Q: Which of the following is the correct expression for the tangent of an angle in a right triangle?

$$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$

Q: Which of the following is the correct expression for the cosine of an angle in a right triangle?

$$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$

Question 1

Which of the following best describes the exponent rule for multiplying two powers with the same base, such as $$a^m 	imes a^n$$?

Accepted Answer

$$a^{m+n}$$

Question 2

If $$y is $$directly proportional to $$x$$, and $$y = 6$$ when $$x = 3$$, what is the value of $$y$$ when $$x = 5$$?

Accepted Answer

$$y = 10$$

Question 3

Given the quadratic equation $$x^2 - 4x + 3 = 0$, which of the following is a correct solution using the quadratic formula?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 4

Which equation represents the slope of a line passing through points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$m = \frac{y_2$ - y_1$}{x_2$ - x_1$}$$

Question 5

If $$f(x) = x^3$, what is the derivative f$$'(x)$$?

Accepted Answer

$$3x^2$$

Question 6

Which of the following is the correct integral of $$f(x) = x^2$ with respect to x$?

Accepted Answer

$$\frac{1}{3}x^3$ + C$$

Question 7

A line has the equation $$y = 2x + 1. $$What is the slope and y-intercept of this line?

Accepted Answer

Slope: $$2$$, y-intercept: $$1$$

Question 8

If $$\sin(	heta) = \frac{3}{5} in a $$right triangle, what is the length of the hypotenuse if the opposite side is $$3$$?

Accepted Answer

$$5$$

Question 9

Which of the following is the general form of a quadratic equation?

Accepted Answer

$$ax^2 + bx + c = 0$

Question 10

If $$y is $$inversely proportional to $$x$$, and $$y = 4$$ when $$x = 2$$, what is $$y$$ when $$x = 8$$?

Accepted Answer

$$y = 1$$

Question 11

Which of the following is the correct rule for dividing exponents with the same base, such as $$a^m \div a^n$$?

Accepted Answer

$$a^{m-n}$$

Question 12

Given the system of equations $$y = 2x$$ and $$x + y = 6$$, what is the solution for $$(x, y)$$?

Accepted Answer

$$(2, 4)$$

Question 13

Which of the following is the correct expression for the tangent of an angle in a right triangle?

Accepted Answer

$$	an(	heta) = \frac{	ext{opposite}}{	ext{adjacent}}$$

Question 14

If $$f(x) = x^2$ + 3x$$, what is $$f'(x)$$?

Accepted Answer

$$2x + 3$$

Question 15

Which of the following is the correct formula for the area under the curve from $$x_0 to$$ $$x_1$$ for a function $$F(x)$$?

Accepted Answer

$$\int_{x_0$}^{x_1$} F(x) dx = F(x_1$) - F(x_0$)$$

Question 16

If $$y is $$jointly proportional to $$x$$ and $$z$$, and $$y = 12$$ when $$x = 2$$ and $$z = 3$$, what is the constant of proportionality $$k in$$ $$y = kxz$$?

Accepted Answer

$$k = 2$$

Question 17

Which of the following is the correct simplification of $$4x + 6 - 3(x + 2)$$?

Accepted Answer

$$x$$

Question 18

If the vertex of a quadratic equation $$y = ax^2$ + bx + c is at$$ $$(h, k)$$, which formula gives the x-coordinate of the vertex?

Accepted Answer

$$h = -\frac{b}{2a}$$

Question 19

Which of the following is the correct expression for the cosine of an angle in a right triangle?

Accepted Answer

$$\cos(	heta) = \frac{	ext{adjacent}}{	ext{hypotenuse}}$$

Mathematical Operations and Functions: Pre-Course Math Review for General Chemistry

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