Question 1

Which of the following is the correct solution to the equation $$2x^2 - 8x + 6 = 0$?

Accepted Answer

$$x = 2 \pm \sqrt{2}$$

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 correct logarithmic form of the equation $$5^x = 125$$?

Accepted Answer

$$x = \log_5$ 125$$

Question 4

Given the function $$f(x) = x^3$ - 4x^2$ + x - 4$$, use synthetic division to determine if $$x = 2 is a $$zero of $$f(x).$$

Accepted Answer

Yes, because the remainder is 0.

Question 5

Which of the following is the correct graph for the function $$y = -2\sin(x) + 1$$?

Accepted Answer

A sine wave with amplitude 2, reflected over the x-axis, shifted up by 1 unit.

Question 6

Solve for $$x$$: $$\log_2$(x) + \log_2$(x-3) = 3.$$

Accepted Answer

Question 7

A rocket is launched at an angle of $$60^\circ$$ with an initial velocity of $$100 m/s. $$What is the vertical component of the velocity?

Accepted Answer

$$100 \sin 60^\circ$$

Question 8

Which of the following is a solution to the equation $$2\sin^2$ x - 1 = 0$$ for $$0 \leq x \u003c 2\pi$$?

Accepted Answer

Question 9

Which of the following is the correct expansion of $$(x + 2)^3$ using the Binomial Theorem?

Accepted Answer

$$x^3$$ + $$6x^2 + 12x + 8$

Question 10

Given the system of equations: $$\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}$$, what is the value of $$x$$?

Accepted Answer

$$x = 2$$

Question 11

Which of the following is the correct formula for the sum of the first $$n$$ terms of an arithmetic sequence with first term $$a_1$$ and common difference $$d$$?

Accepted Answer

$$S_n = \frac{n}{2}(a_1$ + a_n)$$

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

Which of the following is the correct formula for the determinant of a $$2 	imes 2$$ matrix $$\begin{pmatrix} a & b \ c & d \end{pmatrix}$$?

Accepted Answer

$$ad - bc$$

Question 15

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

Accepted Answer

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

Question 16

If $$	an \alpha = 3$$ and $$\alpha is in $$the first quadrant, what is $$\sin \alpha$$?

Accepted Answer

$$\frac{3}{\sqrt{10}}$$

Question 17

Which of the following is the correct formula for the $$nth $$term of a geometric sequence with first term $$a_1$$ and common ratio $$r$$?

Accepted Answer

$$a_n = a_1$ r$$^{n-1}$$

Precalculus Algebra/Trigonometry Syllabus and Course Overview

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드