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# Algebra 1 Final Exam

### Vocabulary for the final exam

Question | Answer |
---|---|

Quadratic Formula | A formula for solving a quadratic equation |

absolute value | The _______ of a number is the number itself or the opposite of the number, whichever is positive (or zero) |

Square property of equality | If two positive numbers are equal, then their positive square roots are equal. |

Square root of a perfect square | To solve the _____________ solve the operation below the vinculum first. |

Discriminant | The expression (b squared) - 4ac which appears in the quadratic formula is called a _________ |

Vertical motion formula | If an object is thrown into the air with an initial upward velocity of r meters per second then it's distance, d meters, above its starting point at time t seconds after it was thrown |

Graph | A chart made up of many small equally sized squares that one uses to record data. |

x-axis | A line on the cartesian coordinate system that moves horizontally |

y-axis | A line on the cartesian coordinate system that moves vertically. |

Ordered Pair | A pair of numbers that are graphed on the x and y axis of a cartesian coordinate system |

Abscissa | The first number in an ordered pair |

Ordinate | The second number in an ordered pair |

Coordinates | The two numbers in an ordered pair are called the _________ of a point in a plane |

Cartesian Coordinate System | A graph with an x-axis, and a y-axis where an ordered pair can be graphed. |

Quadrants | In a cartesian coordinate system there are four of these two on the top and two on the bottom. |

Y-intercept | The _______ is the value of y when x is 0. |

X-intercept | The _______ is the value of x when y is 0. |

Slope | The slope of a line is the ratio |

Slope-intercept form | An equation of the form y=mx+b where ma and b are constants, is in slope=intercept form. The constant m is the slope. The constant b is the y-intercept. |

Slope of horizontal line | __________ have 0 for a slope. |

Slope of a Vertical Line | __________ don't have a a slope. |

Point-slope form | An equation in the form y-y1=m(x-x1) is said to be in ________ |

Equation of horizontal line | If y=constant, the graph is a ________ |

Equation of vertical line | If x=constant, the graph is said to be a ________ |

System of equations | A system is two or more equations with the same variables |

Linear combination | A method for solving a system of equations. A ___________ of two quantities is what you get by multiplying each quantity by a constant, then adding the results. |

Prime number | A prime number is a positive interger that has no positive integers as factors other than 1 and itself |

composite number | A number that can be factored into a product of several primes |

Product of two powers with equal bases | If you multiply two powers, and both bases are equal, then you can add the exponents (and use the same base). |

Power of a product | exponentiation distributes over multiplication. |

Power of a power | If you raise a power to a power, then you can multiply the exponents. |

Power of a quotient | Exponentiation distributes over division |

Quotient of two powers with equal bases | If you divide two powers, and they have equal bases, then you can subtract the exponents(numerator - denominator) and use that same base. |

Negative exponents | For any nonzero number x and for any interger n, x (to the negative n) = 1/x (to the n). |

Zero exponent | For any nonzero number x, x(to the zero) is 1 |

Scientific Notation | A method used to make it easier to read very small or very large numbers using powers of 10. |

Mantissa | In scientific notation the number that has the decimal point after the first digit is called the _______ |

Characteristic | In scientific notation the power of 10 after the first number is usually referred to as the _________ |

Relatively prime | If two integers have no common prime factors their GCF is 1. |

First step in factoring completely | FACTOR THE GCF OF THE TERMS FROM THE POLYNOMIAL. ***DO NOT FORGET THIS*** |

Rational algebraic expression | A _________ is an expression that can be written as a ratio of two polynomials. |

Fractional equation | An equation that has a variable in at least one denominator. |

Canceling | To _________ in a fraction means to divide the numerator and denominator by the same common factor. |

Extraneous solution | An ___________ is a value of the variable that satisfies the transformed equation, but not the original one. |

Domain | The _________ of a variable is the set of numbers that can be values of the variable |

Radical algebraic expression | An expressin such as radical x-16 is called a __________ |

Square root of a product | The _________ of two nonnegative numbers equals the product of the square roots of two numbers. |

Square root of a quotient | The _________ of two positive numbers equals the quotient of the square roots of numbers |

Simple Radical Form | A radical is said to be in _________ if:1. There are no radicals in the denominator2. The radicand(s) in the numerator are as small as possible.3. Reduce number to lowest terms |

Radical equation | A ________ is an equation with a variable under the radical sign |

hypotenuse | In a right triangle the side opposite the right angle is this. |

Pythagorean Theorem | In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs. |

Pythagorean Triples | A right triangle that has all three sides lengths as integers is known as this. |

Cube Root | 5 is a ________ of 125 because 5 (to the third) = 125 |

Fourth Root | 3 is a ________ of 81 because 3 (to the fourth) = 81 |

Fifth Root | 2 is a ________ of 32 because 2 (to the fifth) = 32 |

Nth Root | A _______ of x is a number that, when raised to the ______ power, gives x for the answer. *Hint* th1nk 0f th3 r00t 1nd3x *Hint* |

Root Index | (radical x to the n th), the positive integer n is called the _________ |

Exponent property of n th root | (radical x to the n th) = 1/x(to the n th) |

Rational number | A number that can be written as a ratio of two integers. |

Irrational number | A real number that cannot be written as a ratio of two integers. |

Inequality | a sentence that states one expression is greater than or less than another |

Union | The _____ of sets A and B, abbreviated A U B, is the set of numbers that are either in set A or in set B. |

Intersection | The ___________ of sets A and B, abbreviated A (upside down U) B, is the set of numbers that are in both sets. |

Function | A set of ordered pairs (x,y) for which there is never more than one value of y for any one given value of x. |

Direct variation function | y varies directly with x, or y is directly proportional to x, if and only if y=kx, where k is the proporionality constant. |

Proportionality Constant | The constant by which two terms are directly or inversely proportional |

Inverse variation | y varies inveresely with x, or y is inversely proportional to x, if and only if, y=k/x, where k is the proportionality constant |

General equation | An equation such as y=kx or y=k/x is known as this. |

Particular equation | Equations such as y=kx or y=k/x are known as general equations. However, if the value of k is known: y=3x or y=24/x than these equations are known as _________ |