Question 1

Which of the following correctly applies the rule for multiplying powers with the same base?

Accepted Answer

$$x^a 	imes x^b = x$$^{a+b}$$

Question 2

If $$x^5$$ \div $$x^2 is $$simplified using the rule for dividing powers with the same base, what is the result?

Accepted Answer

$$x^3$$

Question 3

Which of the following is the correct result for $$(x^3)^4$?

Accepted Answer

$$x^{12}$$

Question 4

What is the value of $$x^0$$ for any nonzero $$x$$?

Accepted Answer

$$1$$

Question 5

Which of the following is the correct expression for a negative exponent?

Accepted Answer

$$x^{-n}$$ = \frac{1}{x^n}$$

Question 6

A student simplifies $$\frac{x^7$}{x^3$} as$$ $$x^{21}. $$What algebraic error did the student make?

Accepted Answer

They multiplied the exponents instead of subtracting them.

Question 7

Which of the following is the correct formula for the midpoint between points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$\left( \frac{x_1$ + x_2$}{2}, \frac{y_1$ + y_2$}{2} \right)$$

Question 8

What is the distance between the points $$(1,2)$$ and $$(4,6)$$?

Accepted Answer

$$5$$

Question 9

Which of the following is the correct formula for the area of a circle?

Accepted Answer

$$A = \pi r^2$

Question 10

If $$\log_{10} x = 2$$, what is the value of $$x$$?

Accepted Answer

$$100$$

Question 11

Which of the following is the correct formula for the quadratic formula?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 12

A triangle has sides of length 3, 4, and 5. What is the area of the triangle?

Accepted Answer

$$6$$

Question 13

Which of the following is the correct formula for the Law of Sines?

Accepted Answer

$$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$

Question 14

What is the value of $$\sin(90^\circ)$$?

Accepted Answer

$$1$$

Question 15

Which of the following is the correct formula for the sum of the interior angles of a polygon with $$n$$ sides?

Accepted Answer

$$180(n-2)$$

Question 16

If $$x^2 = 16$, what are the possible values of x$?

Accepted Answer

$$4$$ and $$-4$$

Question 17

Which of the following is the correct formula for the Pythagorean Theorem?

Accepted Answer

$$a^2$$ + $$b^2$$ = $$c^2$$

Question 18

What is the value of $$\cos(0^\circ)$$?

Accepted Answer

$$1$$

Question 19

Which of the following is the correct formula for the slope of a line passing through points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

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

Mathematical Operations and Functions for General Chemistry

Study Guide - Practice Questions