ALGEBRA I BOWL QUESTION #1

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1 ALGEBRA I BOWL QUESTION #1 1) Evaluate the following, given that < 5 < : A) What is the smallest prime number that is GREATER THAN ? B) How many positive integer factors does ( ) have? C) D) X < < Y, where Y and X are integers and Y X = 1. Find Y 2 ALGEBRA I BOWL QUESTION #1 1) Evaluate the following, given that < 5 < : A) What is the smallest prime number that is GREATER THAN ? B) How many positive integer factors does ( ) have? C) D) X < < Y, where Y and X are integers and Y X = 1. Find Y 2

2 ALGEBRA I BOWL QUESTION #2 2) Solve for x : A) 3x + 4 (12x + 2) < 3 B) 12x 3 = 12x + 4 C) x 7 = x D) 2x 6 = 16 ALGEBRA I BOWL QUESTION #2 2) Solve for x : A) 3x + 4 (12x + 2) < 3 B) 12x 3 = 12x + 4 C) x 7 = x D) 2x 6 = 16

3 ALGEBRA I BOWL QUESTION #3 3) Given the equations (1) 3x 4y = 5 and (2) 5x + 12y = 13 A) Find the x-intercept of (1) B) Find the slope of (2) C) Find an equation in Standard Form of the line perpendicular to (1) passing through the point (-12, 6). D) Is the y-intercept of (2) above or below the origin? ALGEBRA I BOWL QUESTION #3 3) Given the equations (1) 3x 4y = 5 and (2) 5x + 12y = 13 A) Find the x-intercept of (1) B) Find the slope of (2) C) Find an equation in Standard Form of the line perpendicular to (1) passing through the point (-12, 6). D) Is the y-intercept of (2) above or below the origin?

4 ALGEBRA I BOWL QUESTION #4 4) Simplify the following, leaving no negative exponents : A) a5 c 2 b 4 a 11 a 8 b 8 B) x 111/3 x C) zz 4 4z 4 + 4z 2 (z 0)(z + 0) D) y 2 z 4 ALGEBRA I BOWL QUESTION #4 4) Simplify the following, leaving no negative exponents : A) a5 c 2 b 4 a 11 a 8 b 8 B) x 111/3 x C) zz 4 4z 4 + 4z 2 (z 0)(z + 0) D) y 2 z 4

5 ALGEBRA I BOWL QUESTION #5 5) For this question, please answer whichever number is the largest in the set , A) { 1 2, 2 3, 3 2, 17 15, π 2 } 3 B) { 10, 26 C) {48 12, } 4, 80} D) { 6 1 8, } ALGEBRA I BOWL QUESTION #5 5) For this question, please answer whichever number is the largest in the set , A) { 1 2, 2 3, 3 2, 17 15, π 2 } 3 B) { 10, 26 C) {48 12, } D) { , 80}, }

6 ALGEBRA I BOWL QUESTION #6 6) Billy G. Oat runs an animal transportation service around the state of Florida. He has a large truck in which he moves many arrangements of livestock to and from farms. The given information will consist of the kinds of animals, the total number of animals on the truck, and how many legs are on the truck (excluding Billy s legs). Your task is to deduce how many of each animal there are. Assume all animals have the normal number of legs unless specified. A) Cows and Chickens; 18 total; 44 legs B) Three-legged cats and four-legged rats; 100 total; 349 legs C) Electric eels and pigs; 51 total; 24 legs D) Humans, Guinea pigs, and spiders; 36 total; 188 legs (Each guinea pig is the pet of a human and each human has only one pet) ALGEBRA I BOWL QUESTION #6 6) Billy G. Oat runs an animal transportation service around the state of Florida. He has a large truck in which he moves many arrangements of livestock to and from farms. The given information will consist of the kinds of animals, the total number of animals on the truck, and how many legs are on the truck (excluding Billy s legs). Your task is to deduce how many of each animal there are. Assume all animals have the normal number of legs unless specified. A) Cows and Chickens; 18 total; 44 legs B) Three-legged cats and four-legged rats; 100 total; 349 legs C) Electric eels and pigs; 51 total; 24 legs D) Humans, Guinea pigs, and spiders; 36 total; 188 legs (Each guinea pig is the pet of a human and each human has only one pet)

7 ALGEBRA I BOWL QUESTION #7 7) Solve for x : A) x 2 + 2x B) 2 3x x 7 = 1 C) x x 3 + 6x 2 13x = 1, x > 0 D) x 1 x + 1 = 0 ALGEBRA I BOWL QUESTION #7 7) Solve for x : A) x 2 + 2x B) 2 3x x 7 = 1 C) x x 3 + 6x 2 13x = 1, x > 0 D) x 1 x + 1 = 0

8 ALGEBRA I BOWL QUESTION #8 8) Let f(x) = x + 2, g(x) = 23x, and h(x) = 2 2. Evaluate the following: x A) h(13) B) f(g(1)) C) g(h(17)) (expressed as a fraction) D) f (g(h(23))) ALGEBRA I BOWL QUESTION #8 8) Let f(x) = x + 2, g(x) = 23x, and h(x) = 2 2. Evaluate the following : x A) h(13) B) f(g(1)) C) g(h(17)) (expressed as a fraction) D) f (g(h(23)))

9 ALGEBRA I BOWL QUESTION #9 9) Wesley has taken a few equally weighted tests in his Algebra class with grades of 88, 81, 93, 78, and 95. Assume a maximum score of 120 and a minimum score of 0. His average for the class is ONLY his test average (no homework, yay!) A) What grade should he get on his final test to ensure an average test grade of exactly 88? B) What grade should he get on his final test to ensure an average test grade of exactly 92? C) What is the lowest grade he could get on the final test to pass the class with an average of at least 70? D) How many more tests should he take and make a 99 on to average at least a 96? ALGEBRA I BOWL QUESTION #9 9) Wesley has taken a few equally weighted tests in his Algebra class with grades of 88, 81, 93, 78, and 95. Assume a maximum score of 120 and a minimum score of 0. His average for the class is ONLY his test average (no homework, yay!) A) What grade should he get on his final test to ensure an average test grade of exactly 88? B) What grade should he get on his final test to ensure an average test grade of exactly 92? C) What is the lowest grade he could get on the final test to pass the class with an average of at least 70? D) How many more tests should he take and make a 99 on to average at least a 96?

10 ALGEBRA I BOWL QUESTION #10 10) For each of the following parts, identify the number or expression which is not like the others. A) B) π φ ε α e C) y = x + 1 y = 5 x + 2 x x 2 + y 2 = 1 y = x 2 + 2x D) ALGEBRA I BOWL QUESTION #10 10) For each of the following parts, identify the number or expression which is not like the others. A) B) π φ ε α e C) y = x + 1 y = 5 x + 2 x x 2 + y 2 = 1 y = x 2 + 2x D)

11 ALGEBRA I BOWL QUESTION #11 Let A be the y-intercept of the line passing through ( 2, 14) and (2, 13.5) The point (B, C) is the midpoint of the line segment connecting the points ( , ) and ( , 169 ) The point (D, D) lies on the line y = 2x + 5 ALGEBRA I BOWL QUESTION #11 Let A be the y-intercept of the line passing through ( 2, 14) and (2, 13.5) The point (B, C) is the midpoint of the line segment connecting the points ( , ) and ( , 169 ) The point (D, D) lies on the line y = 2x + 5

12 ALGEBRA I BOWL QUESTION #12 A) The sum of 5 consecutive integers is 125. What is the middle integer? B) The average of 4 consecutive even integers is 13. What is the largest integer? C) What is the sum of the first 25 positive integers? D) If you label each letter in the alphabet according to its position (i.e. A = 1, B = 2, C = 3, etc.), what is the sum of all letters in FAMAT ALGEBRA I BOWL QUESTION #12 A) The sum of 5 consecutive integers is 125. What is the middle integer? B) The average of 4 consecutive even integers is 13. What is the largest integer? C) What is the sum of the first 25 positive integers? D) If you label each letter in the alphabet according to its position (i.e. A = 1, B = 2, C = 3, etc.), what is the sum of all letters in FAMAT

13 ALGEBRA I BOWL QUESTION #13 13) For this problem, a = 12, b = 3, c = 5, d = 8, e = 15, f = 441 A) a 2 + c 2 f B) d 2 + e 2 C) bc e D) abc d e+f ALGEBRA I BOWL QUESTION #13 13) For this problem, a = 12, b = 3, c = 5, d = 8, e = 15, f = 441 A) a 2 + c 2 f B) d 2 + e 2 C) bc e D) abc d e+f

14 ALGEBRA I BOWL QUESTION #14 A) The sum of the roots of (x + 1) 2 1 = 0 B) The degree of the polynomial (x + x 2 + x 3 ) 6 = 0 C) Solve for x: 1 3 = 1 x + 1 2x D) Compute the square root of the number attained by multiplying thirteen by eleven and adding one. ALGEBRA I BOWL QUESTION #14 A) The sum of the roots of (x + 1) 2 1 = 0 B) The degree of the polynomial (x + x 2 + x 3 ) 6 = 0 C) Solve for x: 1 3 = 1 x + 1 2x D) Compute the square root of the number attained by multiplying thirteen by eleven and adding one.

Ocean Township High School Mathematics Department

Algebra Summer Assignment Name Period Date Ocean Township High School Mathematics Department These are important topics from Algebra 1 that you must be comfortable doing before you can be successful in