An expression is a combination of variables and constants using mathematical operations and grouping symbols.

An equation is a statement that two quantities are equal, built using expressions and an equal sign (=).

A formula is an equation with multiple variables that is used to calculate some quantity that we’re interested in.

The independent variable is sometimes called the input and the dependent variable is sometimes called the output.

To evaluate an expression (or a formula), replace all occurrences of the variable or variables with specific numbers to find a numeric value.

Future Value with Simple Interest

The future value of an account using simple interest is given by A = P + Prt.

Future Value with Compound Interest

The future value of an account using compound interest is given by A = P(1 + r)^t.

In Questions 13 and 14, the new value of an account A is known as the future value, P represents the original amount or principal, r represents the interest rate in decimal form, and t represents the number of time periods.

Equivalent Expressions

Two expressions that would give you the same output no matter what input you choose would be considered equivalent expressions.

Area is the measure of size for two-dimensional objects, like floors, walls, posters, fields, etc.

Area is measured in square units.

Volume is the measure of size for three-dimensional objects, like beer mugs, swimming pools, buildings, and so on.

Volume is measured in cubic units.

Dimensional analysis is the incredibly valuable skill we use in the process for converting units.

It helps ensure that equations make sense dimensionally.

Multiplying any measurement by a conversion factor won’t change the size of the measurement because we’re just multiplying by one; it will change the units used to measure.

This is a fundamental principle in unit conversion.

A rate is a ratio that compares two quantities.

Rates are often expressed as a fraction.

A unit rate is a rate that has a 1 in the denominator.

For example, 60 miles per hour is a unit rate.

Estimation is another name for making an educated guess.

It is often used when exact calculations are not necessary.

A statement that involves one of the symbols >, ≥,

Inequalities express the relationship between two values.

A phrase used to describe

This indicates that one quantity is smaller than another.

A phrase used to describe > is greater than.

This indicates that one quantity is larger than another.

A phrase used to describe ≤ is less than or equal to.

This indicates that one quantity is either smaller than or equal to another.

A phrase used to describe ≥ is greater than or equal to.

This indicates that one quantity is either larger than or equal to another.

The change between two quantities is found by simply subtracting the new value from the old, (xₙ - xₒ).

This gives the absolute change.

The relative change between two quantities measures the change as a fraction of the original value, (xₙ - xₒ) / xₒ.

This is often expressed as a percentage.

When comparing an estimate to an exact value, the error in the estimate can be expressed by subtracting the actual value from the estimated value.

Error = Estimated Value - Actual Value.

The percent error is calculated just like relative change. The idea is to measure how far off the estimate is as a percentage of the actual value.

Percent Error = (Error / Actual Value) × 100%.

The range of a data set is calculated by subtracting the highest value minus the lowest value.

Range = Highest Value - Lowest Value.

Standard deviation, which is often represented by a lowercase Greek sigma (σ), is a measure of how far on average the values are from the mean.

It quantifies the amount of variation in a set of data.

Things like sizes of individuals, IQs, weights of packaged products, and lifespans of batteries or lightbulbs are often normally distributed.

Normal distribution is a common probability distribution.

When a group of data is normally distributed, and we know the mean and standard deviation, the rule that allows us to estimate how many data values fall within certain ranges is known as the empirical rule.

This rule states that approximately 68% of data falls within one standard deviation of the mean.

A combination of two inequalities is known as a compound inequality.

Compound inequalities can be joined by 'and' or 'or'.

The expected value of an event is the value that can be expected, on average, to occur.

It is calculated as the sum of all possible values, each multiplied by its probability.

A grading scale where some assignments count for a bigger portion of the overall grade than others is called a weighted scale.

Weighted scales reflect the importance of different assignments.

A game of chance is called a fair game if the expected value is 0.

In a fair game, the average outcome is neither a gain nor a loss.

Computing measures of average using Excel

Learn to compute mean, median, and mode using Excel.

Evaluating a formula with a calculator or spreadsheet

Use a calculator or spreadsheet to evaluate mathematical formulas.

Computing standard deviation

Understand how to compute standard deviation for a data set.

Table of movie lengths and prepaid calling card values

Use the table to practice computing averages and evaluating formulas.

Unit 2 Review- Making Sense of It All Flashcards

Student preview

100 questions

Show all answers

1.

FLASHCARD QUESTION

Front

Mean

Back

The mean of a set of numbers is found by adding all of the numbers, then dividing by how many numbers there are in the list.

2.

FLASHCARD QUESTION

Front

Median

Back

The median of a list of numbers is the value that lives right in the middle of the set if it’s arranged in order.

3.

FLASHCARD QUESTION

Front

Mode

Back

The mode of a list of numbers is the value that appears most often.

4.

FLASHCARD QUESTION

Front

Variable

Back

A variable is a quantity that is able to change, or vary.

5.

FLASHCARD QUESTION

Front

Constant

Back

A constant is a quantity that can’t vary.

6.

FLASHCARD QUESTION

Front

Dependent Variable

Back

Course grade is an example of a dependent variable because other factors cause your course grade to vary.

7.

FLASHCARD QUESTION

Front

Independent Variable

Back

The amount of time you spend studying is an example of an independent variable because it can change and cause changes in your course grade.

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