Question 1

Which of the following best describes a variable in an algebraic expression?

Accepted Answer

A symbol, usually a letter, that represents an unknown value.

Question 2

What is the value of the expression $$2x + 3y$$ when $$x = 4$$ and $$y = 2$$?

Accepted Answer

$$2(4) + 3(2) = 8 + 6 = 14$$

Question 3

Which property of operations is illustrated by the equation $$a + b = b + a$$?

Accepted Answer

Commutative Property

Question 4

Simplify the expression $$3x + 2x - x.$$

Accepted Answer

Question 5

Which step should be performed first when evaluating the expression $$2(3 + 4)^2$?

Accepted Answer

Add $$3 + 4$$

Question 6

A chemist mixes $$x$$ grams of substance A with $$2x$$ grams of substance B. If the total mixture weighs $$30$$ grams, what is the value of $$x$$?

Accepted Answer

$$x = 10$$

Question 7

Which of the following expressions demonstrates the distributive property?

Accepted Answer

$$a(b + c) = ab + ac$$

Question 8

Evaluate the expression $$4x^2 - 3x + 2$ for x = -2$.

Accepted Answer

$$4(-2)^2 - 3(-2) + 2 = 16 + 6 + 2 = 24$

Question 9

A medical researcher records the number of patients, $$p$$, and the number of treatments, $$t$$, given each day. If the total treatments over $$5$$ days is represented by $$5t$$, and $$t = 12$$, how many treatments were given?

Accepted Answer

$$5 	imes 12 = 60$$

Question 10

Which of the following is an example of an algebraic expression?

Accepted Answer

$$7x - 2$$

Question 11

Simplify the expression $$2x + 3x - 4x + 7.$$

Accepted Answer

$$x + 7$$

Question 12

If $$a = 3$$ and $$b = 5$$, what is the value of $$2a + b^2$?

Accepted Answer

$$2(3) + 5^2$ = 6 + 25 = 31$$

Question 13

Which property allows you to group numbers in any way when adding: $$(a + b) + c = a + (b + c)$$?

Accepted Answer

Associative Property

Question 14

A student is simplifying the expression $$5(x + 2) - 3x. $$What is the simplified form?

Accepted Answer

$$2x + 10$$

Question 15

Which operation should be performed last when evaluating $$2 + 3 	imes 4^2$?

Accepted Answer

Addition

Question 16

A biologist counts $$x$$ birds in the morning and $$y$$ birds in the afternoon. If $$x = 15$$ and $$y = 23$$, what is the total number of birds counted?

Accepted Answer

$$15 + 23 = 38$$

Question 17

Which of the following is NOT a key property of operations discussed in College Algebra?

Accepted Answer

Multiplicative Inverse Property

Question 18

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

Accepted Answer

$$2x + 12$$

Question 19

A historian analyzes the number of artifacts found each year, represented by $$a. If$$ $$a = 7$$ and the total over $$4$$ years is $$4a$$, how many artifacts were found?

Accepted Answer

$$4 	imes 7 = 28$$

Question 20

Which of the following best describes the process of simplifying an algebraic expression?

Accepted Answer

Combining like terms and performing arithmetic operations to write the expression in its simplest form.

Algebraic Expressions and Basic Operations: College Algebra Study Notes

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