Mathematics Exam

16. Let $f (x) = x^{3} + 2 x + 1$ and $g (x) = x^{2} - 1$ be given two polynomial functions. Then which of the following is true?

A.

f (x) + g (x) = x^{3} + x^{2}

B.

f (x) - g (x) = x^{3} - x^{2} + 2 x

C.

f (x) g (x) = x^{5} + x^{3} + x^{2} - 2 x - 1

D.

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

17. Let $a, b \in$ R such that $a < b$ and $f$ be a polynomial function. Then which ane of the following statement states the locahon theorem?

A. If

f (a)

and

f (b)

have the same signs, then there is at least one zero of

\bar{f}

between a and

b

.
B. If

f (a)

and

f (b)

have the same signs, then there exist a unique zeros of

f

between

a

and

b

.
C. If

f (a)

and

f (b)

have opposite signs, then there is a unique zeros of f between a and b .
D. If

f (a)

and

I (b)

have opposite signs, then there is at least one zero of

f

between a and

b

.

18. Which one of the following is the solution set of $5^{x} = 11.2$ ?
[Use $\log 5 = 0, 6990$ and $\log 1.12 = 0.0485$ ]

A. 1.5
B. 1.2
C. 1.69
D. 1.12

19. Given that $\log 4.8 = 0.6812, \log 6.93 = 0.8406$ and $\log 6.84 = 0.8351$ . Then what is the value of $\sqrt{48}$ ?

A. 6.71
B. 6.93
C. 6.84
D. 6.83

20. Consider the equation $\log x + \log (x - 3) = 1$ . Then what is its solution set?

A. {2, -5}
B. {5, -2}
C. {6}
D. {5}

21. If the number of bacteria in a certain laboratory colony grows at the rate of $5 %$ per day and assuming that there are 1000 bacteria present initially, then what would be the approximate number of bacteria present after 3 days?

A. 1102
B. 1158
C. 1050
D. 1105

22. Consider the line sugment PQ with $P = (1, - 1)$ and $Q = (4, 2)$ . Then which of the following point divides $P Q$ intermally in the ratio of $2 : 1$ ?

A.

(2, 0)

B.

(2, 1)

C.

(3, 0)

D.

(3, 1)

23. What is the equation of a line that passes through $(- 2, 5)$ and has a slope $\frac{1}{2}$ ?

A.

y = 2 x + 12

B.

2 y + x = 5

C.

y = \frac{1}{2} x + 5

D.

2 y - x - 12 = 0

24. Let $θ$ be an angle in standard position and $(x, y)$ be a point on the termin side of $θ$ , which is different from the origin. Let $r$ be the distance from ( $x$ , to the origin. Then which of the following defines $\cos θ$ ?

A.

\frac{y}{r}

B.

\frac{r}{x}

C.

- \frac{x}{r}

D.

\frac{r}{y}

25. Censider the gouph of a certain trigonometric function given betow.

Which one of the following functions represents the above graph for $\frac{- π}{2} \leq x \leq \frac{5 π}{2} ?$

A.

y = \sin x

B.

y = \csc x

C.

y = \cos x

D.

y = \sec x

26. Which of the following is true about the cosecant value of the given angles?

A.

\csc 135^{\circ} = - \sqrt{2}

B.

\csc 45^{\circ} = \frac{1}{\sqrt{2}}

C.

\csc 45^{\circ} = \sqrt{2}

D.

\csc 135^{\circ} = - \frac{1}{\sqrt{2}}

27. Consider the figure provided.

If $m (∠ C P E) = 30^{\circ}$ and $m (∠ A F E) = 55^{\circ}$ , then what is the value of $∠ A M C$ ?

A.

30^{\circ}

B.

50^{\circ}

C.

25^{\circ}

D.

60^{\circ}

28. What is the total surface area (in ${cm}^{2}$ ) of the cylinder whose radius is $2 cm$ and height is $7 cm$ ?

A.

28 π

B.

36 π

C.

98 π

D.

49 π

29. If a square pyramid has a base side of $6 cm$ long and its lateral faces are equilateral triangles, then what is its volume (in ${cm}^{3}$ )?

A.

3 \sqrt{2}

B. 48
C.

36 \sqrt{2}

D. 72

30. Which of the following statements defines a frustum of a cone?

A. It is a part of a cone included between the base and a horizontal cross-section made by a plane parallel to the base.
B. It is a part of a cone included between the vertex and a horizontal cross-section made by a plane parallel to the base.
C. It is a part of a cone included between the base and a horizontal cross-section made by a plane.
D. It is a part of a cone included between the vertex and a horizontal cross-section made by a plane.

Mathematics Exam: Part 2

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