Math Trivia 2

15 Points Per Correct Answer - No time limit  

1. Arithmetic: Which of the following is equal to (-5)*(-3)*(-2) ? [Here * denotes multiplication.] 30 -60 60 -30

2. Algebra: Evaluate -x^2 when x = 3. [Be careful here! Note that ^ represents exponentiation.] -9 6 9 -6

3. Geometry: What is true about the two acute angles of a right triangle (in the Euclidean plane?) They are vertical angles. They are supplementary. They are complementary. They are congruent.

4. Trigonometry: For a certain angle, the cosine is negative and the sine is positive. Which quadrant contains this angle? Second quadrant Third quadrant First quadrant Fourth quadrant

5. Analytic Geometry: What do we call the set of all points in the plane for which the sum of the distances from two distinct fixed points is a constant? A parabola A hyperbola An ellipse A circle

6. Calculus: Suppose f is differentiable for all real numbers x and let g(x) = x*f(x). Which of the following is equal to the derivative of g(x)? x + f '(x) f '(x) x*f '(x) + f(x) 1 + f '(x)

7. Analytic Geometry with Vectors: Which of the following is the equation of a line through the origin with normal vector 2i - j? 2x + y = 0 x - 2y = 0 x + 2y = 0 2x - y = 0

8. Elementary Number Theory: How many positive integers less than or equal to 15 are relatively prime to 15? [Relatively prime means they have no common factors other than 1.] 8 10 9 11

9. Basic Set Theory: Let A and B be subsets of a universal set U with A a subset of B. Let A' denote the complement of A and B' denote the complement of B. How are the complements related? The union of A' and B' is U A' is a subset of B' B' is a subset of A' The intersection of A' and B' is the empty set

10. Linear Algebra: Let S denote the subspace of R^3 which consists of all ordered triples of real numbers (x,y,z) which satisfy x + y + z = 0. Which of the following is a well-defined linear transformation T taking S into itself? T(x,y,z) = (x, y, x - y) T(x,y,z) = (x, y, y - x) T(x,y,z) = (x, y, x + y) T(x,y,z) = (x, y, -x - y)

11. Group Theory: What is the smallest order of a nonabelian simple group? 8 48 16 60

12. Ring Theory: Let Z denote the ring of integers and let (10, 15) denote the ideal of Z generated by 10 and 15. Which of the following ideals is also equal to (10, 15)? (30) (10) (5) (15)

13. Real Analysis: Let f(x) be defined for all real numbers x by: f(x) = x * sin(1/x) for x not equal to 0 and f(0) = 0 Which of the following is TRUE? all of these f is differentiable for all x f is continuous for all x f is continuously differentiable for all x

14. Complex Analysis: What is the modulus (absolute value) of the complex number 4 + 3i? 49 25 5 7

15. Basic Topology: Let R denote the set of real numbers with the usual topology and let X denote the closed interval [0,2] with the subspace topology. Let S denote the interval (1,2]. Which of the following is true about S? S is open in X and open in R S is open in X but not open in R S is not open in X but open in R S is not open in X and not open in R