Question 1

Which of the following best defines a variable in algebra?

Accepted Answer

A letter used to represent various numbers.

Question 2

Evaluate the expression $$8 + 6(x - 3)^2$ for x = 13$.

Accepted Answer

$$8 + 6(10)^2$ = 8 + 600 = 608$$

Question 3

What is the value of $$2 + 3(x - 1)^2$ - 4$$ when $$x = 3$$?

Accepted Answer

$$2 + 3(2)^2$ - 4 = 2 + 12 - 4 = 10$$

Question 4

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

Accepted Answer

$$b^n$$

Question 5

Given the formula $$T = 4x^2$ + 341x + 3194$$, what is the value of $$T$$ for the school year ending in 2015?

Accepted Answer

$$T = 4(15)^2$ + 341(15) + 3194 = 4(225) + 5115 + 3194 = 900 + 5115 + 3194 = 9209$$

Question 6

What is the process of finding formulas to describe real-world phenomena called?

Accepted Answer

Mathematical modeling

Question 7

Simplify the expression $$7(4x^2 + 3x$$) + $$2(5x^2 + x$$)$$.

Accepted Answer

$$38x^2 + 23x$

Question 8

Which of the following statements about like terms is correct?

Accepted Answer

Like terms have exactly the same variable factors.

Question 9

Use the formula $$T = 4x^2$ + 341x + 3194 to $$find the average cost of tuition and fees at public U.S. colleges for the school year ending in 2010.

Accepted Answer

$$T = 4(10)^2$ + 341(10) + 3194 = 400 + 3410 + 3194 = 7004$$

Question 10

Simplify the expression $$6(2x^2 + 4x$$) + $$10(4x^2 + 3x$$)$$.

Accepted Answer

$$52x^2 + 54x$

Question 11

Which of the following is NOT a step in simplifying an algebraic expression?

Accepted Answer

Multiplying all terms by zero

Question 12

If $$x = 5$$, what is the value of $$3x^2 - 2x + 7$?

Accepted Answer

$$3(25) - 10 + 7 = 75 - 10 + 7 = 72$$

Question 13

Which of the following best describes a mathematical model?

Accepted Answer

A formula that expresses a relationship between two or more quantities.

Question 14

What is the simplified form of $$5x^2 + 3x$$ + $$2x^2 + 7x$?

Accepted Answer

$$7x^2 + 10x$

Question 15

Which operation should be performed first according to the order of operations in the expression $$2 + 3(x - 1)^2$ - 4$$?

Accepted Answer

Exponentiation: $$(x - 1)^2$

Question 16

A company uses the formula $$C = 5n^2$ + 20n + 100 to $$model its monthly costs, where $$n is $$the number of products made. What is the cost if $$n = 8$$?

Accepted Answer

$$C = 5(64) + 20(8) + 100 = 320 + 160 + 100 = 580$$

Question 17

Which of the following is a correct example of combining like terms?

Accepted Answer

$$3x^2$$ + $$5x^2$$ = $$8x^2$$

Question 18

If $$y = 4$$ and $$z = 2$$, what is the value of $$2y^2 - 3z + 5$?

Accepted Answer

$$2(16) - 6 + 5 = 32 - 6 + 5 = 31$$

Order of Operations and Simplifying Expressions: College Algebra Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard