Mathematics Exam

46. Which of the following statement defines geometric progression?

A. It is a sequence in which the difference between consecutive terms is a positive constant.
B. It is a sequence in which the difference between consecutive terms is a non-zero constant.
C. It is a sequence in which the ratio between consecutive terms is a positive constant.
D. It is a sequence in which the ratio between consecutive terms is a non-zero constant.

47. Given the sequence 3, 6, 12, 24,... Then what is the 10th partial sum of the sequence?

A. 3075
B. 1023
C. 1027
D. 3069

48. Which of the following statement is true about the given infinite series?

A.

\sum_{n = 1}^{\infty} {(\frac{4}{3})}^{n}

is convergent.

B.

\sum_{n = 1}^{\infty} 2^{n}

is divergent.

C.

\sum_{n = 1}^{n} (- 1)^{u} {(\frac{2}{5})}^{n}

is divergent.

D.

\sum_{n = 1}^{\infty} (- 1)^{n} 2^{n}

is convergent.

49. What is the average rate of change of $g (x) = x^{3} - 2 x$ over the interval $1 \leq x \leq 6$ ?

A. 41

B.

\frac{37}{5}

C. 46

D.

\frac{203}{5}

50. Suppose $f (x) = 3 \sqrt{x}$ and $g (x) = \frac{1}{3} x^{4} + 2 x$ be given two functions. Thet which of the following is equal to $(f + g)^{'} (x)$ ?

A.

\frac{2}{3} x^{- 1 / 3} + 4 x^{3} + 2 x

B.

\frac{2}{3} x^{- 1 / 3} + 4 x^{3} + 2

C.

\frac{3}{2} x^{- 1 / 2} + \frac{4}{3} x^{3} + 2

D.

3 x^{- 1 / 2} + 4 x^{3} + 2

51. Let $f (x) = (1 - 2 x)^{\frac{1}{2}}$ . Then what is the values of $f^{'} (x)$ ?

A.

\frac{- 1}{2} \sqrt{1 - 2 x}

B.

\frac{1}{2} \sqrt{1 - 2 x}

C.

- \frac{1}{\sqrt{1 - 2 x}}

D.

\frac{1}{\sqrt{1 - 2 x}}

52. Consider the function f(x) = x³ - 3x² + 3 on (-2, 3). Then which of the following point is local minimum and local maximum of f(x) respectively?

A. (0, 3) and (2, -1)
B. (3, 3) and (-2, -27)
C. (2, -1) and (0, 3)
D. (-2, -27) and (0, 3)

53. Which one of the following statements describes the dispersion of the datavalues?

A. It measures the variability in terms of different units of data.
B. The degree to which numerical data tends to distribute about an average.
C. It helps to describe the degree of similarity of data values.
D. It compares the variability of two or more data that are dependent of the units of measurement.

54. Consider the following data: 13, 16, 19, 19, 19, 19, 24, 27

What is the mean deviation about the mode?

A. 2.75
B. 3.75
C. 3
D. 4

55. What is the coefficient of quartile deviation for the following data?

29, 44, 46, 52, 35, 35, 25, 15, 10, 55, 56

A. 0.35
B. 0.48
C. 2.08
D. 2.85

56. Consider the following data;

1, 3, 7, 9, 11, 13, 18, 28

Then the coefficient of mean deviation about the median is equal to:

A. 8/5
B. 5/8
C. 1/2
D. 1/4

57. Given the objective function Z=-x+2y that is subjected to the constraints
${\begin{matrix} x \geq 3 \\ x + y \geq 5 \\ x + 2 y \leq 6 \\ y \geq 0 \end{matrix}$
What are the maximum and the minimum values of Z respectively?

A. 1 and -2
B. -2 and -6
C. -6 and -2
D. -2 and 1

58. A television company astembles Ind screen and surned scrioen telsemmans. The company has to invest Bur 15,000 to assemble arie flat treceit and Bire 20,000 to assemble one curved serecu televisions. The eomppany allocates a maximum of Birr 900,000 in a week for assembling. The cump, iny gets Bic1800 profit from a sale of one flat screen telesision and Birr 2000 puxtit from a sale of one curved sorcen relevision. Moreover, the company has I store of maximum eapacity of storing 50 relevisions. Let $x$ be the number of flat screens and $y$ be the number of curved screens. Then which one of the following inequalities should model the profit for the objective function $Z = 1800 x + 2000 y$ ?

A.

{\begin{matrix} 15, 000 x + 20, 000 y \leq 900, 000 \\ x + y \leq 50 \\ x, y \geq 0 \end{matrix}

B.

{\begin{matrix} 15, 000 x + 20, 000 y \leq 360, 000 \\ x + y \leq 50 \\ x, y \geq 0 \end{matrix}

C.

{\begin{matrix} 20, 000 x + 15, 000 y \leq 900, 000 \\ x + y \leq 50 \\ x, y \geq 0 \end{matrix}

D.

{\begin{matrix} 20, 000 x + 15, 000 y \leq 360, 000 \\ x + y \leq 50 \\ x, y \geq 0 \end{matrix}

59. A company offers a discount of $25 %$ on one of its product for promotio What is a regular price of the product if it is purchased for Bir 99?

A. Birr 198
B. Birr 125
C. Birr 110
D. Birr 132

60. A worker of a company borrowed Birr 100,000 from the company's credit and saving association. She agreed to pay 10% of the loan during the agreement and on the remaining amount to pay Birr 3000 (monthly plus interest) in 36 monthly installments. What is the total amount of money she paid to the credit and saving association?

A. Birr 118,000
B. Birr 108,000
C. Birr 116,000
D. Birr 106,000

Mathematics Exam: Part 4

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