math terms

Definition of a function.

A function is a set of ordered pairs where every x value is paired with exactly one y value.

When changing from standard form to scientific notation, the leading number needs to be between what two values?

When changing from standard form to scientific notation, the leading number must be greater than or equal to 1 and less than 10.

What is the rule for changing a number in scientific form to standard form when the exponent is negative?

When the exponent is negative, move the decimal point to the left the same number of place as the exponent.

What is the rule for changing a number in scientific form to standard form when the exponent is positive?

When the exponent is positive, move the decimal point to the right the same number of places as the exponent.

Define integers. Give two examples.

Whole numbers and their opposites. Example: -3, 0, 1, -4, 10

Definition of a relation.

A relation is a set of ordered pairs.

Define whole numbers. Give two examples.

All of the natural numbers and 0. Example: 0,1,2,3,4,5...

Define irrational numbers. Give two examples.

An irrational number cannot be expressed as a ratio. The numbers in the decimal would go on forever, without repeating. Example: Pi, square root of 2.

What is the standard form of a line?

Ax + By = C

What letter is the dependent variable?

Dependent Variable = y

What is the rate of change formula?

Difference in the dependent variable/ Difference in the independent variable

What letter is the domain? Range? Output? Input?

Domain/Input = x ; Range/Output = y

What is the definition of a Pythagorean Triple?

What is the definition of a Pythagorean Triple?

Explain how to find the length of the diagonal of a rectangular prism.

Find the length of the "floor" diagonal using the Pythagorean Theorem. Find the length of the "space" diagonal using the Pythagorean Theorem (the height, floor diagonal and space diagonal form a right triangle)

Explain how to use the converse of the Pythagorean Theorem

If a^2+ b^2 = c^2 , then the triangle is a right triangle

If you are given a point and a slope, explain how to find the equation.

If given the slope and a point, use the equation y = mx+b. Using the (x, y) coordinates, substitute the numbers in for x and y. Substitute the slope in for m and solve for b. Using the slope and the "b" that was calculated, write an equation in slope intercept form.

What letter is the independent variable?

Independent Variable = x

What property is modeled by a(b + c) = ab + ac?

It is distributive

How do you use the calculator to solve a cube root?

Math Key, # 4

Rate of change is the same as ___in the context of a word problem.

Slope

Slope is the ratio of the ___________ to ___________.

Slope is the ratio of the rise to run.

What is true about the slopes of parallel lines? Their y-intercepts?

Slopes of parallel lines are equal (same). Y-intercepts are different.

If given two points, how do you use your calculator to get the equation?

Stat; Edit; Enter x coordinates in L1; Enter y coordinates in L2; Stat; Calc; #4

What is the rule for changing a negative exponent into a positive?

To change a negative exponent to a positive, move the base with the negative exponent to the opposite side of the fraction. For example, if the base with the negative exponent is in the denominator, it will be moved to the numerator and the exponent is made positive. If the base with the negative exponent is in the numerator, it will be moved to the denominator and the exponent is made positive.

. How do you use a vertical line test to tell if a graph is a function?

To determine a function using the vertical line test, draw vertical lines on the graph. If the lines touch the graph only once, the graph is a function.

What is the rule for dividing two powers with the same base?

To divide exponents with the same base, subtract the exponents.

Explain how to find the distance between two points on a coordinate plane using the Pythagorean Theorem.

To find the distance between two points on the coordinate plane, create a right triangle on the coordinate plane and use Pythagorean Theorem to find the length.

Explain how to find the x-intercept.

To find the x-intercept, let y=0 and solve for x.

Explain how to find the y-intercept.

To find the y-intercept, let x=0 and solve for y.

What is the rule for multiplying two powers with the same base?

To multiply two powers with the same base, keep the base and add the exponents

What is the shortcut for recognizing a function in ordered pair form?

To recognize a function in ordered pairs, the x value should not repeat itself (with different values for the y).

What is the rule for taking a power to a power?

To take a power to a power, keep the base the same and multiply the powers

How do you know if two monomials are like terms?

Two monomials are like terms if they each have the same variable(s) to the same power.

How many solutions are there to x to the 2nd power = 81?

Two. -9 and 9

What is the slope of a vertical line?

Undefined

Explain how to change 0.5̅ into a fraction.

Use powers of 10 to write two equations that can be subtracted to convert the repeating decimal into a fraction. (Both equations need to have the repeating digit(s) after the decimal point.) Let x =0.5̅.Let 10 x =5.5̅. When you subtract the second and first equations, the result is 9 x=5. Solve for x, x =5/9.

What is the slope of a horizontal line?

Zero

Define rational numbers. Give two examples.

a rational number is any number that can be expressed as the quotient or fraction. Example: 1.787878 or 2/3

List the steps to divide two numbers in scientific notation.

a) Divide the numbers. b) Divide the powers of 10. c) Make adjustments to put in scientific notation.

List the steps to multiply two numbers in scientific notation.

a) Multiply the numbers. b) Multiply the powers of 10. c) Make adjustments to put in scientific notation.

What is the Pythagorean Theorem formula? What kind of triangle do you use it on?

a^2 + b^2 = c^2 ; Right triangles only

Any number to the zero power is equal to what?

any number to the zero power is 1

What does m and b stand for?

m = slope; b = y-intercept

When dividing two numbers in scientific notation using a calculator, you need to use _______________.

parentheses.

Define natural numbers. Give two examples.

the counting numbers. example: 1,2,3,4,5...

What is the special equation of an undefined line?

x = a number

What is the special equation of a zero sloped line?

y = a number

What is the slope intercept form of a line?

y = mx + b

What is the slope formula?

y^2-y^1/x^2-x^1