Practice Test for AP Precalculus - 8 Grade 10 MCQs & solutions - Free

A polynomial function f has the following properties: it touches but does not cross the x-axis at x = −2, crosses the x-axis at x = 1 and x = 3, and both ends of the graph fall toward −∞. Which of the following is most consistent with these observations?

Consider the rational function f(x) = ^{(x2 − 9)}⁄_{(x² − x − 6)}. Which of the following correctly identifies all discontinuities of f?

Let f(x) = x³ − 4x² + x + 6. A student claims that (x − 3) is a factor of f(x). Which of the following correctly evaluates the student’s claim using the Factor Theorem?

What is the horizontal asymptote of the rational function f(x) = ^{(5x3 − 2x + 1)}⁄_{(3x³ + x² − 4)}?

Let f(x) = 2x + 3 and g(x) = e^x. Which of the following correctly expresses (f ∘ g)(x)?

A population of insects is modeled by P(t) = 1200(0.85)^t, where t is measured in years. Which of the following correctly interprets the parameters of this model?

Which of the following expressions is equivalent to log₅(12) using the change of base formula?

A table of values for a function is given below.

Which of the following best classifies the function represented by the table?

Let f(x) = e^{(x − 2)}. Which of the following correctly expresses f⁻¹(x)?

An investment of $5,000 earns interest at an annual rate of 4%, compounded continuously. Which expression gives the value of the investment after t years?

A sinusoidal function is given by f(x) = −3 sin(2x + π) + 5. Which of the following correctly identifies the amplitude and midline of this function?

What is the exact value of sin(5π⁄6)?

The depth of water at a harbor is modeled by a sinusoidal function. The maximum depth is 12 feet and the minimum depth is 2 feet. The period is 12 hours and the maximum depth occurs at t = 0 hours. Which of the following models best represents the depth d (in feet) as a function of time t (in hours)?

Which of the following correctly states the domain of the inverse sine function, arcsin(x)?

Which of the following polar equations represents a limàcon?

A curve is defined parametrically by x(t) = 2t + 1 and y(t) = t² − 3. Which of the following expresses y as a function of x after eliminating the parameter?

Let v = ⟨3, −4⟩. What is the magnitude of v?

A point in polar coordinates is given as (4, π⁄3). Which of the following correctly gives its rectangular coordinates (x, y)?

Let A =

A = [[1, 2], [3, 4]], B = [[0, 1], [2, −1]]

The table below gives selected values of a function f.

What is the average rate of change of f over the interval [2, 4]?

According to the Rational Zero Theorem, which of the following is a possible rational zero of f(x) = 6x³ − 5x² + x − 2?

Solve the equation: log₂(x + 3) + log₂(x − 1) = 5. Which value of x satisfies the equation?

A population is modeled by P(t) = 800(1.06)^t. A student claims that “the growth rate of the population is 1.06.” Which of the following best evaluates this claim?

A polynomial function f(x) has the following end behavior: as x → +∞, f(x) → −∞, and as x → −∞, f(x) → +∞. Which of the following best describes f(x)?

If sin(θ) = 3⁄5 and θ is in Quadrant II, what is the value of cos(θ)?

A particle moves along a path defined by the parametric equations x(t) = cos(t) and y(t) = sin(t) for 0 ≤ t ≤ 2π. Which of the following correctly describes the particle’s path and direction of travel?

Let u = ⟨2, 3⟩ and v = ⟨4, −1⟩. What is the dot product u · v?

A scientist plots ln(y) versus x and obtains a straight line with slope 0.3 and y-intercept 2. Which of the following exponential models is consistent with this linearized data?

A piecewise-defined function is given by:

f(x) = x² + 1, if x < 2
f(x) = 2x − 1, if x ≥ 2

What is the value of f(2) + f(−1)?

Let f(x) = 3x − 6. Which of the following correctly expresses f⁻¹(x)?