Pre-Calculus Summer Homework

Transcription

1 Pre-Calculus Summer Homework In an effort to use less paper, the math department will not be printing off your summer homework. You can go to the homework websites of Mr. Coulson, Mrs. Hopkins, and Mr. Wu on in order to print the homework yourselves. This homework is meant to prepare you for Pre-Calculus in the fall. Please complete the following problems on separate pieces of paper. It will be collected for a grade, and you will be tested over this material during the first week of school. If you need assistance, go to and look on Mr. Coulson s, Mrs. Hopkins, or Mr. Wu s web pages for links to the Kahn Academy, If you have questions about the homework that cannot be answered by using these links, feel free to Mr. Wu at awu@parkwayschools.net, Mrs. Hopkins at ehopkins@parkwayschools.net, or Mr. Coulson at ccoulson@parkwayschools.net. They will be available to answer questions through up until August 1 st.

2 Testimonials Even though you are never supposed to forget the things you learn, sometimes a person does forget. Students forget things, especially when they aren t practicing them. Summer time is the time when you aren t asked to do homework, so all those learned items start to fade. Summer homework is the best way to help you remember what you ve learned. My summer homework really helped me remember all of the math that I had learned the year before. It also prepared me well in advance of my Pre-Calc class. It got me in the habit of doing homework and not slacking. -Sam Markowski When you get back to school in August, there will be a test over the summer homework. For this reason alone, it is very beneficial to actually do the summer homework correctly. And if you decide not to do it over the summer, you ll still have to take the test, and your chances of doing well on it are eactly zero. And then you ll probably be forced into doing the homework during the first week of school, which is a huge pain. It s never good to start the year off behind everyone else. The amount of stress caused by having to do the homework over the summer is much less than the amount caused by feeling lost before the class even starts. -Hailey Cahill Mr. Wu, Mrs. Hopkins, and Mr. Coulson are easily the three best math teachers in the universe. I would do my summer homework for them just because they are so awesome. I have also done a chi-squared analysis on students who do their summer homework versus students who do not. Students who do their summer homework are 178 times more likely to pass their first test than students who do not do their summer homework. Students who do their summer homework are also stronger, taller, faster, smarter, better looking, and end up having a higher average and median salary in their first job after college. Or something like that. -Jason Koehrer

3 Section P.1 For problems 1-6, multiply in the given epressions. 1) ( + 1) = ) ( + 4)( 5) = ) 5) ( 1)( ) + = 4) ( )( 5) + = 6) ( + 1)( 4) = ( 1)( 4 ) + = For problems 7-1, factor the given epressions. 7) 9) 11) + = 8) = 10) = 1) 4 18 = 56 = 6 = For problems 1-0, find a common denominator before adding and subtracting the given fractions. Do not use a calculator. 1) 1 = 14) + 1 = 15) 5 1 = 16) = ) 1 1 = 18) y + = ) 4 = + 0) = + 1 For problems 1-6, multiply or divide the given fractions and then simplify your answer. 1) = + 1 ) = 6 ) 9 1 = + 9 4) = 6 + 5) = 6) 1 + = ) Mr. Wu and Mr. Coulson decide to go see MacGruber. Together they paid $6 for two tickets and two sodas. If a ticket costs $5 more than a soda, how much does a ticket cost? ) Mr. Wu, Mr. Breedencutter, and Mr. Evers are going to a Cardinal s game. For their three tickets, nine hot dogs, and nine sodas, they paid a total of $177. If a hot dog and soda cost $1, and a soda is $ more than a hot dog, how much does each item cost?

4 4) Mr. Wu spent his three day weekend selling lemonade on the streets. He spent $0 on signs, a chair, and a table for his stand. If he sold each cup of lemonade for $.5, but it cost $.09 total for the cup, ice, lemons, and sugar, how many cups of lemonade would Mr. Wu have to sell to break even? 5) Mr. Coulson has $5000 to invest. He splits the money into an IRA and a 40b, which have a return of % and 6% respectively. If he earns $40 total after one year, how much did Mr. Coulson invest into each account? 6) Mr. Wu bought Sour Gummy Worms, Skittles, and Mounds bars for the winners of his Jeopardy games. He remembers buying twelve pieces of candy total and spending $10. He also knows the Gummy Worms cost $, the Skittles cost $1, and the Mounds Bars cost $.50. If he bought four times as many Mounds bars as bags of Skittles, how many bags of Sour Gummy Worms did he buy? 7) A small business owner invests $11,000 to produce a new product. Each unit costs $.56 to make and is sold for $1.7. How many units must be sold for the business to break even? 8) You are offered two jobs selling jalopies. One company offers a yearly salary of $,500 plus a year-end bonus of 1.5% of your total jalopy sales. The other job pays $,000 a year with a bonus of % of your total sales. How much would you need to sell in a year to make the second job a better offer? Section 1.1 For problems 1-4, sketch the line that passes through the given point that has the given slope. 1) (, ) and m = 0 ) ( 4, 1) and m = ) (, 7) and m is undefined 4) 1 (0, 1) and m = For problems 5 and 6, estimate the slope of the line. 5) 6) For problems 7-10, find the equation of the line with the given point and slope. Then sketch the graph by hand. 7) (, 6) and m = 8) (0, 0) and m = 4

5 9) ( 10, 4) and m is undefined 10) (., 8.5) and m = 0 For problems 11 and 1, find the slope-intercept form of the equation of the line that passes through the given points. 11) (4, ) and ( 4, 4) 1) ( 1, 4) and (6, 4) For problems 1 and 14, write the slope-intercept forms of the equations of the lines that travel through the given point that are a) parallel to the given line b) perpendicular to it. 1) (, ) + y = 7 14) ( 4, 1) y + = 0 Section 1. For problems 1-5, determine whether the relationship describes a function or not. Eplain your reasoning. 1) Domain Range ) Domain Range - 5 Year Number of Storms ) 4) Input Input Value Value Output Output Value Value ) Domain = {a, b, c} and Range = {0, 1,, } Ordered Pairs = (a, 1), (c, ), (c, ), (b, ) For problems 6-11, determine whether the equation represents y as a function of. 6) = y 7) y = + 5 8) = y + 5 9) + y = 10) y = 4 11) y = 8

6 For problems 1-14, evaluate the given functions at the specified values of. 1) g( ) = 7 a) g (0) = b) 7 g = c) g( s + ) = 1) V ( r) 4 = π r a) () V = b) V = c) V ( r ) = 14) f ( ) = a) f ( 8) = b) f (1) = c) f ( 8) = For problems 15 and 16, find the value of that makes the f() = 0. 15) 4 f ( ) = 16) 5 1 f ( ) = 5 For problem 17, find the values of such that f() = g(). 17) f = + + ( ) 1 g( ) = + For problems 18-0, find the domain of the given functions. 18) f ( ) 1 = 19) f ( ) = 0) 5 4 f ( ) = + 1) A company produces a toy for which the variable cost is $1.0 per unit with a fied cost of $98,000. The toy sells for $ Let be the number of units produced and sold. a) The total cost for a business is the sum of the variable cost and the fied cost. Write the total cost, C, as a function of. b) Write the revenue, R, as a function of. Section 1. c) Write the profit, P, as a function of. (HINT: Profit = Revenue Cost) For problems 1-, find the domain and range of the given functions. 1) f ( ) 1 = ) f ( ) = 4 ) 1 f ( ) = 5 4

7 For problems 4-6, determine whether the graph represents a function by using the vertical line test. 4) 5) 6) For problems 7 and 8, use the maimum and minimum functions of a graphing calculator to find the relative maimums and minimums of the given functions. Round to the nearest hundredth. 7) f ( ) = 5 8) f ( ) = For problems 9 and 10, sketch the graph of the piece-wise function by hand. 9) f ( ) = 4 > 4 + < 0 10) f ( ) = + 1 0

8 Section 1.4 For problems 1-6, identify the parent function and describe the transformation(s) shown in the graph. Write an equation for the graphed function. 1) ) ) 4) 5) 6)

9 For problems 7-11, g is related to one of the si parent functions. (a) Identify the parent function. (b) describe the transformation(s) that are occurring. (c) Sketch the graph by hand. ( ) = ) g( ) = ( + 10) + 5 8) g ( ) 1 9) g( ) = ( + 1) 10) g ( ) 11) g( ) = Section 1.5 ( ) = + 10 For problems 1-4, find (a) (f + g)(), (b) (f - g)(), (c) (fg)(), and (d) (f/g)(). What is the domain of f/g? 1) f ( ) = 5, g( ) = 1 ) f ( ) = 5, g( ) = 4 ) f ( ) = 4, g( ) = + 1 4) f ( ) =, g( ) = + 1 For problems 5-8, evaluate the indicated function for ( ) 1 f = + and g( ) = 4 algebraically. 5) ( f g)( ) 6) ( f + g)(1) 7) ( fg)( 6) f 8) (0) g For problems 9 and 10, find (a) f g, (b) g f g = f ( g( )) and g f = g( f ( )) ). f, and if possible, (c) ( f g )( 0) (HINT: 9) f ( ) = 1, g( ) = ) f ( ) =, g( ) = 1 For problems 11-1, determine the domains of (a) f, (b) g, and (c) f g. 11) f ( ) = +, g( ) = 1) f ( ) =, g( ) = ) 1 1 f ( ) =, g( ) =

10 Section 1.6 For problems 1-, show algebraically that f and g are inverse functions (HINT: f ( g( )) = g( f ( )) = ) 1) f ( ) 1 =, g( ) 1 = ) f ( ) 9 =, 0; g( ) = 9 ) 1 1 f ( ) =, 0; g( ) =, 0 < 1 1+ For problems 4-9, use the Horizontal Line Test to determine whether the function is one-to-one and has an inverse function. 4) ( ) 1 ( ) 4 f = + 1 5) g( ) = 4 6 6) 9) f ( ) 16 f = 8) f ( ) = ( ) = 7