William Lowell Putnam Mathematical Competition
Description: Welcome to the William Lowell Putnam Mathematical Competition Quiz! This quiz is designed to test your knowledge and skills in various areas of mathematics, including algebra, calculus, geometry, and number theory. The questions are challenging and require critical thinking and problem-solving abilities. Good luck! | |
Number of Questions: 14 | |
Created by: Aliensbrain Bot | |
Tags: mathematics mathematical competitions william lowell putnam mathematical competition |
Let (f(x) = x^3 - 3x^2 + 2x + 1). Find the value of (f(f(1))).
In a triangle (ABC), if (\angle A = 60^\circ), (\angle B = 75^\circ), and (\angle C = 45^\circ), find the ratio of the length of side (a) to the length of side (b).
Find the area of the region bounded by the curves (y = x^2 - 4x + 3) and (y = x - 1).
Let (S) be the set of all positive integers less than 100 that are divisible by 3 or 5. Find the sum of all the elements of (S).
Let (f(x) = \frac{x^2 - 1}{x - 1}). Find the value of (\lim_{x \to 1} f(x)).
Let (A) be a (3 \times 3) matrix with eigenvalues (1, 2, 3). Find the determinant of (A^2).
Find the number of positive integers less than 1000 that are divisible by 7 but not by 11.
Let (f(x) = \frac{x^3 - 1}{x - 1}). Find the value of (f'(2)).
Let (A) be a (3 \times 3) matrix with eigenvalues (1, 2, 3). Find the trace of (A^3).
Let (S) be the set of all positive integers less than 100 that are divisible by 2 or 3. Find the sum of all the elements of (S).
Let (f(x) = \frac{x^2 - 4x + 3}{x - 1}). Find the value of (f'(1)).
Let (A) be a (3 \times 3) matrix with eigenvalues (1, 2, 3). Find the determinant of (A^4).
Let (S) be the set of all positive integers less than 100 that are divisible by 3 or 4. Find the sum of all the elements of (S).
Let (f(x) = \frac{x^3 - 2x^2 + x - 2}{x - 2}). Find the value of (f'(2)).