Miscellaneous Mathematics

15 Points Per Correct Answer - No time limit  

1. We know that if we differentiate f(x) = e^x, we will get the function itself, namely e^x; and if we integrate the function f(x) = e^x, we will get e^x + c. The value of e, namely 2.71828… is an irrational number. It is also known as? Fermat’s number Euler’s number Archimedes’ number Newton’s number

2. In trigonometry, the sine of an angle theta is defined as the ratio of the length of the______ to the length of the ______. hypotenuse; opposite side opposite side; hypotenuse adjacent side; hypotenuse hypotenuse; adjacent side

3. Möbius strip is so-called after the German mathematician August Ferdinand Möbius. The amazing properties of the Möbius strip had also been discovered by another mathematician 2 months earlier in 1858. He was? Edwin Thomson Jaynes Johann Benedict Listing George Barker Jeffery Edward Jan Habich

4. In vectors, scalar products are also known as dot products. Let vector a = a1, a2, a3 and vector b = b1, b2, b3. The scalar product of a dot b is given by? a1 + a2 + a3 + b1 + b2 + b3 a1 x a2 x a3 + b1 x b2 x b3 a1 x b1 + a2 x b2 + a3 x b3 a1 x a2 x a3 x b1 x b2 x b3

5. In mathematics, there are real numbers and imaginary numbers. An imaginary unit, i, is the square root of -1. Which of the following equations is the WRONG one? i^3 = -i i^5 = 1 i^4 = 1 i^2 = -1

6. In elementary linear algebra, the determinant of a 2x2 matrix is given by ad-bc. Meanwhile, the determinant of 3x3 or nxn matrix, where n is equal or greater then 4 can be found by using row or column cofactor expansion. What is the determinant for an 1x1 matrix that contains a single element of b? b^2 1/b b surd b

7. In statistics and probability theory, the normal distribution (the bell-shaped curve) is also known as? The Jouffret distribution The Carl distribution The Laplace-Gaussian distribution The Friedrich distribution

8. In calculus, a very small difference between the real value of f(x) and c on the y-axis is represented by the symbol epsilon. On the other hand, the difference between the value x and c on the x-axis is represented by which symbol? Delta Theta Lambda Kappa

9. The Fourier series are used widely in many fields, such as optics, acoustics, signal and image processing, and spectroscopy. This series was first introduced by a French mathematician, Joseph Fourier in his work on heat conduction. This series is important in analyzing which of the following? Linear functions Quadratic functions Exponential functions Periodic functions

10. In mathematics, conjecture and theorem carry the same meaning. Yes No