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least common multiple (LCM) The smallest number, other than zero, that is a multiple of two or more given numbers Example: 6 9 The LCM of 6 and 9 is 18. x1 6 9 x2 12 18 x3 18 27 x4 24 36 factor A number that is multiplied by another number to get a product Example: 2X3=6 2 and 3 are factors of 6. greatest common factor (GCF) The largest common factor of two or more given numbers Example: 18: 1, 2, 3, 6, 9, 18 30: 1, 2, 3, 5, 6, 10, 15, 30 6 is the GCF of 18 and 30. power The value of a number represented by a base and an exponent Example: 43 = 4 X 4 X 4 = 64 base A number used as a repeated factor Example: 83 = 8 X 8 X 8 The base is 8. It is used as a factor three times. The exponent is 3. exponent The number that indicates how many times the base is used as a factor Example: 43 = 4 X 4 X 4 4 is the base; 3 is the exponent perfect square A number that has an integer as its square root Example: 16 is a perfect square. square number A number that can be represented with a square array Examples: square root One of the two equal factors of a number Example: 6 is the square root of 36 since 62 = 6 X 6 = 36 So, 36 = 6 because we are looking for the one value or factor (which is 6 for this example) that gives us the number below the square root sign. order of operations The order in which the operations are done within an expression 1. Operate inside parentheses. 2. Multiply as indicated by exponents. 3. Multiply and divide from left to right. 4. Add and subtract from left to right. Example: 10 ÷ (2 + 8) X 23 - 4 10 ÷ 10 X 23 - 4 10 ÷ 10 X 8 – 4 1X8–4 8–4 4 Add inside parentheses Solve the exponent Divide Multiply (remember left to right) Subtract Final answer! divisibility rules a way to determine if one number is a factor of another number without actually dividing Characteristic of number Number divisible by: Last digit is EVEN The sum of the digits is divisible by 3 The last two digits form a number divisible by 4 The last digit is 0 or 5 The number is divisible by both 2 and 3 Take the last digit, double it, and subtract it from the rest of the number. If you get an answer divisible by 7 (including zero), then the original number is divisible by seven. If you don’t know the new original number is divisible by seven. If you don’t know the new number’s divisibility, you can apply the rule again. 2 3 4 5 6 7 Example: Check to see if 203 is divisible by 7. • double the last digit: 3x2=6 • subtract that from the rest of the number: 20 - 6 = 14. • check to see if the difference is divisible by 7: 14 is divisible by 7, therefore 203 is also divisible by 7. The last three digits form a number divisible by 8 The sum of the digits is divisible by 9 The numeral ends in 0 8 9 10 Bar Graph A graph that uses separate bars (rectangles) of different heights (lengths) to show and compare data Biased Sample A sample that does not fairly represent the population Box-and-Whisker Graph A graph that shows how far apart and how evenly data are distributed Example: Central Tendency Any of three measures (mean, median, mode) that represent averages of a set of data Circle Graph A graph used to compare the relationship of the parts to the whole Data Information collected about people or things Double-Bar Graph A bar graph showing two or more sets of data at once Frequency Distribution Table A table used to organize a collection of data Example: ** Cumulative means to continuously add the new frequency to all those above it. Histogram A bar graph that shows the frequency of data within equal intervals Example: Distance (in cm) Line Graph A graph in which line segments are used to show changes over time Line Plot A number line with dots or other marks to show frequency Mean (or Equal Sharing) The sum of a set of numbers divided by the number of addends (or the number of entries in our list) 2, 3, 4, 5, 5, 8 (2 + 3 + 4 + 5 + 5 + 8) ÷ 6 = 4.5 number of entries in our list The mean is 4.5 ** Addends are the numbers that we add together. ** Temperature (in oC) Add to the multi-line graph example Census The counting of an entire population Example: The Canadian Census involves collecting information about every single person living in Canada – whether they are Canadian born or have immigrated to the country. Primary Data Information that is YOU collect and use Secondary Data Information that SOMEONE ELSE collects and passes on to another person to use Database An organized set of information, often stored on a computer Name Talia Matteo HB 7-4 8-2 Math 68 72 English 78 65 Phys. Ed. 75 78 Record All the data about one item in the database; for example, one student Name Talia HB 7-4 Math 68 English 78 Phys. Ed. 75 Field A category used as part of a database; for example, Math (yellow cell) Name Talia HB 7-4 Math 68 English 78 Phys. Ed. 75 Entry A single piece of data in a database; for example, English mark for one student (yellow cell) Name Talia HB 7-4 Math 68 English 78 Phys. Ed. 75 Sort Order information from greatest (or first) to least (or last); a database can be sorted by fields Name Matteo Talia HB 8-2 7-4 Math 72 68 English 65 78 Phys. Ed. 78 75 This database is sorted greatest to least by Phys. Ed. marks. (yellow cells) Spreadsheet An orderly arrangement of numerical data using rows and columns. A computer spreadsheet can also use formulas to make calculations for you! Interval The space between two values; for example, 0-9 represents the interval 0 to 9, including 0 and 9. Cell The intersection of a column and a row, where individual data entries are stored; for example cell B2 shows the entry in Column B and in Row 2. 1 2 3 A Name Talia Matteo B HB 7-4 8-2 C Math 68 72 D English 78 65 E Phys. Ed 75 78 In this example, cell B2 has entry 7-4. Formula Calculations made within a cell using data from other cells. Formulas may vary depending on the spreadsheet program you use (Excel, Quattro Pro, TinkerPlots, etc.). Measure of Central Tendency A measure used to describe data; the mean, median, and mode are measures of central tendency Median The middle number or the average of the two middle numbers in an ordered set of data 1, 3, 4, 6, 7 The median is 4. 1, 2, 4, 5, 8, 9 The median is 4.5 (4.5 is the middle value between 4 and 5) Survey A method of gathering information about a population Mode The number or numbers that occur most frequently in a set of data; there can be one mode, more than one mode or no mode. 2, 3, 4, 5, 5, 6, 7, 8, 8, 8, 9, 11 The mode is 8. 2, 3, 4, 5, 5, 5, 7, 8, 8, 8, 9, 11 The modes are 5 and 8. 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 17 There is no mode. Each entry appears an equal number of times in the data set. Multiple-Line Graph A line graph showing two or more sets of data at once 40 35 30 25 20 15 10 5 0 Population The total or entire group to be studied Random Sample A population sample for which every individual in the population had an equal chance of being chosen Random Selection A selection made so that each person or item has an equal chance of being chosen Sample A smaller group of people or objects chosen from a larger group, or population Range The difference between the greatest and the least numbers in a set of data Month Temperature Jun 25oC Jul 32oC Aug 30oC Sept 24oC Oct 20oC Nov 12oC The greatest temperature is 32oC. The least temperature is 12oC. Since 32 - 12 = 20, the range is 20oC. Scatterplot A graph made by plotting points on a coordinate plane to show the relationship between two variables in a data set Example: Stem-and-Leaf Plot A method of organizing intervals or groups of data Number of Sit-Ups Stem Each tens digit is called the stem. 3 4 5 Leaves 4 0 0 Key: 3 6 3 0 8 6 1 8 7 2 7 The ones digits are called the leaves. 6 = 36 Tally Table A table with categories for recording each piece of data as it is collected Favourite Snack Foods Snack Tally Fruit Cereal Chips Cookies Venn Diagram A diagram that is used to show relationships between sets Example: CENSUS In this example, we are looking at whole numbers. All prime numbers and all composite numbers are also ALL COUNTING NUMBERS! That is why they are both inside the purple circle. What are the common factors of 18 and 42? 18 42 9 18 1 2 3 6 7 14 21 42 The common factors are 1, 2, 3, and 6. SEQUENCE An ordered list of numbers Example: 1, 3, 5, 7, 9, … • shows the odd numbers in order Example: 1, 4, 16, 64, 256, . . . 12, 22, 42, 82, 162, … • shows numbers doubling and squared TERM A real number, a variable, or a product of real numbers and variables Example: In the expression 5x + 4, the terms are 5x and 4. TERM A number in a sequence Example: 3, 6, 12, 24, . . . 6 is a term in the sequence TERM One of the numbers in a ratio Example: REAL NUMBERS The set of numbers that includes all rational and all irrational numbers VARIABLE A letter used to represent one or more numbers in an expression, equation, or inequality Examples: 5a 2x = 8 3y + 4 10 a, x, and y are variables. PRODUCT The answer in a multiplication problem Example: The product is 12. EXPRESSION A mathematical phrase that combines operations, numerals, and/or variables to name a number Examples: 35 – 15.5 32 x a ** Notice that there is NO EQUAL sign. COORDINATES An ordered pair, used to describe a location on a grid labeled with an x-axis and a y-axis; Example y-axis 4 3 vertical 3 units 2 1 0 1 2 3 4 x-axis horizontal 2 units The coordinates (2, 3) describe this location VOLUME The number of cubic units needed to occupy a given space Example: The volume of the cube is 8 cubic units. VERTEX A point where two or more rays meet, where sides of a polygon meet, or where edges of a polyhedron meet; the top point of a cone or pyramid; in a network, a point that represents an object Examples: TRIGONOMETRIC RATIOS Ratios which compare the lengths of the sides of a right triangle; the common ratios are tangent, sine, and cosine. Example: TRIANGLE A three-sided polygon Examples: TRAPEZOID A quadrilateral with only one pair of parallel sides Example: TRANSVERSAL A line that intersects two or more lines Example: Line AB is a transversal. THREE-DIMENSIONAL Having length, width, and height Example: The rectangular prism is 3-dimensional. SIMILAR FIGURES Figures that have the same shape but may not have the same size Examples: SURFACE AREA The sum of the areas of all the faces, or surfaces, of a solid figure Example: Area of face A = Area of face B = Area of face C = Area of face D = Area of face E = Area of face F = 11 X 5 = 21 X 11 = 21 X 5 = 21 X 11 = 21 X 5 = 11 X 5 = 55 231 105 231 105 55 55 + 231 + 105 + 231 + 105 + 55 = 782 So, the surface area is 782 m2. SUPPLEMENTARY ANGLES Two angles whose measures have a sum of 180° Example: ABD + DBC = 124° + 56° = 180° SPHERE A solid figure with all points the same distance from the center Example: SQUARE A rectangle with 4 congruent sides Example: The product of a number and itself Example: 25 is the square of 5 because 5 X 5 = 25. 5 X 5 = 52 Read as 5-squared. STRAIGHT ANGLE An angle whose measure is 180° Example: ABC is a straight angle. SOLID FIGURE A three-dimensional figure Examples: SIDE-ANGLE-SIDE (SAS) A triangle congruence rule stating that two sides and the included angle of one triangle match two sides and the included angle of another triangle Example: SIDE-SIDE-SIDE (SSS) A triangle congruence rule stating that three sides of one triangle match three sides of another Example: SEMIREGULAR POLYHEDRON A solid formed from patterns of more than one kind of regular polygon Example: SCALENE TRIANGLE A triangle with no congruent sides Example: RIGHT TRIANGLE A triangle with exactly one right angle Examples: RIGHT ANGLE An angle whose measure is 90° Example: RHOMBUS A parallelogram whose four sides are congruent and whose opposite angles are congruent Example: REGULAR POLYGON A polygon in which all sides and all angles are congruent Example: RECTANGULAR PRISM A polyhedron whose bases are rectangles and whose other faces are parallelograms Example: RECTANGLE A parallelogram with 4 right angles Example: RAY A part of a line that has one endpoint and goes on forever in only one direction Example: RADIUS A line segment with one endpoint at the center of a circle and the other endpoint on the circle Example: PRISM A polyhedron whose two bases are congruent, parallel polygons in parallel planes and whose lateral faces are parallelograms Example: rectangular prism PYTHAGOREAN THEOREM In any right triangle, if a and b are the lengths of the legs and c is the length of the hypotenuse, then a2 + b2 = c2 Example: a2 + b2 = c2 32 + 42 = 52 9 + 16 = 25 25 = 25 Replace the variables with the known lengths. QUADRILATERAL A four-sided polygon Examples: PYRAMID A polyhedron with a base that is a polygon and with lateral faces that are triangles which share a common vertex Example: square pyramid POLYHEDRON A solid figure with flat faces that are polygons Examples: POLYGON A closed plane figure formed by three or more line segments Examples: POINT OF INTERSECTION The point where two or more lines intersect Example: POINT An exact location PLANE FIGURE A figure which lies in a plane Examples: PLANE A set of points forming a flat surface that extends without end in all directions Example: PI () The ratio of the circumference of a circle to the length of its diameter PERSPECTIVE A technique used to make 3-dimensional objects appear to have depth and distance on a flat surface Example: PERPENDICULAR LINES Lines that intersect to form 90° angles, or right angles Example: Read: Line RS is perpendicular to line MN. PERPENDICULAR BISECTOR A line or line segment that intersects a given line segment at its midpoint and forms right angles Example: PERIMETER The distance around a polygon Example: 3 cm + 3 cm + 2 cm = 8 cm The perimeter of this figure is 8 centimeters. PENTAGON A five-sided polygon Examples: PARALLELOGRAM A quadrilateral whose opposite sides are parallel and congruent Example: PARALLEL LINES Lines in a plane that do not intersect Example: Read: Line AB is parallel to line CD. OCTAGON An eight-sided polygon Examples: OBTUSE ANGLE An angle whose measure is greater than 90° and less than 180° Example: NET A connected arrangement of polygons in a plane that can be folded up to form a polyhedron Example: MIDPOINT The point that divides a line segment into two congruent line segments Example: M is the midpoint of . LINE SEGMENT A part of a line or ray, consisting of two endpoints and all points between those endpoints Examples: LINE A set of points that extends without end in opposite directions Example: LEG In a right triangle, either of the two sides that intersect to form the right angle; in an isosceles triangle, one of the two congruent sides Examples: LATERAL SURFACE The curved surface of a cylinder or a cone Example: LATERAL FACE In a prism or a pyramid, a face that is not a base Example: Rectangular Prism ISOSCELES TRIANGLE A triangle with two congruent sides Example: INTERSECTING PLANES Flat surfaces that intersect in a line, such as the sides of a box Example: INTERSECTING LINES Two lines that cross at exactly one point Example: INTERIOR ANGLES Angles on the inner sides of two lines cut by a transversal Example: Angles 3, 4, 5, and 6 are interior angles HYPOTENUSE In a right triangle, the side opposite the right angle; the longest side in a right triangle Example: HORIZON LINE A horizontal line that represents the viewer's eye level Example: HEXAGON A six-sided polygon Examples: HELIX A spiral-shaped curve in space that goes around an axis Examples: FORMULA A rule that is expressed using symbols Examples: The area and the circumference of a circle can be computed by using the following formulas: A = r2 C= d FACE A flat surface of a polyhedron Example: The cube has 6 faces. EXTERIOR ANGLES The angles on the outer sides of two lines cut by a transversal Example: Angles 1, 2, 7, and 8 are exterior angles. EQUILATERAL TRIANGLES A triangle with three congruent sides and three congruent angles Example: EDGE The line segment along which two faces of a polyhedron intersect Example: EDGE A connection between vertices in a network Example: DIAMETER A chord that passes through the center of a circle Example: DIAGONAL A line segment that connects two non-adjacent vertices of a polygon Example: CYLINDER A solid figure with two parallel, congruent circular bases connected by a curved surface Example: CUBE A square prism with six congruent square faces Example: CROSS SECTION The figure formed by the intersection of a plane and a solid figure Example: CORRESONDING ANGLES Angles that are in the same position and are formed by a transversal cutting two or more lines Example: 2 and 6 are corresponding angles. CONGRUENT Having the same size and shape Example: CONE A solid figure with a circular base and one vertex Example: COMPLEMENTARY ANGLES Two angles whose measures have a sum of 90° Example: DBE and EBC are complementary. CIRCUMFERENCE The distance around a circle C= d CIRCLE A closed curve with all points on the curve an equal distance from a given point called the center of the circle Example: CHORD A line segment with endpoints on a circle Example: CENTRAL ANGLE An angle formed by two rays with a common vertex at the center of a circle Example: BISECT To divide into two congruent parts Example: AREA The number of square units needed to cover a given surface Example: The area is 9 square units. BASE A side of a polygon or a face of a solid figure by which the figure is measured or named Examples: A number used as a repeated factor Example: 83 = 8 X 8 X 8 The base is 8. It is used as a factor three times. ANGLE A geometric figure formed by two rays that have a common endpoint Examples: ALTERNATE INTERIOR ANGLES A pair of angles on the inner sides of two lines cut by a transversal, but on opposite sides of the transversal Example: 3 and 6 and 4 and 5 are alternate interior angles. ALTERNATE EXTERIOR ANGLES A pair of angles on the outer sides of two lines cut by a transversal, but on opposite sides of the transversal Example: 1 and 8 and 2 and 7 are alternate exterior angles. ACUTE ANGLE An angle whose measure is greater than 0° and less than 90° Example: ACUTE TRIANGLE A triangle in which all three angles are acute Example: ADJACENT ANGLES Angles that share a common side, have the same vertex, and do not overlap Example: ABD is adjacent to DBC. ANGLE-SIDE-ANGLE (ASA) A triangle congruence rule stating that when two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the two triangles are congruent. Example: ADDITION PROPERTY OF OPPOSITES The property which states that the sum of a number and its opposite is zero Examples: 5 + -5 = 0 -15 + 15 = 0 INTEGERS The set of whole numbers and their opposites. All positive and negative numbers including zero. Example: IDENTITY PROPERTY OF ZERO The property which states that adding zero to a number does not change the number's value Examples: 3+0=3 0+y=y NEGATIVE INTEGER An integer less than zero. Example: -1, -2, -3, -4, . . . OPPOSITE INTEGERS Two numbers that are represented by points on the number line that are the same distance from zero but are on opposite sides of zero. Example: 4 and -4 are opposites POSITIVE INTEGER An integer greater than zero. Example: 1, 2, 3, 4, . . . ZERO PRINCIPLE The sum of two opposite integers equal zero. Examples: (-1) + (+1) = 0 (+20) + (-20) = 0 REGROUP When you group the integers in an equation by their positive and negative values. Example: (+5) + (-7) + (+11) + (+3) + (-8) = (+4) = (-2) + (+11) + (+3) + (-8) + (+3) + (-8) = (+9) = (+12) + (-8) = (+4) (+5) + (+11) + (+3) + (-7) + (-8) = (+4) = (+16) + (+3) + (-7) + (-8) + (-7) + (-8) = (+19) + (-8) = (+12) = (+4) NUMBER LINE A series of numeric values (numbers) listed on a line from least (smallest) to greatest (biggest). -10 -8 -6 -4 -2 0 +2 +4 +6 +8 +10 This number line demonstrates integer values from -10 to +10. NEGATIVE means to go in the OPPOSITE DIRECTION. Example Walk Forward (+) Ascend (+) or Go Up (-) Walk Backward (-) Descend or Go Down Coordinate plane A plane formed by two perpendicular number lines called axes; every point on the plane can be named by an ordered pair of numbers. Axes Two perpendicular lines that intersect to form the coordinate plane. Dilation A transformation that enlarges or reduces a figure. Inequality A mathematical sentence that shows the relationship between quantities that are not equal, using <, >, <, , or . Examples: 6<9 3x > 12 Image The figure in a new position or location as the result of a transformation. Example: A'B'C'D' is the image of ABCD. Tessellation A repeating pattern of congruent plane figures that completely cover a plane with no gaps or overlapping. Ordered pair A pair of numbers used to locate a point on a coordinate plane. Example: (3,2) represents 3 spaces to the right of zero and 2 spaces up. Rotation A type of transformation, or movement, that results when a geometric figure is turned about a fixed point. Example: Origin The point on the coordinate plane where the x-axis and the y-axis intersect, (0,0) Example: Quadrant One of the four regions of the coordinate plane. Translation (slide) A movement of a geometric figure to a new position without turning or flipping it. Example: Rotational symmetry A figure has rotational symmetry when it can be rotated less than 360° around a central point, or point of rotation and still match the original figure. Example: Transformation A change in size, shape, or position of a geometric figure; translations, reflections, rotations, and dilations are transformations. Example: x-axis The horizontal axis on the coordinate plane. Example: x-coordinate The first number in an ordered pair; tells whether to move right or left along the x-axis of the coordinate plane. Example: (3, 2) 3 is the x-coordinate. y-axis The vertical axis on the coordinate plane. Example: y-coordinate The second number in an ordered pair; tells whether to move up or down along the y-axis of the coordinate plane. Example: (3, 2) 2 is the y-coordinate. y-intercept The y-coordinate of the point where the graph of a line crosses the y-axis. Example: The y-intercept of 2x + 3y = 6 is 2. TRINOMIAL The sum of three monomials Example: 3x + 5y + 7 INTERCEPT The place (or point) where a graph crosses the axis Example: The x-intercept is 1 and the y-intercept is -2. SYSTEM OF EQUATIONS Two or more linear equations graphed in the same coordinate plane MONOMIAL An expression that is a number, a variable, or the product of a number and one or more variables Examples: 3x 7 5xy SUBSTITUTE To replace a variable with a value Example: Which of the values 12, 20, and 21 are solutions of x - 4 = 16? Substitute each of the values for x in the equation. Use x = 12. x - 4 = 16 12 - 4 = 16 8 16 not a solution Use x = 20. x - 4 = 16 20 - 4 = 16 16 = 16 solution Use x = 21. x - 4 = 16 21 - 4 = 16 17 16 not a solution POLYNOMIAL A monomial or the sum of two or more monomials Examples: 3a2 + 8 a2 - 4a + 3 SOLUTION The value or values that make an equation an inequality, or system of equations true Examples: x – 4 = 16 x – 4 + 4 = 16 + 4 x = 20 20 is the solution. x+3>9 x+3–3>9–3 x>6 Any number greater than 6 is a solution. NONLINEAR FUNCTION A function whose graph is not a straight line Example: SLOPE The measure of the steepness of a line; the ratio of vertical change to horizontal change Example: NUMERICAL EXPRESSION An expression that includes numbers and at least one operation (addition, subtraction, multiplication, or division) Examples: 6 + 8.1 57 – 48 21.6 – 18.6 LINEAR EQUATION An equation whose graph is a straight line Example: The linear equation for the graph below is y = 2x + 1. TERM A real number, a variable, or a product of real numbers and variables Example: In the expression 5x + 4, the terms are 5x and 4. LINE OF BEST FIT A straight line drawn through as much data as possible on a scatterplot Example: LIKE TERMS Expressions that have the same variables and the same powers of the variables. Example: 8y, -4y, and 9.1y are like terms. BINOMIAL The sum of two monomials Example: 3x + 5y INTERPOLATION An estimated value between two known values Example: Suppose you work for 2.5 hr and are paid $4.50 per hour. Use the graph to predict your earnings. On the horizontal axis of the graph, locate 2.5 Draw a vertical line segment from this point to the line of the graph. From there, draw a horizontal line segment to the vertical axis. It intersects the axis halfway between $9.00 and $13.50. So, if you work 2.5 hr, you will earn $11.25. IDENTITY PROPERTY OF ONE The property which states that multiplying a number by 1 does not change the number's value Examples: 6X1=6 1Xa=a DISTRIBUTIVE PROPERTY OF MULTIPLICATION OVER ADDITION The property which states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products a(b + c) = a X b + a X c Examples: 3(4 + 5) = 3 X 4 + 3 X 5 3(a + b) = 3a + 3b EXTRAPOLATION An estimate or a prediction of an unknown value, based upon known values Example: The trend is an increase with no declines. From 1970 to 1990, the population increased about 25 million every 10 years. Since the population increased about 25 million every 10 years from 1970 to 1990, a good prediction for the year 2000 would be about 250 million + 25 million, or 275 million. COEFFICIENT The number that is multiplied by the variable in an algebraic expression such as 5b ASSOCIATIVE PROPERTY OF MULTICATION The property which states that for all real numbers a, b, and c, their product is always the same, regardless of their grouping: (a X b) X c = a X (b X c) Example: (5 X 6) X 7 = 5 X (6 X 7) ASSOCIATIVE PROPERTY OF ADDITION The property which states that for all real numbers a, b, and c, their sum is always the same, regardless of their grouping: (a + b) + c = a + (b + c) Example: (2 + 3) + 4 = 2 + (3 + 4) COMMUNICATIVE PROPERTY OF MULTIPLICATION The property of multiplication that allows two or more factors to be multiplied in any order without changing the product aXb=bXa Examples: 3Xc=cX3 4 X 5 X y7 = 5 X 4 X y7 COMMUNICATIVE PROPERTY OF ADDITION The property of addition that allows two or more addends to be added in any order without changing the sum; a+b=b+a Examples: c+4=4+c (2 + 5) + 4r = 4r + (2 + 5) ALGEBRAIC EXPRESSION An expression that is written using one or more variables Examples: 3x x–4 2a + 5 RISE The vertical change of a line Example: The rise of line PQ is 2. a+b RUN The horizontal change of a line Example: The run of line PQ is 1. SOLVE To find the correct value of the variable in an equation Example: x + 5 = 17 x + 5 – 5 = 17 – 5 x = 12 SOLUTION The value that makes two sides of an equation equal Example: x+7=9 2+7=9 2 is the solution. SOLUTION OF THE SYSTEM The values for the variables that make each of the equations in a system of equations true; the coordinates of the point where the graphs of the equations in the system intersect Example: The equations of these lines are y = 2x – 1 and y = x + 1 The solution of the system is (2,3). EQUIVALENT FRACTIONS Fractions that name the same number 3 = 6 = 75 4 8 100 EQUIVALENT RATIOS Ratios that make the same comparisons Examples: FACTOR A number that is multiplied by another number to get a product Example: 2X3=6 2 and 3 are factors of 6. SCALE FACTOR The common ratio for pairs of corresponding sides of similar figures Example: SIMILAR FIGURES Figures that have the same shape but may not have the same size Example: SCALE MODEL A proportional model of a solid, or threedimensional object Example: SIMPLEST FORM A fraction is in simplest form when the numerator and denominator have no common factors other than 1. Example: The form of an expression when all like terms are combined Example: 4x + 3x + 2 = 7x + 2 (in its simplest form) INDIRECT MEASUREMENT A method of measuring distances by solving a proportion Example: RECIPROCAL One of two numbers whose product is 1 Example: COMPLEMENTARY ANGLES Two angles whose measures have a sum of 90° Example: DBE and EBC are complementary. EQUIANGULAR TRIANGLE A triangle with three congruent angles and three congruent sides Example: BISECT To divide into two congruent parts Example: PERPENDICULAR BISECTOR A line or line segment that intersects a given line segment at its midpoint and forms right angles Example: ALTERNATE EXTERIOR ANGLES A pair of angles on the outer sides of two lines cut by a transversal, but on opposite sides of the transversal Example: 1 and 8 and 2 and 7 are alternate exterior angles. RIGHT TRIANGLE A triangle with exactly one right angle Examples: ALTERNATE INTERIOR ANGLES A pair of angles on the inner sides of two lines cut by a transversal, but on opposite sides of the transversal Example: 3 and 6 and 4 and 5 are alternate interior angles. SUPPLEMENTARY ANGLES Two angles whose sum equals 180° Example: mABD + mDBC = 124° + 56° = 180° CORRESPONDING ANGLES Angles that are in the same position and are formed by a transversal cutting two or more lines Example: 2 and 6 are corresponding angles. CONGRUENT Having the same size and shape Example: PERPENDICULAR LINES Lines that intersect to form 90° angles, or right angles Example: Read: Line RS is perpendicular to line MN. POINT OF INTERSECTION The point where two or more lines intersect Example: EQUILATERAL TRIANGLE A triangle with three congruent sides and three congruent angles Example: INTERSECTING LINES Two lines that cross at exactly one point Example: INTERIOR ANGLES Angles on the inner sides of two lines cut by a transversal Example: Angles 3, 4, 5, and 6 are interior angles. ISOSCELES TRIANGLE A triangle with two congruent sides Example: LINE A set of points that extends without end in opposite directions Example: LINE SEGMENT A part of a line or ray, consisting of two endpoints and all points between those endpoints Examples: MIDPOINT The point that divides a line segment into two congruent line segments Example: M is the midpoint of . PARALLEL LINES Lines in a plane that do not intersect Example: Read: Line AB is parallel to line CD. RAY A part of a line that has one endpoint and goes on forever in only one direction Example: RIGHT ANGLE An angle whose measure is 90° Example: SCALENE TRIANGLE A triangle with no congruent sides Example: SIMILAR FIGURES Figures that have the same shape but may not have the same size Example: NET A connected arrangement of polygons in a plane that can be folded up to form a polyhedron Example: PRISM A polyhedron whose two bases are congruent, parallel polygons in parallel planes and whose lateral faces are parallelograms Example: rectangular prism VERTEX A point where two or more rays meet, where sides of a polygon meet, or where edges of a polyhedron meet; the top point of a cone or pyramid; in a network, a point that represents an object Examples: SURFACE AREA The sum of the areas of all the faces, or surfaces, of a solid figure Example: Area of face A = 11 X 5 = 55 Area of face B = 21 X 11 = 231 Area of face C = 21 X 5 = 105 Area of face D = 21 X 11 = 231 Area of face E = 21 X 5 = 105 Area of face F = 11 X 5 = 55 55 + 231 + 105 + 231 + 105 + 55 = 782 So, the surface area is 782 cm2. BIASED SAMPLE A sample that does not fairly represent the population COMBINATION An arrangement of items or events in which order does not matter Example: Two-letter combinations of A, B, C, and D: AB AC AD BC BD CD There are 6 combinations. POPULATION The total or entire group to be studied. THEORETICAL PROBABILITY The ratio of the number of favorable outcomes to the number of all possible outcomes EXPERIMENTAL PROBABILITY The ratio of the number of times the event occurs to the total number of trials or times the activity is performed SIMULATION A model of an experiment that would be too difficult or too time-consuming to actually perform. COMPLEMENT In probability, the complement of an event is all outcomes different from the favorable outcome. The sum of the probability of an event and its complement is 1. Example: The number cube is labeled 1-6. PROBABILITY The number used to describe the chance of an event occurring ESTIMATE An answer that is close to the exact answer and is found by rounding, by using front-end digits, by clustering, or by using compatible numbers to compute COMPATIBLE NUMBERS Numbers that are close to a dividend and divisor and divide evenly, with no remainder Example: EVALUATE To find the value INVERSE OPERATIONS Operations that undo each other Examples: 20 – 5 = 15 and 15 + 5 = 20 20 ÷ 5 = 4 and 4 x 5 = 20 PRECISION A property of measurement that is related to the unit of measure used; the smaller the unit of measure used, the more precise the measurement is. Example: 27 mm is more precise than 3 cm.