Question 1

A biologist is studying the population of bacteria in a petri dish. The population is estimated to be $$3.2 	imes 10^7$ at noon and 4.5$$ 	imes $$10^8 at $$midnight. What is the approximate increase in population, expressed in scientific notation?

Accepted Answer

$$4.18 	imes 10^8$

Question 2

Simplify the following expression and write your answer in scientific notation: $$\left(2.5 	imes 10^3$ight) 	imes \left(4 	imes 10^5$ight).$$

Accepted Answer

$$1.0 	imes 10^8$

Question 3

A chemist mixes two solutions. The first has a concentration of $$5.6 	imes 10$$^{-4}$$ mol/L and the second 2.4$$ 	imes $$10^{-3}$$ mol/L. What is the sum of the concentrations, in scientific notation?

Accepted Answer

$$3.0 	imes 10$$^{-3}$$

Question 4

Which of the following is the result of $$\$$left(3x^2$$ - 2x + 5\right) + \$$left(4x^2$$ + 7x - 3\right)$$?

Accepted Answer

$$7x^2 + 5x + 2$

Question 5

A manufacturer is designing a rectangular box with length $$x+3$$, width $$x-2$$, and height $$x. $$What is the polynomial expression for the volume of the box?

Accepted Answer

$$x^3$$ + $$x^2 - 6x - 6$

Question 6

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

Accepted Answer

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

Question 7

Simplify the rational expression: $$\frac{x^2$ - 9}{x^2$ - 6x + 9}.$$

Accepted Answer

$$\frac{(x-3)(x+3)}{(x-3)^2$}$$

Question 8

A pharmacist needs to combine two solutions: $$\frac{2}{x}$$ liters of one and $$\frac{3}{x+1}$$ liters of another. What is the sum, expressed as a single rational expression?

Accepted Answer

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

Question 9

Solve for $$x$$: $$2x - 5 = 9.$$

Accepted Answer

$$x = 7$$

Question 10

Solve the quadratic equation by factoring: $$x^2 - 4x - 21 = 0$.

Accepted Answer

$$x = 7, x = -3$$

Question 11

A projectile is launched from the ground and its height $$h in $$meters after $$t$$ seconds is given by $$h = -5t^2$ + 20t. $$When does it hit the ground again? (Use the quadratic formula.)

Accepted Answer

$$t = 0$$ and $$t = 4$$

Question 12

Simplify: $$(3 + 2i) - (5 - 4i).$$

Accepted Answer

$$-2 + 6i$$

Question 13

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

Accepted Answer

$$11 - 10i$$

Question 14

Solve by factoring: $$x^2 + 2x - 15 = 0$.

Accepted Answer

$$x = -5, x = 3$$

Question 15

Solve the inequality: $$3x - 7 \u003c 2x + 5.$$

Accepted Answer

$$x \u003c 12$$

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

Find the equation of the line perpendicular to $$y = -\frac{1}{2}x + 3$$ and passing through $$(4, -1). $$Express your answer in point-slope form.

Accepted Answer

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

Question 19

A medical researcher is analyzing the concentration of a drug in the bloodstream, modeled by $$C(t) = -0.5t^2$ + 4t + 2$$, where $$t is $$hours after administration. When does the concentration reach zero? (Use the quadratic formula.)

Accepted Answer

$$t = -0.5, t = 8.5$$

College Algebra: Review and Foundations Study Notes

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