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Precalculus NAME _____________________________________ JUNE 2011 PRECALCULUS SUMMER ASSIGNMENT To prepare you for the upcoming year, the Mathematics Department has created this summer assignment as a means of reviewing important skills and concepts that you have learned. The assignment has been divided into different sections. You are responsible for completing this packet on your own. Try and complete most of the assignment without using a calculator. To supplement your knowledge, Ms. Hinrichsen, Mr. Lynch, and Ms. Rossi will have a PDF file of website resources on their websites on their PRECALCULUS pages. Feel free to email any of them with a question. Please consider that it is summer break, and they may not get back to you the same day. The packet will be collected on Wednesday, September 7, 2011. An assessment (quiz/quest) will be given to assess the students’ knowledge of the material. Be sure to SHOW ALL WORK to receive credit. All answers should be EXACT (simplified fractions and radicals). I. 1) COORDINATE GEOMETRY Find the slope, midpoint, and length of the line segment that has the following endpoints (2, -5) and (6, 1). Simplify all answers. Slope ____________ Midpoint _________ Length ___________ MPH/CR 6/11 1 Precalculus 2) Find the x- and y-intercepts for 4x – 9y = 12. 3) A line has a slope of 4) A line has a slope of 5 and contains the points (2, -7) 6 and (x, 4). Find the value of x. a) 4 7 b) 3 Write y x 7 in standard form. 8 6) Write y 7) Write the equation of the line with a slope of -11 and a y-intercept of (0, -2). MPH/CR 6/11 3 2 5 y-int ____________ _________________ perpendicular to it ____________ 5) x ____________ . Identify the slope of a line: parallel to it ____________ 8 x-int in general form. _________________ _________________ _________________ 2 Precalculus 8) Write the equation of a line with a slope of and _________________ Write the equation of a line containing points (3, 7) and (11, -5). _________________ passing through (-10, 3). 9) 2 5 10) Write the equation of the line with zero slope through (-12, 5). _________________ 11) Write the equation of the line parallel to the y-axis passing through (2, 1). _________________ 2x y 4 12) Solve the system using substitution. 7x 3y 13 MPH/CR 6/11 _________________ 3 Precalculus 2x 3y 6 13) Solve the system using linear combinations. 3x 4y 7 (Elimination) _________________ 14) Graph 3x + 4y = -12. II. 1) FACTORING AND POLYNOMIALS Factor each of the following completely. a) y2 – 6y – 40 b) 3a2 + 14a + 8 c) 27x3 + 8y3 d) 5a2 – 45 MPH/CR 6/11 4 Precalculus 3uw2 + 24uw + 45u 1) e) 2) Solve by factoring. a) x2 + 13x = 30 f) 2n3 + 10n2 – 7n - 35 b) 2x3 - 9x2 = 0 3) Solve by completing the square: x2 + 10x – 7 = 0 _________________ 4) Solve using the Quadratic Formula: 2x2 – 2x – 5 = 0 _________________ MPH/CR 6/11 5 Precalculus 5) Solve using synthetic division: 2x3 - x2 – 13x – 6 = 0 _________________ III. RADICALS 1) Simplify (if possible). a) 2 7 6 8 7 11 6 27 11 12 b) 2) _________________ _________________ Simplify (if possible). 2 10 ______________ a) c) 6 5 MPH/CR 6/11 2 ______________ b) d) 12 5 3 ______________ 14 2 ______________ 6 Precalculus 3) Simplify (if possible). a) b) IV. 1) 7 2 3 2 _________________ 54 3 _________________ 2 3 COMPLEX NUMBERS Simplify each expression. a) d) 36 i 130 MPH/CR 6/11 b) e) 48 (4 – 6i) + (11 + 2i) c) i 27 f) (-12 + 5i) - (2 - 7i) 7 Precalculus 2) Given the complex number 4 – 9i, identify: Real Part 3) c) 1) Conjugate Simplify each of the following expressions. a) V. Imaginary Part 6 15 ______________ b) 5 2i ______________ 2 3i _________________ 5 8i FUNCTIONS State the domain of each of the following functions. a) f(x) = 4 – 6x – 7x3 b) g(x) c) h(x) 3x 8 MPH/CR 6/11 2x 10 x 7x 30 2 _________________ _________________ _________________ 8 Precalculus 2) Given the functions below, evaluate each of the following. f(x) = 2x2 – 3 3) g(x) = 4x + 7 a) f(-3) ______________ b) c) h(f(g(2))) ______________ h(x) = 6 x3 g(h(-1)) ______________ For each of the following functions, identify the shape of the graph. Also identify any transformations including shifts and reflections. Be sure to indicate the number of units and the direction. a) f(x) = - |x + 3| Transformations: b) g(x) = (x – 4)2 + 11 Transformations: c) h(x) = x 5 Transformations: d) 3 k(x) = x 7 4 Transformations: MPH/CR 6/11 Shape: ________________________________ ___________________________________________ Shape: ________________________________ ___________________________________________ Shape: ________________________________ ___________________________________________ Shape: ________________________________ ___________________________________________ 9 Precalculus VI. RATIONAL EXPRESSIONS Perform the indicated operation and simplify each expression. 1) 2) 3y 4 y2 8 3x 6 3 4) 2y2 y 3 y2 1 5x x 4 2 2y3 3y2 y2 3y 2 3) 10n n 3n 4 2 2 n1 4 x2 x 5 7 x 2 6x MPH/CR 6/11 10