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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Calculus and Functions | 20% | - Multivariable calculus
|
| Topic 2: Linear Algebra and Matrix Theory | 20% | - Matrix operations
|
| Topic 3: Statistics and Regression Analysis | 20% | - Descriptive statistics
|
| Topic 4: Probability Theory | 25% | - Basic probability concepts
|
| Topic 5: Numerical Methods & Financial Mathematics | 15% | - Root finding and approximation - Basics of risk modeling - Time value of money |
1. Evaluate the derivative of ln(1+ x2) at the point x = 1
A) 2
B) 0.5
C) 0
D) 1
2. Two vectors are orthogonal when:
A) one is a scalar multiple of the other
B) their determinant is zero
C) their components are linearly dependent
D) their scalar product (sum product) is zero
3. If a random variable X has a normal distribution with mean zero and variance 4, approximately what proportion of realizations of X should lie between -4 and +4?
A) 95%
B) 66.60%
C) 99%
D) 90%
4. Your stockbroker randomly recommends stocks to his clients from a tip sheet he is given each day. Today, his tip sheet has 3 common stocks and 5 preferred stocks from Asian companies and 3 common stocks and 5 preferred stocks from European companies. What is the probability that he will recommend a common stock AND/OR a European stock to you when you call and ask for one stock to buy today?
A) None of these
B) 9/16
C) 7/8
D) 11/16
5. Calculate the determinant of the following matrix:
A) 4.25
B) 4
C) 2
D) -4.25
Solutions:
| Question # 1 Answer: D | Question # 2 Answer: D | Question # 3 Answer: A | Question # 4 Answer: D | Question # 5 Answer: C |
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