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Honors Precalculus Summer Review Packet TO: All 2012-2013 Honors Precalculus Students FROM: Honors Precalculus Teachers East: Mr. Gierut – Room 301 Mr. Russ – Room 494 Kevin Volk – Room 352 West: Ms. Cicero – Room C 203 Mrs. Radek–Carreón – Room C 207 We are pleased that you have chosen to continue your math sequence by enrolling in Honors Precalculus for next year. To help ensure your success in Honors Precalculus next year, we have created a summer review work packet. This packet contains material that you must have knowledge of on the 1st day of the course. The packet has problems from Algebra, Geometry, and Advanced Algebra. THIS PACKET IS TO BE COMPLETED IN THE FOLLOWING MANNER: Work must be clearly enumerated and in consecutive order on separate paper. Each problem, with work, counts toward the total grade. Each problem must have WORK! NO WORK =NO CREDIT THE PACKET WITH WORK IS DUE ON THE FIRST FULLDAY OF SCHOOL. THE PACKET IS DUE WHETHER OR NOT YOU ARE PRESENT IN SCHOOL. THE PACKET HAS BEEN DIVIDED IN TO THE FOLLOWING CATEGORIES: Inequalities Linear Equations Linear Systems Quadratics Domain & Range Operations with Exponents Rational Expressions Right Triangle Trigonometry HELPFUL HINTS TO COMPLETING THE PACKET OVER THE SUMMER: Do little of the math packet each day – you are not expected to complete it all in one day Pace yourself, plan to do a portion each week. Resources you may want to use: Use your Algebra, Geometry, or Advanced Algebra notes. khanacademy.org purplemath.com mathforum.org wolframalpha.com Honors Pre-Calculus Supplies Needed: Pencils/Erasers Binder/Notebook Paper Graphing Calculator ***** It is recommended that you have a graphing calculator every day in class and at home. If you don’t already have a TI-83, TI-84, or TI-Nspire and are going to purchase a graphing calculator, we recommend the TI-Nspire CX which will be used extensively in class. Honors Precalculus Summer Review Packet This packet is a review of information you learned in Algebra, Geometry, & Advanced Algebra. You need to know this information to be successful in Precalculus. Therefore, this packet is due on your FIRST DAY IN PRECALCULUS. It is to be completed CORRECTLY, NEATLY, and onSEPARATE sheets of paper. Your Precalculus teacher will collect your work on your FIRST DAY IN PRECALCULUS. Failure to turn in your completed work on your FIRST DAY IN PRECALCULUS may jeopardize your ability to remain in the course. INEQUALITES Solve the following inequalities. 1. 1 4 2. −6 < 4𝑞 − 1 < 0 (𝑥 + 3) − 4𝑥 ≤ 3(1 + 𝑥) 3. 𝑥 2 + 2𝑥 − 35 ≥ 0 4. 𝑥 2 − 5𝑥 ≤ −6 LINEAR EQUATIONS Write the appropriate Linear Equation for each of the following. 5. The point-slope form given (–5, 8) with m= –4. 6. The standard form given (–4,4) & (5,2). 7. The slope-intercept form given (–2, –3) & (8, –1). 8. The slope-intercept form given (6,–5) & perpendicular to –7x–5y= –17. 9. The standard form of the line parallel to the given line y=2x. LINEAR SYSTEMS Solve the following Linear Systems. 10. 2x + 9y – 5 = 0 11. y – 8 = –4(x+5) 5y – x = 26 4x + y = –28 2 7 12. 𝑦 = 3 𝑥 + 3 6y – 4x = 14 13. An apartment building contains 12 units consisting of one-and two- bedroom apartments that rent for $360 and $450 per month, respectively. When all units are rented, the total monthly income is $4,950. What is the number of two-bedroom apartments? 14. For what value of b wouldthe following system of equations have an infinite number of solutions? 3x + 4y = 14 6x + 8y = 7b QUADRATICS Solve by completing the square. 15. x2 + 3x – 9 = 0 16. 49x2 + 15 = 56x Solve the equation using the quadratic formula. 17. x2 – 14x + 40 = 2x2 – 16x + 32 18. 𝑥 2 − 3 = √5𝑥 Solve the equation by factoring. 19. 28x2 + 26x = 0 20. 25x2 + 35x + 12 = 0 Solve by using your Graphing Calculator. 21. x2 – 9x = –18 22. 12x2 + 25x – 2 = –14 DOMAIN & RANGE Determine the domain and range of the following relation or function. 23. (1,2), (8,3), (9,6), (2,5) 24. y + 2x = 3 25. y + 3x2 = x – 2 27. 𝑦 = 8 − |𝑥| 26. 𝑦 = √𝑥 − 3 + 2 OPERATIONS WITH EXPONENTS Simplify the following expressions; assume no variable is equal to zero. 28. (4𝑥 3 )−2 29. 2 6 (𝑥 −3 ) 30. 5𝑥 3 𝑦 9 20𝑥 2 𝑦 −2 31. 𝑥𝑦 9 −7𝑦 ∙ 3𝑦 −2 21𝑥 5 32. (𝑥 2 3 𝑦) (𝑥 −2 𝑦) 1 2 RATIONAL EXPRESSIONS Factor and/or Reduce the following Rational Expressions. 33. If 𝑥 > 2, then 1 𝑥 34. If𝑎 ≠ 𝑏and + 𝑥 2 −𝑥−6 𝑥 2 −4 1 1 = , then 𝑎 𝑏 x=? 35. For which nonnegative value of x is the expression 4+𝑥 16−𝑥 2 36. 3𝑥 2 +7𝑥−6 9𝑥 2 −4 undefined? ( 15𝑥 2 +4𝑥−4 9−𝑥 2 ) RIGHT TRIANGLE TRIGONOMETRY Using right triangle trigonometry, determine the measure of the missing side or angle. 37. 38. 39. 40. Find to the nearest degree, the measure of the smaller acute angle of a right triangle whose sides are 8, 15, and 17. 41. A man standing 30 feet from a flagpole observes the angle of elevation of its top to be 48◦. Find the height of the flagpole to the nearest tenth.