Mathematics Exam: Part 3 | Academic Curator

31. Which one of the following functions is NOT a power function?

A.

f (x) = \sqrt{2} x^{\frac{3}{2}}

B.

f (x) = π x^{5}

C.

f (x) = (\sqrt{3})^{x}

D.

f (x) = x^{\frac{- 3}{5}}

32. Which of the following statements defines the greatest integer function given by $f (x) = ⌊ x ⌋$ ?

A. It is an integer less than or greater than

x

.
B. It is an integer less than or equal to

x

.
C. It is the least integer greater than

x

.
D. It is an integer greater than or equal to

x

.

33. Which one of the following expressions is the correct decomposition of the rational expression $\frac{2 x - 3}{x^{2} + x - 2}$ ?

A.

\frac{1}{3 - 3 x} + \frac{7}{3 x + 6}

B.

\frac{1}{1 - x} + \frac{5}{3 x + 6}

C.

\frac{7}{3 x + 2} - \frac{1}{x + 1}

D.

\frac{5}{3 x + 2} + \frac{1}{x + 1}

34. Consider the graph of the rational function given below.

function is represented?

A.

f (x) = \frac{x}{x^{2} - 1}

B.

f (x) = \frac{x}{x^{2} + 1}

C.

f (x) = \frac{x^{2}}{x^{2} - 1}

D.

f (x) = \frac{x^{2}}{1 - x^{2}}

35. Matrix Equality If $(\begin{matrix} x + y & 2 \\ 5 & 3 \end{matrix}) = (\begin{matrix} 7 & 2 \\ 5 & x - y \end{matrix})$ , then what is the value of $x$ ?

A. -5
B. 5
C. 2
D. -2

36. Which of the following statements is true about the given system of linear equations?

A.

{\begin{cases} 2 x + y = 0 \\ x - 4 y = 0 \end{cases}

is a non-homogeneous system.
B.

{\begin{cases} x + 3 y = 2 \\ 2 x - 5 y = 1 \end{cases}

is a non-homogeneous system.
C.

{\begin{cases} 3 x - y = 1 \\ x + 3 y = 0 \end{cases}

is a homogeneous system.
D.

{\begin{cases} x + 3 y = 6 \\ 2 x - 5 y = 2 \end{cases}

is a homogeneous system.

37. What is the determinant of the matrix $(\begin{matrix} 1 & 2 & 3 \\ 2 & 5 & 3 \\ 7 & 8 & 9 \end{matrix})$ ?

A. 0
B.

\frac{1}{2}

C.

\frac{1}{8}

D. 1

38. Which of the following matrix is the inverse of the matrix $(\begin{matrix} 1 & - 1 & 2 \\ 1 & 0 & 1 \\ 3 & 1 & 3 \end{matrix})$ ?

A.

(\begin{matrix} 1 & 5 & - 1 \\ - 3 & 0 & 1 \\ - 4 & - 1 & 1 \end{matrix})

B.

(\begin{matrix} - 1 & 5 & - 1 \\ 0 & - 3 & 1 \\ 1 & - 4 & 1 \end{matrix})

C.

(\begin{matrix} - 1 & 0 & 1 \\ 5 & 3 & 4 \\ 1 & - 1 & 1 \end{matrix})

D.

(\begin{matrix} - 1 & 0 & 1 \\ 5 & - 3 & - 4 \\ - 1 & 1 & 1 \end{matrix})

39. Which of the following statements describes the difference between scalar and vector quantities?

A. Physical quantities that only have magnitude are scalars, while those that have both magnitude and direction are vectors.
B. Physical quantities that only have magnitude are vectors, while those that have both magnitude and direction are scalars.
C. Physical quantities that only have direction are scalars, while those that have both magnitude and direction are vectors.
D. Physical quantities that only have direction are vectors, while those that have both magnitude and direction are scalars.

40. Which statement is true about types of data?

A. The height of students is qualitative data.
B. The weight of students is qualitative data.
C. The gender of students is quantitative data.
D. The age of students in a class is quantitative data.

41. Consider the following grouped frequency distribution table:

X	0-9	10-19	20-29	30-39	40-49
f	4	3	6	5	2

Then what is the class midpoint of the fourth class?

A. 34.5
B. 35.5
C. 24.5
D. 55.5

42. The table given below shows the ages distribution of children in a small village in years.

Age interval	Frequency(f)
2-4	4
5-7	1
8-10	2
11-13	3

Then what is the mean age of the children's (in years)?

A. 6.9
B. 7.5
C. 7.2
D. 6.6

43. Which one of the following distribution is multimodal?

A. 6, 10, 9, 6, 10, 4
B. 8, 7, 11, 13, 17, 9, 8, 7, 6, 11
C. 12, 13, 26, 15, 25, 38, 28, 27, 32
D. 18, 14, 15, 10, 11, 3, 18, 12

44. Suppose that we have 4 objects chosen 3 at a time. Then which of the following statement is true?

A. The number of combinations is 24.
B. The number of permutations is 24.
C. The number of permutations is 6.
D. The number of combinations is 6.

45. Which one of the following statements defines favorable outcomes in a random experiment?

A. The outcomes containing all sample elements.
B. The outcomes containing only one sample element.
C. The outcomes that have equal chance of being chosen.
D. The outcomes that insure the occurrence of a particular result.

2016 - Mathematics Exam: Questions 31 -45

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