Name: PreCalculus (Level 1 & Honors) Summer Assignment

Transcription

1 o PreCalculus (Level 1 & Honors) Summer Assignment Name: Welcome to the start of your PreCalc experience! It s going to be an exciting journey. Over time PreCalculus teachers have come to realize that students struggle, not with the PreCalculus part of many problems, but with the Algebra 1 and Algebra 2 parts and skills that have been forgotten or need more practice. If you can come to PreCalculus next year confident that you can do all the problems in this assignment and other problems of this type, you will be off to a great start! What comes next will then be dependent on our collective efforts. You are reuired to complete this packet prior to the first day of school. I will NOT be collecting and grading this packet. I will check it for completion and we will review the correct answers. You will have a UNIT 1 TEST on the material during the first week of school. If you are unsure about how to complete a uestion, remember! All of this content came from Algebra 1 and Algebra 2. Use old notes, watch tutorial videos online, use KHAN Academy and/or work with your classmates! If you lose this copy there will be extras left in Guidance; it is your responsibility to get a new one and complete it on time! You can also access a digital copy by visiting the East Hartford High School main page ( In addition to having a Unit 1 Test on this content during the first week, your completion of this Summer Assignment will count as your first uiz grade of Quarter 1. You must SHOW ALL YOUR WORK to receive full credit. If you have any uestions over the summer either on this packet or about the course in general, please do not hesitate to one of the PreCalculus teachers listed here: PreCalc Honors: blaisdell.kl@easthartford.org (Ms. Kelly Blaisdell) PreCalc Level 1: beauchamp.jm@easthartford.org (Ms. Jenae Beauchamp) beauchamp.na@easthartford.org (Ms. Nicole Beauchamp) Once you have your schedule, please the following information to your teacher. ing this information acknowledges receipt of the packet and an understanding that completion of this prereuisite assignment is a reuirement for PreCalculus (Level 1 and Honors). The completed packet is due on the first day of class. A test of the material will happen the first week of school. Name: Grade: Favorite part of math class: Least favorite part of math class: Parent/guardian Name and Something uniue about yourself: School activities and/or hobbies: *** Reuired materials for PreCalculus (Level 1 and Honors) TI 84 (recommended) or TI 83 Graphing Calculator o Level 1 Reuired: Only a few are available to sign out for the year for special circumstances, not enough for all. Must purchase your own if possible (approx. $ from Amazon/Walmart). Honors Optional: Class set available for use in-class only. These stay in the classroom, it is strongly recommended you purchase your own for personal use. Pencils and erasers Different color pens or highlighters (strongly recommended) Level 1 Reuired: 1.5inch or 2inch 3-ring binder with loose-leaf lined paper

2

3 Section 1.1: Linear Functions 1. Calculate the slope given the graph or points on the line: a. b. The line passes through (-11, 0) and (4, -5) 2. Write the euation of the line that contains the point (-8, -2) and has a slope of Write the euation of the line that contains the points (2, 7) and (-4, -5) in all three forms. Slope-Intercept Form: Point-Slope Form: : Standard Form: : 4. A car initially is filled with 16 gallons of gas. On a long highway trip, gas is used at the rate of 2 gallons per hour. Write a linear model to represent the amount of gas in the tank, y, based on the number of hours elapsed, x.

4 5. Determine if the lines are parallel, perpendicular, or neither. a. Line 1 contains (4, 5) and (-16, 5) b. 4 x 2y = 18 Line 2 contains (1, 5) and (1, 21) 6x + 3y = Graph each of the following. a. y + 2 = 3( x 1) b. y = 2 x Suppose Line A can be graphed with the following euation: 4 12=. a. Write the euation of a line that is parallel to Line A and passes through the point (16, 3). b. Write the euation of a line that is perpendicular to Line A and passes through the point (0, 5).

5 8. For 1986 through 1991, retail sales of American bookstores increased at a rate that was approximately linear. In 1986, the retail sales were $4.9 billion. In 1991, the retail sales were $7.9 billion. a. Write a linear model for the retail sales, y (billions of dollars), based on the year, x. b. Use your model to predict the amount of retail sales in c. Based on your model, when will the retail sales reach $20 billion? Section 1.2: Functions 1. Does the following table represent a function? Explain your reasoning. Input (x) Output f(x) Given the function f(x), evaluate f (x 4) = Use the function below to answer the following: = +5, , >1 a. 6 b. 2

6 4. Find the values of such that =0. = For each graph shown answer each of the following: a. Is it a function? b. What is the domain? c. What is the range? Function? Domain? Range? Function? Domain? Range?

7 Section 1.3: Graphs and Functions Analyzing Graphs of Functions Use the graph above to answer each of the following uestions: 1.) Evaluate f(2). 2.) Identify the coordinates (points) for any zeros of the function (x-intercepts). 3.) Provide the coordinates of any y-intercepts of the function. 4.) Over what interval(s) is the function constant? 5.) Over what interval(s) is the function increasing? 6.) On what interval is the function decreasing? 7.) State the domain of the function. 8.) State the range of the function. 9.) For what value(s) of x is f(x) = 1?

8 Section 1.4: Shifting, Reflecting, and Graphing Functions 1. For each euation below, identify the shape of the graph (either in words or with a picture). Then, describe any shifts (left/right or up/down), or reflections, in your own words. a) = +1 b) h = 5 c) = Sketch each of the parent functions below. a. = b. = c. h = 3. Graph each of the functions below. a. = 4 +3 b. h = 2 2

9 1.5: Combinations of Functions 2 1. Find f + g x andb + ggbg 4 for fbg x = 3x + x 3 and b gbg f gbg x = 3 + 4x + 5x 2. F HG I f x KJbg bg = bg = f 2 2. Find x for 16 x and g x 4 x. Simplify your answer. g 1.6: Inverse Functions 1. Given f(x), find the coordinates of its inverse. Use appropriate notation. f(x) = {(4, -1), (-2, 2), (-7, 0)} 2. Explain the relationship between the domain and range of a function, f(x), and the domain and range of its inverse,. Be thorough and use appropriate vocabulary. 3. Find the inverse,, of each given function. a. f(x) = 4 b. f(x) =! 3

10 c. = "# $ d. = %" e. h = f. & = "' $ Section 2.1: Quadratic Functions 1. Given the function, answer each of the following: = 4+3 a. Does the parabola open up or down? How do you know? b. Find the coordinates of the vertex of the parabola. c. Find the x-intercepts of the function. d. Find the y-intercept of the function. 2. Convert the uadratic to standard form (( +)+*: h ( x) = 6( x + 4) 2 + 3

11 PreCalc Summer Packet CONT. T v2n0g1r8c lkuuqtaax vsso[fjtzwfaorlee CL]LgC\.g Z ^AClvlI r^iegrhptysc yrsedszeurkv_etde. Show ALL work on seperate paper (lined, blank, or graph paper) Simplify. 1) (5 + 8i)(5-2i) 2) (-7i)(-1-4i) + 8(7i) ID: 1 3) (-4i)(-4-7i) + 5(-3 + 6i) 4) (-4i)(5 + 8i) - (i)(1-6i) Simplify each expression. 5) 7n3-70n 2 6n - 54 n2-16n n ) 2a2-2a 2a 2 + 4a a2 + 4a - 12 a 2-4 7) 5x x x x x ) x + 3 9x 2-45x 9x2-90x 7x ) m 2-16 m 2-4m - 32 m2 + 3m - 28 m 2 + 8m ) p + 7 p 2-8 p + 12 p2-9 p + 14 p 2-49 Solve each euation. 11) 243 2m + 2 = 27 12) 3 2 p - 2 = ) 3 n + 3 = ) 8-3v = 64 15) log 2 (x - 7) + log 2 10 = 4 16) log 7 3x 2 - log 7 3 = 4 17) log 7 4x 2 + log 7 9 = 4 18) log 7 x - log 7 (x - 2) = 1 19) log 8 2x 2 - log 8 2 = 2 20) log log 6 (x - 2) = 4 Condense each expression to a single logarithm. 21) log 7 a + 5 log 7 b + 3 log 7 c 22) 2 log 9 u - log 9 w - 6 log 9 v 23) 12 log 3 z + 12 log 3 x - 3 log 3 y 24) log 7 b + log 7 c + log 7 d + log 7 a 2 c K2O0a1Q8J dkru_tiat YSpopfEtIwoakrwew UL`LrCa.[ S fawlplg XrWiDgmhOtos\ DrMeos\eGrBvgeQdQ.R PMiaadEe_ ZwiiMtAhb LILnVfaiRn]iwt^ed eawldgeekbur`ap M2u. -1- Worksheet by Kuta Software LLC

12 Expand each logarithm. 25) log 9 (z xy 3 ) 2 26) log ( z 6 3 x y) 27) log 7 ( ) 28) log Divide. 29) (6x x x 2-22x + 10) (x + 5) 30) (3 p 3-15 p 2-26 p + 43) ( p - 6) Factor each (Factoring "Tool Box": Basic factoring, Quadratic Formula, Factor by Grouping, "Quadratic-Like", Sum/Difference of Cubes). 31) x 6 + 4x 4-25x = 0 32) x 3 + 5x 2-5x - 25 = 0 33) x x = 0 34) x 4-14x = 0 35) x 4 + x 3-12x 2 = 0 36) x x = 0 37) x 3-3x 2 + 3x - 9 = 0 38) x = 0 Sketch the graph of each function. 39) f (x) = 1 2 x2 + 4x y 40) f (x) = -2(x + 1) 2-2 y x x Find the measure of each angle indicated. Round to the nearest tenth. 41) C 42) C A B B A B f2b0u1p8^ dkfuct\ai HS`oYfet\wJaarDeB SLPLCF.z W \AJlJlT lrkiogqhvtmsw YrxeFsteFrCvGeVdb.i e ^MNaZdEeh owliitehi iinufdirnmintuek ballfgresbyrcar i2q. -2- Worksheet by Kuta Software LLC

13 Find the measure of each side indicated. Round to the nearest tenth. 43) A 44) A B 30 x 4.8 C B x C Find the value of the trig function indicated. (Reminder - Use the Pythagorean Theorem to find the missing side length first!) 45) sec 46) cos ) cos 20 48) tan ) csc ) sin ) cot 10 52) cos ) csc ) cot l g2o0e1q8f kkmuytiav CScohfatVw]aprIer YLILdCQ.F Z KAzlklx DrwiVg`h^tlsJ _rae\suenrzvhesdx.b T dmeaodaes vwriktahh ziqntfbivnjixtuep SABlCgAeRbhr`aJ r2r. -3- Worksheet by Kuta Software LLC

14 Answers to Show ALL work on seperate paper (lined, blank, or graph paper) (ID: 1) 1) i 2) i 3) i 4) 26-21i 7n 2 5) 6) a - 1 7) 5x x ) n - 9 a + 6 7(x - 5) 9) m ) 11) m - 8 p - 6 { ) {3} 10 } 13) {-7} 14) { } 15) { 43 16) {49, -49} 5 } 17) { 49 6, } 18) { 7 19) {8, -8} 20) {164} 3 } 21) log 7 ( ac 3 b 5 ) u 2 z 12 x 12 24) log 22) log 9 23) log 7 (dcb a) wv 6 3 y 3 25) 2 log 9 z + 2 log 9 x + 6 log 9 y 26) 6 log z + log x + log y ) 5 log log log ) 3 log log log ) 6x 3 + 7x 2-5x x ) 3 p p p ) (x 2 + 4)(x 2-5)(x 2 + 5) = 0 32) (x + 5)(x 2-5) = 0 33) (x + 5)(x 2-5x + 25)(x + 1)(x 2 - x + 1) = 0 34) (x 2-7) 2 = 0 35) x 2 (x + 4)(x - 3) = 0 36) (x 2 + 7) 2 = 0 37) (x - 3)(x 2 + 3) = 0 38) (x + 3)(x 2-3x + 9) = 0 39) 40) y x ) ) ) ) ) 12 47) 3 48) ) ) ) ) ) y x 53) ) 4 3 A s2r0b1b8o mk`uct`ax dsuozfdtzwbadroeo vlkllcc.j [ rapljl_ erdi_g[hptesy MrCeCsceLrRvxe\dc.M ] mmla`diei twjisthk _InntfTipnuiEtPeH PAolmg]egbYryaT D2T. -4- Worksheet by Kuta Software LLC