Pre-Calculus Summer Assigment

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1 Pre-Calculus Summer Assigment To All Future Pre-Calculus Students- You have successfully completed Algebra 2. It is now time to prepare for Pre-Calculus. This assignment will be the first homework grade for the class. Complete the packet prior to the first day of school. The packet includes topics covered in Algebra 1 and Algebra 2. There are no new concepts included in this packet. If you are unable to answer a question, do not skip it! Research the topic on the internet and make a solid effort at attempting the problem. The packet will be graded on effort and not accuracy of your answers. Therefore, answer all questions. Work must be included to receive full credit. When we return to school in September, we will spend class time going over the packet in detail and provide additional problems, if necessary on any specific topic. Students will be assessed on the material contained in this packet. Enjoy your summer and we look forward to meeting you in the Fall. The Pre-Calculus Teachers

2 Name Pre-Calculus Date Summer Assignment Directions: Please do all work on a separate sheet of paper. Number all problems on the separate sheet so it is easy to follow. Place the solution on the line provided. It is strongly recommended that the problems be completed without the aid of a calculor, unless directed to use one. You may use the calculator to check your work. Good Luck! Write an equation in slope-intercept form for the line that satisfies each set of conditions. 1) slope 4, passes through (6, 9) 2) passes through (-8, -5) and (3, -10) 3) passes through (-6, -6), parallel to 4x 3y = -24 4) passes though (4,2), perpendicular to y = -2x + 3 Find the x-intercept and the y-intercept of each equation. 5) 2x 3y + 8 = 0 6) f(x) = 4x 10 Graph each linear equation. 7) y = 1 2 x 3 8) y = 2

3 9) y = - 3 x ) x + 3y = -6 2 Graph each linear inequality 11) y > 3x ) 10 5y 2x

4 Solve each system by graphing x = 3 2x + y = 5 13) { y = 2 x 1 14) { 8x + 4 = 4y 3 Solve each system algebraically (substitution or elimination) y + 16 = 5x 15) { 2x + 3y = 3 2x 3y = 1 16) { 4x 5y = 7 5x 2y = 12 17) { 5 x + 1 y = Solve the systems of inequalities by graphing y < 3x 1 18) { 3x 6y > 6 y 1 x ) { y 3 x 3 2 x + y 2

5 Simplify each expression using the law of exponents. No negative exponents in your final 20) (-2x 3 y 2 ) 5 21) (2x -3 y 3 )(-7x 5 y -6 ) 22) ( 3a3 b 4 ) 2 23) 15c 5 d 3 18c 2 d 7 Simplify each expression 24) (3m + 4)(2m 5) 25) (2x + 5y) 2 26) (2x + 5)(4x 2 10x + 25) 27) 5c(2c 2 3c + 4) -2c(7c 8) 28) 4a 3 b 6ab+2ab 2 2ab 29) (3x 2) 3 Simplify each radical expression. No decimal approximations! 30) - 36x 8 y ) 27b 18 c ) 81(x + 4) 4

6 3 33) 75 34) 32 35) 40 36) 12c 6 d ) 8x 3 y 2 4 * 2x 5 y 2 38) ) ) 32x ) (7-3)(7 + 3) Rationalize each denominator. (Use conjugates to rationalize binomial denominators). 42) ) ) ) Evaluate each expression involving rational exponents. 46) ) ) ) Perform each operation if f(x) = 3x 7 and g(x) = x ) f(20) 51) g(a 4) 52) g[f(-1)] 53) f[g(x)]

7 Graph the quadratic function and complete the chart: 54) 55)

8 Mr. Goodman, who knows a lot about physics, is going to fire a rocket to start off this year s Battle of the Classes. He has done testing on the rocket to ensure it will not hit any students. If the rocket is launched upwards with an initial velocity of 200 feet per second, its height h(t) (in feet) can be found by the function h(t) = -16t t, where t is the number of seconds since it was launched. 56) How long will it take for the rocket to reach its highest point? 57) What is the maximum height that the rocket will reach? Factor each completely. 58) 8ab 2 4ab 59) x 2 + 4x 21 60) 25x xy + y 2 61) 9c 2 49d 2 62) 3x 3 3x 2 90x 63) 3x x ) x 3 + 5x 2 2x 10 65) 6x 2 + 7x 3 66) 16x 3 y - 81xy 67) x 4 4x ) 8x ) 18a 2-31ab + 6b 2

9 The imaginary unit I is defined as the principal square root of -1 and is written i = 1. Since I = 1, it naturally follows that (i) 2 = -1. Simplify each expression. 70) i 14 71) 64 72) 24 73) (-3 i) (4 5i) 74) (5 + i) 2 75) 1+2i 2 3i Solve each equation by factoring. Include all solutions (real and imaginary) 76) 20x 2 11x 3 = 0 77) 2x 3 12x 2 = -18x 78) x 4 = 4 3x 2 Solve each equation by using the Quadratic Formula. Include all solutions (real and imaginary). Answer in simplified radical form, if necessary. 79) 2x 2 + 6x 3 = 0 80) x = 6x - 5 Solve each quadratic equation using any method. Answer in simplified radical form, if necessary. 81) (x + 5)(x 3) = 33 82) x 2 4x + 7 = 0 83) Normal systolic blood pressure is a function of age. For a woman, the normal systolic blood pressure (in millimeters of mercury) is given by the function P =.01x x + 107, where x is the woman s age. Use this function to find the age of a woman whose systolic blood pressure is measured to be 121 millimeters of mercury. (Hint: Use the Quadratic Formula)

10 Simplify the expression. List any values of x that make the expression undefined. 84) 2k 2 k 15 k 2 13k+30 85) 2u 3 y 15xz 5 25x3 14u 2 y 2 86) 8x 2x 14 x x 87) 5 6ab 7 8a 2 88) x+3 x+7 89) 4 x+1 3x+6 x ) 1+ y x 1 y + 1 x Match each equation to the graphs. a) f(x) = 1 x b) f(x) = x c) f(x) = x d) f(x) = x 2 e) f(x) = 2 x f) f(x) = log 2x g) f(x) = x 3 h) f(x) = x

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