Math Trivia 1

15 Points Per Correct Answer - No time limit  

1. Arithmetic: What is the value of 3 + 2*7 ? Here * denotes multiplication. 17 20 35 13

2. Basic Algebra: Which of the following is equal to (2x - 7)^2 ? 4x^2 + 49 4x^2 - 14x + 49 4x^2 - 28x + 49 4x^2 - 49

3. Geometry: The perpendicular bisectors of the sides of a triangle are concurrent in this point. The circumcenter The centroid The incenter The orthocenter

4. Analytic Geometry: What can you say about the eccentricity e of a hyperbola? e = 0 e = 1 e is greater than 1 e is between 0 and 1

5. Calculus: Suppose f(x) is a differentiable function for all real numbers x which also satisfies: f '(4) = 0, f '(x) is negative for all x less than 4, f '(x) is positive for all x greater than 4 What can be said about the critical value x = 4? f(x) has a local maximum at x = 4 nothing can be said, we must use the second derivative test f(x) does not have a local extrema at x = 4 f(x) has a local minimum at x = 4

6. Advanced Calculus: Let f(x,y,z) = xyz. What is the gradient of f? The vector (yz, xz, xy) The vector (xz, yz, xy) The vector (xy, xz, yz) The vector (xz, xy, yz)

7. Basic Set Theory: How many 2 element subsets does a 4 element set have? 6 3 4 12

8. Linear Algebra: Let A be a square matrix with the property that there exists a positive integer k such that A^k is the zero matrix. A is said to be which of the following? orthogonal idempotent symmetric nilpotent

9. Elementary Number Theory: Which of the following numbers is congruent to 3 mod 7? 27 17 37 47

10. Basic Probability: A box contains 2 good and 2 bad light bulbs. 2 light bulbs are selected from the box without replacement. Find the probability that both light bulbs selected were good. 1/6 1/4 1/2 2/3

11. Real Analysis: Let f be a continuous function with domain the closed interval [0,1]. Which of the following is not necessary true? f attains a maximum value at some c in [0,1] f is differentiable at some value c in the interval f is Riemann integrable on the interval [0,1] The image of f is compact

12. Group Theory: Let G be a group. What is the name given to the subgroup that consists of all elements of G that commute with every element of G? The commutator subgroup of G The center of G The trivial subgroup The Sylow p-subgroup

13. Ring Theory: Let R be a commutative ring with 1 and let m be a maximal ideal. Which of the following is FALSE? The quotient R/m is a field There exists an ideal J not equal to R or m with m a subset of J a subset of R The quotient R/m is an integral domain m is a prime ideal

14. Complex Analysis: Which of the following is NOT a sixth root of 1? e^(i*pi/2) e^(2i*pi/3) e^(i*pi/3) e^(i*pi)

15. Basic Topology: Let X be a Hausdorff topological space and C a compact subset of X. What must be true of the complement of C? It must be closed It must be empty It must be compact It must be open