Q: Which of the following is the correct formula for the sum of a geometric series with first term $$a$$ and common ratio $$r$$ ($$r \\neq 1) $$over $$n$$ terms?

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

Q: Which of the following is the correct formula for the distance between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$) in $$the plane?

$$\\sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

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

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

Question 1

Which of the following is the correct definition of a rational expression?

Accepted Answer

An expression that can be written as the ratio of two polynomials.

Question 2

A student is solving the inequality $$2x - 5 \u003e 7. $$What is the solution set?

Accepted Answer

$$x \u003e 6$$

Question 3

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

Accepted Answer

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

Question 4

A chemical reaction requires the temperature $$T (in $$degrees Celsius) to be at least $$5$$ times the concentration $$C (in $$mol/L) minus $$10. $$Which inequality models this requirement?

Accepted Answer

$$T \geq 5C - 10$$

Question 5

Which of the following is the correct definition of the domain of a function?

Accepted Answer

The set of all possible input values for which the function is defined.

Question 6

Given the function $$f(x) = x^2$ - 4x + 3$$, what is the value of $$f(2)$$?

Accepted Answer

$$-1$$

Question 7

A hospital uses the formula $$C = 2t + 50 to $$estimate the cost $$C (in $$dollars) of a procedure that takes $$t$$ minutes. If the procedure takes $$30$$ minutes, what is the estimated cost?

Accepted Answer

$$C = 110$$

Question 8

Which of the following is the correct solution to the equation $$3(x - 2) = 9$$?

Accepted Answer

$$x = 5$$

Question 9

A biologist models the population $$P of a $$species after $$t$$ years by $$P = 1000e$$^{0.05t}$$. What is the population after 10$ years? (Round to the nearest whole number)

Accepted Answer

$$1649$$

Question 10

Which of the following is the correct formula for the sum of a geometric series with first term $$a$$ and common ratio $$r$$ ($$r \neq 1) $$over $$n$$ terms?

Accepted Answer

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

Question 11

A student is asked to solve the system of equations: $$x + y = 5$$ and $$x - y = 1. $$What is the value of $$x$$?

Accepted Answer

$$x = 3$$

Question 12

Which of the following is the correct definition of an exponential function?

Accepted Answer

A function of the form $$f(x) = a^x$$ where $$a \u003e 0$$ and $$a \neq 1.$$

Question 13

A medical researcher uses the formula $$A = P(1 + r)^n to $$calculate the amount $$A$$ after $$n$$ years, where $$P is $$the initial amount and $$r is $$the annual growth rate. If $$P = 500$$, $$r = 0.04$$, and $$n = 5$$, what is $$A$$? (Round to the nearest dollar)

Accepted Answer

$$608$$

Question 14

Which of the following is the correct solution to the equation $$x^2 - 9 = 0$?

Accepted Answer

$$x = 3 or$$ $$x = -3$$

Question 15

A student is asked to factor the polynomial $$x^2 + 5x + 6$. Which of the following is the correct factorization?

Accepted Answer

$$(x + 2)(x + 3)$$

Question 16

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

Accepted Answer

$$\sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Question 17

A student is asked to solve the equation $$\frac{2}{x} = 4. $$What is the value of $$x$$?

Accepted Answer

$$x = 0.5$$

Question 18

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

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

Question 19

A student is asked to solve the inequality $$x^2$$ \u003c 16$$. What is the solution set?

Accepted Answer

$$-4 \u003c x \u003c 4$$

Question 20

Which of the following is the correct formula for the vertex of the parabola $$y = ax^2$ + bx + c$$?

Accepted Answer

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

Precalculus Syllabus: Algebra & Trigonometry with Interactive Assignments

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