ATI TEAS Version 7 Math Comprehensive Review

Practice flashcards covering the math concepts of fractions, algebra, statistics, measurements, and geometry as taught in the ATI TEAS Version 7 comprehensive review.

What does the numerator of a fraction represent?

The number above the fraction line that represents how many parts of a whole you have.

What does the denominator of a fraction represent?

The bottom number below the fraction line that represents how many equal parts the whole is being divided into.

According to the lecture, what is an example of equivalent fractions?

$\frac{2}{8}$ and $\frac{1}{4}$ because they represent the same quantity once simplified.

What is the result of dividing a tenth by $10$?

One over $100$ or one hundredth (the hundredths place).

What is the value of the digit in the thousandths place in the number $1,234.567$?

$0.007$ (seven thousandths).

What is the Latin origin and meaning of the word 'percent'?

It derives from the Latin word 'centum', meaning $100$, so percent translates to 'per $100$' or 'out of a $100$'.

How do you convert a fraction to a decimal?

Divide the numerator by the denominator (e.g., $\frac{3}{4} = 0.75$).

How do you convert a decimal to a percentage?

Multiply by $100$ and move the decimal point two places to the right.

What is the order of operations acronym provided in the transcript?

PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

When performing multiplication and division in PEMDAS, which operation takes precedence?

Neither; you perform them moving from left to right.

Define a rational number.

Any number that can be expressed as a ratio of two integers where the denominator is not zero.

What are examples of irrational numbers mentioned in the lecture?

$\pi$, the number $e$, and the square root of any number that is not a perfect square (e.g., $\sqrt{2}$, $\sqrt{3}$, $\sqrt{15}$).

What is 'the stacking method' for comparing decimals?

Stacking numbers vertically and lining up the decimal points to compare place values from left to right.

What does the 'alligator analogy' represent in math?

The alligator's mouth always opens toward the greater number ($>$ or $<$).

In the expression $15x + 5$, what is the term for the number $15$?

The coefficient.

What is a 'constant' in an algebraic expression?

A number that stands alone without a variable attached to it (e.g., the $5$ in $15x + 5$).

What is the 'multiplicative inverse' of a whole number $b$?

The reciprocal, which is $\frac{1}{b}$, such that $b \times \frac{1}{b} = 1$.

How do you solve a proportion involving two fractions with an equal sign (e.g., $\frac{x}{3} = \frac{4}{6}$)?

Cross-multiply the fractions to obtain an equation ($6x = 12$) and then isolate the variable ($x = 2$).

What real-world object is approximately one meter tall?

A doorknob.

What is the estimated weight of a standard paperclip?

Approximately $1$ gram.

How should the phrase 'four less than a number' be translated into algebra?

$x - 4$, where $x$ is the number.

What is the formula for percent proportions?

$$\frac{\text{is}}{\text{of}} = \frac{\text{percent}}{100}$$

What is a 'unit rate'?

A form of rate where the denominator is $1$ (e.g., $\$12$ per hour).

What inequality symbol represents 'at most' or a 'maximum capacity'?

$\le$ (less than or equal to).

Define the 'constant of proportionality' $k$.

The consistent rate at which one quantity increases or decreases relative to another in the equation $y = kx$.

What is the 'mean' of a dataset?

The average number, calculated by adding all numbers together and dividing by the total number of items.

How do you find the 'median' of a dataset with an even number of data points?

Find the average of the two middle numbers.

What is the 'mode' of a dataset?

The most frequent number in the set; it can be unimodal, bimodal, or have no mode.

How is the 'range' of a dataset calculated?

The difference between the highest and lowest numbers (Highest $-$ Lowest).

Using the 'toe analogy', how can you identify a right-skewed distribution?

It mirrors your right foot, where the 'great toe' is tallest on the left (the peak/mode) and the data trails off to the right.

What is the probability of an impossible event and a certain event on the probability line?

Impossible is $0$ and Certain is $1$.

If an event is described as 'event A AND event B occurring', what math operation do you use for their probabilities?

Multiplication.

What is the name of the graph consisting of two perpendicular axes ($x$ and $y$) meeting at an origin?

Cartesian coordinate chart.

Which type of graph is best for examining the relationship and correlation between two numerical variables?

Scatter plot.

In a scatter plot, which axis should represent the independent variable?

The $x$-axis.

Which graph type is ideal for observing changes over time?

Line graph.

What are the three common trends for graphs discussed in the video?

Linear, Exponential, and Quadratic.

Describe the appearance of a quadratic function on a graph.

A classic $U$-shaped curve that is symmetrical.

What is the relationship between the distance traveled and time at a constant speed?

Direct proportionality ($y = kx$).

What is an example of inverse proportionality?

The relationship between the number of workers assigned to a task and the time taken to complete it (more workers = less time).

What is the formula for the circumference of a circle?

$C = \pi \times d$ (Cherry Pie is Delicious).

What is the formula for the area of a circle?

$A = \pi \times r^2$ (Apple Pies Are $r^2$).

What is the formula for the area of a trapezoid?

$$\frac{(b_1 + b_2) \times h}{2}$$

How do you calculate the volume of a square or rectangular prism?

$$\text{Length} \times \text{Width} \times \text{Height}$$

What is the mnemonic to remember metric prefixes from kilo to milli?

King Henry Doesn't Usually Drink Cold Milk.

How many feet are in one mile?

$5,280$ feet.

How many pounds are in one kilogram?

$2.2$ pounds ($1\,kg = 2.2\,lbs$).

How many tablespoons are in one cup based on the Big G/Super G breakdown?

The Big G covers gallons to cups; specifically, $1$ gallon = $16$ cups.

What is the specific conversion between tablespoons and teaspoons?

$1$ tablespoon = $3$ teaspoons.