College Entrance Math Test

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College Entrance Mathematics Test (50 Items) Instructions: Choose the best answer for each question. Algebra Simplify: $3(x - 2) - 2(x + 5)$ a) $x - 16$ b) $x - 4$ c) $x + 1$ d) $x + 16$ If $2x + 5 = 11$, what is the value of $x$? a) $2$ b) $3$ c) $4$ d) $8$ Factor the expression: $x^2 - 9$ a) $(x - 3)^2$ b) $(x + 3)^2$ c) $(x - 3)(x + 3)$ d) $(x - 9)(x + 1)$ Solve for $y$: $3y - 7 = 5y + 3$ a) $-5$ b) $-2$ c) $2$ d) $5$ What is the value of $x^2 - 4x + 4$ when $x = 3$? a) $1$ b) $4$ c) $7$ d) $25$ Which of the following is an equation of a line with slope $2$ and y-intercept $3$? a) $y = 3x + 2$ b) $y = 2x + 3$ c) $y = -2x + 3$ d) $y = 3x - 2$ Solve the inequality: $2x + 1 > 7$ a) $x 3$ c) $x 4$ If $f(x) = x^2 + 3$, what is $f(-2)$? a) $-1$ b) $1$ c) $7$ d) $9$ Simplify: $(a^3 b^2)^4$ a) $a^7 b^6$ b) $a^{12} b^8$ c) $a^{12} b^2$ d) $a^3 b^8$ What is the solution set for the system of equations: $x + y = 5$ and $x - y = 1$? a) $(2, 3)$ b) $(3, 2)$ c) $(4, 1)$ d) $(1, 4)$ Functions and Equations What is the domain of the function $f(x) = \sqrt{x - 4}$? a) $x > 4$ b) $x \ge 4$ c) $x Find the roots of the quadratic equation $x^2 - 5x + 6 = 0$. a) $x=2, x=3$ b) $x=-2, x=-3$ c) $x=1, x=6$ d) $x=-1, x=-6$ If $log_2 8 = x$, what is $x$? a) $2$ b) $3$ c) $4$ d) $16$ What is the equation of the parabola with vertex $(0,0)$ and focus $(0, 2)$? a) $y^2 = 8x$ b) $x^2 = 8y$ c) $y^2 = -8x$ d) $x^2 = -8y$ Solve for $x$: $e^{2x} = 1$ a) $x = 0$ b) $x = 1/2$ c) $x = 1$ d) $x = \ln(1/2)$ Which of the following is equivalent to $a^{\frac{m}{n}}$? a) $\sqrt[m]{a^n}$ b) $\sqrt[n]{a^m}$ c) $a^{mn}$ d) $a^{m-n}$ If a function is even, then $f(-x) = ?$ a) $-f(x)$ b) $f(x)$ c) $1/f(x)$ d) $f(x^2)$ What is the range of the function $f(x) = x^2$? a) All real numbers b) $y \ge 0$ c) $y \le 0$ d) $y > 0$ Which transformation describes $g(x) = f(x - 3)$ compared to $f(x)$? a) Shift left by 3 b) Shift right by 3 c) Shift up by 3 d) Shift down by 3 The inverse of $f(x) = 2x + 1$ is: a) $f^{-1}(x) = \frac{x - 1}{2}$ b) $f^{-1}(x) = \frac{x + 1}{2}$ c) $f^{-1}(x) = 1 - 2x$ d) $f^{-1}(x) = 2x - 1$ Geometry What is the area of a circle with radius $5$ units? a) $5\pi$ b) $10\pi$ c) $25\pi$ d) $100\pi$ A triangle has angles $30^\circ$ and $90^\circ$. What is the measure of the third angle? a) $30^\circ$ b) $45^\circ$ c) $60^\circ$ d) $90^\circ$ What is the perimeter of a rectangle with length $8$ cm and width $3$ cm? a) $11$ cm b) $22$ cm c) $24$ cm d) $48$ cm The distance between points $(1, 2)$ and $(4, 6)$ is: a) $3$ b) $4$ c) $5$ d) $7$ What is the volume of a cube with side length $4$ cm? a) $16 \text{ cm}^3$ b) $24 \text{ cm}^3$ c) $48 \text{ cm}^3$ d) $64 \text{ cm}^3$ Lines $L_1$ and $L_2$ are parallel. If $L_1$ has a slope of $3$, what is the slope of $L_2$? a) $-3$ b) $1/3$ c) $-1/3$ d) $3$ In a right-angled triangle, if the two shorter sides are $3$ and $4$, what is the length of the hypotenuse? a) $5$ b) $6$ c) $7$ d) $25$ What is the measure of each interior angle of a regular hexagon? a) $90^\circ$ b) $108^\circ$ c) $120^\circ$ d) $135^\circ$ If two angles are supplementary and one angle measures $70^\circ$, what is the measure of the other angle? a) $20^\circ$ b) $110^\circ$ c) $180^\circ$ d) $70^\circ$ What is the midpoint of the segment connecting $(2, -1)$ and $(6, 5)$? a) $(4, 2)$ b) $(3, 3)$ c) $(8, 4)$ d) $(2, 4)$ Trigonometry What is $\sin(30^\circ)$? a) $0$ b) $1/2$ c) $\sqrt{3}/2$ d) $1$ If $\cos(\theta) = 3/5$ and $\theta$ is in the first quadrant, what is $\sin(\theta)$? a) $3/5$ b) $4/5$ c) $1$ d) $5/3$ Convert $90^\circ$ to radians. a) $\pi/4$ b) $\pi/2$ c) $\pi$ d) $2\pi$ What is the value of $\tan(45^\circ)$? a) $0$ b) $\sqrt{3}/3$ c) $1$ d) $\sqrt{3}$ The amplitude of $y = 3\sin(2x)$ is: a) $1$ b) $2$ c) $3$ d) $2\pi$ In a right triangle, the opposite side to angle $\theta$ is $6$ and the adjacent side is $8$. What is $\tan(\theta)$? a) $6/8$ b) $8/6$ c) $6/10$ d) $8/10$ What is the period of $y = \cos(x)$? a) $\pi/2$ b) $\pi$ c) $2\pi$ d) $4\pi$ Which identity is correct? a) $\sin^2\theta - \cos^2\theta = 1$ b) $\tan\theta = \frac{\cos\theta}{\sin\theta}$ c) $\sin^2\theta + \cos^2\theta = 1$ d) $\sec\theta = \frac{1}{\sin\theta}$ If $\sin(\theta) = -1/2$ and $\theta$ is in the third quadrant, what is $\cos(\theta)$? a) $1/2$ b) $\sqrt{3}/2$ c) $-\sqrt{3}/2$ d) $-1/2$ What is the value of $\csc(30^\circ)$? a) $1/2$ b) $2$ c) $\sqrt{3}/2$ d) $1$ Statistics and Probability What is the mean of the numbers: $2, 4, 6, 8, 10$? a) $5$ b) $6$ c) $7$ d) $8$ What is the median of the numbers: $10, 5, 12, 8, 5$? a) $5$ b) $8$ c) $10$ d) $12$ What is the mode of the numbers: $3, 5, 7, 3, 8, 5, 3$? a) $3$ b) $5$ c) $7$ d) $8$ A fair coin is tossed twice. What is the probability of getting two heads? a) $1/4$ b) $1/2$ c) $3/4$ d) $1$ A bag contains $3$ red marbles and $2$ blue marbles. What is the probability of picking a red marble? a) $1/5$ b) $2/5$ c) $3/5$ d) $4/5$ In a survey, $60\%$ of students like math. If there are $200$ students, how many like math? a) $60$ b) $80$ c) $100$ d) $120$ What is the range of the data set: $15, 20, 10, 25, 5$? a) $5$ b) $10$ c) $20$ d) $25$ How many different ways can $3$ books be arranged on a shelf? a) $3$ b) $6$ c) $9$ d) $12$ What is the probability of rolling a number greater than $4$ on a standard six-sided die? a) $1/6$ b) $1/3$ c) $1/2$ d) $2/3$ The standard deviation measures: a) The midpoint of the data b) The most frequent value c) The spread of the data d) The sum of the data