Mr. Neil Rinaldi
Ellington High School
Principal 37 MAPLE STREET
ELLINGTON, CT 06029 Mr. Dan Uriano (860) 896-2352 Fax (860) 896-2366 Assistant Principal Mr. Peter Corbett Lead Teacher Mrs. Suzanne Markowski Guidance Director Mr. Tim McCluskey
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 rapidly changing global community. We expect all members of our learning community to demonstrate responsibility, integrity, respect, cultural understanding, and ethical behavior.
It has been discovered that students regress in skills over the summer months. To help you succeed next fall- and perhaps to help you learn some lessons that you did not master the first time through – we have
prepared the following set of math exercises to be completed over the summer. Your high school mathematics courses are cumulative. This means that you will need to utilize concepts previously learned to be successful. The reason for this review is to reacquaint you with necessary skills to be successful in next year’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 you work, you may find that you only need to do math a few days each week. Working on this set of math exercises will be most effective if you do work throughout the summer, so try not to skip weeks.
This assignment will be due the first day 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 you do not perform as expected, you will need to stay after school to continue your review of these topics.
Should you misplace this set of math exercises, you will be able to print another copy off the EHS website.
PRE-CALCULUS (Academic)
Summer Work and List of Topical UnderstandingsFor students to successfully complete the objectives of the Pre-Calculus curriculum, the student must demonstrate a high level of independence, capability, dedication, and effort. This summer packet will help you maintain/improve your skills. This packet is a requirement for those entering the Pre-Calculus course and is due on the first day of class. Your attempt to complete this packet by the first day will be combined with a pre-test on the material to form your first grade of the Pre-Calculus course. Complete as much of this packet on your own as you can, then get together with a friend, e-mail your 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 your work on a separate piece of paper.
Be sure all problems are neatly organized and all writing is legible.
We expect you 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/x-intercepts of rational and polynomial functions Simplifying radicals and complex numbers
Completing the square Write the equation of a line Quadratic formula
Composite function and notation Domain/Range
Interpreting and comprehending word problems .
Finally, it is suggested to not wait until the last two weeks of summer to begin on this packet. If you spread it out, you will most likely retain the information much better. Once again, this is due, completed with quality, on the first day of class. It is intended to help you be successful in the coming year.
Problem Set of Required Math Skills for
Pre-Calculus (Academic)
Skill 1:
All students should be able to complete operations involving fractions and recall exponent facts quickly and accurately without the use of a calculator.
1. 1 1 2 4 2. 2 5 2 3 3 3. 4 20 5 7 4. 3 1 5 2 5. 16 2 3 6. 5 2 7 7. 1 5 15 8. 7 1 16 20 9. 2 1 1 3 2 10. 2 3 4 11. 1 3 2 12. 0 5 7 13. 82 14. 53 15. 6-3 16. 25 17. -34 18. (-3)-4 19. 2 33 20. (-2)-6 21. (2-5)3 22. x2 = 16 23. x3 = -27. 24. x2 – 1 = -7 Simplify 25. 300 26. 192 2 27. 18 2 28. 3 1 2 2 Skill 2:
All students should be familiar with all concepts of graphing linear equations in various forms, including graphically, in equations (slope-intercept, point-slope and standard form) and formulas, and numerically in a chart of ordered pairs.
Graph each of the following:
1. 1 5 4 ) (x x f 2. y 1 2(x 4) 3. y 4 x 1 4. 4x – 3y = -12 5. x y 5 6. x = 4
Find the slopes of the lines described.
7. The line passing through 8. The line 4x – 2y = 5 (-1, 6) and (4, -9).
9. The line with x intercept 3 and 10. Any line parallel to
y intercept -2. 2 4 3 x y
11. Any line perpendicular to. 12. Any horizontal line.
1 5 2y x
13. The line x = 0. 14. The line through (9, 1) and (9, -4).
Write the equation of each line indicated. Give answers in slope-intercept form.
15. The line passing through 16. The line passing through
(-1, 6) and (4, -9). (4, 2) and (-6, 2).
17. The line with x intercept 3 and 18. The line parallel to
y intercept -2. y 2x 2 and containing (4, 1).
19. The line graphed below. 20. A linear function for which
f(1) = 7 and f(-1) = 5.
Shade the half-plane that represents the solution to the linear inequality.
Skill 3:
All students should be able to solve a system of equations.
Solve using substitution, elimination, or graphing.
1. 3 3 18 4 5 x y x y 2. 3. 2 3 8 5 2 1 x y x y Skill 4:
All students should be able to multiply, factor add and subtract polynomials and to use these skills to simplify expressions and solve equations involving quadratic, polynomial, and rational terms.
Factor: 1. 2 11 26 b b 2. t2 17t 30 3. x2 81 4. 2 12 25 36m n 5. 5x2 7x 6 6. 100x2 75 7. 2 3x 5x 2 8. 9 + 8x – x2 9. x3 64 10. xy xz 4y 4z 11. 4x2 8x 4 12. x6+ 5x3y2 - 24y4
Multiply, Add, subtract or divide.
13. 2 2 2 2 3x y 2xy 7xy 4x y 2xy 8xy 14. 2x 1 2 15. 5 2 5 2 5 3 5 3x yz x yz 16. 3x 13 17. 2 4 4 x x y y 18. 2 4 8 2 2 x x x x 19. v t 4 2 20. 2 3 4 5 2 x x 21. xy y x x y x 2 1 22. 32 2 5 2 4 6 2 x x x x Solve: 23. 3x(x – 1) – x(x – 8) = 3 24. 2 2x 7x 15 25. 2 4x 20 26. 2 14 45 0 x x 27. 2 144 0 x 28. 3 5 0 x x 29. 2 4 10 0 x x 30. 3x2 8x 5 0 31. 2 4x 7x 6 0 32. 4 2 17 16 0 x x 2 3 1 x y 12 2 3y x
Skill 5:
All students should be able to apply the rules of exponents to simplify and expand expressions, evaluate expressions and to solve equations. (Give answers with no negative exponents)
Simplify: 1. 8 n 3 x x 2. 2 1 4 49 3. 4 3 2x 4. 3 12 y y 5. 2 2 4 y y x 6. 1 0 3 5 z w y x 7. 65 72 v t v t 8. y x x 2 9. v v t 1 10. 2 4 x 11. x 5 2 12. 9 2 3 2 x x 13. 3 5 6 14. 2 2 1 x 15. 2 3 3x 16. If 2 ( ) 5 12 g x x x then find: a. g(-6) b. g(2) c. g(0) d. g(3a) e. g(x - 2)
17. Given the following functions, f(x) 3x 22 1 and
5 3 2 ) ( x x x g , find: a. f(g(2)) b. g(f(2))
