Definitions - Regular Math
Chapter One
1.1
1. Numerical Expression- An expression that contains only numbers and operations.
2. Order of Operations- A rule for evaluating expressions: first perform the operations in the parentheses, then compute powers and roots, then perform all multiplication and division from left to right, and then perform all addition and subtraction from left to right.
1.2
3. Commutative Property- The property that states that two or more numbers can be added in any order without changing their sum.
4. Associative Property- The property that states that for all real numbers a, b, and c, the sum is always the same regardless of their grouping.
5. Identity Property- The property that states that the product of 1 and any numbers is that number.
6. Distributive Property- For all real numbers, a, b, and c, a(b+c)=ab+ac and a(b-c)=ab-ac.
1.3
7. Variable- A symbol used to represent a quantity that can change.
8. Constant- A value that does not change.
9. Algebraic Expressions- An expression that contains at least one variable.
10. Evaluate- To find the value of a numerical or algebraic expression.
1.4 – None
1.5
11. Term- the parts of an expression that are added or subtracted.
12. Coefficient- The number that is multiplied by the variable in an algebraic expression.
Chapter Two
2.1
1. Opposite- Two numbers that are an equal distance from zero on a number line; also called additive inverse.
2. Additive Inverse- The opposite of a number.
3. Integer- The set of whole numbers and their opposites.
4. Absolute Value- The distance a number is from zero on a number line.
2.2 – None
2.3 – None
2.4 – None
2.5 – None
2.6
5. Terminating Decimal- A decimal number that ends, or terminates.
6. Repeating Decimal- A decimal in which one or more digits repeat infinitely.
2.7
7. Rational Number- Any number that can be expressed as a ratio of two integers.
Chapter Three
3.1 – None
3.2 – None
3.3 – None
3.4 – None
3.5 – None
3.6 – None
3.7
1. Reciprocal- One of two numbers whose product is 1; also called multiplicative inverse.
2. Multiplicative Inverse- The product of a nonzero number and its reciprocal, or multiplicative inverse, is one.
3.8 – None
Chapter Four
4.1
1. Rate- A ratio that compares two quantities measured in different units.
2. Unit Rate- A rate in which the second quantity in the comparison is one unit.
4.2
3. Equivalent Ratios- Ratios that name the same comparison.
4. Proportion- An equation that states that two ratios are equivalent.
4-3
5. Cross Product- The product of numbers on the diagonal when comparing two ratios.
4.4
6. Similar- Figures with the same shape but not necessarily the same sizes are similar.
7. Corresponding Sides- Matching sides of two or more polygons.
8. Corresponding Angles- Angles in the same relative position in polygons with an equal number of sides.
4.5
9. Indirect Measurement- The technique of using similar figures and proportions to find a measure.
4.6
10. Scale Drawing- A drawing that uses a scale to make an object smaller than or larger than the real object.
11. Scale Factor- The ratio used to enlarge or reduce similar figures.
12. Scale Model- A proportional model of a three-dimensional object.
13. Scale- The ratio between two sets of measurements.
Chapter Five
5.1
1. Coordinate Plane- A plane formed by the intersection of a horizontal number line called the x-axis and a vertical number line called the y-axis.
2. X-Axis- The horizontal axis on a coordinate plane.
3. Y-Axis- The vertical axis on a coordinate plane.
4. Origin- The point where the x-axis and y-axis intersect on the coordinate plane; (0, 0).
5. Quadrant- The x- and y- axes divide the coordinate plane into four regions, each region is called a quadrant.
6. Ordered Pair- A pair of numbers that can be used to locate a point on the coordinate plane.
5.2 – None
5.3
7. Slope- A measure of the steepness of a line on a graph; the rise divided by the run.
8. Rate of Change- A ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable.
5.4
9. Direct Variation- A linear relationship between two variables, x and y, that can be written in the form y=kx, where k is a nonzero constant.
10. Constant of Variation- The constant k in direct and inverse variation equations.
Chapter Six
6.1 – None
6.2 – None
6.3 – None
6.4
1. Percent of Change- The amount stated as a percent that a number increases or decreases.
2. Percent of Increase- A percent change describing an increase in a quantity.
3. Percent of Decrease- A percent change describing a decrease in a quantity.
6.5
4. Commission- A fee paid to a person for making a sale.
5. Commission Rate- The fee paid to a person who makes a sale, expressed as a percent of the selling price.
6.6
6. Interest- The amount of money charged for borrowing or using money, or the amount of money earned by saving money.
7. Simple Interest- A fixed percent of the principal. It is found using the formula I=Prt where P represents the principal, r the rate of interest, and tthe time.
8. Principal- The initial amount of money borrowed or saved.
9. Rate of Interest- The percent charged or earned on an amount of money.
Chapter Seven
7.1
1. Mean- The sum of the items in a set of data divided by the number of items in the set; also called average.
2. Median- The middle number, or mean (average) of the two middle numbers, in an ordered set of data.
3. Mode- The number or numbers that occur most frequently in a set of data; when all numbers occur with the same frequency, we say there is no mode.
4. Range- The difference between the greatest and least values in a data set.
5. Outlier- A value much greater or much less than the others in a data set.
7.2
6. Box-and-Whisker Plot- A graph shows how data are distributed by using the median, quartiles, least value and greatest value; also called abox plot.
7. Lower Quartile- The median of the lower half of a set of data.
8. Upper Quartile- The median of the upper half of a set of data.
9. Interquartile Range- The difference between the upper and lower quartiles in a box-and-whisker plot.
7.3
10. Population- The entire group of objects or individuals considered for a survey.
11. Sample- A part of the population.
12. Convenience Sample- A sample based on members of the population that are readily available.
13. Biased Sample- A sample that does not fairly represent the population.
Chapter Eight
8.1
1. Point- An exact location that has no size.
2. Line- A straight path that has no thickness and extends forever.
3. Plane- A flat surface that has no thickness and extends forever.
4. ray- A part of a line that starts at one endpoint and extends forever in one direction.
5. Line Segment- A part of a line made of two endpoints and all points between them.
6. Congruent- Having the same size and shape, the symbol is .
8.2
7. Angle- A figure formed by two rays with a common endpoint called a vertex.
8. Vertex- On an angle or polygon, the point where two sides intersect.
9. Right Angle- An angle that measures 90°
10. Acute Angle- An angle that measures greater than 0° and less than 90°.
11. Obtuse Angle- An angle whose measure is greater than 90° but less than 180°.
12. Straight Angle- An angle that measures 180°.
13. Complementary Angles- Two angles whose measures add to 90°.
14. Supplementary Angles-Two angles whose measures have a sum of 180°.
8.3
15. Perpendicular Lines- Lines that intersect to form right angles.
16. Parallel Lines- Lines in a plane that do not intersect.
17. Skew Lines- Lines that lines that lie in different planes that are neither parallel nor intersecting.
18. Adjacent Angles- Angles in the same plane that have a common vertex and a common side.
19. Vertical Angles- A pair of opposite congruent angles formed by intersecting lines.
20. Transversal- A line that intersects two or more lines.
8.4
21. Diagonal- A line segment that connects two non-adjacent vertices of a polygon.
8-5
22. Side-Side-Side Rule- States that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
Chapter Nine
9.1
1. Perimeter- The distance around a polygon
2. Circumference- The distance around a circle.
3. Pi- The ratio of the circumference of a circle to the length of its diameter.
9.2 – None
9.3
4. Composite Figure- A figure made up of simple geometric shapes.
9.4
5. Face- A flat surface of a polyhedron.
6. Edge- The line segment along which two faces of a polyhedron intersect.
7. Polyhedron- A three-dimensional figure in which all surfaces or faces are polygons.
8. Vertex- On an angle or polygon, the point where two sides intersect.
9. Base- A face of a three-dimensional figure by which the figure is measured or classified.
10. Prism- A polyhedron that has two congruent polygon-shaped bases and other faces are all parallelograms.
11. Pyramid- A polyhedron with a polygon base and triangular sides that all meet at a common vertex.
12. Cylinder- A three-dimensional figure with two parallel, congruent circular bases connected by a curved lateral surface.
13. Cone- A three- dimensional figure with one vertex and one circular base.
14. Sphere- A three-dimensional figure will all points the same distance from the center.
9.5
15. Volume- The number of cubic units needed to fill a given space.
9-6
16. Net- An arrangement of two dimensional figures that can be folded to form a polyhedron.
17. Surface Area- The sum of the areas of the faces, or surfaces of a three-dimensional figure.
18. Lateral Face- A face of a prism or pyramid that is not a base.
19. Lateral Area- The sum of the areas of the faces of a prism or pyramid, or the area of the lateral surface of a cylinder.
Chapter Ten
10.1
1. Experiment- In a probably, any activity based on chance, such as tossing a coin.
2. Trial- Each repetition or observation of an experiment.
3. Outcome- A possible result of a probability experiment.
4. Event- An outcome or set of outcomes of an experiment or situation.
5. Probability- A number from 0 to 1 (or 0% to 100%) that describes how likely an event is to occur.
6. Simple Event- An event consisting of only one outcome.
7. Compound Event- An event made up of two or more simple events.
8. Complement- The set of all outcomes that are not the event.
10.2
9. Experimental Probability- The ratio of the number of times an event occurs to the number of trials, or times that the activity is performed.
10.3
10. Sample Space- All possible outcomes of an experiment.
11. Fundamental Counting Principle-If one event has m possible outcomes and a second event has n possible outcomes after the first event has occurred, then there area total possible outcomes for the two events.
10.4
12. Theoretical Probability- The ratio of the number of ways an event can occur to the total number of equally likely outcomes.
13. Equally Likely- Outcomes that have the same probability.
14. Fair- When all outcomes of an experiment are equally likely, the experiment is said to be fair.
10.5
15. Prediction- Something you can reasonably expect to happen in the future.
10.6
16. Independent Events- Events for which the outcome of one event does not affect the probability of the other.
17. Dependent Events-Events for which the outcome of one event affects the probability of the second event.
10.7
18. Combination- An arrangement of items or events in which order does not matter.
10-8
19. Permutation- An arrangement of items or events in which order is important.
20. Factorial- The product of all whole numbers except zero that are less than or equal to a number.
10.9 – None
Chapter Eleven
11.1 – None
11.2 – None
11.3 – None
11.4
1. inequality- A mathematical sentence that shows the relationship between quantities that are not equivalent.
2. Algebraic Inequality- An inequality that contains at least one variable.
3. Solution Set- The set of values that make a statement true.
4. Compound Inequality- A combination of more than one inequality.
11.5 – None
11.6 – None
11.7 – None
1.1
1. Numerical Expression- An expression that contains only numbers and operations.
2. Order of Operations- A rule for evaluating expressions: first perform the operations in the parentheses, then compute powers and roots, then perform all multiplication and division from left to right, and then perform all addition and subtraction from left to right.
1.2
3. Commutative Property- The property that states that two or more numbers can be added in any order without changing their sum.
4. Associative Property- The property that states that for all real numbers a, b, and c, the sum is always the same regardless of their grouping.
5. Identity Property- The property that states that the product of 1 and any numbers is that number.
6. Distributive Property- For all real numbers, a, b, and c, a(b+c)=ab+ac and a(b-c)=ab-ac.
1.3
7. Variable- A symbol used to represent a quantity that can change.
8. Constant- A value that does not change.
9. Algebraic Expressions- An expression that contains at least one variable.
10. Evaluate- To find the value of a numerical or algebraic expression.
1.4 – None
1.5
11. Term- the parts of an expression that are added or subtracted.
12. Coefficient- The number that is multiplied by the variable in an algebraic expression.
Chapter Two
2.1
1. Opposite- Two numbers that are an equal distance from zero on a number line; also called additive inverse.
2. Additive Inverse- The opposite of a number.
3. Integer- The set of whole numbers and their opposites.
4. Absolute Value- The distance a number is from zero on a number line.
2.2 – None
2.3 – None
2.4 – None
2.5 – None
2.6
5. Terminating Decimal- A decimal number that ends, or terminates.
6. Repeating Decimal- A decimal in which one or more digits repeat infinitely.
2.7
7. Rational Number- Any number that can be expressed as a ratio of two integers.
Chapter Three
3.1 – None
3.2 – None
3.3 – None
3.4 – None
3.5 – None
3.6 – None
3.7
1. Reciprocal- One of two numbers whose product is 1; also called multiplicative inverse.
2. Multiplicative Inverse- The product of a nonzero number and its reciprocal, or multiplicative inverse, is one.
3.8 – None
Chapter Four
4.1
1. Rate- A ratio that compares two quantities measured in different units.
2. Unit Rate- A rate in which the second quantity in the comparison is one unit.
4.2
3. Equivalent Ratios- Ratios that name the same comparison.
4. Proportion- An equation that states that two ratios are equivalent.
4-3
5. Cross Product- The product of numbers on the diagonal when comparing two ratios.
4.4
6. Similar- Figures with the same shape but not necessarily the same sizes are similar.
7. Corresponding Sides- Matching sides of two or more polygons.
8. Corresponding Angles- Angles in the same relative position in polygons with an equal number of sides.
4.5
9. Indirect Measurement- The technique of using similar figures and proportions to find a measure.
4.6
10. Scale Drawing- A drawing that uses a scale to make an object smaller than or larger than the real object.
11. Scale Factor- The ratio used to enlarge or reduce similar figures.
12. Scale Model- A proportional model of a three-dimensional object.
13. Scale- The ratio between two sets of measurements.
Chapter Five
5.1
1. Coordinate Plane- A plane formed by the intersection of a horizontal number line called the x-axis and a vertical number line called the y-axis.
2. X-Axis- The horizontal axis on a coordinate plane.
3. Y-Axis- The vertical axis on a coordinate plane.
4. Origin- The point where the x-axis and y-axis intersect on the coordinate plane; (0, 0).
5. Quadrant- The x- and y- axes divide the coordinate plane into four regions, each region is called a quadrant.
6. Ordered Pair- A pair of numbers that can be used to locate a point on the coordinate plane.
5.2 – None
5.3
7. Slope- A measure of the steepness of a line on a graph; the rise divided by the run.
8. Rate of Change- A ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable.
5.4
9. Direct Variation- A linear relationship between two variables, x and y, that can be written in the form y=kx, where k is a nonzero constant.
10. Constant of Variation- The constant k in direct and inverse variation equations.
Chapter Six
6.1 – None
6.2 – None
6.3 – None
6.4
1. Percent of Change- The amount stated as a percent that a number increases or decreases.
2. Percent of Increase- A percent change describing an increase in a quantity.
3. Percent of Decrease- A percent change describing a decrease in a quantity.
6.5
4. Commission- A fee paid to a person for making a sale.
5. Commission Rate- The fee paid to a person who makes a sale, expressed as a percent of the selling price.
6.6
6. Interest- The amount of money charged for borrowing or using money, or the amount of money earned by saving money.
7. Simple Interest- A fixed percent of the principal. It is found using the formula I=Prt where P represents the principal, r the rate of interest, and tthe time.
8. Principal- The initial amount of money borrowed or saved.
9. Rate of Interest- The percent charged or earned on an amount of money.
Chapter Seven
7.1
1. Mean- The sum of the items in a set of data divided by the number of items in the set; also called average.
2. Median- The middle number, or mean (average) of the two middle numbers, in an ordered set of data.
3. Mode- The number or numbers that occur most frequently in a set of data; when all numbers occur with the same frequency, we say there is no mode.
4. Range- The difference between the greatest and least values in a data set.
5. Outlier- A value much greater or much less than the others in a data set.
7.2
6. Box-and-Whisker Plot- A graph shows how data are distributed by using the median, quartiles, least value and greatest value; also called abox plot.
7. Lower Quartile- The median of the lower half of a set of data.
8. Upper Quartile- The median of the upper half of a set of data.
9. Interquartile Range- The difference between the upper and lower quartiles in a box-and-whisker plot.
7.3
10. Population- The entire group of objects or individuals considered for a survey.
11. Sample- A part of the population.
12. Convenience Sample- A sample based on members of the population that are readily available.
13. Biased Sample- A sample that does not fairly represent the population.
Chapter Eight
8.1
1. Point- An exact location that has no size.
2. Line- A straight path that has no thickness and extends forever.
3. Plane- A flat surface that has no thickness and extends forever.
4. ray- A part of a line that starts at one endpoint and extends forever in one direction.
5. Line Segment- A part of a line made of two endpoints and all points between them.
6. Congruent- Having the same size and shape, the symbol is .
8.2
7. Angle- A figure formed by two rays with a common endpoint called a vertex.
8. Vertex- On an angle or polygon, the point where two sides intersect.
9. Right Angle- An angle that measures 90°
10. Acute Angle- An angle that measures greater than 0° and less than 90°.
11. Obtuse Angle- An angle whose measure is greater than 90° but less than 180°.
12. Straight Angle- An angle that measures 180°.
13. Complementary Angles- Two angles whose measures add to 90°.
14. Supplementary Angles-Two angles whose measures have a sum of 180°.
8.3
15. Perpendicular Lines- Lines that intersect to form right angles.
16. Parallel Lines- Lines in a plane that do not intersect.
17. Skew Lines- Lines that lines that lie in different planes that are neither parallel nor intersecting.
18. Adjacent Angles- Angles in the same plane that have a common vertex and a common side.
19. Vertical Angles- A pair of opposite congruent angles formed by intersecting lines.
20. Transversal- A line that intersects two or more lines.
8.4
21. Diagonal- A line segment that connects two non-adjacent vertices of a polygon.
8-5
22. Side-Side-Side Rule- States that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
Chapter Nine
9.1
1. Perimeter- The distance around a polygon
2. Circumference- The distance around a circle.
3. Pi- The ratio of the circumference of a circle to the length of its diameter.
9.2 – None
9.3
4. Composite Figure- A figure made up of simple geometric shapes.
9.4
5. Face- A flat surface of a polyhedron.
6. Edge- The line segment along which two faces of a polyhedron intersect.
7. Polyhedron- A three-dimensional figure in which all surfaces or faces are polygons.
8. Vertex- On an angle or polygon, the point where two sides intersect.
9. Base- A face of a three-dimensional figure by which the figure is measured or classified.
10. Prism- A polyhedron that has two congruent polygon-shaped bases and other faces are all parallelograms.
11. Pyramid- A polyhedron with a polygon base and triangular sides that all meet at a common vertex.
12. Cylinder- A three-dimensional figure with two parallel, congruent circular bases connected by a curved lateral surface.
13. Cone- A three- dimensional figure with one vertex and one circular base.
14. Sphere- A three-dimensional figure will all points the same distance from the center.
9.5
15. Volume- The number of cubic units needed to fill a given space.
9-6
16. Net- An arrangement of two dimensional figures that can be folded to form a polyhedron.
17. Surface Area- The sum of the areas of the faces, or surfaces of a three-dimensional figure.
18. Lateral Face- A face of a prism or pyramid that is not a base.
19. Lateral Area- The sum of the areas of the faces of a prism or pyramid, or the area of the lateral surface of a cylinder.
Chapter Ten
10.1
1. Experiment- In a probably, any activity based on chance, such as tossing a coin.
2. Trial- Each repetition or observation of an experiment.
3. Outcome- A possible result of a probability experiment.
4. Event- An outcome or set of outcomes of an experiment or situation.
5. Probability- A number from 0 to 1 (or 0% to 100%) that describes how likely an event is to occur.
6. Simple Event- An event consisting of only one outcome.
7. Compound Event- An event made up of two or more simple events.
8. Complement- The set of all outcomes that are not the event.
10.2
9. Experimental Probability- The ratio of the number of times an event occurs to the number of trials, or times that the activity is performed.
10.3
10. Sample Space- All possible outcomes of an experiment.
11. Fundamental Counting Principle-If one event has m possible outcomes and a second event has n possible outcomes after the first event has occurred, then there area total possible outcomes for the two events.
10.4
12. Theoretical Probability- The ratio of the number of ways an event can occur to the total number of equally likely outcomes.
13. Equally Likely- Outcomes that have the same probability.
14. Fair- When all outcomes of an experiment are equally likely, the experiment is said to be fair.
10.5
15. Prediction- Something you can reasonably expect to happen in the future.
10.6
16. Independent Events- Events for which the outcome of one event does not affect the probability of the other.
17. Dependent Events-Events for which the outcome of one event affects the probability of the second event.
10.7
18. Combination- An arrangement of items or events in which order does not matter.
10-8
19. Permutation- An arrangement of items or events in which order is important.
20. Factorial- The product of all whole numbers except zero that are less than or equal to a number.
10.9 – None
Chapter Eleven
11.1 – None
11.2 – None
11.3 – None
11.4
1. inequality- A mathematical sentence that shows the relationship between quantities that are not equivalent.
2. Algebraic Inequality- An inequality that contains at least one variable.
3. Solution Set- The set of values that make a statement true.
4. Compound Inequality- A combination of more than one inequality.
11.5 – None
11.6 – None
11.7 – None