sample qp - 2014

8/20/2019 Sample QP - 2014

1/22

ACET: Practice Exam – Questions Page 1

The Actuarial Education Company © IFE: 2014 Examinations

Practice Exam – Questions

Question E1

What is 0.040783 rounded to 2 significant figures?

A 0.04

B 0.041

C 0.0408

D 0.04078 [1]

FAC 2 1

Question E2

What is na a x

log x log y

Ê ˆ - Á ˜ Ë ¯

A ( 1) a an log x log y- +

B ( )a x ynx a --

C

n

alog x

Ê ˆ

-Á ˜ Ë ¯

D1n

a

xlog

-Ê ˆ Á ˜ Ë ¯

[1]

FAC 4 1

Question E3

Solve 11 3 2 15 x- £ - <

A 7 6 x- £ < B 7 x ≥ and 6 x < - C 7 6 x≥ > - D 7 x £ - and 6 x > [1]

FAC 4 4

8/20/2019 Sample QP - 2014

2/22

Page 2 ACET: Practice Exam – Questions

© IFE: 2014 Examinations The Actuarial Education Company

Question E4

Which of these is the graph of n y x= where n is an even number:

A

x

y

B

x

y

C

x

y

D

x

y

[1]

FAC 3 1

8/20/2019 Sample QP - 2014

3/22



Question E5

Interest rates at the start of the year are set at 2.5%. At the end of the year they are

2.75%. What is the absolute change in the interest rate over the year?

A 10%

B 250 basis points

C 9.09%

D 25 basis points [1]

FAC 5 2

Question E6

What is the result if (2 3 )i+ is multiplied by its complex conjugate?

A 5 12i- + B 5- C 13

D 5 12i- - [1]FAC 5 7

Question E7

Differentiate 5 y x= with respect to x .

A 25 --

B ½52

x

C 3 252

x

D5

2 x [1]

FAC 6 3

8/20/2019 Sample QP - 2014

4/22



Question E8

Find ( ) f x¢ where2

3( )

x f x

e= .

A2

3

2 xe

B2

3

2 xe-

C2

6 xe

-

D2

6 xe

[1]

FAC 6 4

Question E9

What is

14

0

3 xe dxÚ ?

A 19.17

B 40.20

C 160.79

D 643.18 [1]

FAC 7 2

8/20/2019 Sample QP - 2014

5/22



Question E10

What is the integral of3

1 1

x x- ?

A4

41 c

x- +

B4

1ln

4c

x- +

C2

21 c

x- +

D2

1ln

2c

x+ + [1]

FAC 7 1

Question E11

If

1

2

2

Ê ˆ Á ˜ = -Á ˜ Ë ¯

a and

2

3

5

-Ê ˆ Á ˜ =Á ˜ Ë ¯

b then 2-b a is:

A 4.24B 5.83

C 8.12

D 12.37 [1]

FAC 8 1

Question E12

If3 4

2 5

- -Ê ˆ = Á ˜ Ë ¯ B then | |B is given by:

A 23- B 7- C 7

D 23 [1]

FAC 8 2

8/20/2019 Sample QP - 2014

6/22



Question E13

The abbreviation etc means:

A for exampleB compared with

C that is to say

D and so on [1]

FAC Gloss

Question E14

The histogram below shows the age distribution of the last 100 policyholders to take out

an insurance policy with a life insurance company.

0.6

5.6

4.2

1.6

0.7 0.48 f r e q u e n c y

d e n s i t y

age

0 15 20 25 35 55 80

1

2

3

4

5

6

Determine the number of policyholders in the 35 to 55 age group.

A 7

B 14

C 56

D 70 [1]SP 1 3

8/20/2019 Sample QP - 2014

7/22



Question E15

A company employs 32 skilled labourers and 19 unskilled labourers. The mean salary

of the skilled labourers is £24,638, and the mean salary of the unskilled labourers is

£13,942.

Calculate the mean salary of all 51 labourers.

A £17,926.78

B £19,290.00

C £20,653.22

D £22,428.22 [1]

SP 2 2

Question E16

The numbers of claims last year on a group of home insurance policies was recorded

and resulted in the following frequency distribution:

Number of claims, 0 1 2 3

Number of policies, f 70 30 15 5

Calculate the sample median number of claims per policy.

A 0

B 0.625

C 0.864

D 1.5 [1]

SP 2 3

8/20/2019 Sample QP - 2014

8/22



Question E17

For independent events A and B , you are given:

( ) 0.5 ( ) 0.3 P A P B

Determine ( or ) P A B .

A 0.65

B 0.72

C 0.80

D 0.95 [1]

SP 4 2&3

Question E18

A contest has 3 prizes and 8 competitors. Each competitor can receive at most one

prize. How many ways are there of allocating the prizes to the competitors?

A 56

B 168

C 336

D 1512 [1]SP 6 2

Question E19

The number of claims, X , arise on a policy according to the following probability

distribution:

x 0 1 2 3

P X x 0.2 a b 0.4

If the mean number of claims is 1.72, then the value b a- is:

A 0.16- B 0

C 0.12

D 0.28 [1]

SP 7 4

8/20/2019 Sample QP - 2014

9/22



Question E20

A discrete random variable X has the following probability function:

1 2 3

( ) P X x= 0.45 0.35 0.2

Calculate2

E X

Ê ˆ Á ˜ Ë ¯

.

A 1.143

B 1.383

C 1.75

D 2 [1]SP 7 5

Question E21

If 5.2 E X and 4.49 sd X , the second moment about zero is:

A 9.69

B 25.36

C 31.53

D 47.20 [1]

SP 7 8

Question E22

The probability density function of a random variable Y is given by:

2364( ) 0 4 f y y y

Calculate ( 2) P Y .

A 0.125

B 0.1875

C 0.8125

D 0.875 [1]

SP 9 3

8/20/2019 Sample QP - 2014

10/22



Question E23

A continuous random variable X has a mean of 50 and a standard deviation of 8.

Calculate

4 7

var 10

X -Ê ˆ Á ˜ Ë ¯ .

A 1.28

B 3.2

C 10.24

D 25.6 [1]

SP 9 6

Question E24

The random variable X is uniformly distributed on the interval (1,4) . The CDF of X

is given by:

A1

3

B1

4

C

1

3

x -

D4

x [1]

SP 10 1

8/20/2019 Sample QP - 2014

11/22



Question E25

Which of the following scattergraphs is most likely to be the relationship between the

number of cold drinks sold by a cafe and the temperature?

A

B

C

D

[1]

SP 12 2

8/20/2019 Sample QP - 2014

12/22



Question E26

Simplify the expression(3 1)! (2 2)

(3 1)(2 )!

n n

n n

- G +G +

, where n is an integer.

A(2 2)(2 1)

(3 1)(3 )

n n

n n

+ ++

B(2 2)(2 1)

3

n n

n

+ +

C(2 1)

(3 1)(3 )

n

n n

++

D(2 1)

3

n

n

+ [2]

FAC 3 3

Question E27

Calculate21 (5 4.712)

2.306 0.106310 2.82596

Ï ¸-Ô Ô+ ¥Ì ˝Ô ÔÓ ˛

.

A 0.088B 0.270

C 0.338

D 0.741 [2]

FAC 2 2

Question E28

Solve the quadratic equation 27 4 0 x x- - = giving your solutions to 1 DP.

A 5.3 and 1.3 x = - B 0.2 and 0.8 x = - C 10.6 and 2.6 x = - D The equation has no real solutions [2]

FAC 4 2

8/20/2019 Sample QP - 2014

13/22



Question E29

Use the result( 1) ( 1)( 2)2 32! 3!

(1 ) 1 p p p p p p x px x x

- - -+ = + + + + to expand the

expression ( ) 1.21 x -+ as far as the term in 3 x and hence evaluate it when 0.4 x = - .

A 0.641088

B 1.358912

C 1.781312

D 1.845944 [2]

FAC 4 9

Question E30

Solve for x and : 2 22 33 x y+ = 3 x y+ = -

A 21 x = - and 18 y = B 4 x = - and 1 y = C 5 x = and 2 y = - or 1 x = - and 4 y = D 5 x = - and 2 y = or 1= and 4 y = - [2]

FAC 4 3

Question E31

Calculate the sum of the first 10 terms in the sequence 5, 6, 7.2, 8.64, ...

A 103.995

B 129.793

C 155.752

D 160.752 [2]FAC 4 7

8/20/2019 Sample QP - 2014

14/22



Question E32

A population increases by 5% every year. Calculate the minimum whole number of

years until the population has doubled in size.

A 9

B 12

C 15

D 18 [2]

FAC 5 1

Question E33

Given 3 i= + is a complex root of the cubic 3 24 2 20 0 x x x- - + = , find the othertwo roots.

A 3 or 2 x i= - - B ( ) ( )3 or 2i i= - - + C 3 or 3 x i= - D 3 or 2 x i= - - - [2]

FAC 5 7

Question E34

Finddy

diwhere

41 (1 )i y

i

-- += .

A4 5

2

(1 ) 4 (1 ) 1i i i

i

- -+ - + -

B

4 3

2

(1 ) 4 (1 ) 1i i i

i

- -+ - + -

C4 5

2

(1 ) 4 (1 ) 1i i i

i

- -+ + + -

D4 3

2

(1 ) 4 (1 ) 1i i i

i

- -+ + + - [2]

FAC 6 4

8/20/2019 Sample QP - 2014

15/22



Question E35

Find the second derivative of ( 1)( )t e M t e m -= evaluated at 0t = , where m is a constant.

A (0) M m =¢¢

B 2(0) M m =¢¢

C 2(0) M m m = +¢¢

D 2(0) e m =¢¢ [2]FAC 6 5

Question E36

What is ( ) ( )( )2

2 3axy b xy c xy

x y

∂+ +

∂ ∂?

A ( ) ( )2

2 3a b yx c yx+ +

B ( ) ( )2

4 9a b yx c yx+ +

C

2 3

2 3

yx yxaxy b c

Ê ˆ Ê ˆ + +Á ˜ Á ˜ Ë ¯ Ë ¯

D

2 3 4

2 3 4

yx yx yxa b c

Ê ˆ Ê ˆ Ê ˆ + +Á ˜ Á ˜ Á ˜ Ë ¯ Ë ¯ Ë ¯ [2]

FAC 6 7

8/20/2019 Sample QP - 2014

16/22



Question E37

What is 2 48 (3 2) x dx+Ú ?

A2 58 (3 2)

5

x xc

++

B2 58(3 2)

5

xc

++

C2 54(3 2)

15

xc

++

D3 58 ( 2)

5

x xc

++ [2]

FAC 7 3

Question E38

What is

5 2

1 1

(3 4 )

x y

y dy dx

= =

+Ú Ú ?

A24

B 60

C 66

D 84 [2]

FAC 7 5

Question E39

Using the trapezium rule and 6 ordinates, what is the value of

1

3

0

xe dxÚ ?

A 4.330

B 6.552

C 13.103

D 65.516 [2]

FAC 7 6

8/20/2019 Sample QP - 2014

17/22



Question E40

If1 2

3 4

Ê ˆ = Á ˜

-Ë ¯

A then T A A is given by:

A5 5

5 20

Ê ˆ Á ˜ -Ë ¯

B2 16

9 2

-Ê ˆ Á ˜ - -Ë ¯

C 1 0

0 1

Ê ˆ Á ˜ Ë ¯

D 10 1010 20-Ê ˆ Á ˜ -Ë ¯

[2]

FAC 8 2

Question E41

The eigenvalues of1 2

2 2

Ê ˆ Á ˜ -Ë ¯

are:

A 2 and 3- B 1 and 6- C 4.37 and 1.37- D do not exist [2]

FAC 8 2

8/20/2019 Sample QP - 2014

18/22



Question E42

The stem and leaf diagram below shows the values of 20 claim amounts from a certain

portfolio of policies. The stem unit is $1,000 and the leaf unit is $100.

1 2458

2 03899

3 35677

4 1448

5 03

Determine the upper quartile of this sample.

A $4,100

B $4,175

C $4,325

D $4,400 [2]

SP 1 3 & 3 2

Question E43

Calculate the standard deviation of the following data set:

35 40 41 45 45 51 53

A 5.83

B 6.29

C 33.92

D 39.57 [2]

SP 3 3

Question E44

In a certain population, 55% of the lives are male, 30% of males are over 60 and 35% of

females are over 60. A life is randomly selected from this population. What is the

probability that this life is female, given that the life is under 60?

A 0.4317

B 0.4884

C 0.5683

D 0.6775 [2]

SP 5 2

8/20/2019 Sample QP - 2014

19/22



Question E45

Amit has a bunch of 12 bananas. The probability of any banana in the bunch being

unripe is 0.1. Calculate the probability that there are 3 unripe bananas in the bunch.

A 0.001

B 0.000387

C 0.0852

D 0.22 [2]

SP 6 4

Question E46

The random variable, X , has probability function:

( 0) 0.4 ( 1) 0.6 P X P X

Calculate the third-order moment of X about 0.8.

A 0.200- B 0.2096

C 0.28

D 0.6 [2]

SP 7 8

Question E47

Given that ~ (1.2) X Poi , calculate ( )2 | 0 P X X = > .

You are given that the probability function of a Poisson distribution with mean is:

( )!

x

P X x e x

A 0.217

B 0.310

C 0.690

D 0.783 [2]

SP 8 4

8/20/2019 Sample QP - 2014

20/22



Question E48

A continuous random variable X has PDF:

2 0.1( ) 0.005 x X f x x e-= for 0 x >

Calculate the mode of X .

A 0.2

B 2

C 20

D X has no mode. [2]

SP 9 4

Question E49

The random variable X has an exponential distribution with PDF:

0.2( ) 0.2 0 x f x e x

The median of this distribution is:

A 0.2

B 3.466

C 4.581

D 5 [2]

SP 10 2

Question E50

If ~ 120, 25 X N calculate 113 8 P X

.

You are given that ( 0.04) 0.51595 P Z , ( 0.2) 0.57926 P Z ,

( 0.6) 0.72575 P Z and ( 3) 0.99865 P Z .

A 0.2098

B 0.2417

C 0.41939

D 0.5779 1 [2]

SP 11 4

8/20/2019 Sample QP - 2014

21/22



Question E51

You are given that

( ) ( ) ( ) ( )4 3 2

6.6 2 2 2

11 1 1 PV

ii i i

-= + + +

++ + +. By trial and error and

interpolation, calculate the value of i to 2 significant figures such that 0 PV = .

Evaluate the formula(1 ) 1n

n

i s

i

+ -= , using the value of i obtained, where 4n = .

A 4.246n

s =

B 4.297n

s =

C 4.310n

s =

D 4.375n s = [5]FAC 5 5

Question E52

Find and distinguish between the turning points of the function 3 5( ) 15 f x x x= - .

A minima at 1.225 x = ± and point of inflexion at 0 x = B minimum at 3 x = - , point of inflexion at 0 x = and maximum at 3 x = C maximum at 3 x = - , point of inflexion at 0 x = and minimum at 3 x = D maxima at 1.225 x = ± , point of inflexion at 0 x = [5]

FAC 6 6

Question E53

What is

22 0.5

1

2 x x e dx-Ú ?

A 8.437

B 4.218

C 2.109

D 0.875- [5]FAC 7 3

8/20/2019 Sample QP - 2014

22/22


Question E54

The random variable, X , has the following PF:

x 0 1 2 3

P X x 0.5 0.35 0.1 0.05

The coefficient of skewness,3

3

[( ) ] E X

, is:

A 0.507

B 0.938

C 1.113

D 1.861 [5]

SP 7 7

Question E55

The probability density function of a random variable W is given by:

3( ) (1 ) 0 1 f w kw w x

The variance of W is:

A 0.005

B 0.0317

C 0.476

D 0.667 [5]

SP 9 6

sample qp - 2014

Documents