Q: A nurse needs to prepare a $$20\%$$ saline solution. If she mixes $$100 mL of$$ $$10\%$$ saline with $$x mL of$$ $$30\%$$ saline, which equation represents the total amount of salt in the mixture?

$$0.1 \times 100 + 0.3x = 0.2(100 + x)$$

Question 1

Which of the following is the correct order of operations when evaluating the expression $$8 + 2 	imes (3^2$ - 1)$$?

Accepted Answer

First evaluate the parentheses, then multiply, then add.

Question 2

A chemist mixes $$\frac{3}{4}$$ liter of solution A with $$\frac{2}{3}$$ liter of solution B. What is the total volume of the mixture in liters?

Accepted Answer

$$\frac{17}{12}$$

Question 3

Which property of real numbers is illustrated by the equation $$a(b + c) = ab + ac$$?

Accepted Answer

Distributive Property

Question 4

Solve for $$x in $$the equation $$5x - 7 = 18.$$

Accepted Answer

$$x = 5$$

Question 5

A nurse needs to prepare a $$20\%$$ saline solution. If she mixes $$100 mL of$$ $$10\%$$ saline with $$x mL of$$ $$30\%$$ saline, which equation represents the total amount of salt in the mixture?

Accepted Answer

$$0.1 	imes 100 + 0.3x = 0.2(100 + x)$$

Question 6

Which of the following is the simplified form of $$\frac{2x^2$ - 8}{4x}$$?

Accepted Answer

$$\frac{x^2$ - 4}{2x}$$

Question 7

If $$f(x) = 2x + 3$$, what is $$f(-2)$$?

Accepted Answer

$$-7$$

Question 8

Which of the following is the solution set for the inequality $$2x - 5 \u003c 9$$?

Accepted Answer

$$x \u003c 7$$

Question 9

A rectangle has a length of $$2x + 3$$ and a width of $$x - 1. $$Which expression represents its area?

Accepted Answer

$$(2x + 3)(x - 1)$$

Question 10

Which of the following is the factored form of $$x^2 - 9$?

Accepted Answer

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

Question 11

A car travels at a constant speed and covers $$180$$ miles in $$3$$ hours. What is the speed of the car in miles per hour?

Accepted Answer

$$60$$

Question 12

Which of the following is equivalent to $$\sqrt{50}$$?

Accepted Answer

$$5\sqrt{2}$$

Question 13

If $$y = 3x - 4$$, what is the slope of the line?

Accepted Answer

$$3$$

Question 14

Which of the following is the solution to the quadratic equation $$x^2 - 5x + 6 = 0$?

Accepted Answer

$$x = 2 or$$ $$x = 3$$

Question 15

A recipe calls for $$\frac{2}{3}$$ cup of sugar for every $$4$$ servings. How much sugar is needed for $$12$$ servings?

Accepted Answer

$$2$$ cups

Question 16

Which of the following is the correct simplification of $$(x^3)^2$?

Accepted Answer

$$x^6$$

Question 17

If $$a = 2$$ and $$b = -3$$, what is the value of $$|a + b|$$?

Accepted Answer

$$1$$

Question 18

Which of the following is the solution to $$\frac{2x}{5} = 8$$?

Accepted Answer

$$x = 20$$

Question 19

A student scored $$85\% on a $$test with $$40$$ questions. How many questions did the student answer correctly?

Accepted Answer

$$34$$

Question 20

Which of the following is the graph of the equation $$y = -2x + 5$$?

Accepted Answer

A straight line with slope $$-2$$ and $$y-$$intercept $$5$$

Essentials in Mathematics I and II: Syllabus and Course Structure Overview

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