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# Algebra 1 Final Exam

### Vocabulary for the final exam

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 _________
Created by: ahastings