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# Math

Term | Definition |
---|---|

Scale Factor of Dilation | The ratio of the side lengths of the image to the corresponding side lengths of the original figure |

Transversal | A line that intersects two or more lines |

Convex Polygon | A polygon is convex when every line segment connecting any two vertices lies entirely inside the polygon |

Concave Polygon | A polygon is concave when at least one line segment connecting any two vertices lies outside the polygon |

Indirect Measurement | uses similar figures to find a missing measure when it is difficult to find directly |

Linear Equation | an equation whose graph is a line |

Slope | the rate of change between any two points on a line. It is a measure of the steepness of a line |

Slope Intercept Form | A linear equation written in the form y=mx+b is in slope-intercept form |

Standard Form of a Linear Equation | Ax+By=C where a and b are not both zero |

Point Slope Form | y-y1=m(x-x1) |

System of Linear Equations | A set of two or more linear equations with the same variables |

Solution of a System of Linear Equations | the point of intersection of the graphs of the equations. |

Relation | pairs inputs with outpust |

Mapping Diagram | a way to represent a relation |

Function | A relation that pairs each input with exactly one output |

Function Rule | An equation that describes the relationship between inputs and outputs |

Linear Function | A function whose graph is a straight line |

Nonlinear Function | A function whose graph is not a straight line |

Perfect Square | A number with integers as its square roots |

Perfect Cube | A number that can be written as the cube of an integer |

Theorem | A mathematical rule |

Legs | The two sides of a right triangle that form the right angle |

Hypotenuse | The side of the right triangle opposite the right angle |

Pythagorean Theorem | In any right triangle the sums of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse |

Irrational Number | A number that cannot be written as the ratio of two integers |

Real Numbers | The set of all rational and irrational numbers |

Distance Formula | d = √[( x₂ - x₁)² + (y₂ - y₁)²] |

Sphere | The set of all points in space that are the same distance from a point called the center |

Similar Solids | Solids that have the same shape and proportional corresponding dimensions |

Joint Frequency | Each entry in a two way table |

Marginal Frequency | The sums of the rows and columns in a two way table |

Power | A product of repeated factors |

Base | The base of a power is the common factor |

Scientific Notation | A number is written in scientific notation when it is represented as the product of a factor and a power of 10. The factor must be greater than or equal to 1 and less than 10 |

Open Sentence | An equation that contains one or more variables |

Natural Numbers | The counting numbers |

Rational Number | A real number that can be written as a ratio of two integers. Rational numbers in decimal form are terminating or repeating |

Counter example | Any example that proves a statement false |

Deductive Reasoning | A process of reasoning logically from given facts to a conclusion |

Consecutive integers | Integers that differ by one |

Equivalent equations | Equations that have the same solution |

Identity | An equation that is true for every value |

Literal equation | An equation involving two or more variables |

Mean | sum of data items divided by number of data items |

Median | The middle value in an ordered set of numbers |

Mode | The data item that occurs the greatest number of times in a data set. A data set may have no mode, one mode, or more than one mode |

Measure of Central tendency | Mean, median, and mode. They are used to organize and summarize a set of data. |

range | The difference between the greatest and the least data values for a set of data |

uniform motion | The motion of an object moving at a constant rate |

Compound inequalities | Two inequalities that are joined by AND or OR |

equivalent inequalities | have the same set of solutions |

solution of an inequality | Any ordered pair that makes the inequality true |

Complement of an event | All possible outcomes that are not in the event |

dependent events | Two events in which the occurrence of one event affects the probability of the second event |

experimental probability | The ration of the number of times an event actually happens to the number of times the experiment is done. The probability of an event is the number of times an event happens divided by the number of times the experiment is done |

greatest possible error | One half of the measuring unit, for any measurement. |

independent events | Two events for which the outcome of one does not affect the other |

means of a proportion | In the proportion a/b = c/d, b and c are the means |

outcome | The result of a single trial in a probability experiment |

percent error | The ratio of the greatest possible error to the measurement |

percent of change | The ratio of the amount of change to the original amount expressed as a percent |

percent of decrease | The percent of change found when the original amount decreases |

percent of increase | The percent of change found when the original amount increases |

probability | How likely it is that an event will occur |

sample space | All possible outcomes of an event |

scale drawing | An enlarged or reduced drawing similar to an actual object or place |

similar figures | Figures that have the same shape, but not necessarily the same size |

theoretical probability | The ratio of the number of favorable outcomes to the number of possible outcomes if all outcomes have the same chance of happening. Number of favorable outcomes divided by number of possible outcomes |

unit analysis | The process of selecting conversion factors to produce the appropriate units |

unit rate | A rate with a denominator of 1 |

arithmetic sequence | A number sequence formed by adding a fixed number to each previous term |

conjecture | Conclusion reached by inductive reasoning |

constant of variation for direct variation | The nonzero constant k in the function y=kx |

domain | The set of all first coordinates in the ordered pairs of a relation |

function notation | To write a rule in function notation, you use the symbol f(x) in place of y |

function rule | An equation that describes a function |

inductive reasoning | Making conclusions based on observed patterns |

relation | Any set of ordered pairs |

vertical line test | A method used to determine if a relation is a function or not. If a vertical line passes through a graph more than once, the graph is not the graph of a function. |

absolute value equation | Equation whose graph forms a V that opens up or down |

correlation coefficient | A number that tells how closely the equation of best fit models the data. The value r of the correlation coefficient is in the range -1 ≤ r ≤ 1. |

line of best fit | The most accurate trend line on a scatter plot showing the relationship between two sets of data |

negative reciprocal | A number of the form -b/a, where a/b is a nonzero rational number. The product of a number and its negative reciprocal is -1 |

elimination method | A method for solving a system of linear equations. You add or subtract the equations to eliminate a variable |

infinitely many solutions | The number of solutions of a system of equations in which the graphs of the equations are the same line |

linear inequality | A mathematical sentence that describes a region of the coordinate plane having a boundary line. Each point in the region is a solution of the inequality |

no solution | When the graphs of the equations in a system are parallel with no point of intersection. |

solution of a system of linear equations | Any ordered pair in a system that makes all the equations of that system true |

solution of a system of linear inequalities | Any ordered pair that makes all of the inequalities in the system true |

solutions of an inequality | Any value or values of a variable in the inequality that makes an inequality true. |

substitution method | A method of solving a system of equations by replacing one variable with an equivalent expression containing the other variable |

system of linear equations | Two or more linear equations using the same variables |

system of linear inequalities | Two or more linear inequalities using the same variables |

common ratio | The fixed number used to find terms in a geometric sequence |

compound interest | Interest paid on both the principal and the interest that has already been paid |

decay factor | The base b in the exponential function y = ab with an exponent of x, where 0<b<1 |

exponential decay | A situation modeled with a function of the form y = ab with an exponent of x , where a>0 and 0 < b< 1 |

exponential function | A function that repeatedly multiplies an initial amount by the same positive number. You can model all exponential functions using y = ab with an exponent of x, where a is a nonzero constant, b>0, and b is not equal to 1 |

exponential growth | A situation modeled with a function of the form y = ab with an exponent of x, where a>0 and b>1 |

geometric sequence | A number sequence formed by multiplying a term in a sequence by a fixed number to find the next term |

growth factor | The number b in an exponential growth function of the form y = ab with an exponent of x, where b > 1 |

interest period | The length of time over which interest is calculated |

binomial | A polynomial of two terms |

degree of a monomial | The sum of the exponents of the variables of a monomial |

degree of a polynomial | The degree of the term with the greatest exponent for a polynomial in one variable |

factor by grouping | A method of factoring that uses the distributive property to remove a common binomial factor of two pairs of terms |

monomial | An expression that is a number, a variable, or a product of a number and one or more variables |

perfect square trinomial | Any trinomial of the form a squared + 2ab +b squared or a squared - 2ab + b squared |

polynomial | A monomial or the sum or difference of two or more monomials. A quotient with a variable in the denominatior is not a polynomial |

standard form of a polynomial | The form of a polynomial in which the degree of the terms decreases from left to right ( also descending order ) |

trinomial | A polynomial of three terms |

axis of symmetry | The line that divides a parabola into two matching halves |

completing the square | A method of solving quadratic equations. Completing the square turns every quadratic equation into the form x squared = c |

discriminant | The quantity b squared - 4ac is the discriminant of ax squared + bx + c = 0 |

maximum | The y-coordinate of the vertex of a parabola that opens downward |

minimum | The y-coordinate of the vertex of a parabola that opens upward |

negative square root | A number of the form negative square root of b |

parabola | The graph of a quadratic function |

principal square root | A number of the form positive square root of b |

quadratic equation | An equation you can write in the standard form ax squared + b + c = 0 where a does not equal 0 |

quadratic formula | If ax squared plus bx plus c equals zero and a doesn't equal zero, then x equals negative b ± the square root of (b squared -4ac) and all of that is divided by 2a |

quadratic function | A function of the form y equals ax squared + bx + c where a doesn't equal zero the graph of a quadratic function is a parabola, a U shaped curve that opens up or down |

radicand | The expression under the radical sign |

standard form of a quadratic function | The form of a quadratic function written y = ax squared + bx + c where a does not equal zero |

standard form of a quadratic equation | The form of a quadratic equation written ax squared + bx + c = 0 |

Zero product Property | For all real numbers a and b, if ab = 0 then a = 0 or b = 0 |

angle of depression | An angle from the horizontal down to a line of sight It is used to measure heights indirectly |

angle of elevation | An angle from the horizontal up to a line of sight It is used to measure heights indirectly |

conclusion | In conditional the part following then |

conditional | an if-then statement |

conjugates | The sum and the difference of the same two terms |

converse | The statement obtained by reversing the if and then parts of an if-then statement |

cosine (cos) | In a right triangle, such as ABC with right angle C the cosine of angle A is equal to the length of side adjacent to angle A divided by length of hypotenuse OR A =b/c |

extraneous solution | An apparent solution of the equation that does not satisfy the original equation |

hypothesis | The part following if in a conditional |

like radicals | Radical expressions with the same radicands |

midpoint | The point that divides a segment into to equal segments |

midpoint formula | The midpoint of a line segment with endpoints A (x1, y1) and B (x2, y2) is (x1 +x2 divided by 2 , y1+y2 divided by 2) |

radical equation | An equation that has a variable in a radicand |

radical expression | Expression that contains a radical |

rationalize | Rewrite as a rational number. Rationalizing the denominator of a radical expression may be necessary to obtain the simplest radical form |

sine (sin) | In a right triangle sine of angle A is equal to the length of side opposite angle A divided by length of hypotenuse or sine A = a/c |

square root function | A function that contains the independent variable in the radicand |

tangent (tan) | In a right triangle tangent of angle A equals length of side opposite angle A divided by length of side adjacent to angle A OR tangent A = a/b |

trigonometric ratios | The ratios of the sides of a right triangle |

unlike radicals | Radical expressions that do not have the same radicands |

asymptote | A line the graph of a function gets closer to as x or y gets larger in absolute value |

combination (you can use the notation nCr to write the number of combinations of n objects chosen r at a time) | An arrangement of some or all of a set of objects without regard to order. The number of combinations equals total number of permutations divided by number of times the objects in each group are repeated |

Constant of variation for direct variation | The nonzero constant k in the function y=kx |

Inverse variation | A function that can be written in the form xy = k or y = k/x The product of the quantities remains constant so as one quantity increases the other decreases |

multiplication counting principle | If there are m ways to make the first selection and n ways to make the second selection there are m*n ways to make the two selections |

permutation | An arrangement of some or all of a set of objects in a specific order. YOu can use the notation nPr to express the number of permutations, where n equals the number of objects available and r equals the number of selections to make |

rational equation | An equation containing rational expressions |

rational expression | A ratio of two polynomials. The value of the variable cannot make the denominator equal to 0 |

rational function | A function that can be written in the form f(x) = polynomial/polynomial. The value of the variable cannot make the denominator equal to 0 |

Constant of variation for inverse variation | The nonzero constant k in the function y = k/x |

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22holmei