Clearview Regional High School District Summer Assignment Coversheet

Transcription

1 Clearview Regional High School District Summer Assignment Coversheet Course Honors Pre-Calculus Mathematics Ms. Mary Marks Supervisor Due Date Thursday 9/6 Grade Category Weight for Q1 Common Core and/or NJ Core Curriculum Content Standards covered Description of Assignment Purpose of Assignment Specific Expectations Students will take a quiz on the material in the packet. The quiz will tentatively be scheduled for Monday, September 10 th, after opportunity has been provided in class to go over questions that students may have. Algebra: Expressions (A-SSE 1, 2, ), Operations with Monomials and Polynomials (A-APR 1,, 6), Equations (A-CED 1, 2, ), and Reasoning (A-REI 1, 2,, 4, 5, 6, 10) Functions: Interpreting (F-IF 1, 2, 4, 6, 7, 8), Building (F-BF 1), Linear and Quadratic Models (F- LE 2) Algebra Review Packet in preparation for Honors Pre-Calculus The purpose of Honors Pre-Calculus is to prepare students for a college-level Calculus course. The skills contained in this packet are prerequisite skills that they should know from their previous math courses. If they find they are deficient in any of these skills, they may want to seek additional practice prior to the start of school. The packet should be completed prior to the start of school. Solutions should be checked once they are posted in August. Students should practice with skills that they find they are deficient in prior to the start of school and mark any questions that they have for the teacher. Time will be allotted in class for questions about problems in the packet, but not for the complete re-teaching of the skills in the packet.

2 Where to Locate Assignment Helpful Resource(s) District Website Khan Academy: IXL.com: (20 problems per day can be practiced for free) The Virtual Mathlab: hlab/ Math.com: SOS Mathematics: Algebra Help: See you in September!

3 Clearview Regional High School Math Department Summer Course Work Honors Pre-Calculus Name The purpose of Honors Pre-Calculus is to prepare you for a college-level Calculus course. The skills contained in this packet are prerequisite skills that you should know from your previous math courses. If you find you are deficient in any of these skills, you may want to seek additional practice prior to the start of school. You will be quizzed on the material in this packet the first week of school. I will be available to answer questions prior to the quiz the first few days of school. Solutions will be posted the last Monday in August. 1. (x 2 + )(x 7) I look forward to meeting you in September! FOIL PRACTICE: (First, Outside, Inside, Last) 2. (x 4)( x 2 + x 5). (-2x + 1)(x ) 4. (5x 6)(-x + ½) 5. ( 2 + x)( 8 x)

4 FACTORING PRACTICE Factor each. 1. y 2 12y x 2 25y 2. 12z 2 z p 51p 2 15p 5. 6a b a 2 b 210ab 4 Simplify. RATIONALIZING RADICALS xy x

5 Solve by using the substitution method. SOLVING SYSTEMS OF EQUATIONS 1.) 2x + y = 4 2.) y = x 27 x + 2y = 1 y = ½ x 7 Solve by using the elimination method..) u + 5v = ) 2a b = 8 2u v = -8 6a b = -9 SIMPLIFYING SQUARE ROOTS 1.) ) 15 1/.) 20x 2 4.) )

6 LINEAR EQUATIONS Standard Form Put the following equations into standard form. 1. y 5 = 0 2. y = 2 x x + y = (x + 2) 7(y 4) = 2x Slope-Intercept Find the slope-intercept form of an equation of the line that has a slope of and passes through. 5. slope - 2 1, passes through (2,-) 6. slope 4, passes through the origin Graph the following equations. GRAPHING EQUATIONS 7. 2x + 5y = x 4 - y = 2

7 9. 4y = x 10. 5x + 6y = 4x 2 PARALLEL AND PERPENDICULAR LINES Write an equation in slope-intercept form of the line that passes through and is perpendicular to the line whose equation is. 11. passes through (-9,5), equation y = -x passes through (4,6), equation y = x +

8 Solve for x in each equation: SOLVING LINEAR EQUATIONS a. (2x 5) 1 = -2(x + 4) b. 4x 2 = 5x 1 c. t x p m = y d. 2x 12y = 10 e. 2 x = 4

9 Standard Form Put the following equations into standard form. 1. f(x) = 2(x 1) 2 5 QUADRATIC EQUATIONS 2. f(x) = -(x + 2) 2 + Graphing Quadratics Identify the vertex, axis of symmetry, direction of opening, and y-intercept for each quadratic equation given and then graph below.. f(x) = -2x 2 4x + 4. f(x) = (x ) f(x) = -x

10 SOLVING QUADRATIC EQUATIONS Remember that quadratic functions can be solved in a variety of ways, by graphing, factoring, completing the square, and the quadratic formula. You must be comfortable determining the most appropriate method and solving. Solve the following x 2 = x 2-10x + 25 = 0. x 2 5x = x 2 + x 28 = x 2 11x = x 2 + 7x 1 = 0

11 MANIPULATING RADICALS Simplify the following. Express in radical form. 1) 4 4 b 2) a b c ) 8 z b 4) 2 64 a b 6 9 b 5) 4 a 6) a b 4 c

12 ( a ) m n n a a a b b mn n n EXPONENT RULES a a a n m n a nm 1 n a ( ab) n a n b n m n n m n a a or a m You are expected to know the above rules. Use them to simplify the following. Answers may not be expressed with negative exponents! 1) 2x 6x 2 7 y y 4 5 t t m p k 2) p k m ) x y 2 4x 4) 1 2 2x 6 x y x t 5) x t x p 6) 2 6 x p

13 DISTANCE AND MIDPOINT You are expected to have the distance and midpoint formulas memorized from Algebra 2. A rectangle has vertices located at A(2,1), B(10,1), C(10,16), and D(2,16). A. What is the horizontal width of the rectangle from A to B? B. What is the length of the diagonal AC? C. What are the coordinates of the point midway between A and D? D. What are the coordinates of the intersection of diagonals AC and BD? E. What is the slope of diagonal BD? F. What is the slope of a line perpendicular to diagonal AC?

14 A significant portion of this course will be calculator-free. You may want to brush up on basic arithmetic without the use of a calculator. FRACTIONS Complete without a calculator. Leave all answers as simplified fractions. a x x b. + 8 c. 4 x 9 x 4 x 9 8 d. 5q8 25q6 9p 5 10p 5 e. ( p mt ) ( pt m ) f. x x x 2 4

15 OPERATIONS Simplify #1-16 without the use of a calculator (5-) 2. ( ). Find the value of 2X 2 X-4 when X = - Subtract: (-0.8) (-1.1) ( 1) ( 2) Multiply: (-12.8) (-12.1) Divide Add: