Question 1

A pharmaceutical company is testing a new drug and records the concentration of the drug in the bloodstream at two different times: at 2 hours, the concentration is 5 mg/L, and at 6 hours, it is 3 mg/L. Assuming the concentration decreases linearly, what is the equation of the line representing concentration $$C (in mg/L) as a $$function of time $$t (in $$hours)?

Accepted Answer

Question 2

Solve the quadratic equation $$x^2 - 6x + 8 = 0$ using the quadratic formula.

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 3

A biologist measures the distance between two nests at coordinates $$(1, 2)$$ and $$(4, 6). $$What is the distance between the nests?

Accepted Answer

$$5$$

Question 4

Solve the linear equation $$3x - 7 = 2x + 5$$ for $$x.$$

Accepted Answer

Question 5

A chemical reaction requires the midpoint temperature between two readings: $$20^	ext{o}C $$and $$36^	ext{o}C. $$What is the midpoint temperature?

Accepted Answer

$$28^	ext{o}C$$

Question 6

Solve the rational equation $$\frac{2}{x} + 1 = \frac{4}{x}$$ for $$x.$$

Accepted Answer

$$x = 2$$

Question 7

A medical researcher needs to solve the radical equation $$\sqrt{x + 5} = 4. $$What is the value of $$x$$?

Accepted Answer

$$x = 11$$

Question 8

Solve the absolute value equation $$|2x - 3| = 7$$ for $$x.$$

Accepted Answer

$$x = 5 or$$ $$x = -2$$

Question 9

A city engineer is designing a circular park. If the center is at $$(2, -1)$$ and the radius is $$5$$ units, what is the equation of the circle in standard form?

Accepted Answer

$$(x - 2)^2$ + (y + 1)^2$ = 25$$

Question 10

Solve the linear inequality $$2x - 3 \u003c 7$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, 5)$$

Question 11

A physicist records two points on a graph: $$(0, 0)$$ and $$(3, 9). $$What is the slope of the line passing through these points?

Accepted Answer

$$m = 3$$

Question 12

Solve the combined inequality $$-2 \u003c x + 1 \leq 5$$ and express the solution in interval notation.

Accepted Answer

$$(-3, 4]$$

Question 13

A business tracks profit using the equation $$y = 4x - 10. $$What is the y-intercept of the graph?

Accepted Answer

$$-10$$

Question 14

Add the complex numbers $$(3 + 2i)$$ and $$(1 - 5i). $$What is the result?

Accepted Answer

$$4 - 3i$$

Question 15

Solve the absolute value inequality $$|x - 4| \u003c 3$$ and express the solution in interval notation.

Accepted Answer

$$(1, 7)$$

Question 16

A scientist wants to find the equation of a line passing through $$(2, 5)$$ with slope $$-3. $$What is the equation in point-slope form?

Accepted Answer

$$y - 5 = -3(x - 2)$$

Question 17

Given the equation $$y^2$$ = $$x^2$$, which type of symmetry does its graph have?

Accepted Answer

Symmetric with respect to the y-axis, x-axis, and origin

Question 18

A circle has the equation $$x^2$$ + $$y^2 - 4x + 6y = 12$. What is the center and radius of the circle?

Accepted Answer

Center $$(2, -3)$$, radius $$5$$

Question 19

A line passes through $$(1, 2)$$ and $$(4, 8). $$What is the equation of the line in slope-intercept form?

Accepted Answer

$$y = 2x$$

Exam 1 Review: Equations, Inequalities, and Graphs in Precalculus

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