Math

What is an exponent?

An operation used as shorthand for a number multiplied or divided by itself for a defined number of times: 3^7 = 3 x 3 x 3 x 3 x 3 x 3 x 3

A student gets an 85% on a test with 20 questions. How many answers did the student solve correctly? a.) 15 b.) 16 c.) 17 d.) 18

Answer. C: 85% of a number means that number should be multiplied by 0.85.

How do you convert a fraction to a percent?

Divide the numerator by the denominator to get a decimal: 9/12 = 0.75 Then convert the decimal to a percentage: 0.75 = 75%

What is covariance?

How two variables move in relation to each other.

How would you describe a set of data?

In terms of its center, spread, shape, and any unusual features.

What are perfect squares?

Numbers with whole number square roots. The list begins with 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

What's the primary reason for plugging data into a table?

So readers can easily interpret the information.

What is the arc of a circle?

The distance between two points on a circle.

What is associative property?

The grouping of numbers doesn't matter in an addition problem. The formula is (a + b) + c = a + (b + c).

What are factors?

The numbers multiplied to achieve a product. For example, the factors of 45 are 1, 3, 5, 9, 15 and 45, because these numbers all divide into 45 evenly.

How do you convert a percentage to a fraction?

With a denominator of 100. Example: 35% = 35/100

What is the perimeter and area of a circle?

- Circumference is measured by multiplying the diameter by Л. The formula is C = 2 Л r. - Area is calculated through the formula A = (Л)(r^2)

How would you find the perimeter and area of a rectangle?

- Measured by adding all sides together. The formula is P = 2 (| + w). - Length multiplied by the width. The formula is A = (l)(w).

How would you find the perimeter and area of a square?

- Measured by adding together all of the sides. The formula is P = 4 x s. - The length of a side squared. The formula is A = s^2

What is the perimeter and area of a triangle?

- Measured by adding together the three sides, so the formula is P = a + b + c. - The product of one-half the base and height, so the formula is: A = bh / 2

What is a chart?

A broad term that refers to a variety of ways to represent data.

What is a ratio?

A comparison between the relative sizes of two parts of a whole, separated by a colon. Example: if 3 pieces of an 8-piece pie were eaten, the number of uneaten parts expressed as a ratio to the number of eaten parts would be 5:3.

What is a common factor?

A factor shared by two numbers. Let's take 45 and 30 and find the common factors: The factors of 45 are: 1, 3, 5, 9, 15, and 45. The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30. The common factors are 1, 3, 5, and 15.

What is a decimal number?

A number written out with a decimal point instead of as a fraction. Example: 1.25 instead of 5/4. It is terminating if it stops at some point. It is called repeating if it never stops, but repeats a pattern over and over.

What are composite numbers?

A positive integer that is formed by multiplying two smaller integers together. They can be divided evenly by numbers other than 1 or itself. Example: 24, 66, 2348, 10002, because they are the result of multiplying two smaller integers together. In particular, these are all divisible by 2.

What are whole numbers?

A set of numbers that does not contain any fractions or decimals. The set of numbers includes zero. Example: 0, 1, 2, 3, 4, 189, 293.

What is the decimal system?

A way of writing out numbers that uses ten different numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. This is also called a "base ten" or "base 10" system. Other bases are also used. Example: computers work with a base of 2. This means they only use the numerals 0 and 1.

How do you find the mean of a data set?

Add up all the data points, then divide by the total number of data points.

What is multiplication?

Adding together multiple copies of a number. It is indicated by a " x " symbol or a number immediately outside of a parenthesis. Example: 5 x 6 or 5 (8 - 2)

What is distributive property?

Allows the multiplication to be distributed through parentheses. The formula is a x (b + c) = ab + ac.

What are independent variables?

Also controlled by the scientist, but they are the same only for each group or trial in the experiment.

What are numbers?

An adjective representing a quantity of objects. They function as placeholders for a value. They can be better understood by their type and related characteristics.

What is a fraction?

An equation that represents a part of a whole, but can also be used to present ratios or division problems. Example: x/y; In this example, x is called the numerator, while y is the denominator.

Johnny earns $2334.50 from his job each month. He pays $1437 for monthly expenses. Johnny is planning a vacation in 3 months' time that he estimates will cost $1750 total. How much will Johnny have left over from three months' of saving once he pays for his vacation? a.) $948.50 b.) $584.50 c.) $852.50 d.) $942.50

Answer. D: First, subtract $1437 from $2334.50 to find Johnny's monthly savings; this equals $897.50. Then, multiply this amount by 3 to find out how much he will have (in three months) before he pays for his vacation: this equals $2692.50. Finally, subtract the cost of the vacation ($1750) from this amount to find how much Johnny will have left: $942.50.

A school has 15 teachers and 20 teaching assistants. They have 200 students. a.) 3:20 b.) 4:17 c.) 3:2 d.) 7:40

Answer. D: The total faculty is 15 + 20 = 35. So the ratio is 35 : 200. Then, divide both of these numbers by 5, since 5 is a common factor to both, with a result of 7 : 40.

Using the following diagram, calculate the total circumference, rounding to the nearest decimal place. a.) 25.0 cm b.) 15.7 cm c.) 78.5 cm d.) 31.4 cm

Answer. D: To calculate the circumference of a circle, use the formula C = 2 Л r, where r equals the radius or half of the diameter of the circle and Л = 3.14... . Substitute the given information, 2 Л 5 = 31.4...

What are even numbers?

Any number that can be divided by 2 evenly, meaning the answer has no decimal or remainder portion. Example: 2, 4, 9082, -2, -16, -504. It does not matter whether the number is positive or negative.

What are rational numbers?

Any number that can be expressed as a fraction, with a non-zero denominator. Since any integer can be written with 1 in the denominator without changing its value, all integers are considered rational. They have a decimal expression that terminates or repeats.

What are odd numbers?

Any number that does not divide evenly by 2. Example: 1, 21, 541, 3003, -9, -63, -1257.

How do you convert a percentage to a fraction?

By making the number in the percentage the numerator and putting 100 as the denominator: 97% = 97/100 43% = 43/100

How are decimals multiplied?

Calculate the product as if the decimals are not there, then count the number of decimal places in the original problem. Use that total to place the decimal the same number of places over in your answer, counting from right to left. Example: 0.5 x 1.25 can be rewritten and multiplied as 5 x 125, which equals 625. Then the decimal is added three places from the right for .625.

What is rate of change?

Calculates the steepness of the line over a given interval. It is also known as the slope or rise/run. The TEAS will focus on the rate of change for linear functions which are straight lines. The slope is given by the change in y divided by the change in x.

What is a decimal place?

Denotes how far to the right of the decimal point a numeral is. The first digit to the right of the decimal point is in the tenths place. The next is the hundredths. The third is the thousandths.

What are real numbers?

Describe rational and irrational numbers.

What are decimal numbers?

Designated by a decimal point which indicates that what follows the point is a value that is less than 1 and is added to the integer number preceding the decimal point. The digit immediately following the decimal point is in the tenths place, the digit following the tenths place is in the hundredths place, and so on.

How do you convert a fraction to a decimal?

Divide the numerator by the denominator: 5/20 = .25

How are decimals added together?

Each number in columns needs to be lined up by the decimal point. For each number being added, the zeros to the right of the last number need to be filled in so that each of the numbers has the same number of places to the right of the decimal. Then, the columns can be added together. Example: 2.450 1.300 +8.891

How are decimals subtracted from each other?

Each number in columns needs to be lined up by the decimal point. For each number, the zeros to the right of the last number need to be filled in so that each of the numbers has the same number of places to the right of the decimal. Example: 7.89 - 4.235 written in column form: 7.890 - 4.235 3.655

What are dependent variables?

Experience change caused by the independent variable and are what is being measured or observed.

What is the square root symbol?

Expressed as ⎷ and is commonly known as the radical. Taking the root of a number is the inverse operation of multiplying that number by itself some amount of times. Example: ⎷36 = 6 because 6 multiplied by 6 equals 36. Note, the square root of 36 is also -6 since -6 x -6=36. This can be indicated using a plus/minus symbol like this: + 6.

What is estimation?

Finding a value that is close to a solution but is not the exact answer. Example: if there are values in the thousands to be multiplied, then each value can be estimated to the nearest thousand and the calculation performed. This value provides an approximate solution that can be determined very quickly.

How do you divide two fractions?

Flip the numerator and denominator of the second fraction, and then proceed as if it were a multiplication problem. Example: 7/8 ÷ 4/5 = 7/8・5/4 = 35/32

What is the remainder in division?

If a divisor doesn't divide into a dividend an integer number of times, whatever is left over is termed the remainder.

How do you find the median of a data set?

In a data set, find the point in the middle. The middle refers to the point where half the data comes before it and half comes after, when the data is recorded in numerical order.

What is a prime factorization?

Involves an additional step after breaking a number down to its factors: breaking down the factors until they are all prime numbers. Let's break 129 down into its prime factors. First, the factors are 3 and 43. Both 3 and 43 are prime numbers, so we're done. But if 43 was not a prime number, then it would also need to be factorized until all of the factors are expressed as prime numbers.

What are irrational numbers?

Irrational numbers are numbers which cannot be written as a finite decimal. The most common is Pi, which has an endless and non-repeating decimal, but there are other well-known irrational numbers, such as e and ⎷2.

How do you convert a decimal to a percentage?

Move the decimal point two places to the right and add a % sign. Example: 0.65 = 65% 0.33 = 33% 0.215 = 21.5% 0.9999 = 99.99% 5.00 = 500% 7.55 = 755%

What is commutative property?

Numbers in an addition equation can be switched without altering the result. The formula is a + b = b + a.

What are time numbers?

Numbers that are only evenly divisible, resulting in no remainder or decimal, by 1 and itself. Example: 2, 3, 7, 13, 113, because they can only be evenly divided by 1 and itself.

Describe proper and improper fractions and mixed numbers.

Proper fractions have a numerator less than the denominator, such as 3/8, but improper fractions have a numerator greater than the denominator, such as 15/8. Mixed numbers combine a whole number with a proper fraction, such as 3 1/2.

What do graphs do?

Provide a visual representation of data.

What are constant variables?

Remain unchanged by the scientist across all trials. They can either be controlled by the scientist directly like the nutrition, water, and sunlight given to plants, or they can be selected by the scientist specifically for an experiment, like using a certain animal species or choosing to investigate only people of a certain age group.

How are parentheses used in math problems?

Separate different parts of an equation, and operations within them should be thought of as taking place before the outside operations take place.

How do you multiply two fractions?

Simply multiply the numerators, multiply the denominators, and place the products as a fraction. Example: 2/5・3/4 = 6/20 = 3/10

What is subtraction?

Taking away one number from another, so their quantities are reduced. The sign designating this operation is the " - " symbol, and the result is called the difference. Example: 9 - 6 = 3.

What is addition?

The combination of two numbers so their quantities are added together cumulatively. The sign for this operation is the + symbol. For example, 9+6=15.

How do you find the mode of a data set?

The data point that appears most frequently. If two or more data points all tie for the most frequent appearance, then each of them is considered a mode.

What is the greatest common factor?

The largest number among the shared, common factors.

What is perimeter?

The measurement of a distance around something or the sum of all sides of a polygon.

What is the order of operations?

The order is as follows: Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right. A popular pneumonic device to help remember the order is Please Excuse My Dear Aunt Sally (PEMDAS).

What does it mean to solve an equation in one variable?

The process of isolating a variable on one side of the equation. X is commonly used as a variable, though any letter can be used. Example: x + 8 = 20 x + 8 - 8 = 20 - 8 x = 12

What is the slope of a line?

The rise over run: slope = rise/run The rise is the change vertically on the y-axis and the run is the change horizontally on the x-axis.

What is division?

The signs designating this operation are the ÷ and / symbols. The second number divides into the first. The number before the division sign is called the dividend or, if expressed as a fraction, the numerator. The number after the division sign is called the divisor or, if expressed as a fraction, the denominator.

What is the least common multiple?

The smallest number that's a multiple of two numbers. Let's try to find the least common multiple of 4 and 9. The multiples of are 4, 8, 12, 16, 20, 24, 28, 32, 36, and so on. For 9, the multiples are 9, 18, 27, 36, 45, 54, etc. Thus, the least common multiple of 4 and 9 is 36, the lowest number where 4 and 9 share multiples.

What is area?

The space occupied by a defined enclosure, like a field enclosed by a fence.

What is an absolute value?

The value of a number regardless of its sign. The symbol for absolute value is | |. Example: The absolute value of 24 is 24 or | 24 |= 24. The absolute value of -693 is 693 or | -693 | = 693.

To add and subtract fractions, what needs to happen?

These operations require the fractions to have the same denominator, also called a common denominator.

How can ratios and rates be used together, and how are they related to the conversion factor?

They can be used together to convert rates into different units. Example: if someone is driving 50 kilometers per hour, that rate can be converted into miles per hour by using a ratio known as the conversion factor.

What do unit rate word problems ask you to do?

To calculate the rate or quantity of something in a different value. Example: a problem might say that a car drove a certain number of miles in a certain number of minutes and then ask how many miles per hour the car was traveling. These questions involve solving proportions.

How are decimals divided?

Use long division first by ignoring the decimal point. Then, the decimal point is moved the number of places given in the problem. Dividing by another decimal requires changing the divisor to a whole number by moving its decimal point.

What are integers?

Whole numbers and their negative counterparts. Note that zero does not have a negative counterpart here. Instead, zero is its own negative. Example: -1, -2, -3, -4, -5, 0, 1, 2, 3, 4, 5 are all integers. -1, -2, -3, -4, -5 are considered negative integers and 1, 2, 3, 4, 5 are considered positive integers.