NLN PAX: Mathematics Test: Algebra, Complete Solution

NLN PAX: Mathematics Test: Algebra, Complete Solution Numbers basic building blocks of mathematics. Integers set of whole positive and negative numbers, including zero. These do not include fractions, decimals, or mixed numbers. Prime Number whole number greater than 1 that has only two factors, itself and 1; a number that can be divided evenly by 1 itself. Composite Number whole number greater than 1 that has more than two different factors; any whole number that is not a prime number. Even Number any integer that can be divided by 2 without leaving a remainder. Odd Number any integer that cannot be divided evenly by 2. Decimal Number a number that uses a decimal point to show the part of the number that is less than one. Decimal Point symbol used to separate the ones place from the tenths place in decimals or dollars from cents in currency. Decimal Place position of a number to the right of the decimal point. Decimal or Base 10 System number system that uses ten different digits. Rational Number all integers, decimals, and fractions. Any terminating or repeating decimal number is a rational number. Irrational Number cannot be written as fractions or decimals because the number of decimal places is infinite and there is no recurring pattern of digits within the number. Real Numbers set of all rational and irrational numbers. Mathematical Operations addition, subtraction, multiplication, division Addition increases the value of one quantity by the value of another results in sum Subtraction opposite operation to addition; it decreases the value of one quantity by the value of another quantity results in difference. Multiplication repeated addition; one number tells how many times to add the other number to itself (order doesn't matter). Division opposite operation to multiplication; one number tells us how many parts to divide the other number into (order does matter) Exponent superscript number placed next to another number at the top right that indicates how many times the base number is to be multiplied by itself. Squared number with an exponent of 2 Power value of a number raised to an exponent Cubed number with an exponent of 3 Negative Exponent reciprocal of a positive exponent. Parentheses designate which operations should be done first when there are multiple operations. Order of Operations set of rules that dictates the order in which we must perform each operation in an expression so that we will evaluate it accurately. P operations inside the parentheses E simplify the exponents MD multiplication and division from left to right. AS addition and subtraction from left to right. Root another way of writing a fractional exponent; uses radical symbol to indicate the operation. Radical number underneath the bar, and sometimes have a number in the upper left. Square Root a number raised to the one-half power. Perfect Square number that has an integer for its square root. Scientific Notation way of writing large numbers in a shorter form. Absolute Value distance away from zero a number is on the number line. Signs are the same add the absolute values. Signs are different take absolute values of the addends and subtract the smaller value from the larger value, then apply the original sign of the larger value to the difference. Factors numbers that are multiplied together to obtain a product. Prime Number only two factors (1 and itself), but other numbers can have many factors. Common Factor number that divides exactly into two or more other numbers. Prime Factor also, a prime number Greatest Common Factor (GCF) largest number that is a factor of two or more numbers. Least Common Multiple (LCM) smallest number that is a multiple of two or more numbers. Fraction number that is expressed as one integer written above another integer, with a dividing line between them fractions can be manipulated by multiplying or dividing both the numerator and denominator by the same number. Numerator top number of a fraction that represents the number of parts under consideration. Denominator bottom number of a fraction that represents the total number of equal parts. Undefined fraction that cannot have a denominator of zero Equivalent Fractions two fractions that have the same value but are expressed differently. Common Denominator when two fractions are manipulated and end up having the same denominator. Proper Fraction fraction whose denominator is greater than the numerator. Improper Fraction fraction whose numerator is greater than its denominator. Mixed Number number that contains both an integer and a fraction. Percentages fractions that are based on a whole of 100. Percent per hundred. Decimals to percentages move the decimal point two places to the right. Percentage to a decimal move the decimal point two places to the left. Ratio comparison of two quantities in a particular order. Proportion relationship between two quantities that dictates how one changes when the other changes. Direct Proportion relationship in which a quantity increases by a set amount for every increase in the other quantity or decreases by that same amount for every decrease in the other quantity. Inverse Proportion relationship in which an increase in one quantity is accompanied by a decrease in the other or vice versa. Cartesian Coordinate Plane two number lines placed perpendicular to each other and intersecting at the zero point. Origin zero point of a cartesian coordinate plane. X-axis horizontal number line with positive values to the right of the origin and negative values to the left of the origin. Y-axis vertical number line with positive values above the origin and negative values below the origin. Coordinate any point on the plane can be identified by an ordered pair in the form (x, y). Abscissa x-value of the coordinate Ordinate y-value of the coordinate. Slope a ratio of the change in the vertical distance to the change in horizontal distance. Slope Formula (Y2-Y1)/(X2-X1) if value is positive slope is positive and line slopes upward from the left to right. If value is negative slope is negative and line slopes downward from left to right. Horizontal Line y-coordinates are the same for both points, the slope is 0. Vertical Line x-coordinates are the same for both points, there is no slope. Parallel Line two or more lines that have equal slopes. Perpendicular Line slopes that are negative reciprocals of each other. Monomial single variable or product of constants and variables. Polynomials algebraic expressions which use addition and subtraction to combine two or more monomials. Binomial two terms Trinomial