algebraic expression angle base (of a power) coordinate plane equation exponent expression factor
A figure formed by two rays with the same endpoint An expression that contains numbers, operations, and one or more symbols 8 + x, 6 a b vertex A coordinate plane is formed by the intersection of a horizontal number line and a vertical number line. The base of a power is the repeated factor. Quadrant II x-axis 5 4 3 2 1 y Quadrant I y-axis See power. 5 4 3 2 O 2 3 4 Quadrant III 5 1 2 3 4 5 x Quadrant IV The origin is at (0, 0). The exponent of a power indicates the number of times a base is used as a factor. A mathematical sentence that uses an equal sign to show that two expressions are equal See power. 4x = 16, a + 7 = 21 When whole numbers other than zero are multiplied together, each number is a factor of the product. A mathematical phrase containing numbers, operations, and/or variables 2 3 4 = 24, so 2, 3, and 4 are factors of 24. 12 + 6, 18 + 3 4 8 + x, 6 a b
negative number ordered pair origin percent polygon polyhedron positive number power
A pair of numbers (x, y) used to locate a point in a coordinate plane; The first number is the x-coordinate, and the second number is the y-coordinate. ( 2, 1) 1 y A number less than 0 0.25, 10, 500 2 O 1 2 x The x-coordinate of the point ( 2, 1) is 2, and the y-coordinate is 1. A part-to-whole ratio where the whole is 100 37% = 37 out of 100 = 37 100 The point, represented by the ordered pair (0, 0), where the horizontal and vertical number lines intersect in a coordinate plane See coordinate plane. A solid whose faces are all polygons A closed figure in a plane that is made up of three or more line segments that intersect only at their endpoints A product of repeated factors A number greater than 0 base exponent 0.5, 2, 100 5 1 1 1 1 1 1 = 2 2 2 2 2 2 1 power is used as a factor 5 times. 2
prism pyramid quadrilateral ray regular polygon solid solution (of an equation) terms (of an algebraic expression)
A polyhedron that has one base; The lateral faces are triangles. A polyhedron that has two parallel, congruent bases; The lateral faces are parallelograms. lateral face base base base lateral face A part of a line that has one endpoint and extends without end in one direction A polygon with four sides A three-dimensional figure See three-dimensional figure. A polygon with congruent sides and congruent angles The parts of an algebraic expression A value that makes an equation true The terms of 4x + 7 are 4x and 7. 6 is the solution of the equation x 4 = 2.
three-dimensional figure two-dimensional figure variable vertex (of an angle) whole numbers x-axis y-axis
A figure that has only length and width A figure that has length, width, and depth; also known as a solid The point at which the two sides of an angle meet See angle. A symbol that represents one or more numbers x is a variable in 2x + 1. The horizontal number line in a coordinate plane The numbers 0, 1, 2, 3, 4, See coordinate plane. The vertical number line in a coordinate plane See coordinate plane.
absolute value additive inverse Chapter 1 Chapter 1 Additive Inverse Property integers Chapter 1 Chapter 1 opposites Chapter 1
The opposite of a number The additive inverse of 8 is 8. The distance between a number and 0 on a number line; The absolute value of a number a is written as a. 5 = 5 5 = 5 The set of whole numbers and their opposites 3, 2, 1, 0, 1, 2, 3, The sum of an integer and its additive inverse is 0. 8 + ( 8) = 0 Two numbers that are the same distance from 0, but on opposite sides of 0 3 and 3 are opposites.
rational number repeating decimal Chapter 2 Chapter 2 terminating decimal Chapter 2
A decimal that has a pattern that repeats 0.555... = 0.5 1.727272... = 1.72 A number that can be written as a b where a and b are integers and b 0 3 3 =, 1 1 0.25 =, 4 2 2 = 5 5 1 4 1 = 3 3 A decimal that ends 1.5, 2.58, 5.605
Addition Property of Equality Division Property of Equality Chapter3 Chapter 3 equivalent equations factoring an expression Chapter 3 Chapter 3 like terms linear expression Chapter 3 Chapter 3 Multiplication Property of Equality simplest form (of an algebraic expression) Chapter 3 Chapter 3
Dividing each side of an equation by the same number produces an equivalent equation. Adding the same number to each side of an equation produces an equivalent equation. 3y = 18 3y 18 = 3 3 y = 6 x 5 = 1 + 5 + 5 x = 4 Writing an expression as a product of factors ( x ) 5x 15 = 5 3 Equations that have the same solutions 2x 8 = 0 and 2x = 8 An algebraic expression in which the exponent of the variable is 1 1 4 x, 3x + 5, 5 x 6 Terms of an algebraic expression that have the same variables raised to the same exponents 4 and 8, 2x and 7x An algebraic expression is in simplest form when it has no like terms and no parentheses. Multiplying each side of an equation by the same number produces an equivalent equation. 2 6a + 9 a, 3t + 5 x = 6 3 x 3 = 3 6 3 x = 18 ( )
Subtraction Property of Equality Chapter 3
Subtracting the same number from each side of an equation produces an equivalent equation. w + 5 = 25 5 5 w = 20
Addition Property of Inequality Division Property of Inequality Chapter 4 Chapter 4 graph of an inequality inequality Chapter 4 Chapter 4 Multiplication Property of Inequality solution of an inequality Chapter 4 Chapter 4 solution set Subtraction Property of Inequality Chapter 4 Chapter 4
When you divide each side of an inequality by the same positive number, the inequality remains true. When you divide each side of an inequality by the same negative number, the direction of the inequality symbol must be reversed for the inequality to remain true. 4x > 12 4x 12 > 4 4 x > 3 5x > 30 5x 30 < 5 5 x < 6 When you add the same number to each side of an inequality, the inequality remains true. x 3 > 10 + 3 + 3 x > 7 A mathematical sentence that compares expressions; It contains the symbols <, >,, or. A graph that shows all the solutions of an inequality on a number line x 4 < 14, x + 5 12 x > 2 3 2 1 0 1 2 3 A value that makes an inequality true A solution of the inequality x + 3 > 9 is x = 2. When you multiply each side of an inequality by the same positive number, the inequality remains true. When you multiply each side of an inequality by the same negative number, the direction of the inequality symbol must be reversed for the inequality to remain true. x x < 9 < 3 2 6 x 2 < 2 ( 9) x 6 > 6 3 2 6 x < 18 x > 18 When you subtract the same number from each side of an inequality, the inequality remains true. The set of all solutions of an inequality x + 7 > 20 7 x 7 > 27
complex fraction constant of proportionality Chapter 5 Chapter 5 cross products Cross Products Property Chapter 5 Chapter 5 direct variation proportion Chapter 5 Chapter 5 proportional rate Chapter 5 Chapter 5
The number k in the direct variation equation y = kx A fraction that has at least one fraction in the numerator, denominator, or both The constant of proportionality in the equation y = 2 x is 2. 1 4 1 2 The cross products of a proportion are equal. 2 4 = 3 6 2 6 = 3 4 a c In the proportion =, the products a d b d and b c are called cross products. 2 4 = 3 6 2 6 and 3 4 An equation stating that two ratios are equivalent 3 12 = 4 16 Two quantities x and y show direct variation when y = kx, where k is a number and k 0. The graph of y = kx is a line with a slope of k that passes through the origin. 3 2 1 3 2 1 y y = 2x 1 2 3 x 3 A ratio of two quantities with different units You read 3 books every 2 weeks. Two quantities that form a proportion are proportional. Because 3 4 3 4 and 12 16 and 12 16 are proportional. form a proportion,
ratio slope Chapter 5 Chapter 5 unit rate Chapter 5
A ratio of the change in y (vertical change) to the change in x (horizontal change) between any two points on a line; It is a measure of the steepness of a line. slope = change in y change in x y 7 6 5 4 3 2 1 3 2 3 Slope = 2 A comparison of two quantities using division; where b 0 can be written The ratio of a to b ( ) a as a to b, a : b, or. b 4 to 1, 4 : 1, or 4 1 1 2 3 4 5 6 7 x A rate with a denominator of 1 The speed limit is 65 miles per hour.
discount interest Chapter 6 Chapter 6 markup percent of change Chapter 6 Chapter 6 percent of decrease percent error Chapter 6 Chapter 6 percent of increase principal Chapter 6 Chapter 6
Money paid or earned for the use of money See simple interest. A decrease in the original price of an item The original price of a pair of shoes is $95. The sale price is $65. The discount is $30. The percent that a quantity changes from the original amount percent of change amount of change = original amount The percent of change from 20 to 25 is: 25 20 5 = = 25% 20 20 The increase from what a store pays to the selling price A store buys a hat for $12 and sells it for $20. The markup is $8. The percent that an estimated quantity differs from the actual amount percent error amount of error = actual amount Estimated length: 16 feet Actual length: 21 Percent error: 21 16, or 23.8% 21 The percent of change when the original amount decreases percent of decrease original amount new amount = original amount The price of a shirt decreases from $20 to $10. The percent of decrease is 20 10, or 50%. 20 An amount of money borrowed or deposited You deposit $200 in an account that earns 4% simple interest per year. The principal is $200. The percent of change when the original amount increases percent of increase new amount original amount = original amount The price of a shirt increases from $20 to $30. The percent of increase is 30 20, or 50%. 20
simple interest Chapter 6
Money paid or earned only on the principal Simple Interest I = Prt Annual interest rate (in decimal form) Principal Time (in years) You put $200 into an account. The account earns 5% simple interest per year. The interest earned after 3 years is $200 0.05 3, or $30. The account balance is $200 + $30 = $230 after 3 years.
adjacent angles complementary angles Chapter 7 Chapter 7 congruent angles congruent sides Chapter 7 Chapter 7 kite scale Chapter 7 Chapter 7 scale drawing scale factor (of a scale drawing) Chapter 7 Chapter 7
Two angles whose measures have a sum of 90 Two angles that share a common side and have the same vertex 30 60 1 2 1 2 4 3 1 and 2 are adjacent. 2 and 4 are not adjacent. Sides that have the same length Angles that have the same measure B G 60 60 A F Side AB and side FG are congruent sides. 120 120 A ratio that compares the measurements of a drawing or model with the actual measurements 12 cm : 1 cm 2 in. 15 ft A quadrilateral with two pairs of congruent adjacent sides and opposite sides that are not congruent A scale without units See ratio. A proportional, two-dimensional drawing of an object A blueprint or a map
scale model supplementary angles Chapter 7 Chapter 7 vertical angles Chapter 7
Two angles whose measures have a sum of 180 A proportional, three-dimensional model of an object 135 45 3 4 The angles opposite each other when two lines intersect; Vertical angles are congruent angles. 4 1 3 2 1 and 3 are vertical angles. 2 and 4 are vertical angles.
center (of a circle) circle Chapter 8 Chapter 8 circumference composite figure Chapter 8 Chapter 8 diameter (of a circle) pi Chapter 8 Chapter 8 radius (of a circle) semicircle Chapter 8 Chapter 8
The set of all points in a plane that are the same distance from a point called the center circle center The point inside a circle that is the same distance from all points on the circle See circle. A figure made up of triangles, squares, rectangles, semicircles, and other two-dimensional figures The distance around a circle C triangle d square r The ratio of the circumference of a circle to its diameter The value of π can be approximated as 3.14 or 22. 7 The distance across a circle through the center See circumference. One-half of a circle The distance from the center of a circle to any point on the circle See circumference.
cross section lateral surface area (of a prism) Chapter 9 Chapter 9 regular pyramid slant height (of a pyramid) Chapter 9 Chapter 9
The sum of the areas of the lateral faces of a prism 3 cm 5 cm 4 cm ( )( ) ( )( ) Lateral surface area = 2 4 3 + 2 5 3 = 24 + 30 = 54 cm 2 A two-dimensional shape formed by the intersection of a plane and a solid The intersection of the plane and the cone is a circle. The height of each triangular face of a pyramid A pyramid whose base is a regular polygon slant height
biased sample compound event Chapter 10 Chapter 10 dependent events event Chapter 10 Chapter 10 experiment experimental probability Chapter 10 Chapter 10 favorable outcomes Fundamental Counting Principle Chapter 10 Chapter 10
An event that consists of two or more events Spinning a spinner and flipping a coin A sample that is not representative of a population; One or more parts of the population are favored over others. You want to estimate the number of students in your school who like to play basketball. You survey 100 students at a basketball game. A collection of one or more outcomes of an experiment Flipping heads on a coin Two events such that the occurrence of one event affects the likelihood that the other event(s) will occur A bag contains 3 red marbles and 4 blue marbles. You randomly draw a marble, do not replace it, then randomly draw another marble. The events first marble is blue and second marble is red are dependent events. Probability that is based on repeated trials of an experiment An investigation or procedure that has varying results ( event) P = number of times the event occurs total number of trials Rolling a number cube A basketball player makes 19 baskets in 28 attempts. The experimental probability that the player makes a basket is 19, or about 68%. 28 An event M has m possible outcomes and event N has n possible outcomes. The total number of outcomes of event M followed by event N is m n. You have 7 shirts, 5 pairs of pants, and 2 pairs of shoes. You can make 7 5 2 = 70 different outfits. The outcomes of a specific event When rolling a number cube, the favorable outcomes for the event rolling an even number are 2, 4, and 6.
independent events outcomes Chapter 10 Chapter 10 population probability Chapter 10 Chapter 10 relative frequency sample Chapter 10 Chapter 10 sample space simulation Chapter 10 Chapter 10
The possible results of an experiment The outcomes of flipping a coin are heads and tails. Two events such that the occurrence of one event does not affect the likelihood that the other event(s) will occur You flip a coin and roll a number cube. The events flipping tails and rolling a 4 are independent events. A number from 0 to 1 that measures the likelihood that an event will occur See experimental probability and theoretical probability. An entire group of people or objects Population: All of the 14-year-old females in the United States Sample: All of the 14-year-old females in your town A part of a population See population. The fraction or percent of the time that an event occurs in an experiment You flip a coin 20 times. If you flip heads 11 times, the relative frequency of flipping heads is 11, or 55%. 20 An experiment that is designed to reproduce the conditions of a situation or process The set of all possible outcomes of one or more events You flip a coin twice. The outcomes in the sample space are HH, HT, TH, and TT.
theoretical probability unbiased sample Chapter 10 Chapter 10
A sample that is representative of a population; It is selected at random and is large enough to provide accurate data. You want to estimate the number of students in your school who like to play basketball. You survey 100 students at random during lunch. The ratio of the number of favorable outcomes to the number of possible outcomes when all possible outcomes are equally likely P ( event) number of favorable outcomes = number of possible outcomes When rolling a number cube, the theoretical probability of rolling a 4 is 1. 6