Ellington High School Principal

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1 Mr. Neil Rinaldi Ellington High School Principal 7 MAPLE STREET ELLINGTON, CT 0609 Mr. Dan Uriano (860) 896- Fa (860) Assistant Principal Mr. Peter Corbett Lead Teacher Mrs. Suzanne Markowski Guidance Director Mr. Tim McCluske Athletic Director Where Children Come First Summer Review For Students Entering Academic Pre Calculus We believe in creating a challenging academic environment. All students should gain the skills and knowledge to prepare them for a lifetime of learning in a rapidl changing global communit. We epect all members of our learning communit to demonstrate responsibilit, integrit, respect, cultural understanding, and ethical behavior. It has been discovered that students regress in skills over the summer months. To help ou succeed net fall- and perhaps to help ou learn some lessons that ou did not master the first time through we have prepared the following set of math eercises to be completed over the summer. Your high school mathematics courses are cumulative. This means that ou will need to utilize concepts previousl learned to be successful. The reason for this review is to reacquaint ou with necessar skills to be successful in net ear s math course. It is clear that most students do not want to spend their entire summer doing math work. Based on how fast or slow ou work, ou ma find that ou onl need to do math a few das each week. Working on this set of math eercises will be most effective if ou do work throughout the summer, so tr not to skip weeks. This assignment will be due the first da of school. This assignment will also serve as a basis of preparing for a review assessment which will be given during the first week of school. If ou do not perform as epected, ou will need to sta after school to continue our review of these topics. Should ou misplace this set of math eercises, ou will be able to print another cop off the EHS website.

2 PRE-CALCULUS (Academic) Summer Work and List of Topical Understandings For students to successfull complete the objectives of the Pre-Calculus curriculum, the student must demonstrate a high level of independence, capabilit, dedication, and effort. This summer packet will help ou maintain/improve our skills. This packet is a requirement for those entering the Pre-Calculus course and is due on the first da of class. Your attempt to complete this packet b the first da will be combined with a pre-test on the material to form our first grade of the Pre-Calculus course. Complete as much of this packet on our own as ou can, then get together with a friend, our teacher, or google the topic. (math.com is also a good resource) SHOW YOUR BEST WORK. Requirements The following are guidelines for completing the summer work packet You must show all of our work on a separate piece of paper. Be sure all problems are neatl organized and all writing is legible. We epect ou to come in with certain understandings that are prerequisite to Pre-Calculus. A list of these topical understandings is below. Topical understandings within summer work Factoring Zeros/roots/-intercepts of rational and polnomial functions Simplifing radicals and comple numbers Completing the square Write the equation of a line Quadratic formula Composite function and notation Domain/Range Interpreting and comprehending word problems. Finall, it is suggested to not wait until the last two weeks of summer to begin on this packet. If ou spread it out, ou will most likel retain the information much better. Once again, this is due, completed with qualit, on the first da of class. It is intended to help ou be successful in the coming ear.

3 Problem Set of Required Math Skills for Pre-Calculus (Academic) Skill : All students should be able to complete operations involving fractions and recall eponent facts quickl and accuratel without the use of a calculator (-) (-) -6. (-). = 6. = -7.. = -7 0 Simplif Skill : All students should be familiar with all concepts of graphing linear equations in various forms, including graphicall, in equations (slope-intercept, point-slope and standard form) and formulas, and numericall in a chart of ordered pairs. Graph each of the following: f. ( ).. ( ). = =

4 Find the slopes of the lines described. 7. The line passing through 8. The line = (-, 6) and (, -9). 9. The line with intercept and 0. An line parallel to intercept -.. An line perpendicular to.. An horizontal line.. The line = 0.. The line through (9, ) and (9, -). Write the equation of each line indicated. Give answers in slope-intercept form.. The line passing through 6. The line passing through (-, 6) and (, -9). (, ) and (-6, ). 7. The line with intercept and 8. The line parallel to intercept -. and containing (, ). 9. The line graphed below. 0. A linear function for which f() = 7 and f(-) =. Shade the half-plane that represents the solution to the linear inequalit... 6.

5 Skill : All students should be able to solve a sstem of equations. Solve using substitution, elimination, or graphing Skill : All students should be able to multipl, factor add and subtract polnomials and to use these skills to simplif epressions and solve equations involving quadratic, polnomial, and rational terms. Factor:. b b 6. t 7t m n z z Multipl, Add, subtract or divide z t v z Solve:. ( ) ( 8) =

6 Skill : All students should be able to appl the rules of eponents to simplif and epand epressions, evaluate epressions and to solve equations. (Give answers with no negative eponents) Simplif:.. t v t v n w z t. 9. v v 6. If g( ) then find: a. g(-6) b. g() c. g(0) d. g(a) e. g( - ) 7. Given the following functions, f ( ) and g ( ), find: a. f (g()) b. g(f())

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