Welcome to Precalculus-Statistics!

Transcription

1 Welcome to Precalculus-Statistics! Congratulations! You are currently enrolled in Precalculus-Statistics for the Fall of 018. This course will prepare you for the IB Math SL, which you will take in school year. This course consists of three marking periods of Precalculus topics, and one marking period of Statistics. This course is very demanding, runs at fast pace, and requires from you consistent work and your best effort. Prior to the Fall 018 year, it is necessary for you to review some fundamental concepts that you had learned in Algebra and Geometry. The attached packet represents the level of required knowledge in order to be successful with less stress possible. Therefore, completion of this packet would help you to get properly prepared for the upcoming year. Directions: When completing this packet, you may use notes or other resources to refresh your memory. Bring the completed packet with you on the first day of school. This packet will be checked for completeness. All problems should be done or well attempted. Show work on every problem. Write neatly, so you can use it as a reference-guide in the beginning of the school year. During the first few weeks of classes you will be given an opportunity to ask some questions in class, as we will review main concepts and address all the difficulties you might have with any of the problems. You will be tested on this prerequisite material during 3 rd week of September. The TI-84, TI-84 Plus or TI-84 Plus CE calculator is required for the course. Please review the basics of the calculator prior to the fall semester. If you do not have a manual, visit my Wiki page friendlymath.pbworks.com and its Useful links with the uploaded manuals. Entering this course, you should be able to graph a function, create a table of values for that function, and find zeros of a function. If you have any questions over the summer you can me at yoygenblik@ctemc.org, and I will be more than happy to help you. Have a GREAT summer and I will see you in September! Mrs. Oygenblik

2 SUMMER PACKET for students entering IB MATH SL1 Name Precalculus-Stat Evaluate the algebraic expression for the given value or values of the variable(s). 1) 4 4( х 4)3 ; x 6 ) y x ; 7 x xy Solve. x, y 5 3) The winning times (in seconds) in a speed-skating event for men can be represented by the formula T x where x represents the year, with x = 0 corresponding to 190. (For example in 199, x would be According to the formula, what was the winning time in 1987? Round to the nearest hundredth. 1) ) 3) Find the intersection of the two sets. 4) { 1, 3, 5, 9} { 5, 6, 1} 4) Find the union of the two sets. 5) {, 10, 5, 9} { 5, 11, } 5) List all numbers from the given set B that are members of the given Real Number subset. 6) 6) 7 B = { 17, 7, 1, 0,, 4, 0., 0.07} Rational numbers 8 Rewrite the expression without absolute value bars. 7) 7 9 7) Evaluate the expression for the given values of x and y. 8) x y ; x 3 and y 4 x y 8) Write the algebraic expression without parentheses. 9) (7 z 4w 3 y) 9)

3 Simplify the exponential expression. 10) x y z xyz 10) 11) xy 11 6x y 11) 1) x y z 3 3 3xy z 1) Perform the indicated computation. Write the answer in scientific notation ) 13) 14) ) Use the product rule to simplify the expression. 15) 10x 70x 15) Use the quotient rule to simplify the expression. 16) 4 7x 3x 17) The time, in seconds, that it takes an object to fall a distance d, in feet, is given d by the algebraic expression 16. Find how long it will take a ball dropped from 16) 17) the top of a building 38 feet tall to hit the ground. Write the answer in simplified radical form. Add or subtract terms whenever possible. 18) 5x5 15x 7 180x 18) Rationalize the denominator. 19) ) 3

4 0) ) Add or subtract terms whenever possible. 1) ) ) y 189x 875xy ) Simplify by reducing the index of the radical. 3) y z 3) 4) The algebraic expression d describes the duration of a storm, in hours, whose diameter is d miles. Use a calculator to determine the duration of a storm with a diameter of 1 miles. Round to the nearest hundredth. 4) Simplify using properties of exponents x 8x 5) 5) Perform the indicated operations. Write the resulting polynomial in standard form. 6x 9 9x 8 x 7 6 x 9 5x 8 6x 7 7 6) 6) Find the product. 9x1 x 5x 1 7) 7) 8) Write a polynomial in standard form that represents the volume of the open box. 8) 4

5 9) Write a polynomial in standard form that represents the area of the shaded region. 9) Find the product. 30) 9x 4 30) 31) 8 9x 31) 3) x 4 3 3) 33) 4x ) 34) 6y 7x 6y 7x 34) 35) 4x 8y 54x 8y 5 35) 36) 4x4 7y 36) Factor out the greatest common factor. x x4 x 4 37) 37) Factor by grouping. Assume any variable exponents represent whole numbers. 38) 3 x 8xx 16 38) 5

6 Factor the trinomial, or state that the trinomial is prime. 39) 5x 14x 3 39) 40) 7x 3xy 0y 40) 41) 1x 5xy 1y 41) Factor: 4) 144x 5y 4) 43) 4x 4x 1 43) Factor using the formula for the sum or difference of two cubes. 44) 3 15x 64 44) 45) 3 64x 7 45) Factor completely, or state that the polynomial is prime. 46) 5 y 65y 46) 47) 49x 16x81 64y 47) Factor and simplify the algebraic expression x9 x 9 48) 48) 49) x 7 x ) Find all numbers that must be excluded from the domain of the rational expression. 50) x 3 x 64 50) 6

7 Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. 51) x 6x9 x 1x7 51) Find all numbers that must be excluded from the domain of the rational expression. 5) x 4 x 9x0 5) Multiply or divide as indicated. 53) x 14x4 x 8x7 x 11x10 x 5x6 53) 54) x 4x144 11x13 x 4 54) Add or subtract as indicated. 55) x 6 x 16 x 5x4 55) 56) 3x 4 6 x x x ) Simplify the complex rational expression. 57) x 1 x x 36 57) 58) x 3 x x x 58) 7

8 Simplify the expression. 59) 1 x 5 x x 59) 60) x 6 x 6 x 6 x 60) 61) 1 1 x 3 x 3 61) Rationalize the numerator. 6) x 6 x 6) 6 63) x y x y 63) Solve the linear equation. 64) 6x67( x1) 6x 7 64) Solve the equation. 65) x9 47 x ) 66) x x x ) First, write the value(s) that make the denominator(s) zero. Then solve the equation. 67) x3 3 x1 67) 8

9 Solve the formula for the specified variable. AP 1 nr for r 68) 68) Solve the absolute value equation or indicate that the equation has no solution. 69) 6x ) Solve the quadratic equation by factoring. 70) 4x 5 19x 70) Solve the quadratic equation by the square root property. 71) 3x ) Solve the equation by the method of your choice. x6 x5 6 7) 7) Solve the quadratic equation by completing the square. 73) 3x x4 0 73) Solve the radical equation, and check all proposed solutions. 74) 14x7 3 x 74) 75) For a culture of 60,000 bacteria of a certain strain, the number of bacteria N that will survive x hours is modeled by the formula N x. After how many hours will 18,000 bacteria survive? 75) 9

10 76) Employment statistics show that 5,480 of the residents of Bear Valley were unemployed last month. This was a decrease of 9% from the previous month. How many residents were unemployed in the previous month? 76) 77) A 6-ft-tall ladder is placed so that it reaches 5 ft up on the wall of a house. How far is the base of the ladder from the wall of the house? If necessary, round to the nearest tenth foot. 77) 78) A rectangular parking lot has a length that is yards greater than the width. The area of the parking lot is 55 square yards. Find the length and the width. 78) 79) Use the formula Distance traveled Time traveled =. Average Velocity A passenger train can travel 40 miles in the same amount of time it takes a freight train to travel 160 miles. If the average velocity of the freight train is 15 miles per hour slower than the average velocity of the passenger train, find the average velocity of each. 79) Use graphs to find the set. 80) (-, 8) [ -, 17) 80) 81) ( 6, ) [ 11, ) 81) Solve the linear inequality. Use interval notation to express the solution set and graph the solution set on a number line. 8) 4x75x 5 8) 10

11 83) 5(x10) 15x 0 83) 84) x x ) 85) Claire has received scores of 85, 88, 87, and 80 on her algebra tests. What score must she receive on the fifth test to have an overall test score average of at least 8? 85) Solve the compound inequality. Use interval notation to express the solution set and graph the solution set on a number line. 86) 113x ) 87) Parts for an automobile repair cost $736. The mechanic charges $3 per hour. If you receive an estimate for at least $98 and at most $1056 for fixing the car, what is the time interval, in hours, that the mechanic will be working on the job? 87) Solve the absolute value inequality. Use interval notation to express the solution set and graph the solution set on a number line. 88) x ) 89) x ) 90) 8x ) 11