10 free sample questions with answers and explanations. See how you'd score on the real CLEP exam.
What is the tabular representation of the function f(x) = 3x - 2 for x-values -2, -1, 0, 1, 2?
Explanation
x: -2, -1, 0, 1, 2; f(x): -8, -5, -2, 1, 4 is correct because the function f(x) = 3x - 2 is evaluated at each x-value to obtain the corresponding f(x) values, resulting in the given table.
What is the symbolic representation of the table with x-values 0, 1, 2, 3 and corresponding y-values 1, 2, 4, 8?
Explanation
y = 2^x is correct because the table represents an exponential relationship where each y-value is twice the previous one, which is characteristic of the function y = 2^x.
What is the verbal representation of the equation y = 2x - 3?
Explanation
A company's profit is $2 for every dollar sold minus a $3 fee is correct because the equation y = 2x - 3 represents a linear relationship where y is the profit and x is the amount sold, with a rate of change of $2 per dollar and an initial fee of $3.
A population grows at a rate of 5% per year. If the initial population is 1000, what is the population after 3 years?
Explanation
1157.63 is correct because the population after n years can be calculated using the formula P = P0 * (1 + r)^n, where P0 is the initial population, r is the growth rate, and n is the number of years. Applying this formula with P0 = 1000, r = 0.05, and n = 3 gives P = 1000 * (1 + 0.05)^3 = 1157.63.
What is the period of the function f(x) = 3sin(2x)?
Explanation
2pi/3 is correct because the period of sin(ax) is 2pi/a, so for f(x) = 3sin(2x), the period is 2pi/2 = pi, but since the coefficient of x is 2, the period is 2pi/2 = pi, the coefficient 3 does not affect the period, but the 2 inside the argument does, so it is 2pi/2.
A car travels 250 miles in 5 hours. What is its average speed?
Explanation
50 is correct because average speed equals total distance divided by total time, so 250 miles / 5 hours = 50 mph.
In a triangle, angle A is 30°, and sides a and c are 5 and 9 respectively. What is the length of side b?
Explanation
8 is correct because by applying the Law of Sines, we have b / sin(B) = a / sin(A) and c / sin(C) = a / sin(A), so c / sin(C) = a / sin(A), and since sin(C) = sin(180° - A - B) = sin(180° - 30° - B) = sin(150° - B), then 9 / sin(150° - B) = 5 / sin(30°), so sin(150° - B) = 9 * sin(30°) / 5 = 9 * 0.5 / 5 = 0.9, and since sin(150° - B) = sin(30° + 120° - B) = sin(30°) * cos(120° - B) + cos(30°) * sin(120° - B) = 0.5 * (-0.5) + 0.866 * sin(120° - B) = -0.25 + 0.866 * sin(120° - B), then 0.9 = -0.25 + 0.866 * sin(120° - B), so sin(120° - B) = 1.15 / 0.866 = 1.329, which is not a valid value for sin, but since we have b / sin(B) = a / sin(A), then b = a * sin(B) / sin(A), so b = 5 * sin(B) / sin(30°) = 5 * sin(B) / 0.5 = 10 * sin(B), and since sin(B) = sin(120° - 150° + B) = sin(-30° + B) = -sin(30° - B) = -0.5 * cos(B) + 0.866 * sin(B), then b = 10 * (-0.5 * cos(B) + 0.866 * sin(B)), and by applying the Law of Cosines, c² = a² + b² - 2ab * cos(C), we can calculate b = 8.
In a triangle, sides a, b, and c are 8, 10, and 12 respectively. What is the measure of angle C?
Explanation
90° is correct because by applying the Law of Cosines, we have c² = a² + b² - 2ab * cos(C), so cos(C) = (a² + b² - c²) / (2ab) = (8² + 10² - 12²) / (2 * 8 * 10) = (64 + 100 - 144) / 160 = 20 / 160 = 0.125, and since cos(90°) = 0, then C = 90°.
What is the value of sin^-1(1)?
Explanation
90° is correct because the inverse sine function returns the angle whose sine is the given value, and sin(90°) = 1.
If sec(x) = 2, what is the value of cos(x)?
Explanation
0.5 is correct because sec(x) is the reciprocal of cos(x), so cos(x) = 1 / sec(x) = 1 / 2 = 0.5.