June Dear prospective Pre-Calculus student,

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1 Dear prospective Pre-Calculus student, June 017 We are pleased that you have decided to take Pre-Calculus next year. Pre-Calculus is a challenging class that requires that you have mastered the concepts that were taught in Algebra II. We cover a lot of new and interesting topics, such as conic sections, trigonometry, functions, logarithms, sequences and series, and limits. By the time you finish the class, you will have learned all of the topics necessary to go on to Calculus. By accepting the challenge to take Pre-Calculus, you are making a commitment to put in the effort required to excel in the class. You will be required to do homework before each class covering the material learned in the previous class. If you are having trouble with the challenging material presented in the class that is OK (that s what challenging means) but you will need to take advantage of opportunities to get help during flex, open lunch periods, and before or after school as offered. The biggest factor in whether you will succeed is how much you want to succeed. Whether or not math comes easy to you is of little importance compared to how much work you are willing to put into the class. You can start to show your level of dedication and commitment to the class by completing the summer assignment that comes with this letter. Please attempt to complete as much of this packet as possible without the use of a calculator. There will be calculator and non-calculator sections on assessments. Therefore, a calculator will be used for this course. Should your child want a calculator, a TI-84 Plus Family (84, 84 Plus, 84 Plus C, 84 CE) is sufficient for this course and AB Calculus it is also allowed on the SAT/ACT. This packet will be turned in the first week of school. An assessment will be given covering this material during the first weeks of school. Have a wonderful summer, Mrs. Amy McDowell and Mr. Matt Glover The Pre-Calculus Teachers

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3 Pre-Calculus Summer Packet Name: Write Answers ONLY on the blanks attach a page per section to show your work (as needed) Problems that you need to ask next school year: 1) ) ) 4) 5) 6) 7)

4 SECTION 1 (Simplify Radicals) Rationalize if needed. 1) ) 5 ) 1 4) 5 5) 9 6) 1

5 SECTION (Functions) 1) Solve the system of equations: 5x y 4 x y 5 ) Write the equation of the line that is perpendicular to y x 10 and passes through the point 6,1. ) Solve the non-linear system: x y 7 0 x 6x 1 y 4) See Below Evaluate the function for the given value of x. f a) f 4 = b) f = c) f 1 = x 6, x x 1 x 5, x 5) Solve for y in terms of x. 4xy y 1 6) Solve for y in terms of x. x y y

6 SECTION (Factoring) Factor the following polynomials completely. Factor completely showing ALL work. Show ALL steps IF it is more than a one step factoring problem. Section I: 1) ) ) 4) 5) y 64 7m 1 15n 16 5x 0 81 x Section II: 6) 7) 8) 9) x x x 1 y y y x x x y 100y y 4 Section III: 10) 11) 1) 1) 4 x 65 4 x 7x 6 5 y y 6 4 6m 1m m Section IV: 14) 15) 16) 17) 6 x y x n 7 n x 1 7ac bc 7ad bd 49x 4xy 9y Section V: Write f(x) in factored form given a factor or zero of f(x). Use synthetic or long division to reduce to a quadratic equation to factor fully. 18) f ( x ) x 10x 19x 0; x 6 19) 0) f x x x x f ( ) ; ( ) 0 f x x x x x ( ) 61 0; 5

7 SECTION 4 (Polynomial Equations) Solve for x. 1) 6x = 1x + 5 ) x 15 Simplify answers completely no decimals allowed. Solve Quadratic Equations: 1) Square Root Both Sides (Don t forget ±) ) Factor and apply Zero Product Property ) Complete the Square 4) Quadratic Formula ) Solve by completing the square: x + 6x = 7 4) Solve by completing the square: x 4x = 5) Solve by completing the square: x + 6x = 1 6) Solve by completing the square: 7 5 x x x x Solve by factoring completely. 7) y 5y 0 11) 6 4 x 4x 9x 6 0 8) 18x 50 x 1) 5 48x 7x 9) 10) g g g 0 5 4x 84x 1) 5 x x Find the vertex using completing the square: 14) 15) y x x 10 y x x ) 17) y x x y x x 7

8 1) Graph the given function: Parent Points: x Quadratic: y x Cubic: y SECTION 5 (Graphing) f x x. Graph showing ALL points possible WITHOUT using a calculator Vertex for Quadratic Eqs: b x a x h f1 f x y f x vertex ) Graph the given functions, x 6y 1, x y x 4, x then find: f f 0 f 5 f ) Graph the function: f x, x 1 x x 4, x 1 4) Find the following information: a) Domain: b) Range: c) Increasing Interval: d) Decreasing Interval: e) Local Minimum: f) Local Maximum: g) Intercepts:

9 1) Solve: x 6 SECTION 6 (Radical Equations and Exponents) ) Solve: 1 7 x ) Solve: 4 x ) Simplify: x x 5) Simplify: x 6) Completely Simplify: 5 x x 5 (Hint: Look at bases in your 1 st answer)

10 SECTION 7 (Rational Expressions/Equations) Simplify each expression. Solve each equation. x 7 1) Simplify: x x 4 ) Simplify: x x x x x x 1 ) Simplify: x 4x x x 16 x 4 4) Solve, if possible: 4 x x 1 x 5) Solve, if possible: x x 1 6) Solve, if possible: 1 x 1 x x x

11 SECTION 8 (Geometry Review: Right Triangle Review & SOH-CAH-TOA) Find the value of x. Write answer in simplest radical form. Use Special Right Triangles. O A O S ; C ; T Solve the right triangle using the Trigonometric Functions H H A a b c Round answers to the nearest hundredth. Find the value of each variable. Write answer in simplest radical form. Use Special Right Triangles.

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