QUESTION 01
The inverse function of \(y = 3x - 2\) is \(\bbox[10px, border: 2px solid red]{(\: \dotso \: )}\)
(A) \(y = \dfrac {x + 3}{2}\)
(B) \(y = \dfrac {x - 3}{2}\)
(C) \(y = \dfrac {x - 2}{3}\)
(D) \(y = \dfrac {x + 2}{3}\)
QUESTION 02
The solution set of the inequality \(\dfrac {x - 3}{x + 1} \geq 0\) is \(\bbox[10px, border: 2px solid red]{(\: \dotso \: )}\)
(A) \((- \sim, -1] \cup [3, + \sim) \)
(B) \((- \sim, -1) \cup [3, + \sim) \)
(C) \((- \sim, -3] \cup [1, + \sim) \)
(D) \((- \sim, -3] \cup (1, + \sim) \)
QUESTION 03
The distance from a point P(−1,2) to another point Q(2,3) is \(\bbox[10px, border: 2px solid red]{(\: \dotso \: )}\)
(A) \(3\)
(B) \(4\)
(C) \(\sqrt{26}\)
(D) \(\sqrt{10}\)
QUESTION 04
If \(a < b, \: c < d\), which of the following is correct ? \(\bbox[10px, border: 2px solid red]{(\: \dotso \: )}\)
(A) \(a^2 < b^2 \)
(B) \(a - c < b - d\)
(C) \(ac < bd \)
(D) \(c^3 < d^3 \)
QUESTION 05
If \(\cos \alpha = - \dfrac 14\), then \(\cos 2 \alpha = \bbox[10px, border: 2px solid red]{(\: \dotso \: )}\)
(A) \(- \dfrac 78\)
(B) \(- \dfrac {3}{16}\)
(C) \(- \dfrac 12\)
(D) \( \dfrac 34\)
QUESTION 06
The foci of the hyperbola \(\dfrac {x^2}{4} - \dfrac {y^2}{5} = 1\) have coordinates \(\bbox[10px, border: 2px solid red]{(\: \dotso \: )}\)
(A) \((0, \pm 3 )\)
(B) \((\pm 3, 0 )\)
(C) \((0, \pm 1 )\)
(D) \((\pm 1, 0 )\)
QUESTION 07
If the sum of the first \(n\) terms of the sequence \(\{a_n\}\) is given by \(S_n = n^2 + 1\), then \(a_{10} = \bbox[10px, border: 2px solid red]{(\: \dotso \: )}\).
(A) 18
(B) 19
(C) 20
(D) 21
QUESTION 08
Which of the following lines is parallel to \(3x - y + 1 = 0\). \(\bbox[10px, border: 2px solid red]{(\: \dotso \: )}\)
(A) \(x - 3y + 2 = 0 \)
(B) \(x + 3y - 2 = 0 \)
(C) \(6x - 2y - 3 = 0 \)
(D) \(6x + 2y + 1 = 0 \)
QUESTION 09
If \(\cos \alpha = - \dfrac 12, \pi < \alpha < \dfrac {3 \pi}{2}\), then \(\sin \dfrac {\alpha}{2} = \bbox[10px, border: 2px solid red]{(\: \dotso \: )}\)
(A) \(\dfrac {\sqrt{3}}{2} \)
(B) \(- \dfrac {\sqrt{3}}{2} \)
(C) \(\pm \dfrac {\sqrt{3}}{2} \)
(D) \(\dfrac 12 \)
QUESTION 10
The domain of the function \(y = 5 \tan \left( x - \dfrac {\pi}{4} \right)\) is \(\bbox[10px, border: 2px solid red]{(\: \dotso \: )}\)
(A) \(\left \{ x | x \neq k \pi + \dfrac {3 \pi}{4}, k \in Z \right \}\)
(B) \(\left \{ x | x \neq k \pi + \dfrac {\pi}{4}, k \in Z \right \} \)
(C) \(\left \{ x | x \neq 2k \pi + \dfrac {3 \pi}{4}, k \in Z \right \} \)
(D) \(\left \{ x | x \neq 2k \pi + \dfrac {\pi}{4}, k \in Z \right \} \)
QUESTION 11
A sequence \(\{a_n\}\) has \(a_1 = 2, a_n = 1 + \dfrac {1}{a_{n - 1}} \: (n \geq 2)\). Then \(a_4 = \bbox[10px, border: 2px solid red]{(\: \dotso \: )}\)
(A) \(\dfrac 32 \)
(B) \(\dfrac 53 \)
(C) \(\dfrac 85 \)
(D) \(\dfrac {13}{8} \)
QUESTION 12
The solution set of the inequality \(\log_2 (3 - x) < 0\) is \(\bbox[10px, border: 2px solid red]{(\: \dotso \: )}\)
(A) \((1, 3) \)
(B) \((-\sim, 3) \)
(C) \((2, +\sim) \)
(D) \((2, 3) \)
QUESTION 13
If a function satisfies \(f(2x + 1) = x - 3\), then \(f(-3) = \bbox[10px, border: 2px solid red]{(\: \dotso \: )}\)
(A) \(-3 \)
(B) \(0 \)
(C) \(-6 \)
(D) \(-5 \)
QUESTION 14
Which of the following is correct? \(\bbox[10px, border: 2px solid red]{(\: \dotso \: )}\)
(A) \((0.3)^{-2.1} > (0.2)^{-2.1} \)
(B) \((2.1)^{0.12} < (2.2)^{0.12} \)
(C) \((3.2)^{-1.1} > (3.2)^{-0.9} \)
(D) \((0.25)^{1.5} > (0.25)^{1.4} \)
QUESTION 15
Let \(\vec a = (-1,2), \vec b = (2,-1)\) be two vectors. Then \(2 \vec a + \vec b = \bbox[10px, border: 2px solid red]{(\: \dotso \: )}\)
(A) \((1,1) \)
(B) \((0,3) \)
(C) \(-4 \)
(D) \((-2,-2) \)
QUESTION 16
A bag contains five equal sized balls. Three of them are black and two of them are red. Two balls are drawn randomly from the bag. The probability that the balls have the same color is \(\bbox[10px, border: 2px solid red]{(\: \dotso \: )}\)
(A) \(\dfrac 15 \)
(B) \(\dfrac 25 \)
(C) \(\dfrac 35 \)
(D) \(\dfrac 45 \)
QUESTION 17
Suppose that the center of an ellipse C is at the origin, and the foci are on the x -axis. Suppose also that it has a vertex at (0,1) , and an eccentricity of \(\dfrac {2 \sqrt{5}}{5}\). The equation of C is \(\bbox[10px, border: 2px solid red]{(\: \dotso \: )}\)
(A) \(\dfrac {x^2}{20} + \dfrac {y^2}{4} = 1\)
(B) \(\dfrac {x^2}{4} + \dfrac {y^2}{20} = 1 \)
(C) \(x^2 + \dfrac {y^2}{5} = 1 \)
(D) \(\dfrac {x^2}{5} + y^2 = 1 \)
QUESTION 18
Suppose that a complex number \(z\) satisfies \((1 - i)^2 z = 3 + 2i\), where \(i\) is the unit imaginary number. Then \(z = \bbox[10px, border: 2px solid red]{(\: \dotso \: )}\)
(A) \(- \dfrac 32 + i \)
(B) \(- \dfrac 32 - i \)
(C) \(-1 - \dfrac 32 i \)
(D) \(-1 + \dfrac 32 i \)
QUESTION 19
The maximum value of the function \(f(x) = 2x^3 - 3x^2 - 36x + 1\) over the interval \([-3,4]\) is \(\bbox[10px, border: 2px solid red]{(\: \dotso \: )}\)
(A) \(-63 \)
(B) \(1 \)
(C) \(28 \)
(D) \(45 \)
QUESTION 20
The angle between the planes \(x - 2y + z - 1 = 0\) and \(2x + y - z + 3 = 0\) is \(\bbox[10px, border: 2px solid red]{(\: \dotso \: )}\)
(A) \(\dfrac {\pi}{3} \)
(B) \(\dfrac {2 \pi}{3} \)
(C) \(\arccos \dfrac 16 \)
(D) \(\pi - \arccos \dfrac 16 \)