           ## Math Vocabulary

 Understanding the math vocabulary is crucial when preparing for the 8th grade CRCT math test. This glossary explains the meaning of a variety of math terms by using simple definitions, examples, images, diagrams, tables, and graphs.
 Absolute Value The absolute value of a number equals to the distance from that number to zero on a number line. The absolute value of a positive number is the number itself. The absolute value of a negative number is the opposite number (the same numeral but without the minus sign in front of it). Examples: Absolute Value Equation An equation in witch the variable (or an expression containing the variable) is between the bars of the absolute value symbol is called an absolute value equation. Example: Absolute Value Inequality An inequality in which the variable (or an expression containing the variable) is between the bars of the absolute value symbol is called an absolute value inequality. Examples: Acute Angle An acute angle is an angle measuring less than 90 degrees. Example: Acute Triangle An acute triangle is a triangle in which all of its angles are acute (each angle measure less than 90 degrees). Examples: Algebraic Expression An algebraic expression is a combination of mathematical symbols such as numbers, variables (letters), and operations. Examples: Alternate Exterior Angles Alternate exterior angles are formed when two lines are cut by a transversal. If the lines are parallel, the two alternate exterior angles are congruent. Alternate exterior angles are located on oposite sides of the transversal, and outside the parallel lines. Examples: Angles < 1 and < 2 are alternate exterior. Angles < 3 and < 4 are also alternate exterior. Alternate Interior Angles Alternate interior angles are formed when two lines are cut by a transversal. If the lines are parallel, the two alternate interior angles are congruent. Alternate interior angles are located on oposite sides of the transversal, and inside the area formed by the parallel lines. Examples: Angles < 5 and < 6 are alternate interior. Angles < 7 and < 8 are also alternate interior. Base In the expression , m is the base. Example: 2 is the base of the expression . Closed Half-Plane A closed half-plane is a half-plane that contains its boundary line. A solid line is used to indicate the boundary of a closed half-plane. Example: The half-plane in this picture is closed because its boundary line (the solid red line) is part of the half-plane. Complement of a Set The complement of a set is the set of all elements in the universal set that are not in the initial set. Example: The complement of the set A in the above picture is set A' indicated in yellow. Congruent Triangles Two triangle are congruent if all corresponding sides and angles are congruent. Example: Triangles ABC and A'B'C' above are congruent. Congruent Polygons Two ploygons are congruent if all corresponding sides and angles are congruent. Example: The two pentagons in this picture are congruent. Corresponding Angles Corresponding angles are formed when two lines are cut by a transversal. If the lines are parallel, the two correspondent angles are congruent. Corresponding angles are located on the same side of the transversal; one angle is inside the area formed by the parallel lines, and the other area is outside the parallel lines. Examples: Angles < 3 and < 6 are correspondent. Angles < 4 and < 5 are also correspondent. Disjoint Sets Two sets are disjoint if they have NO common elements (their intersection is the null set). Example: Sets A = {1,2,3,4} and B = {5,6} are disjoint because their intersection is the empty set (they do not have any common elements). Empty Set A set with no elements is called empty set or null set. We use this symbol to indicate an empty set. Equation An equation is a mathematical sentence that indicates that two numbers or mathematical expressions are equal. Example: 3m - 4 = -19 is an equation. The equal sign indicates that the expression located on the left side of this equation (3m - 4) is equal to the right side of the equation (number -19). Exponent In the expression , x is the exponent. It indicates the number of time the base is multiplied by itself. Example: 5 is the exponent of the expression . Function A function is a correspondence between two sets in which each element of the first set has one and only one correspondent in the second set. Example: The relation between sets A and B is a function. Hypotenuse The longest side of a righ triangle is called the hypotenuse. The hypotenuse opposes the right angle of the triangle. Example: Independent Events Two events whose outcomes do not influence each other are called independent events. Example: Tossing a coin and rolling a number cube are two independent events. Inequality A mathematical sentence comparing two quantities that are not equal is called an inequality. Example: 2 + 3 < 97 - 82 Integers Whole numbers and their opposites are called integers. Examples: 67, -13, 8, 90, -1005, 3, 0, -546 Intersection of Sets A set formed by all common elements to two or more sets is called intersection of sets. Example: Inverse operation An operation is the inverse of another operation if it undoes its effect. Example: Addition and subtraction are inverse operations.               Multiplication and division are inverse operations. Irrational Number An irrational number is any number that can not be written as a fraction of two integers. Examples: Legs The two shorter sides of a right triangle are called legs. They are the sides of the right angle. Line of Best Fit The line of best fit is a line used in a scatter plot to represent the trend of a data. Example: The red line in the above scatter plot is a line of best fit because all points in this graph cluster around it. Linear Equation A linear equation is an equation whose graph is a straight line in the coordinate plane. Example: y = 2x - 3 is a linear equation because its graph (the red line below) is a straight line. Null Set A set with no elements is called null set or empty set. We use this symbol to indicate a null set. Open Half-Plane An open half-plane is a half-plane that does not contain its boundary line. A dashed line is used to indicate that the boundary is NOT a part of the open half-plane. Example: The half-plane in this picture is open because its boundary line (the dashed red line) is NOT part of the half-plane. Parallel Lines Two coplanar lines that have no common points are called parallel lines. Their intersection is the null set. Example: Pattern A pattern is a numerical sequence that follows a certain rule for getting from one number to the next. Example: The sequence 1,5,9,13,17,... is a pattern because to get from one term to the next, we have to always add four. Perfect Square A number is a perfect square if it can be written as the square of a whole number. Example: 25 is a perfect square because . Perpendicular Lines Two lines are perpendicular if they intersect and form four right angles. Example: Lines a and b in the above figure are perpendicular. Probability A ratio that measures the likelihood that an event will happen is called probability. Pythagorean Theorem Pythagorean Theorem: The sum of the squares of the legs in a right triangle equals to the square of the hypotenuse. Radical The radical sign is this symbol and it is used when calculating the root of a number. Radicand A number located under the radical symbol is called radicand Example: Rate A rate is a comparison between two quantities through division. Examples: 2/3, 5 out of 7, 6:9 , 3 to 4 Rational Numbers A rational number is a number that can be written as a fraction of two integers. Examples: 6/7, 35, 0.25, -401 Relation A relation is a correspondence between the elements of two sets. Example: Repeating Decimal A decimal whose last digit (or group of digits) is repeating is called a repeating decimal. The bar notation is used to indicate the repeating digit(s). Examples: Right Triangle A right triangle is a triangle that has one right angle (an angle that measures 90 degrees). Example: Scatter Plot A scatter plot is a graph in which points are plotted in a coordinate plane to investigate the correlation between two variables. Example: Scientific Notation Scientific Notation is a way of writing large or small numbers as the product between a power of ten and a decimal that is at least 1, but less then 10. Example: Sequence A sequence is an ordered list of terms such as numbers, letters, or other objects. Example: 1, -3, 9, -27, 81, ... Set A set is a collection of distinct elements. Example: A = {0, 1, 2, 4, 7, 9} Slope Slope is a ratio used to measure the steepness of a line. It is equal to the ratio between the rise (or vertical change) and the run (or horizontal change). Slope-Intercept Form The slope-intercept form of a linear equation is given by the following formula: y = mx + b ;(where m is the slope and b is the y-intercept). Solution The solution of an equation is a number that makes the equation true when we replace the variable with it. Example: 7 is the solution of the equation 3y - 5 = 16. Square Root The square root of a number is a number whose square is the initial number. Example: 49 has two square roots, 7 and -7, because Subset Set A is a subset of set B if all of its elements are also in set B. Example: System of Equations A system of equations is a collection of two or more equations that are considered together and are graphed in the same coordinate plane. Example:  System of Linear Inequalities A system of inequalities is a collection inequalities that are considered together and are graphed in the same coordinate plane. Example:  Terminating Decimal A terminating decimal is a decimal that has a finite number of digits. Examples: 7.6 ; 100.25 ; 0.0004 Transversal A transversal is a line that intersects other lines at different points. Example: The red line, t, is a transversal because it intersects lines a, b, and c in different points. Tree Diagram A tree diagram is an intuitive method used to show the outcomes of several independent events. Example: The above tree diagram can be used to show the outcomes of tossing a coin and rolling a die. Union of Sets A set formed by all elements of two or more sets is called the union of those sets. Example: Unknown An unknown is a variable to be solved for in an equation or an inequality. Example: The unknow in the equation 1-5x = 21 is letter x. Variable A variable is a letter representing one or more numbers. Example: 2m - 1 = 5 (m is the variable in this equation) Venn Diagram Venn diagrams are figures (such as circles, ovals, or rectangles) used to illustrate data. Example: The above Ven diagram can be used to show how different types of quadrilaterals relate to each other. Vertical Line Test The vertical line test is a test used to determine if a relation is also a function. If any vertical line intersects the graph in one and only one point, the relation is a function. Example: The vertical line test in the above figure proves that the graph is not a function because a vertical line intersects the graph in 2 different points. X-Intercept The x-intercept is the point of intersection between the graph of a function and the x-axis. Example: Y-Intercept The y-intercept is the point of intersection between the graph of a function and the y-axis. Example: Return from the Math Vocabulary page to the CRCT Preparation homepage.