ALGEBRA I MARCH REGIONAL TEAM QUESTION #1

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1 ALGEBRA I MARCH REGIONAL TEAM QUESTION #1 On a Cartesian Plane, Brandon Bug is crawling along a path defined by the equation B(x) = 5x -. Lindsay Lizard is slithering along a path defined by the equation L(x) = -7x + 4. A : (x, y) is the x-intercept of B(x). A = x (expressed as a fraction) B : (x, y) is the y-intercept of L(x). B = y C : Brandon texts Lindsay to meet up so they can talk. C = the ordered pair, expressed in fractions, of the point where Brandon and Lindsay meet if they continue along the same paths. D : David Donkey is walking along a path at point (-14, 6) perpendicular to Lindsay s path. D = the equation, in Slope-Intercept Form, of the path David is walking. ALGEBRA I MARCH REGIONAL TEAM QUESTION #1 On a Cartesian Plane, Brandon Bug is crawling along a path defined by the equation B(x) = 5x -. Lindsay Lizard is slithering along a path defined by the equation L(x) = -7x + 4. A : (x, y) is the x-intercept of B(x). A = x (expressed as a fraction) B : (x, y) is the y-intercept of L(x). B = y C : Brandon texts Lindsay to meet up so they can talk. C = the ordered pair, expressed in fractions, of the point where Brandon and Lindsay meet if they continue along the same paths. D : David Donkey is walking along a path at point (-14, 6) perpendicular to Lindsay s path. D = the equation, in Slope-Intercept Form, of the path David is walking.

2 ALGEBRA I MARCH REGIONAL TEAM QUESTION # A ball thrown in the air by Alex follows a path determined by y = -0.5x +.5x + 4 where y = the height of the ball, in meters, after x seconds. A = the maximum height the ball reaches, in meters. B = the time, in seconds, when the ball reaches its maximum height. C = the time, in seconds, when the ball hits the ground after being thrown. Express your answer in simple radical form. D = the height of the ball, in meters, three seconds after Alex threw it. ALGEBRA I MARCH REGIONAL TEAM QUESTION # A ball thrown in the air by Alex follows a path determined by y = -0.5x +.5x + 4 where y = the height of the ball, in meters, after x seconds. A = the maximum height the ball reaches, in meters. B = the time, in seconds, when the ball reaches its maximum height. C = the time, in seconds, when the ball hits the ground after being thrown. Express your answer in simple radical form. D = the height of the ball, in meters, three seconds after Alex threw it.

3 ALGEBRA I MARCH REGIONAL TEAM QUESTION #3 A : Simplify x +1x+36 if x is a Real Number. B : Multiply and simplify. ( )( ) C, D : Simplify to the form C- D ALGEBRA I MARCH REGIONAL TEAM QUESTION #3 A : Simplify x +1x+36 if x is a Real Number. B : Multiply and simplify. ( )( ) C, D : Simplify to the form C- D

4 ALGEBRA I MARCH REGIONAL TEAM QUESTION #4 A = the number of sets of numbers natural, whole, integers, and transcendental. 65 belongs to. Choose from rational, irrational, B = written as a fraction in simplest form. Given D ABC C = the length of side c if the length of side a = 7 and the length of side b = 4. D = the length of side b if the length of side a = 6160 and the length of side c = ALGEBRA I MARCH REGIONAL TEAM QUESTION #4 A = the number of sets of numbers natural, whole, integers, and transcendental. 65 belongs to. Choose from rational, irrational, B = written as a fraction in simplest form. Given D ABC C = the length of side c if the length of side a = 7 and the length of side b = 4. D = the length of side b if the length of side a = 6160 and the length of side c = 6161.

5 ALGEBRA I MARCH REGIONAL TEAM QUESTION #5 Factor completely. A : 49w 16x 4x 9 C : x 4 5x 3 + x + x - 30 B : a n+ + a b + a n c n + b c n D : 3x 6 y 15x 5 y 3 150x 4 y 4 ALGEBRA I MARCH REGIONAL TEAM QUESTION #5 Factor completely. A : 49w 16x 4x 9 C : x 4 5x 3 + x + x - 30 B : a n+ + a b + a n c n + b c n D : 3x 6 y 15x 5 y 3 150x 4 y 4

6 ALGEBRA I MARCH REGIONAL TEAM QUESTION #6 A : The amount of interest earned on a savings account is directly proportional to the amount of money in the account. If $5000 earns $350 interest in a year, how much interest is earned in a year on an investment of $8000? B : A car is purchased at a cost of $9,000. It is estimated the car will be used for 11 years before being sold for $785. If the car depreciates linearly, what is the annual rate of depreciation? C : Hayden signs a contract to work with Google!! His salary the first year (05) is $100,000 and he gets a salary increase of 10% per year. How much will his salary be his fourth year at Google, 08? D : Hayden is so excited about his newfound wealth, he goes out and buys a BMW i8 Roadster (a car!) for just $150,000. Unfortunately, the car depreciates at 10% per year. How much will Hayden s car be worth two years after he buys it? ALGEBRA I MARCH REGIONAL TEAM QUESTION #6 A : The amount of interest earned on a savings account is directly proportional to the amount of money in the account. If $5000 earns $350 interest in a year, how much interest is earned in a year on an investment of $8000? B : A car is purchased at a cost of $9,000. It is estimated the car will be used for 11 years before being sold for $785. If the car depreciates linearly, what is the annual rate of depreciation? C : Hayden signs a contract to work with Google!! His salary the first year (05) is $100,000 and he gets a salary increase of 10% per year. How much will his salary be his fourth year at Google, 08? D : Hayden is so excited about his newfound wealth, he goes out and buys a BMW i8 Roadster (a car!) for just $150,000. Unfortunately, the car depreciates at 10% per year. How much will Hayden s car be worth two years after he buys it?

7 ALGEBRA I MARCH REGIONAL TEAM QUESTION #7 A : Simplify. Leave no negative exponents in your answer. B : Simplify. Leave no negative exponents in your answer. 4w x 6w x (5rs ) (5r s) y y C : Write the largest of the roots for 4x 3 + 4x x 6 = 0 D : The tens digit of a two-digit number is 3 less than the square of the units digit. If 7 is subtracted from the number, the result is the number with the digits reversed. Find the original number. ALGEBRA I MARCH REGIONAL TEAM QUESTION #7 A : Simplify. Leave no negative exponents in your answer. B : Simplify. Leave no negative exponents in your answer. 4w x 6w x (5rs ) (5r s) y y C : Write the largest of the roots for 4x 3 + 4x x 6 = 0 D : The tens digit of a two-digit number is 3 less than the square of the units digit. If 7 is subtracted from the number, the result is the number with the digits reversed. Find the original number.

8 ALGEBRA I MARCH REGIONAL TEAM QUESTION #8 When a positive integer is divided by a smaller positive integer, the integer part of the quotient is and the remainder is 9. The sum of the integers is 48. A = the larger integer B = the smaller integer At his new job at Publix, Jason accidently peels off the labels to 300 cans of tomato soup and 500 cans of chicken noodle soup. The cans of soup are not identifiable and Jason, ever the jokester, mixes the cans up. C : If 100 cans are chosen at random, how many cans of chicken noodle soup would you expect to get? C = the number of cans of chicken noodle soup rounded to the nearest whole number. D : How many cans, total, would you have to take in order for the expected number of cans of tomato soup to be 60? D = the number of cans of tomato soup. ALGEBRA I MARCH REGIONAL TEAM QUESTION #8 When a positive integer is divided by a smaller positive integer, the integer part of the quotient is and the remainder is 9. The sum of the integers is 48. A = the larger integer B = the smaller integer At his new job at Publix, Jason accidently peels off the labels to 300 cans of tomato soup and 500 cans of chicken noodle soup. The cans of soup are not identifiable and Jason, ever the jokester, mixes the cans up. C : If 100 cans are chosen at random, how many cans of chicken noodle soup would you expect to get? C = the number of cans of chicken noodle soup rounded to the nearest whole number. D : How many cans, total, would you have to take in order for the expected number of cans of tomato soup to be 60? D = the number of cans of tomato soup.

9 ALGEBRA I MARCH REGIONAL TEAM QUESTION #9 Given : x -7x+10 1 x+1 x -6x+5 x- x -4x+4 A = the excluded value(s) for this expression B = the expression when most simplified Given : x -6x-16 x +4x+3 x-8 x -x-15 C = the excluded value(s) for this expression D = the expression when most simplified ALGEBRA I MARCH REGIONAL TEAM QUESTION #9 Given : x -7x+10 1 x+1 x -6x+5 x- x -4x+4 A = the excluded value(s) for this expression B = the expression when most simplified Given : x -6x-16 x +4x+3 x-8 x -x-15 C = the excluded value(s) for this expression D = the expression when most simplified

10 ALGEBRA I MARCH REGIONAL TEAM QUESTION #10 Michael is driving home from a football game. The number of kilometers Michael is away from home is a linear function that depends on the number of minutes he has been driving. Suppose Michael is 11 km from home when he has been driving for 10 minutes and 8 km from home after he has been driving for 15 minutes. A : Find Michael s distance from home after he has been driving for 0 minutes. B : When was Michael 7 kilometers from home? C : What does the distance-intercept equal? D : What is the domain of this function? ALGEBRA I MARCH REGIONAL TEAM QUESTION #10 Michael is driving home from a football game. The number of kilometers Michael is away from home is a linear function that depends on the number of minutes he has been driving. Suppose Michael is 11 km from home when he has been driving for 10 minutes and 8 km from home after he has been driving for 15 minutes. A : Find Michael s distance from home after he has been driving for 0 minutes. B : When was Michael 7 kilometers from home? C : What does the distance-intercept equal? D : What is the domain of this function?

11 ALGEBRA I MARCH REGIONAL TEAM QUESTION #11 A = the sum of the integers in the solution set for x + 3 < 6 B = the sum of the integers in the solution set for x-1 ³ 6 C : Write in Scientific Notation D : Write.4 x x 10 8 in Scientific Notation ALGEBRA I MARCH REGIONAL TEAM QUESTION #11 A = the sum of the integers in the solution set for x + 3 < 6 B = the sum of the integers in the solution set for x-1 ³ 6 C : Write in Scientific Notation D : Write.4 x x 10 8 in Scientific Notation

12 ALGEBRA I MARCH REGIONAL TEAM QUESTION #1 A : The largest whole number less than 300 that is divisible by 18. B : Which is greater? or 3 C : Jack has 40 chickens and pigs on his farm. There are a total of 114 legs. How many of chickens does Jack own? Assume all animals have the appropriate number of legs. D : Two times the number of fracks equal a frick. Three times the number of fracks equal a frink. Together, there are 4 fricks, fracks, and frinks. How many frinks are there? ALGEBRA I MARCH REGIONAL TEAM QUESTION #1 A : The largest whole number less than 300 that is divisible by 18. B : Which is greater? or 3 C : Jack has 40 chickens and pigs on his farm. There are a total of 114 legs. How many of chickens does Jack own? Assume all animals have the appropriate number of legs. D : Two times the number of fracks equal a frick. Three times the number of fracks equal a frink. Together, there are 4 fricks, fracks, and frinks. How many frinks are there?

13 ALGEBRA I MARCH REGIONAL TEAM QUESTION #13 -A + B 4A - B = 5 3 Solve the system of equations on the left. This will provide for the answers for A and B. A+ 1-B = 3 9 Camren s age is 3 David s age. Four years ago, David s age was 5 3 of Camren s age. C = Camren s current age D = David s current age. ALGEBRA I MARCH REGIONAL TEAM QUESTION #13 -A + B 4A - B = 5 3 Solve the system of equations on the left. This will provide for the answers for A and B. A+ 1-B = 3 9 Camren s age is 3 David s age. Four years ago, David s age was 5 3 of Camren s age. C = Camren s current age D = David s current age.

14 ALGEBRA I MARCH REGIONAL TEAM QUESTION #14 Luke and Leia are trapped in a room (say, the garbage compactor) on the Death Star. The room is 0 meters long and 15 meters wide. However, the length is decreasing by a rate of meters per minute and the width is increasing by a rate of 3 meters per minute. A : Let A(t) be the area of the room in square meters after t minutes. Write the equation for A(t) in Standard Form. B : Set A(t) = 0 and completely factor the result from part A. C : When will the area of the room be zero? D : After how many minutes does the room reach maximum area? ALGEBRA I MARCH REGIONAL TEAM QUESTION #14 Luke and Leia are trapped in a room (say, the garbage compactor) on the Death Star. The room is 0 meters long and 15 meters wide. However, the length is decreasing by a rate of meters per minute and the width is increasing by a rate of 3 meters per minute. A : Let A(t) be the area of the room in square meters after t minutes. Write the equation for A(t) in Standard Form. B : Set A(t) = 0 and completely factor the result from part A. C : When will the area of the room be zero? D : After how many minutes does the room reach maximum area?