Question 1

A biologist is studying the population of bacteria in a petri dish. The population is estimated to be $$3.2 	imes 10^7$ at noon. If the population doubles every 3 hours, what will the population be at midnight (12 hours later)? Express your answer in scientific notation.

Accepted Answer

$$2.56 	imes 10^8$

Question 2

Simplify the following expression and write your answer in scientific notation: $$\left(4.5 	imes 10^5$ight) 	imes \left(2 	imes 10^3$ight).$$

Accepted Answer

$$9.0 	imes 10^7$

Question 3

A chemist mixes two solutions. The first solution contains $$2x^2 + 3x - 5$ grams of a compound, and the second contains -x^2$ + 4x + 7$$ grams. What is the total amount of compound after mixing?

Accepted Answer

$$x^2 + 7x + 2$

Question 4

Multiply the polynomials: $$(x - 2)(x^2$ + 3x + 4). $$What is the result?

Accepted Answer

Question 5

Factor the polynomial: $$x^2 - 5x + 6$.

Accepted Answer

$$(x - 2)(x - 3)$$

Question 6

A rectangular garden has an area of $$x^2 - 9$ square meters. Which of the following represents the factored form of the area?

Accepted Answer

$$(x - 3)(x + 3)$$

Question 7

Simplify the rational expression: $$\frac{x^2$ - 4}{x^2$ + 2x}.$$

Accepted Answer

$$\frac{(x - 2)(x + 2)}{x(x + 2)} = \frac{x - 2}{x}$$

Question 8

Divide the rational expressions: $$\frac{3x}{x^2$ - 9} \div \frac{x}{x + 3}.$$

Accepted Answer

$$\frac{3}{x - 3}$$

Question 9

Add the rational expressions: $$\frac{2}{x} + \frac{3}{x + 1}.$$

Accepted Answer

$$\frac{2(x + 1) + 3x}{x(x + 1)} = \frac{2x + 2 + 3x}{x(x + 1)} = \frac{5x + 2}{x(x + 1)}$$

Question 10

Solve the linear equation for $$x$$: $$5x - 3 = 2x + 9.$$

Accepted Answer

$$x = 4$$

Question 11

A pharmacist needs to prepare a solution by mixing two solutions: one with 20% concentration and one with 50% concentration. If she wants 100 mL of a 30% solution, how many mL of the 50% solution should she use? (Let $$x be $$the amount of 50% solution.)

Accepted Answer

$$\boxed{33.3}$$

Question 12

Solve the quadratic equation by factoring: $$x^2 - 7x + 12 = 0$.

Accepted Answer

$$x = 3,\ 4$$

Question 13

Use the quadratic formula to solve: $$2x^2 - 4x - 6 = 0$.

Accepted Answer

$$x = 3,\ -1$$

Question 14

Add the complex numbers: $$(3 + 2i) + (5 - 7i).$$

Accepted Answer

$$8 - 5i$$

Question 15

Multiply the complex numbers: $$(2 + 3i)(4 - i).$$

Accepted Answer

$$11 + 10i$$

Question 16

Solve the inequality: $$2x - 5 \u003c 7.$$

Accepted Answer

$$x \u003c 6$$

Question 17

Find the equation of the line passing through the point $$(2, 5)$$ with slope $$-3 ($$use point-slope form).

Accepted Answer

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

Question 18

Find the equation of the line parallel to $$y = 2x - 7$$ that passes through $$(1, 4).$$

Accepted Answer

$$y - 4 = 2(x - 1)$$

Question 19

A road is perpendicular to a street with equation $$y = -\frac{1}{2}x + 3$$ and passes through the point $$(2, 1). $$What is the equation of the road?

Accepted Answer

$$y - 1 = 2(x - 2)$$

College Algebra: Review and Foundations Study Notes

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