AP® Precalculus Exam Section I

AP® Precalculus Practice Exam flashcards

What are all intervals on which p(x) ≥ 0, given p(x) = −x(x − 4)(x + 2)?

(−∞, −2] ∪ [0, 4]

Which of the following is an equivalent form for f(x) = 9 * (25)^x ?

f(x) = 9 * (5^2)^x = 9 * (5^(2x))

On which interval is f increasing and the graph of f concave down, given a graph with labeled zeros, extrema, and inflection points A, B, C, D, and E?

The interval from A to B

Describe the end behavior of f(x) = (5/6)x^3 - 3x^2 - 3.

lim x->∞ f(x) = ∞ and lim x->-∞ f(x) = -∞

Which expression is equivalent to 2ln(x^(3/2) * y) - ln(3)?

ln((x^3 * y^2) / 3)

Describe the zeros of p(x) = x^3 + 3x^2 - 2x - 15.

p has exactly one distinct real zero and two non-real zeros.

In the xy-plane, the graph of a rational function f has a vertical asymptote at x = -5. Which of the following could be an expression for f(x)?

(x-3) / ((x-3)(x+5))

What is the period of the sinusoidal function f?

4

Describe the transformation of the graph for y = f(x + 1/2) - 2.

Shift left by 1/2 and down by 2

For the exponential function f(x) = ab^x, given the table values, which statement is true?

f demonstrates exponential growth because a > 0 and b > 1.

Which of the following is an expression for f(g(x)), given f(x) = x^2 + 1 and g(x) = (x-3)/x?

(x^2 - 6x + 9 + x^2) / x^2

Based on the table, which of the following claim and explanation statements best fits these data for function g?

g is best modeled by a quadratic function, because the change in the average rates of change over consecutive equal-length input-value intervals is constant.

Which of the following is an equivalent form for g(x) = 7sin(2x)?

g(x) = 14cos(x)sin(x)

If the function g has the property that for each time the input values double, the output values increase by 1, which of the following could be the graph of y = g(x) in the xy-plane?

Logarithmic

A complex number is represented by rectangular coordinates (3, 3). Which of the following is one way to express the complex number using its polar coordinates?

(3√2) * (cos(π/4) + i*sin(π/4))

The terminal ray of the angle intersects the circle at point P (x, y), and point R also lies on the circle. The coordinates of R are (x, -y). Which of the following is true about the sine of θ?

sin(θ) = y/5 because it is the ratio of the vertical displacement of P from the x-axis to the distance between the origin and P.

The function f is given by f(x) = 3x^2 + x + 1. The graph of which of the following functions is the image of the graph of f after a vertical dilation of the graph of f by a factor of 2?

k(x) = 6x^2 + 2x + 2, because this is a multiplicative transformation of f that results from multiplying f(x) by 2.

Let h be the function defined by h(x) = f(g(x)). What is the value of h(0)?

-2

Which of the following sequences of transformations maps the graph of f to the graph of g in the same xy-plane?

A horizontal dilation of the graph of f by a factor of 1/2, followed by a horizontal translation of the graph of f by 4 units.

Which of the following could be an expression for f(x), given the graph of a trigonometric function f?

3sin(2(x - π/4)) - 1

What are the location of holes and vertical asymptotes of f?

The graph of f has a hole at x = 1 and a vertical asymptote at x = 7.

If a model is constructed to represent these data, which of the following best applies to this situation?

y = 20(3/2)^t

Given polynomial function k(x) = -ax^4 - bx + 15, where a and b are nonzero real constants. Each of the zeros of k has multiplicity 1. In the xy-plane, an x-intercept of the graph of k is (17.997, 0). A zero of k is −0.478 − 0.801i. Which of the following statements must be true?

-0.478 + 0.801i is a zero of k.

What are all x-coordinates of the points of intersection of the graphs of f and g?

x = 3 only

What are all values of θ, for 0 ≤ θ < 2π, where 2sin(2θ) = -sin θ?

0, π, 7π/6, and 11π/6

If the domain of f is restricted to 0 ≤ θ ≤ π/2, the portion of the given graph that remains consists of two pieces. One of those pieces is the portion of the graph in Quadrant I from C to E. Which of the following describes the other remaining piece?

The portion of the graph in Quadrant III from E to D

If a patient pedals 1 revolution per second, which of the following could be an expression for h(t), the height, in inches, of the bicycle pedal above level ground at time t seconds?

12 - 8sin(2πt)

Which of the following statements is true about the distance between the point with polar coordinates (f(θ), θ) and the origin?

The distance is increasing for 0 ≤ θ ≤ π/2 because f(θ) is positive and increasing on the interval.

Which of the following graphs could depict this situation, where time, in hours, is the independent variable, and the volume of water in the pool, in gallons, is the dependent variable?

Piecewise function

What was the population of the colony on day 6 based on the simulation?

14,000

Based on the model, at what value of t does the rate of people entering the subway car change from increasing to decreasing?

5.505

Which of the following graphs could represent these data in a semi-log plot, where the vertical axis is logarithmically scaled?

Exponential

Based on the model, which of the following is true?

The maximum height of the tide is 13.8 ft.

What are the values of a and d?

a = 1 and d = 3

What is the value of S(12)?

175,325

What is the first time t that sales predicted by the logarithmic model will be 0.1 thousand units more than sales predicted by the linear model?

4.324

Using the period of f , which of the following is the number of complete cycles of the graph of f in the xy-plane on the interval 0 ≤ x ≤ 1000?

318

What is the maximum value of g?

5

What are the zeros of g on the interval 0 ≤ x ≤ π?

1.540 and 2.471

Which of the following functions is an appropriate model for this situation?

f(t) = 2sin(12πt)