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試験番号：8002問題集
試験科目：PRMIA 「PRM Certification - Exam II: Mathematical Foundations of Risk Measurement」
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NO.1 You intend to invest $100 000 for five years. Four different interest payment options are available.
Choose the interest option that yields the highest return over the five year period.
A. a lump-sum payment of $22 500 on maturity (in five years)
B. an annually compounded rate of 4.15%
C. a quarterly-compounded rate of 4.1%
D. a continuously-compounded rate of 4%
Answer: C
PRMIA問題集 8002 8002 8002 8002認定証
NO.2 When a number is written with a fraction as an exponent, such as , which of the following is the correct
computation?
A. Take the square-root of 75 and raise it to the 5th power
B. Divide 75 by 2, then raise it to the 5th power
C. Multiply 75 by 2.5
D. Square 75, then take the fifth root of it
Answer: A
PRMIA認定試験 8002認定資格 8002 8002 8002
NO.3 Find the roots, if they exist in the real numbers, of the quadratic equation
A. 4 and -2
B. -4 and 2
C. 1 and 0
D. No real roots
Answer: D
PRMIA 8002問題集 8002 8002認証試験 8002 8002
NO.4 Which of the following statements is true?
A. Discrete and continuous compounding produce the same results if the discount rate is positive.
B. Continuous compounding is the better method because it results in higher present values compared to
discrete compounding.
C. Continuous compounding can be thought as making the compounding period infinitesimally small.
D. The constant plays an important role in the mathematical description of continuous compounding.
Answer: C
PRMIA 8002 8002 8002練習問題 8002問題集
NO.5 Let a, b and c be real numbers. Which of the following statements is true?
A. The commutativity of multiplication is defined by
B. The existence of negatives is defined by
C. The distributivity of multiplication is defined by
D. The associativity of multiplication is defined by
Answer: C
PRMIA 8002認定試験 8002
NO.6 What is the sum of the first 20 terms of this sequence: 3, 5, 9, 17, 33, 65, ?
A. 1 048 574
B. 1 048 595
C. 2 097 170
D. 2 097 172
Answer: C
PRMIA認定証 8002 8002認定試験
NO.7 What is the 40th term in the following series: 4, 14, 30, 52, ?
A. 240
B. 4598
C. 4840
D. 4960
Answer: C
PRMIA 8002問題集 8002認定証 8002 8002認証試験 8002
NO.8 You invest $2m in a bank savings account with a constant interest rate of 5% p.a. What is the value of
the investment in 2 years time if interest is compounded quarterly?
A. $2,208,972
B. $2,210,342
C. $2.205,000
D. None of them
Answer: A
PRMIA 8002認定試験 8002 8002認証試験
NO.9 Which of the following statements is not correct?
A. Every linear function is also a quadratic function.
B. A function is defined by its domain together with its action.
C. For finite and small domains, the action of a function may be specified by a list.
D. A function is a rule that assigns to every value x at least one value of y.
Answer: D
PRMIA認証試験 8002 8002認定証 8002問題集
NO.10 Solve the simultaneous linear equations: x + 2y - 2 = 0 and y - 3x = 8
A. x = 1, y = 0.5
B. x = -2, y = 2
C. x = 2, y = 0
D. None of the above
Answer: B
PRMIA 8002 8002認定試験
NO.11 Identify the type and common element (that is, common ratio or common difference) of the following
sequence: 6, 12, 24
A. arithmetic sequence, common difference 2
B. arithmetic sequence, common ratio 2
C. geometric sequence, common ratio 2
D. geometric sequence, common ratio 3
Answer: C
PRMIA参考書 8002 8002過去問
NO.12 For a quadratic equation, which of the following is FALSE?
A. If the discriminant is negative, there are no real solutions
B. If the discriminant is zero, there is only one solution
C. If the discriminant is negative there are two different real solutions
D. If the discriminant is positive there are two different real solutions
Answer: C
PRMIA問題集 8002 8002過去問 8002認定証 8002問題集
NO.13 The sum of the infinite series 1+1/2+1/3+1/4+1/5+.... equals:
A. 12
B. Infinity
C. 128
D. 20
Answer: B
PRMIA過去問 8002 8002 8002認証試験 8002
NO.14 Which of the following is not a sequence?
A. , , , , , o
B. , , , ,
C. , , , , , ,
D. 30
Answer: D
PRMIA 8002認証試験 8002
NO.15 The natural logarithm of x is:.?
A. the inverse function of exp(x)
B. log(e)
C. always greater than x, for x>0
D. 46
Answer: A
PRMIA参考書 8002 8002認証試験 8002
NO.16 Which of the following properties is exhibited by multiplication, but not by addition?
A. associativity
B. commutativity
C. distributivity
D. invertibility
Answer: C
PRMIA練習問題 8002認定資格 8002 8002 8002
NO.17 For each of the following functions, indicate whether its graph is concave or convex:
Y = 7x2 + 3x + 9
Y = 6 ln(3x)
Y = exp(-4x)
A. concave, concave, concave
B. concave, convex, convex
C. convex, concave, concave
D. convex, convex, concave
Answer: C
PRMIA参考書 8002認定試験 8002過去問 8002 8002
NO.18 Which of the provided answers solves this system of equations?
2y
3x = 3y +x
y2 + x2 = 68
A. x = 1; y = square root of 67
B. x = 2; y = 8
C. x = 2; y = -8
D. x = -2; y = -8
Answer: C
PRMIA問題集 8002 8002 8002認定試験
NO.19 What is the simplest form of this expression: log2(165/2)
A. 10
B. 32
C. 5/2 + log2(16)
D. log2 (5/2) + log2(16)
Answer: A
PRMIA認定証 8002 8002認定資格 8002参考書
NO.20 You invest $100 000 for 3 years at a continuously compounded rate of 3%. At the end of 3 years, you
redeem the investment. Taxes of 22% are applied at the time of redemption. What is your approximate
after-tax profit from the investment, rounded to $10?
A. $9420
B. $7350
C. $7230
D. $7100
Answer: B
PRMIA 8002認定試験 8002過去問 8002
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