Question 1

Evaluate the expression $$5 + 3x$$ for $$x = 4.$$

Accepted Answer

$$17$$

Question 2

Which algebraic expression represents 'three more than the quotient of a number $$x$$ and $$11$$'?

Accepted Answer

$$3 + \dfrac{x}{11}$$

Question 3

Translate the sentence: 'Nine less than four times a number is twenty-six' into an algebraic equation.

Accepted Answer

$$4x - 9 = 26$$

Question 4

Determine whether $$x = 3 is a $$solution to the equation $$2x + 7 = 13.$$

Accepted Answer

Yes, because $$2(3) + 7 = 13$$

Question 5

If $$b = 5$$ and $$c = 2$$, evaluate the expression $$4b - 3c.$$

Accepted Answer

$$14$$

Question 6

Which of the following is the correct order of operations for evaluating algebraic expressions?

Accepted Answer

Grouping symbols, multiplication/division, addition/subtraction

Question 7

A mathematical model for the percentage of marriages ending in divorce after $$n$$ years, when the wife is under $$18$$, is $$d = 4n + 5. $$What is $$d$$ after $$10$$ years?

Accepted Answer

$$45$$

Question 8

Given the formula $$d = 2.3n + 1.5$$ for the percentage of marriages ending in divorce after $$n$$ years (wife over $$25$$), what is the percentage after $$12$$ years?

Accepted Answer

$$29.1$$

Question 9

Which of the following best describes a variable in algebra?

Accepted Answer

A letter that represents a variety of different numbers

Question 10

If $$x = 2$$ and $$y = 5$$, evaluate the expression $$3x^2 - 2y$.

Accepted Answer

$$2$$

Question 11

Which of the following is an algebraic expression?

Accepted Answer

$$7x - 4$$

Question 12

A formula is best described as:

Accepted Answer

An equation that expresses a relationship between two or more variables

Question 13

Which equation represents 'the product of $$8$$ and a number $$x is$$ $$48$$'?

Accepted Answer

$$8x = 48$$

Question 14

Suppose a cricket chirps $$60$$ times per minute. If the temperature formula is $$T = 0.5C + 40$$, where $$C is $$the number of chirps per minute, what is the temperature?

Accepted Answer

$$70$$

Question 15

Which of the following is NOT a solution to the equation $$x^2 - 4 = 0$?

Accepted Answer

$$3$$

Question 16

If $$x = 5$$, which of the following expressions has a value of $$40$$?

Accepted Answer

$$8x$$

Question 17

A mathematical model predicts $$65\% of $$marriages end in divorce after $$15$$ years for wives under $$18. $$The actual value from the graph is $$60\%. $$What is the difference and does the model overestimate or underestimate?

Accepted Answer

The model overestimates by $$5\%$$

Question 18

Which of the following is the correct translation for 'twice a number, decreased by $$6$$'?

Accepted Answer

$$2x - 6$$

Question 19

If $$x = 2$$ and $$y = 3$$, what is the value of $$5(x + y^2$)$$?

Accepted Answer

$$55$$

Question 20

Which of the following best describes mathematical modeling?

Accepted Answer

The process of finding formulas to describe real-world phenomena

Chapter 1: Variables, Real Numbers, and Mathematical Models – Study Notes

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