Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{2x - 5}$$?

Accepted Answer

Question 2

A population of bacteria triples every 4 hours. If the initial population is 200, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 200 \cdot 3$$^{t/4}$$

Question 3

Which of the following is the inverse function of $$f(x) = 2x + 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 7}{2}$$

Question 4

Which of the following equations represents a circle with center at $$(3, -2)$$ and radius $$5$$?

Accepted Answer

$$(x - 3)^2$ + (y + 2)^2$ = 25$$

Question 5

A right triangle has legs of length $$7$$ and $$24. $$What is the length of the hypotenuse?

Accepted Answer

$$25$$

Question 6

Which of the following is equivalent to $$\log_2$(8x)$$?

Accepted Answer

$$3 + \log_2$(x)$$

Question 7

If $$f(x) = x^2$ - 4x + 7$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 3)$$

Question 8

Which of the following is the solution to the equation $$2^{x} = 10$?

Accepted Answer

$$x = \log_2$(10)$$

Question 9

A Ferris wheel has a radius of $$20$$ meters and rotates once every $$60$$ seconds. If a rider starts at the lowest point, which trigonometric function best models the rider's height $$h$$ above the ground as a function of time $$t (in $$seconds)?

Accepted Answer

$$h(t) = 20 - 20 \cos\left(\frac{2\pi t}{60}\right)$$

Question 10

Which of the following is the correct formula for the sum of a finite geometric series with first term $$a$$, common ratio $$r 
eq 1$$, and $$n$$ terms?

Accepted Answer

$$S_n = a \frac{1 - r^n}{1 - r}$$

Question 11

If $$\sin(	heta) = \frac{3}{5}$$ and $$	heta is in $$the first quadrant, what is $$\cos(	heta)$$?

Accepted Answer

$$\frac{4}{5}$$

Question 12

Which of the following is the correct expression for the period of the function $$f(x) = 5 \sin(3x)$$?

Accepted Answer

$$\frac{2\pi}{3}$$

Question 13

A radioactive substance decays according to the formula $$A(t) = A_0$ e$$^{-kt}$$. If the half-life is 10$ years, what is the value of k$?

Accepted Answer

$$k = \frac{\ln 2}{10}$$

Question 14

Which of the following is the correct solution to the equation $$	an(x) = \sqrt{3}$$ for $$0 \leq x \u003c 2\pi$$?

Accepted Answer

$$x = \frac{\pi}{3}, \frac{4\pi}{3}$$

Question 15

If $$f(x) = \ln(x^2$ + 1)$$, what is the domain of $$f$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 16

A triangle has sides of length $$7$$, $$8$$, and $$9. $$Which law would you use to find the measure of the largest angle?

Accepted Answer

Law of Cosines

Question 17

Which of the following is the correct polar form of the complex number $$-1 + i\sqrt{3}$$?

Accepted Answer

$$2 \left( \cos\left(\frac{2\pi}{3}\right) + i \sin\left(\frac{2\pi}{3}\right) \right)$$

Question 18

Which of the following is the correct solution to the equation $$e^{2x} = 7$?

Accepted Answer

$$x = \frac{1}{2} \ln 7$$

Question 19

A ball is thrown upward from a height of $$2$$ meters with an initial velocity of $$10 m/s. $$Its height after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 10t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$7.1$$ meters

Question 20

Which of the following is the correct expression for the sum of the infinite geometric series $$1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots$$?

Accepted Answer

$$2$$

Precalculus Course Syllabus and Study Guide

Guida di studio - Domande di pratica

Study guide - Flashcard