Question 1

Which of the following numbers is an example of an irrational number?

Accepted Answer

$$\sqrt{2}$$

Question 2

Which set of numbers includes all integers, rational numbers, and irrational numbers?

Accepted Answer

The set of real numbers

Question 3

Simplify the following expression: $$3(x - 2) + 4x$$

Accepted Answer

$$7x - 6$$

Question 4

Which of the following is the correct factorization of the polynomial $$x^2 - 9$?

Accepted Answer

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

Question 5

A chemist mixes two solutions: one with a concentration of $$20\%$$ salt and another with $$50\%$$ salt. If she wants to make $$100 mL of a$$ $$30\%$$ salt solution, how many mL of the $$50\%$$ solution should she use?

Accepted Answer

$$33.33 mL$$

Question 6

Which of the following is NOT a polynomial?

Accepted Answer

$$x^{-2} + 3$

Question 7

Given the sets $$A = \{1, 2, 3, 4\}$$ and $$B = \{3, 4, 5, 6\}$$, what is $$A \cap B$$?

Accepted Answer

$$\{3, 4\}$$

Question 8

Which of the following rational expressions is equivalent to $$\frac{x^2$ - 9}{x + 3}$$ for $$x 
eq -3$$?

Accepted Answer

$$x - 3$$

Question 9

A medical researcher is analyzing the heights of a large group of patients. If the heights are normally distributed with a mean of $$170 cm $$and a standard deviation of $$10 cm$$, what is the $$z-$$score for a patient who is $$185 cm $$tall?

Accepted Answer

$$1.5$$

Question 10

Which of the following is the correct simplification of the rational expression $$\frac{2x^2$ - 8}{4x}$$ for $$x 
eq 0$$?

Accepted Answer

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

Question 11

A company wants to estimate the proportion $$p of $$defective products in a large shipment. If a random sample of $$200$$ products contains $$16$$ defectives, what is the point estimate for $$p$$?

Accepted Answer

$$0.08$$

Question 12

Which of the following is the correct result of multiplying $$(x + 2)(x - 5)$$?

Accepted Answer

$$x^2 - 3x - 10$

Question 13

If $$A = \{x | x 	ext{ is an even integer}\}$$ and $$B = \{x | x 	ext{ is a multiple of } 4\}$$, which statement is true?

Accepted Answer

$$B \subseteq A$$

Question 14

A biologist records the weights of a sample of frogs. The sample mean is $$50$$ grams, and the standard deviation is $$5$$ grams. According to the Central Limit Theorem, what is the standard deviation of the sample mean for samples of size $$25$$?

Accepted Answer

$$1$$ gram

Question 15

Which of the following is the correct factorization of $$x^2 + 5x + 6$?

Accepted Answer

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

Question 16

A student is asked to solve the equation $$2(x - 3) = x + 5. $$What is the solution?

Accepted Answer

$$x = 11$$

Question 17

Which of the following is the correct simplification of $$\frac{3x^2$y}{6xy^2$}$$ for $$x 
eq 0, y 
eq 0$$?

Accepted Answer

$$\frac{x}{2y}$$

Question 18

A survey found that $$60\% of $$people prefer coffee over tea. If $$10$$ people are randomly selected, what is the expected number of people who prefer coffee?

Accepted Answer

$$6$$

Question 19

Which of the following is the correct result of dividing $$x^2 - 4x$ by x$ for x$$ 
eq 0$$?

Accepted Answer

$$x - 4$$

Question 20

If $$A = \{1, 2, 3\}$$ and $$B = \{2, 3, 4, 5\}$$, what is $$A \cup B$$?

Accepted Answer

$$\{1, 2, 3, 4, 5\}$$

Intermediate Algebra Study Notes: Algebraic Expressions, Polynomials, Rational Expressions, and Problem Solving

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