question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field. Answer Choice: (A) 0 (B) 1 (C) 2 (D) 3

answer: The answer is (B). #### B


question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G. Answer Choice: (A) True, True (B) False, False (C) True, False (D) False, True

answer: The answer is (B). #### B


question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements. Answer Choice: (A) True, True (B) False, False (C) True, False (D) False, True

answer: The answer is (C). #### C


question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian. Answer Choice: (A) True, True (B) False, False (C) True, False (D) False, True

answer: The answer is (A). #### A


question: Find the characteristic of the ring 2Z. Answer Choice: (A) 0 (B) 3 (C) 12 (D) 30

answer: The answer is (A). #### A


question: Let V be the set of all real polynomials p(x). Let transformations T, S be defined on V by T:p(x) -> xp(x) and S:p(x) -> p'(x) = d/dx p(x), and interpret (ST)(p(x)) as S(T(p(x))). Which of the following is true? Answer Choice: (A) ST = 0 (B) ST = T (C) ST = TS (D) ST - TS is the identity map of V onto itself.

answer: The answer is (D). #### D


question: A tank initially contains a salt solution of 3 grams of salt dissolved in 100 liters of water. A salt solution containing 0.02 grams of salt per liter of water is sprayed into the tank at a rate of 4 liters per minute. The sprayed solution is continually mixed with the salt solution in the tank, and the mixture flows out of the tank at a rate of 4 liters per minute. If the mixing is instantaneous, how many grams of salt are in the tank after 100 minutes have elapsed? Answer Choice: (A) 2 (B) 2 - e^-2 (C) 2 + e^-2 (D) 2 + e^-4

answer: The answer is (D). #### D


question:
Let A be a real 2x2 matrix. Which of the following statements must be true?
I. All of the entries of A^2 are nonnegative.
II. The determinant of A^2 is nonnegative.
III. If A has two distinct eigenvalues, then A^2 has two distinct eigenvalues. Answer Choice: (A) I only (B) II only (C) III only (D) II and III only

answer: The answer is (B). #### B


question: Suppose that f(1 + x) = f(x) for all real x. If f is a polynomial and f(5) = 11, then f(15/2) Answer Choice: (A) -11 (B) 0 (C) 11 (D) 33/2

answer: The answer is (C). #### C


question: Let A be the set of all ordered pairs of integers (m, n) such that 7m + 12n = 22. What is the greatest negative number in the set B = {m + n : (m, n) \in A}? Answer Choice: (A) -5 (B) -4 (C) -3 (D) -2

answer: The answer is (B). #### B


question: The population of the city where Michelle was born is 145,826. What is the value of the 5 in the number 145,826? Answer Choice: (A) 5 thousands (B) 5 hundreds (C) 5 tens (D) 5 ones

answer: The answer is (A). #### A


question: Olivia used the rule "Add 11" to create the number pattern shown below. 10, 21, 32, 43, 54 Which statement about the number pattern is true? Answer Choice: (A) The 10th number in the pattern will be an even number. (B) The number pattern will never have two even numbers next to each other. (C) The next two numbers in the pattern will be an even number then an odd number. (D) If the number pattern started with an odd number then the pattern would have only odd numbers in it.

answer: The answer is (B). #### B


question: A total of 30 players will play basketball at a park. There will be exactly 5 players on each team. Which statement correctly explains how to find the number of teams needed? Answer Choice: (A) Add 5 to 30 to find 35 teams. (B) Divide 30 by 5 to find 6 teams. (C) Multiply 30 and 5 to find 150 teams. (D) Subtract 5 from 30 to find 25 teams.

answer: The answer is (B). #### B


question: A store sells 107 different colors of paint. They have 25 cans of each color in storage. The number of cans of paint the store has in storage can be found using the expression below. 107 × 25. How many cans of paint does the store have in storage? Answer Choice: (A) 749 (B) 2,675 (C) 2,945 (D) 4,250

answer: The answer is (B). #### B


question: Which expression is equivalent to 5 x 9? Answer Choice: (A) (5 x 4) x (6 x 5) (B) (5 x 5) + (5 x 4) (C) (5 x 5) + (5 x 9) (D) (5 x 9) x (6 x 9)

answer: The answer is (B). #### B


question: Joe was in charge of lights for a dance. The red light blinks every two seconds, the yellow light every three seconds, and the blue light every five seconds. If we include the very beginning and very end of the dance, how many times during a seven minute dance will all the lights come on at the same time? (Assume that all three lights blink simultaneously at the very beginning of the dance.) Answer Choice: (A) 3 (B) 15 (C) 6 (D) 5

answer: The answer is (B). #### B


question: Five thousand dollars compounded annually at an $x\%$ interest rate takes six years to double. At the same interest rate, how many years will it take $\$300$ to grow to $\$9600$? Answer Choice: (A) 12 (B) 1 (C) 30 (D) 5

answer: The answer is (C). #### C


question: The variable $x$ varies directly as the square of $y$, and $y$ varies directly as the cube of $z$. If $x$ equals $-16$ when $z$ equals 2, what is the value of $x$ when $z$ equals $\frac{1}{2}$? Answer Choice: (A) -1 (B) 16 (C) -\frac{1}{256} (D) \frac{1}{16}

answer: The answer is (C). #### C


question: Simplify and write the result with a rational denominator: $$\sqrt{\sqrt[3]{\sqrt{\frac{1}{729}}}}$$ Answer Choice: (A) \frac{3\sqrt{3}}{3} (B) \frac{1}{3} (C) \sqrt{3} (D) \frac{\sqrt{3}}{3}

answer: The answer is (D). #### D


question: Ten students take a biology test and receive the following scores: 45, 55, 50, 70, 65, 80, 40, 90, 70, 85. What is the mean of the students’ test scores? Answer Choice: (A) 55 (B) 60 (C) 62 (D) 65

answer: The answer is (D). #### D