = - 1 0) x + = 7 x 1) x x + = x - x x x +

5 ) (x + 7)(x - 1) = (x + 1) ) 1 x - 7 = -1 x x - 1x + 98 A) {1} B) {7, 1} C) {7} D) no solution ) 10x + = x A) {- 8 } B) {-, 1} C) {1} D) no real solution Solve the equation by first setting = 0, then factoring. ) x - 11x = 0 6) x(x - 8) + 1 = 0 7) x + 8x - = 0 8) 8x + 16 x = - (hint = first mult by com den) 9) (x - ) + (x - ) - 18 = 0 0) x + x = 16x + 0 A) {-, 0} B) {-, } C) {-, -,} D) {-,} Solve the equation by taking first the square root of both sides. 1) x = 9 ) (x - ) = 16

6 Solve the equation by completing the square. ) x + 8x - = 0 A) { + 19} B) {- - 19,- + 19} C) {- - 19, } D) {-1-19, } Find the real solutions, if any, of the equation. Use the quadratic formula. ) x + 1x + = 0 A) { C) { -6-61, -6-11, } B) { } D) { -6-11, , } } Solve the formula for the indicated variable. ) S = rh + r for h A) h = (S - r) B) h = S - r r C) h = S - r D) h = S r - 1 6) A = P(1 + rt) for t A) t = - A + P rp B) t = A - P rp C) t = A + P rp D) t = P - A rp Write the expression in the standard form a + bi. 7) 6 + 8i A) i B) i C) + i D) - i 8) ( - i) A) 16-0i + i B) -9 C) 1-0i D) -9-0i 9) i7 A) i B) -1 C) -i D) 1 Solve the problem by WRITING ONE OR MORE EQUATIONS and showing your steps to solve it. 0) 1 - i is a solution of a quadratic equation with real coefficients. Find the other solution. A) 1 - i B) -1 + i C) 1 + i D) -1 - i

7 Solve the equation in the complex number system. 1) x + x + 8 = 0 A) { 1-1, } B) { 1-1 i, i} C) {- 1-1 i, i} D) {-1, } ) x - x - = 0 (hint = factor first) A) {,} B) {- i, -i} C) { i, i} D) {-,, i, -i} Without solving, determine the character of the solutions of the equation in the complex number system. ) x - x + = 0 A) two unequal real solutions B) a repeated real solution C) two complex solutions that are conjugates of each other ) x + x + 6 = 0 A) two unequal real solutions B) two complex solutions that are conjugates of each other C) a repeated real solution Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols. ) The total cost of producing refrigerators in one production line is $00 plus $0 per unit produced. A) If C is the total cost and x is the number of units produced, then C = 00x + 0. B) If C is the total cost and x is the number of units produced, then C = x. C) If C is the total cost and x is the number of units produced, then C = 00 0x. D) If C is the total cost and x is the number of units produced, then C = (00 + 0)x. Solve the problem by WRITING ONE OR MORE EQUATIONS and showing your steps to solve it. 6) The area of a vegetable garden is 60 square feet. If the length of the garden is 7 feet longer than its width, what are the dimensions? A) ft by 1 ft B) ft by 1 ft C) ft by 11 ft D) 6 ft by 1 ft 6

8 7) A 1-inch-square TV is on sale at the local electronics store. If 1 inches is the measure of the diagonal of the screen, use the Pythagorean theorem to find the length of the side of the screen. A) 1 in. B) 1 in. C) 1 in. D) 1681 in. 8) Suppose that an open box is to be made from a square sheet of cardboard by cutting out -inch squares from each corner as shown and then folding along the dotted lines. If the box is to have a volume of 00 cubic inches, find the original dimensions of the sheet of cardboard. A) 10 in. by 10 in. B) 18 in. by 18 in. C) 10 in. by 10 in. D) 0 in. by 0 in. Solve the equation. 9) 8x + = 7 60) 10 - x = Write the inequality using interval notation. 61) t -7 A) [-7, ] B) (-7, ] C) (-7, ) D) [-7, ) Write the interval as an inequality involving x. 6) [-8, 1) A) -8 < x < 1 B) -8 < x 1 C) -8 x 1 D) -8 x < 1 6) (-, -8) A) x -8 B) x < -8 C) x > -8 D) -8 x Solve the inequality by showing your steps. Express your answer using interval notation. Graph the solution set. 6) -1 -x - < -9 A) [, ) B) (, ] C) [-, -) D) (-, -] 7

9 6) x A) [-10, -] B) [-10, 1] C) (-10, -) D) Solve the problem by WRITING ONE OR MORE EQUATIONS and showing your steps to solve it. 66) Express the fact that x differs from -7 by more than as an inequality involving absolute value. Solve for x. A) x + 7 < ; {x -10 < x < -} B) x + 7 < ; {x x < -10 or x > -} C) x + 7 > ; {x -10 < x < -} D) x + 7 > ; {x x < -10 or x > -} 67) A landscaping company sells 0-pound bags of top soil. The actual weight x of a bag, however, may differ from the advertised weight by as much as 0.7 pound. Write an inequality involving absolute value that expresses the relationship between the actual weight x of a bag and 0 pounds. Over what range may the weight of a 0-pound bag of to soil vary? A) x ; {x 9. x 0.7} B) x - 0 < 0.7; {x 9. < x < 0.7} C) x ; {x x 9. or x 0.7} D) x ; {x 9. x 0.7} Find the exact value. Do not use a calculator. 68) sin (- ) 69) cos 70) tan 71) csc 6 7) cot 8

10 Find the exact value of the expression. Do not use a calculator. 7) sin - cos 6 A) B) 1 C) - 1 D) 0 Name the quadrant in which the angle lies. 7) cot < 0, cos > 0 A) I B) II C) III D) IV 7) tan < 0, sin < 0 A) I B) II C) III D) IV 76) sin = 1, cos = 1 Find tan. A) 1 B) C) 1 1 D) 1 1 In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. 77) (, 7 ) Find sin t. A) 7 B) 7 C) 7 7 D) Solve the equation on the interval 0 <. 78) cos + 1 = 0 A), B), C), D) 79) cos + cos + 1 = 0 A) B), C), 7 D) 80) sin = sin A), B),,, C) 6, 6 D) 0,, 6, 6 Complete the identity. First multiply then simplify. 81) tan (cot - cos ) =? A) 1 B) 0 C) 1 - sin D) -sec 9

11 8) Graph y sin x 8) Graph y sin x 8) Graph y cos x 8) Graph y tan x 11

12 86) Two sides of a right triangle ABC (C is the right angle) are a = 7 and b =. Find sin(a). 87) Solve the right triangle using the given information Round answers to two decimal places. b 8, ; find a, c, and For #88-89, solve the problem by drawing a diagram, writing a trig equation, and showing your steps to solve it. 88) 89) 90) Use the graph of f(x) given below a) Evaluate f() b) What values of x satisfy f(x) = 0? c) How many times does the line y = 1 intersect f(x)? d) For what values of x is f(x) < 0? e) What is the domain of f(x)? f) Range? 1

13 91) Find the equation of the line with slope -/ passing through the point (, -1) A. x + y = 10 B. x + y = C. x + y = 7 D. x y = 11 9) Find the equation of the line parallel to x + y = passing through (-1, 6) A. x y + 0 = 0 B. x + y 9 = 0 C. x + y 16 = 0 D. x + y 17 = 0 9) Write the equation of the line (in point-slope form) perpendicular to 7x y 1 = 0 through (7, -1). 9) Given f(x) = x x, find f(x 1) A. x x 1 B. x x C. x x + D. x x + 9) The graph of f(x) is: The following graph is a transformation of f(x): What is the equation of this new graph? A. (f(x + ) + 1) B. (1 f(x )) C. f(x ) + 1 D. f(x + ) ) The vertex of the parabola y = x + 10x + 0 is: A. (-, ) B. (-, -) C. (, -) D. (, ) 1