Enochs Pre-AP SM3 Summer Assignment

Transcription

1 Enochs Pre-AP SM Summer Assignment 07-8 In 07-8 school year, Pre-AP SM classes will be taught by Mrs Dodds & Mrs Rubalcava Both teachers require the same Summer Assignment However, in order to acquire more information specific to each teacher, please see below Mrs Karolin Dodds Enochs High School Phone: (09) Website: Mrs Christina Rubalcava Enochs High School Phone: (09) Schoology Classroom Code: JCFN7-TFMNB (login to your schoology account, click courses, click join and type in the code) Mrs Dodds s Class Material: - Math Only Binder with Graph & Regular Paper, - Pen, Pencil, eraser, highlighter, - TI-8 Plus Graphing or scientific calculator Notes, assignments, & handouts will be organized & saved in the Math Binder Your binder will be your best resource for studying & preparing for any Quiz or Test Mrs Rubalcava s class materials: - Graph-ruled notebook (at least ), - Math binder or section of a binder, - Colored pencils, pencils/erasers, pens, - Highlighters & Pen tip whiteboard marker - Graphing or scientific calculator All notes, which include important definitions, formulas, & examples shown in class should be done in your notebook The teacher has the discretion to perform random notebook checks for a grade In fairness to all, calculators with a computer algebraic system (CAS) will NOT be used on Quizzes or Tests Be noted that you will be taught to do calculations in this class with & without a calculator; thus, you will be Quizzed and Tested in both ways SUMMER ASSIGNMENT: TAKE THE SUMMER ASSIGNMENT VERY SERIOUSLY! The first Test in this class is at the end of The First Week of School, and it will cover the content standards assigned in the Summer Assignment Packet and there are NO RETAKES! This Test contains Free Response Questions without a calculator; this means you are required to show the mastery of essential skills covered in this packet PAGE

2 Enochs Pre-AP SM Summer Assignment 07-8 Pre-AP Secondary Math III (SM) Summer Assignment Mrs Karolin Dodds & Mrs Christina Rubalcava These problems must be completed on binder paper & be Ready to Turn in on the First Day of School Note: you must offer legible & legitimate work that supports your answer Use the offered resources to refresh your memory & re-learn the required skills Positive, Negative, & Rational Exponents Simplify without using a calculator! ] 0 8x ] 9] 5 ] 4x y 5 9 0] ] 4] 4 xy 6 xy 5 x 5x 5] 7 x ] 6 9x 4 5 x 6] ] x x ] 6xy 5x y 4] 4 8] 5 a b c a b c 5] 8 6x y 6] 54 y 4 9 x 7] 8x y 9y 5x y x 8] ] 8y 50y Solve for x without using logarithm 0] x x ] x ] 64 ] 6 x x 4] 7 9 5] x Add, Subtract, & Multiply Polynomials Perform the given operations and write the answer in standard form ] x x 6 x 5x 4 ] x 5 x 7x ] 4y y y y 6y 4 4] 4x x 5] k mk m k 0] x x m 9] 6] x 7] 5 5 4y ] x x 4 x ] 4 x 8] x x ] x 5 PAGE

3 Enochs Pre-AP SM Summer Assignment 07-8 Factor each polynomial expression completely 5 ] x 5x ] x 0x Factor Polynomials x ] 9 6 y 4] 6 x 5] y 64 6] 9k 4k 6 7] 8m 7 8] 6y 5y 9] 0m m 0] x y xy ] 6 4 a ab b ] x x x ] 4y 0y 5y 7] 4] x 6x 4x 5] x 4x 5 x x x 6 8] x 5x 9] 4 6] 5x x Solve each equation Solving Equations Algebraically Do Not use Calculator! 4 k ] x 4] x x ] 4x 5 x 8 6x ] 5 4k 5k 4x 5 5] x 4 6] k k 5 4 7] 6x 5 0 8] x ] x 4 0] x 40 7 ] x 96 ] x Solving Equations by Variety of Methods Solve each Equation using the Recommended Method Do Not use Calculator! Factoring: ] x 6x 0 ] x 7x ] x 8 x 4] x x 7x Quadratic Formula: 5] x 0x 5 6] x x 4 0 7] x x 8] x x 4 Completing The Square: 9] x 0x 0 0] x 0x ] x 4x 6 ] x x 0 Extracting The Root: ] x 7 5 4] x 5 5] 5x Solve each equation using your method of choice Should you check for extraneous solutions! 6] 0 x x 7] x 7 x 8] x 6 x 4 9] x 8 x 0] x 0 x ] x 8 x PAGE

4 Enochs Pre-AP SM Summer Assignment 07-8 Solving Absolute Value Equations Solve each absolute value equation Do Not use Calculator! ] 4 x 5 9 ] x 9 8 ] 7 x 0 4] x 4x 5 Operations with Complex Numbers Write the sum or difference in standard form ] i 4i ] i 9i 4] 7 i 5 8 5] ] 5 i Write the product in standard from 6] 4 i i 7] 5i4 i 8] 4 i 6 5i Multiply each complex number with its conjugate & write the result in standard form 9] 5 6i 0] i ] 4 i Write each complex number in standard form 7 i ] ] i i 4] i i 5] i 4i 6] 6 i Solve using quadratic Formula 7] x 4x 9 8] x 8x9 5 The examples below show how to write the solution to an inequality in interval notations Also, interval notations are used to express the domain, range, increasing, & decreasing intervals of a function Real Number Line Graphs Interval Notation Inequality , Set of all real #s x such that x,,, Set of all real #s x such that x, Set of -5 all -4 real -#s x - such - that 0 x,, Set of all real #s x such that x, Set of all real #s x such that x, PAGE 4 x

5 Enochs Pre-AP SM Summer Assignment 07-8 Solving Linear Inequalities Solve each Inequality algebraically & write the solution in Interval Notation x ] x 6x 8 ] 5 x 7 ] 5 x 6 4x 4 4 5] x x x 6] 8 x 7 7] 6 8 4] 4 7 x 8] x 5x Graphing Functions and Analyzing their Details ] y x ] f ( x) x Zero(s): 4 y-intercept: Domain: Range: Zero(s): y-intercept: Domain: Range: ] x 4] y Zero(s): y-intercept: Domain: Range: Zero(s): y-intercept: Domain: Range: PAGE 5

6 Enochs Pre-AP SM Summer Assignment ] y x 4 6] y x Zero(s): y-intercept: Domain: Range: Zero(s): y-intercept: Domain: Range: y 8] y x 7] x 4 Zero(s): y-intercept: Domain: Range: Zero(s): y-intercept: Domain: Range: 9] y x 5 Zero(s): 0] y x 4x 5 y-intercept: Domain: Range: Zero(s): y-intercept: Domain: Range: PAGE 6

7 Enochs Pre-AP SM Summer Assignment 07-8 y ] y x ] x 4x 6 ] ( x ) ( y ) 6 Zero(s): y-intercept: Domain: Range: Zero(s): 6 6 Zero(s): y-intercept: Domain: Range: y-intercept: Domain: Range: 4] x x) x x ( x f 5] x x 5 f ( x) x 8x,,, x x x 4 Zero(s): y-intercept: Domain: Range: PAGE 7 Zero(s): y-intercept: Domain: Range:

8 Enochs Pre-AP SM Summer Assignment 07-8 Sequences/Functions Determine if the pattern given is linear, exponential, quadratic, or neither Next, give the recursive & explicit equations Figure Figure Figure Figure 4 Type of Sequence: Recursive Rule: Explicit Rule: At the beginning Day One Day Two Type of Sequence: Recursive Rule: Explicit Rule: Describe the pattern of change or rate of change for a linear, exponential, and a quadratic function Linear- Exponential- Quadratic- 4 Which type of function grows the fastest? x5 6x 5 8 Fraction Operations (Answers in Reduced Form) 7 5n 9n 8n 4x x 0 4x 4 8x x 6 7x For 7-8, write as a single fraction PAGE x + 0x 8 5 4x 4 6x

9 Enochs Pre-AP SM Summer Assignment 07-8 Quadratic Functions Use each function to identify the vertex, intercepts, vertical stretch, and graph it y x x 0 4 y x x vertex: x-intercepts: y-intercepts: stretch or compress: y x vertex: x-intercepts: y-intercepts: stretch or compress: 6 vertex: x-intercepts: y-intercepts: stretch or compress: Write the equation in vertex form 5 y x x y x x 7 7 y x x 9 Inverse Functions Find the inverse of the function, graph both the original function and its inverse on the graph provided f ( x) x Find the inverse of the given function f x x f x x 5 PAGE 9

10 Enochs Pre-AP SM Summer Assignment 07-8 Absolute Value Functions Graph the absolute value function and write it as a piecewise function Absolute Value: f x x Absolute Value: f ( x) x 4 { { Piece-Wise: f( x) Piece-Wise: f( x) Right Triangle Trigonometry Use the figure to write the following trigonometric ratios sin( A) cos( A) tan( A) 4 sin( B) 5 cos( B) 6 tan( B) Solve the right triangles (list all side and angle measures for the triangle) 7 A 8 X Y C B 8 A 4-foot ladder forms a 65 angle with the ground The top of the ladder rests against a building Draw a diagram to find to how high up the building the ladder is to the nearest hundredth of a foot PAGE 0

11 Enochs Pre-AP SM Summer Assignment 07-8 Radian & Degree Measure Write the radian measure of the angle given in degrees Write the degree measure of the angle given in radians 6 π 7 π 8 π 9 π 4 0 9π 4 For problems &, find the arc length and sector area in degrees Give EXACT answers PAGE

12 Enochs Pre-AP SM Summer Assignment 07-8 You are advised to use the next few pages of examples to help refresh your memory or relearn the essential mathematical skill that you may have not fully mastered Simplifying Radicals Solving Absolute Value Equations Factoring PAGE

13 Enochs Pre-AP SM Summer Assignment 07-8 Solving Equations by Factoring Multiplying Rational Expressions PAGE

14 Enochs Pre-AP SM Summer Assignment 07-8 Dividing Rational Expressions Adding & Subtracting Rational Expressions PAGE 4

15 Enochs Pre-AP SM Summer Assignment 07-8 Law of Exponents Multiplying Monomials Multiplying Polynomials Dividing Monomials PAGE 5

16 Enochs Pre-AP SM Summer Assignment 07-8 Graphing a Piecewise Function Solution graph Greatest Integer Funtion PAGE 6

17 Enochs Pre-AP SM Summer Assignment 07-8 Quadratic Function (Polynomial of degree ): Shape of the graph of a quadratic function is a Parabola Three parabolas are shown below with important points labeld The graph of a quadratic funciton: - can open either upward or downward - always has a vertex which is either the maximum or minimum - always has exactly one y-intercept - can have 0,, x-intercepts * A parabola is symmetric about a line through the vertex called the axis of symmetry * A quadratic function can be written in Transformation Form which is f x y abx h k h * In Transformation Form, the vertex is, k b and line of symmetry is h x b * A quadratic function can be written in Polynomial Form which is f x y ax bx c b b * In Polynomial Form, the vertex is, f a a and line of symmetry is b x a Changing from Polynomial Form to Transformation Form PAGE 7

18 Enochs Pre-AP SM Summer Assignment 07-8 Nine Basic Funcitons of Algebra PAGE 8

19 Enochs Pre-AP SM Summer Assignment 07-8 Complex Numbers: The complex number system contains a number, denoted i, such that i Every complex number can be written in standard form a bi PAGE 9

20 Enochs Pre-AP SM Summer Assignment 07-8 Logarithmic Rules Composition of Fucntions: PAGE 0