Test #1
1-1
1. Algebraic Expression- An expression consisting of one or more numbers and variables along with one or more arithmetic operations.
2. Variables- 1. Symbols used to represent unspecified numbers or values. 2. A characteristic of a group of people or objects that can assume different values.
3. Term- A number, a variable, or the product or quotient of numbers and variables.
4. Factors- In an algebraic expression, the quantities being multiplied are called factors.
5. Product- In an algebraic expression, the result of quantities being multiplied is called the product.
6. Power- An expression of the form xn, read x to the nth power.
7. Exponent- In an expression of the form xn, the exponent is n. it indicates the number of times x is used as a factor.
8. Base- In an expression of the form xn, the base is x.
1-2
9. Evaluate- To find the value of an expression.
10. Order of Operations- Process used to solve mathematical expressions
1-3
11. Equivalent Expressions- Expressions that denote the same value for all values of the variable(s).
12. Additive Identity- For any number a, a+0=0+a=a
13. Multiplicative Identity- For any number a, a∙1=1∙a=a
14. Multiplicative Zero Property- The product of any number and zero is equal to 0.
15. Multiplicative Inverses- Two numbers with a product of 1.
16. Reciprocals- The Multiplicative inverse of a number.
17. Commutative Property- The order in which you add or multiply numbers does not change their sum or product.
18. Associative Property- The way you group three or more numbers when adding or multiplying does not change their sum or product.
19. Proof- A logical argument in which each statement you make is supported by a statement that is accepted as true.
1-4
20. Distributive Property- For any numbers a, b, and c, a(b+c) = ab+ac. And, for any numbers a, b, and c, (b+c)a = ba + ca.
21. Like Terms- Terms that contain the same variables, with corresponding variables having the same exponent.
22. Simplest Form- An expression is in simplest form when it is replaced by an equivalent expression having no like terms or parentheses.
23. Coefficient- The numerical factor of a term.
1-5
24. Open Sentence- A mathematical statement with one or more variables.
25. Equation- A mathematical sentence that contains an equals sign, =.
26. Solving- Finding a value for a variable that makes a sentence true.
27. Solution- A replacement value for the variable in an open sentence.
28. Replacement Set- A set of numbers from each which replacements for a variable may be chosen.
29. Set- A collection of objects or numbers that is often shown using braces.
30. Element- Each object or number in the set.
31. Solution Set- The set of elements from the replacement set that make an open sentence true.
32. Identity- An equation that is true for every value of the variable.
1-6
33. Coordinate System- The grid formed by the intersection of two number line, the horizontal axis and the vertical axis.
34. Coordinate Plane- The plane containing the x- and y-axes.
35. Y-Axis- The vertical number line on a coordinate plane.
36. X-Axis- The horizontal number line on a coordinate plane.
37. Origin- The point where the two axes intersect at their zero points.
38. Ordered Pair- A set of numbers or coordinates used to locate any point on a coordinate plane, written in the form (x, y).
39. X-Coordinate- The first number in an ordered pair.
40. Y-Coordinate- The second number in an ordered pair.
41. Relation- A set of ordered pairs.
42. Mapping- Illustrates how each element of the domain is paired with an element in the range.
43. Domain- The set of the first numbers of the ordered pairs in a relation.
44. Range- 1. The set of second numbers of the ordered pairs in a relation. 2. The difference between the greatest and least data values.
45. Independent Variable- The variable in a function with a value that is subject to choice.
46. Dependent Variable- The variable in a relation with a value that depends on the value of the independent variable.
1-7
47. Function- A relation in which each element of the domain is paired with exactly one element of the range.
48. Discrete Function- A function of points that are not connected.
49. Continuous Function- A function that can be graphed with a line or a smooth curve.
50. Vertical Line Test- If any vertical line passes through no more than one point of the graph of a relation, then the relation is a function.
51. Function Notation- A way to name a function that is defined by an equation. In function notation, the equations y=3x-8 is written as f(x)=3x-8.
52. Nonlinear Function- A function with a graph that is not a straight line.
1-8
53. Intercepts- Points on a graph where the graph intercepts and axis.
54. Y-Intercept- The y-coordinate of a point where a graph crosses the y-axis.
55. X-Intercept- The x-coordinate of a point where a graph crosses the x-axis.
56. Positive- A function is positive on a portion of its domain where its graph lies above the x-axis.
57. Negative- A function is negative on portion of its domain where its graph lies below the x-axis.
58. Increasing- The graph of a function goes up on a portion of its domain when viewed from left to right.
59. Decreasing- The graph of a function goes down on a portion of its domain when viewed from left to right.
60. Extrema- Points of relatively high or low function values.
61. Relative Minimum- The point with the least y-coordinate.
62. Relative Maximum- The point with the greatest y-coordinate.
63. End Behavior- Describes how the values of a function behave at each end of the graph.
Test #2
2-1
1. Formula- A Equation that states a rule for the relationship between certain quantities.
2-2
2. Solving an Equation- The process of finding all values of the variable that make the equation a true statement.
3. Equivalent Equations- Equations that have the same solution.
4. Subtraction Property of Equality- If an equation is true and the same number is subtracted from each side of the equation, the resulting equivalent equation is also true.
5. Multiplication Property of Equality- If an equation is true and each side is multiplied by the same nonzero number, the resulting equation is equivalent.
6. Division Property of Equality- If an equation is true and each side is divided by the same nonzero number, the resulting equation is equivalent.
2-3
7. Multi-Step Equation- Equations with more than one operation.
8. Consecutive Integers- Integers in counting order.
9. Number Theory- The study of numbers and the relationships between them.
2-4
10. Identities- An equation that is true for every value of the variable.
2-5 None
2-6
11. Ratio- A comparison of two numbers by division.
12. Proportion- An equation of the form a/b=c/d, where b≠0, stating that two ratios are equivalent.
13. Means- The middle terms of the proportion.
14. Extremes- In the ratio a/b=c/d, a and d are the extremes.
15. Rate-The ratio of two measurements having different units of measure.
16. Unit Rate- A ratio of two quantities, the second of which is one unit.
17. Scale- The relationship between the measurements on a drawing or model and the measurements of the real object.
18. Scale Model- A model used to represent an object that is too large or too small to be built at actual scale.
2-7
19. Percent of Change- When an increase or decrease is expressed as a percent.
20. Percent of Increase- The ratio of an amount of increase to the previous amount, expressed as a percent.
21. Percent of Decrease- The ratio of an amount of decrease to the previous amount, expressed as a percent.
2-8
22. Literal Equation- A formula or equation with several variables.
23. Dimensional Analysis- The process of carrying units throughout a computation.
24. Unit Analysis- The process of including units of measurement when computing.
2-9
25. Weighted Averages- The sum of the product of the number of units and the value per unit divided by the sum of the number of units represented by M.
26. Mixture Problems- Problems in which two or more parts are combined into a whole.
27. Uniform Motion Problems- Problems in which an object moves at a certain speed, or rate.
28. Rate Problems- Problems in which an object moves at a certain speed, or rate.
Test #3
3-1
1. Linear Equation- A equation in the form Ax+By=C, with a graph that is a straight line.
2. Standard Form- The standard form of a linear equation is Ax+By=C, where A≥0, A and B are not both zero, and A, B, and C are integers with a greatest common factor of 1.
3. Constant- A monomial that is a real number.
4. X-intercept- The x-coordinate of a point where a graph crosses the x-axis.
5. Y-intercept- The y-coordinate of a point where a graph crosses the y-axis.
3-2
6. Linear Function- A function with ordered pairs that satisfy a linear equation.
7. Parent Function-
8. Family of Graphs- Graphs and equations of graphs that have at least one characteristic in common.
9. Root- The solutions of a quadratic equation.
10. Zeros- The x-intercepts of the graph of a function; the points for which f(x)=0.
3-3
11. Rate of Change- How a quantity is changing with respect to a change in another quantity.
12. Slope- The ratio of the change in the y-coordinates (rise) to the corresponding change in the x coordinates (run) as you move from one point to another along the line.
3-4
13. Direct Variation- A equation of the form y=kx, where k is not equal to zero.
14. Constant of Variation- The number k in equations of the form y=kx.
15. Constant of Proportionality- Another term for constant of variation.
3-5
16. Sequence- A set of numbers in a specific order.
17. Terms of the Sequence- The numbers in a sequence.
18. Arithmetic Sequence- A numerical pattern that increases or decreases at a constant rate or value. The difference between successive terms of the sequence is constant.
19. Common Difference- The difference between the terms in an arithmetic sequence.
3-6 None
Test #4
4-1
1. Slope Intercept Form- An equation of the form y=mx+b, where m is the slope and b is the y-intercept.
2. Constant Functions- A linear function in the form y=b.
4-2
3. Constraint- A condition that a solution must satisfy. Equations can be viewed as constraints in a problem situation. The solutions of the equation meet the constraints of the problem.
4. Linear Extrapolation- The use of a linear equation to predict values that are outside the range of data.
4-3
5. Point-Slope Form- An equation of the form y-y1=m(x-x1), where m is the slope and (x1, y1) is a given point on a nonvertical line.
4-4
6. Parallel Lines- Lines in the same plane that do not intersect and either have the same slope or are vertical.
7. Perpendicular Lines- Lines that intersect to form a right angle.
4-5
8. Bivariate Data- Data with two variables.
9. Scatter Plot- Shows the relationship between a set of data with two variables, graphed as ordered pairs on a coordinate plane.
10. Line of Fit- A line that describes the trend of data in a scatter plot.
11. Linear Interpolation- The use of a linear equation to predict values that are inside the data range.
4-6
12. Best-Fit Line- The line that most closely approximates the data in a scatter plot.
13. Linear Regression- An algorithm to find a precise line of fit for a set of data.
14. Correlations Coefficient- A value that shoes how close data points are to a line.
15. Residual- The difference between an observed y-value and its predicted y-value on a regression line.
16. Median-Fit Line- A type of best-fit line that is calculated using the medians and the coordinates of data points.
4-7
17. Inverse Relation- A set of ordered pairs obtained by exchanging the x-coordinates with the y-coordinates of each ordered pair in a relation.
Test #5
5-1
1. Inequality- An open sentence that contains the symbol <, ≤, >, or ≥.
2. Addition Property of Inequalities- If the same number is added to each side of a true inequality, the resulting inequality is also true.
3. Set-Builder Notation- A concise way of writing a solution set. For example, {t|t<17} represents the set of all numbers t such that t is less than 17.
4. Subtraction Property of Inequalities- If the same number is subtracted from each side of a true inequality, the resulting inequality is also true.
5-2
5. Multiplication Property of Inequalities- If both sides of an inequality that is true are multiplied by a positive number, the resulting inequality is also true. If both sides of an inequality that is true are multiplied by a negative number, the direction of the inequality sign is reversed to make the resulting inequality also true.
6. Division Property of Inequalities- If both sides of a true inequality are divided by a positive number, the resulting inequality is also true. If both sides of a true inequality are divided by a negative number, the direction of the inequality sign is reversed to make the resulting inequality also true.
5-3 None
5-4
7. Compound Inequality- Two or more inequalities that are connected by words and or or.
8. Intersection- The graph of a compound inequality containing and; the solution is the set of elements common to both inequalities.
9. Union- The graph of a compound inequality containing or; the solution is a solution of either inequality, not necessarily both.
5-5 None
5-6
10. Boundary- A line or curve that separates the coordinate plane into regions.
11. Half-Planes- The region of the graph of an inequality on one side of a boundary.
12. Closed Half-Plane- The solution of a linear inequality that includes the boundary line.
13. Open Half-Plane- The solution of a linear inequality that does not include the boundary line.
Test #6
6-1
1. System of Equations- A set of equations with the same variable.
2. Consistent- A system of equations that has at least one ordered pair that satisfies both equations.
3. Independent- A system of equations with exactly one solution.
4. Dependent- A system of equations that has an infinite number of solutions.
5. Inconsistent- A system of equations with no ordered pair that satisfy both equations.
6-2
6. Substitution- Use algebraic methods to find an exact solution of a system of equations.
6-3
7. Elimination- The use of addition or subtraction to eliminate on variable and solve a system of equations.
6-4 None
6-5 None
6-6
Systems of Inequalities- A set of two or more inequalities with the same variables.Test #7
7.1
1. Monomial- A number, a variable, or a product of a number and one or more variables.
2. Constant- A monomial that is a real number.
7-2
3. Zero Exponent- For any nonzero number a, a0=1. Any nonzero number raised to the zero power is equal to 1.
4. Negative Exponent- For any real number a≠0 and any integer n, and
5. Order of Magnitude- The order of magnitude of a quantity is the number rounded to the nearest power of 10.
7-3
6. Rational Exponents- For any positive real number b and any integers m and n>1, .
7. Cube Root- If a3=b, then a is the cube root of b.
8. nth Root- If an=b for a positive integer n, then a is an nth root of b.
9. Exponential Equation- An equation in which he variable occur as exponents.
7-4
10. Scientific Notation- A number in scientific notation is expressed as a·10n, where 1≤a<10 and n is an integer.
7-5
11. Exponential Function- A function that can be described by an equation of the form y=ax, where a<0 and a≠1
12. Exponential Growth Functions- When an initial amount increases by the same percent over a given period of time.
13. Exponential Decay Functions- When an initial amount decreases by the same percent over a given period of time.
7-6
14. Compound Interest- A special application of exponential growth involving money.
7-7
15. Geometric Sequence- A sequence in which each term after the first is found by multiplying the previous term by a constant r, called the common ration.
16. Common Ratio- The ratio of successive terms of a geometric sequence.
7-8
17. Recursive Formula- Each term is formulated from one or more previous terms.
Test #8
8-1
1. Polynomial- A monomial or sum of monomials.
2. Binomial- The sum of two monomials.
3. Trinomial- The sum of three monomials.
4. Degree of a Monomial- The sum of the exponents of all its variables.
5. Degree of a Polynomial- The greatest degree of any term in the polynomial.
6. Standard form of a Polynomial- A polynomial that is written with the terms in order from greatest degree to least degree.
7. Leading Coefficient- The coefficient of the term with the highest degree in a polynomial.
8-2 None
8-3
8. FOIL method- To multiply two binomials, find the sum of the products of the first terms, the outer terms, the inner terms, and the last terms.
9. Quadratic Expression- An expression in one variable with a degree of 2 written in the form ax2+bx+c.
8-4 None
8-5
10. Factoring- To express a polynomial as the product of monomials and polynomials.
11. Factoring by Grouping- The use of the Distributive Property to factor some polynomials having four or more terms.
12. Zero Product Property- If the product of two factors is 0, then at least one of the factors must be 0.
8-6
13. Quadratic Equation- An equation of the form ax2+bx+c=0, where a≠0.
8-7
14. Prime Polynomial- A polynomial that cannot be written as a product of two polynomials with integral coefficients.
8-8
15. Difference of Two Squares- Two perfect squares separated by a subtraction sign.
8-9
16. Perfect Square Trinomials- A trinomial that is the square of a binomial.
Test #9
9-1
1. Quadratic Functions- An equation of the form ax2+bx+c, where a≠0.
2. Standard Form of a Quadratic Function- The standard form of a linear equation is f(x)=ax2+by+c, where a≠0.
3. Parabola- The graph of a quadratic function.
4. Axis of Symmetry- The vertical line containing the vertex of a parabola.
5. Vertex- The maximum or minimum point of a parabola.
6. Minimum- The lowest point on the graph of a curve.
7. Maximum- The highest point on the graph of a curve.
9-2
8. Double Root- The roots of a quadratic function that are the same number.
9-3
9. Transformation- A movement of a geometric figure.
10. Translation- A transformation where a figure is slid from one position to another without being turned.
11. Dilation- A transformation that alters the size of a figure, but not its shape.
12. Reflection- A transformation where a figure, line, or curve, is flipped across a line.
13. Vertex Form- A quadratic function in the form f(x)=a(x-h)2+k.
9-4
14. Completing the Square- Too add a constant term to a binomial of the form x2+bx so that the resulting trinomial is a perfect square.
9-5
15. Quadratic Formula- The solutions of a quadratic equation in the form , where a≠0, are given by the formula .
16. Discriminant- In the Quadratic Formula, the expression under the radical sign, b2-4ac.
9-6 None
9-7
17. Step Function- A function with a graph that is a series of horizontal line segments.
18. Piecewise-Linear Function- A function written using two or more linear expressions.
19. Greatest Integer Function- A step function, written as , where f(x) is the greatest integers less than or equal to x.
20. Absolute Value Function- A function written as f(x)=|x|, in which f(x)≥0 for all values of x.
21. Piecewise-Defined Function- A function that is using two or more expressions.
Test #10
10-1
1. Square Root Function- Function that contains the square root of a variable.
2. Radical Function- A function that contains radicals with variable in the radicand.
3. Radicand- The expression that is under the radical sign.
10-2
4. Radical Expression- An expression that contains a square root.
5. Rationalize the Denominator- A method used to eliminate radicals from the denominator of a function.
6. Conjugates- Binomials of the form and .
10-3 None
10-4
7. Radical Equations- Equations that contain radicals with variables in the radicand.
8. Extraneous Solutions- Results that are not solutions to the original equation.
10-5
9. Hypotenuse- The side opposite the right angle in a right triangle.
10. Legs- The sides of a right triangle that form the right angle.
11. Converse- The statement formed by exchanging the phrases after if and then of in if-then statement.
12. Pythagorean Triple- Counting numbers that satisfy the Pythagorean Theorem.
10-6
13. Trigonometry- The study of the properties of triangles and trigonometric functions and their applications.
14. Trigonometric Ratio- A ration of the lengths of sides of a right triangle.
15. Sine- For an acute angle of a right triangle, the ratio of the measure of the leg opposite the acute angle to the measure of the hypotenuse.
16. Cosine- For an acute angle of a right triangle, the ratio of the measure of the leg adjacent of the acute angle to the measure of the hypotenuse.
17. Tangent- For an acute angle of a right triangle. The ratio of the measure of the leg opposite the acute angle to the measure of the leg adjacent to the acute angle.
18. Solving the Triangle- Finding the measures of all the angles and sides of a triangle.
19. Inverse Sine- If is an acute angle and the sine of A is x, then the in inverse sine of is the measure of
20. Inverse Cosine- If is an acute angle and the cosine of A is x, then the inverse cosine of x is the measure of .
21. Inverse Tangent- If is an acute angle and the tangent of A is x, then the inverse tangent of x is the measure of .
Test #11
11-1
1. Inverse Variation- An equation in the form xy=k, where k≠0.
2. Product Rule- If (x1, y1) and (x2, y2) are solutions to an inverse variation, then y1x1=y2x2
11-2
3. Rational Function- An equation in the form f(x)=p(x)/q(x), where p(x) and q(x) are polynomial functions and q(x) ≠0
4. Excluded Values- Any valunes of a variable that result in a denominator of 0 must be excluded from the domain of that variable.
5. Asymptote- A line that a graph approaches.
11-3
6. Rational Expression- An algebraic fraction with a numerator and denominator that re polynomials.
11-4 None
11-5 None
11-6
7. Least Common Multiple (LCM)- The least number that is a common multiple of two or more numbers.
8. Least Common Denominator (LCD)- The least common multiple of two or more numbers.
11-7
9. Mixed Expression- An expression that contains the sum of a monomial and a rational expression.
10. Complex Fraction- A fraction that has one or more fractions in the numerator or denominator.
11-8
11. Rational Equation- Equations that contain rational expressions.
12. Extraneous Solutions- Results that are not solutions to the original equation.
13. Work Problems- Rational equations are used to solve problems involving work rates.
14. Rate Problems- Problems in which an object moves at a certain speed or rate.
Test #12
Test #13
1-1
1. Algebraic Expression- An expression consisting of one or more numbers and variables along with one or more arithmetic operations.
2. Variables- 1. Symbols used to represent unspecified numbers or values. 2. A characteristic of a group of people or objects that can assume different values.
3. Term- A number, a variable, or the product or quotient of numbers and variables.
4. Factors- In an algebraic expression, the quantities being multiplied are called factors.
5. Product- In an algebraic expression, the result of quantities being multiplied is called the product.
6. Power- An expression of the form xn, read x to the nth power.
7. Exponent- In an expression of the form xn, the exponent is n. it indicates the number of times x is used as a factor.
8. Base- In an expression of the form xn, the base is x.
1-2
9. Evaluate- To find the value of an expression.
10. Order of Operations- Process used to solve mathematical expressions
1-3
11. Equivalent Expressions- Expressions that denote the same value for all values of the variable(s).
12. Additive Identity- For any number a, a+0=0+a=a
13. Multiplicative Identity- For any number a, a∙1=1∙a=a
14. Multiplicative Zero Property- The product of any number and zero is equal to 0.
15. Multiplicative Inverses- Two numbers with a product of 1.
16. Reciprocals- The Multiplicative inverse of a number.
17. Commutative Property- The order in which you add or multiply numbers does not change their sum or product.
18. Associative Property- The way you group three or more numbers when adding or multiplying does not change their sum or product.
19. Proof- A logical argument in which each statement you make is supported by a statement that is accepted as true.
1-4
20. Distributive Property- For any numbers a, b, and c, a(b+c) = ab+ac. And, for any numbers a, b, and c, (b+c)a = ba + ca.
21. Like Terms- Terms that contain the same variables, with corresponding variables having the same exponent.
22. Simplest Form- An expression is in simplest form when it is replaced by an equivalent expression having no like terms or parentheses.
23. Coefficient- The numerical factor of a term.
1-5
24. Open Sentence- A mathematical statement with one or more variables.
25. Equation- A mathematical sentence that contains an equals sign, =.
26. Solving- Finding a value for a variable that makes a sentence true.
27. Solution- A replacement value for the variable in an open sentence.
28. Replacement Set- A set of numbers from each which replacements for a variable may be chosen.
29. Set- A collection of objects or numbers that is often shown using braces.
30. Element- Each object or number in the set.
31. Solution Set- The set of elements from the replacement set that make an open sentence true.
32. Identity- An equation that is true for every value of the variable.
1-6
33. Coordinate System- The grid formed by the intersection of two number line, the horizontal axis and the vertical axis.
34. Coordinate Plane- The plane containing the x- and y-axes.
35. Y-Axis- The vertical number line on a coordinate plane.
36. X-Axis- The horizontal number line on a coordinate plane.
37. Origin- The point where the two axes intersect at their zero points.
38. Ordered Pair- A set of numbers or coordinates used to locate any point on a coordinate plane, written in the form (x, y).
39. X-Coordinate- The first number in an ordered pair.
40. Y-Coordinate- The second number in an ordered pair.
41. Relation- A set of ordered pairs.
42. Mapping- Illustrates how each element of the domain is paired with an element in the range.
43. Domain- The set of the first numbers of the ordered pairs in a relation.
44. Range- 1. The set of second numbers of the ordered pairs in a relation. 2. The difference between the greatest and least data values.
45. Independent Variable- The variable in a function with a value that is subject to choice.
46. Dependent Variable- The variable in a relation with a value that depends on the value of the independent variable.
1-7
47. Function- A relation in which each element of the domain is paired with exactly one element of the range.
48. Discrete Function- A function of points that are not connected.
49. Continuous Function- A function that can be graphed with a line or a smooth curve.
50. Vertical Line Test- If any vertical line passes through no more than one point of the graph of a relation, then the relation is a function.
51. Function Notation- A way to name a function that is defined by an equation. In function notation, the equations y=3x-8 is written as f(x)=3x-8.
52. Nonlinear Function- A function with a graph that is not a straight line.
1-8
53. Intercepts- Points on a graph where the graph intercepts and axis.
54. Y-Intercept- The y-coordinate of a point where a graph crosses the y-axis.
55. X-Intercept- The x-coordinate of a point where a graph crosses the x-axis.
56. Positive- A function is positive on a portion of its domain where its graph lies above the x-axis.
57. Negative- A function is negative on portion of its domain where its graph lies below the x-axis.
58. Increasing- The graph of a function goes up on a portion of its domain when viewed from left to right.
59. Decreasing- The graph of a function goes down on a portion of its domain when viewed from left to right.
60. Extrema- Points of relatively high or low function values.
61. Relative Minimum- The point with the least y-coordinate.
62. Relative Maximum- The point with the greatest y-coordinate.
63. End Behavior- Describes how the values of a function behave at each end of the graph.
Test #2
2-1
1. Formula- A Equation that states a rule for the relationship between certain quantities.
2-2
2. Solving an Equation- The process of finding all values of the variable that make the equation a true statement.
3. Equivalent Equations- Equations that have the same solution.
4. Subtraction Property of Equality- If an equation is true and the same number is subtracted from each side of the equation, the resulting equivalent equation is also true.
5. Multiplication Property of Equality- If an equation is true and each side is multiplied by the same nonzero number, the resulting equation is equivalent.
6. Division Property of Equality- If an equation is true and each side is divided by the same nonzero number, the resulting equation is equivalent.
2-3
7. Multi-Step Equation- Equations with more than one operation.
8. Consecutive Integers- Integers in counting order.
9. Number Theory- The study of numbers and the relationships between them.
2-4
10. Identities- An equation that is true for every value of the variable.
2-5 None
2-6
11. Ratio- A comparison of two numbers by division.
12. Proportion- An equation of the form a/b=c/d, where b≠0, stating that two ratios are equivalent.
13. Means- The middle terms of the proportion.
14. Extremes- In the ratio a/b=c/d, a and d are the extremes.
15. Rate-The ratio of two measurements having different units of measure.
16. Unit Rate- A ratio of two quantities, the second of which is one unit.
17. Scale- The relationship between the measurements on a drawing or model and the measurements of the real object.
18. Scale Model- A model used to represent an object that is too large or too small to be built at actual scale.
2-7
19. Percent of Change- When an increase or decrease is expressed as a percent.
20. Percent of Increase- The ratio of an amount of increase to the previous amount, expressed as a percent.
21. Percent of Decrease- The ratio of an amount of decrease to the previous amount, expressed as a percent.
2-8
22. Literal Equation- A formula or equation with several variables.
23. Dimensional Analysis- The process of carrying units throughout a computation.
24. Unit Analysis- The process of including units of measurement when computing.
2-9
25. Weighted Averages- The sum of the product of the number of units and the value per unit divided by the sum of the number of units represented by M.
26. Mixture Problems- Problems in which two or more parts are combined into a whole.
27. Uniform Motion Problems- Problems in which an object moves at a certain speed, or rate.
28. Rate Problems- Problems in which an object moves at a certain speed, or rate.
Test #3
3-1
1. Linear Equation- A equation in the form Ax+By=C, with a graph that is a straight line.
2. Standard Form- The standard form of a linear equation is Ax+By=C, where A≥0, A and B are not both zero, and A, B, and C are integers with a greatest common factor of 1.
3. Constant- A monomial that is a real number.
4. X-intercept- The x-coordinate of a point where a graph crosses the x-axis.
5. Y-intercept- The y-coordinate of a point where a graph crosses the y-axis.
3-2
6. Linear Function- A function with ordered pairs that satisfy a linear equation.
7. Parent Function-
8. Family of Graphs- Graphs and equations of graphs that have at least one characteristic in common.
9. Root- The solutions of a quadratic equation.
10. Zeros- The x-intercepts of the graph of a function; the points for which f(x)=0.
3-3
11. Rate of Change- How a quantity is changing with respect to a change in another quantity.
12. Slope- The ratio of the change in the y-coordinates (rise) to the corresponding change in the x coordinates (run) as you move from one point to another along the line.
3-4
13. Direct Variation- A equation of the form y=kx, where k is not equal to zero.
14. Constant of Variation- The number k in equations of the form y=kx.
15. Constant of Proportionality- Another term for constant of variation.
3-5
16. Sequence- A set of numbers in a specific order.
17. Terms of the Sequence- The numbers in a sequence.
18. Arithmetic Sequence- A numerical pattern that increases or decreases at a constant rate or value. The difference between successive terms of the sequence is constant.
19. Common Difference- The difference between the terms in an arithmetic sequence.
3-6 None
Test #4
4-1
1. Slope Intercept Form- An equation of the form y=mx+b, where m is the slope and b is the y-intercept.
2. Constant Functions- A linear function in the form y=b.
4-2
3. Constraint- A condition that a solution must satisfy. Equations can be viewed as constraints in a problem situation. The solutions of the equation meet the constraints of the problem.
4. Linear Extrapolation- The use of a linear equation to predict values that are outside the range of data.
4-3
5. Point-Slope Form- An equation of the form y-y1=m(x-x1), where m is the slope and (x1, y1) is a given point on a nonvertical line.
4-4
6. Parallel Lines- Lines in the same plane that do not intersect and either have the same slope or are vertical.
7. Perpendicular Lines- Lines that intersect to form a right angle.
4-5
8. Bivariate Data- Data with two variables.
9. Scatter Plot- Shows the relationship between a set of data with two variables, graphed as ordered pairs on a coordinate plane.
10. Line of Fit- A line that describes the trend of data in a scatter plot.
11. Linear Interpolation- The use of a linear equation to predict values that are inside the data range.
4-6
12. Best-Fit Line- The line that most closely approximates the data in a scatter plot.
13. Linear Regression- An algorithm to find a precise line of fit for a set of data.
14. Correlations Coefficient- A value that shoes how close data points are to a line.
15. Residual- The difference between an observed y-value and its predicted y-value on a regression line.
16. Median-Fit Line- A type of best-fit line that is calculated using the medians and the coordinates of data points.
4-7
17. Inverse Relation- A set of ordered pairs obtained by exchanging the x-coordinates with the y-coordinates of each ordered pair in a relation.
Test #5
5-1
1. Inequality- An open sentence that contains the symbol <, ≤, >, or ≥.
2. Addition Property of Inequalities- If the same number is added to each side of a true inequality, the resulting inequality is also true.
3. Set-Builder Notation- A concise way of writing a solution set. For example, {t|t<17} represents the set of all numbers t such that t is less than 17.
4. Subtraction Property of Inequalities- If the same number is subtracted from each side of a true inequality, the resulting inequality is also true.
5-2
5. Multiplication Property of Inequalities- If both sides of an inequality that is true are multiplied by a positive number, the resulting inequality is also true. If both sides of an inequality that is true are multiplied by a negative number, the direction of the inequality sign is reversed to make the resulting inequality also true.
6. Division Property of Inequalities- If both sides of a true inequality are divided by a positive number, the resulting inequality is also true. If both sides of a true inequality are divided by a negative number, the direction of the inequality sign is reversed to make the resulting inequality also true.
5-3 None
5-4
7. Compound Inequality- Two or more inequalities that are connected by words and or or.
8. Intersection- The graph of a compound inequality containing and; the solution is the set of elements common to both inequalities.
9. Union- The graph of a compound inequality containing or; the solution is a solution of either inequality, not necessarily both.
5-5 None
5-6
10. Boundary- A line or curve that separates the coordinate plane into regions.
11. Half-Planes- The region of the graph of an inequality on one side of a boundary.
12. Closed Half-Plane- The solution of a linear inequality that includes the boundary line.
13. Open Half-Plane- The solution of a linear inequality that does not include the boundary line.
Test #6
6-1
1. System of Equations- A set of equations with the same variable.
2. Consistent- A system of equations that has at least one ordered pair that satisfies both equations.
3. Independent- A system of equations with exactly one solution.
4. Dependent- A system of equations that has an infinite number of solutions.
5. Inconsistent- A system of equations with no ordered pair that satisfy both equations.
6-2
6. Substitution- Use algebraic methods to find an exact solution of a system of equations.
6-3
7. Elimination- The use of addition or subtraction to eliminate on variable and solve a system of equations.
6-4 None
6-5 None
6-6
Systems of Inequalities- A set of two or more inequalities with the same variables.Test #7
7.1
1. Monomial- A number, a variable, or a product of a number and one or more variables.
2. Constant- A monomial that is a real number.
7-2
3. Zero Exponent- For any nonzero number a, a0=1. Any nonzero number raised to the zero power is equal to 1.
4. Negative Exponent- For any real number a≠0 and any integer n, and
5. Order of Magnitude- The order of magnitude of a quantity is the number rounded to the nearest power of 10.
7-3
6. Rational Exponents- For any positive real number b and any integers m and n>1, .
7. Cube Root- If a3=b, then a is the cube root of b.
8. nth Root- If an=b for a positive integer n, then a is an nth root of b.
9. Exponential Equation- An equation in which he variable occur as exponents.
7-4
10. Scientific Notation- A number in scientific notation is expressed as a·10n, where 1≤a<10 and n is an integer.
7-5
11. Exponential Function- A function that can be described by an equation of the form y=ax, where a<0 and a≠1
12. Exponential Growth Functions- When an initial amount increases by the same percent over a given period of time.
13. Exponential Decay Functions- When an initial amount decreases by the same percent over a given period of time.
7-6
14. Compound Interest- A special application of exponential growth involving money.
7-7
15. Geometric Sequence- A sequence in which each term after the first is found by multiplying the previous term by a constant r, called the common ration.
16. Common Ratio- The ratio of successive terms of a geometric sequence.
7-8
17. Recursive Formula- Each term is formulated from one or more previous terms.
Test #8
8-1
1. Polynomial- A monomial or sum of monomials.
2. Binomial- The sum of two monomials.
3. Trinomial- The sum of three monomials.
4. Degree of a Monomial- The sum of the exponents of all its variables.
5. Degree of a Polynomial- The greatest degree of any term in the polynomial.
6. Standard form of a Polynomial- A polynomial that is written with the terms in order from greatest degree to least degree.
7. Leading Coefficient- The coefficient of the term with the highest degree in a polynomial.
8-2 None
8-3
8. FOIL method- To multiply two binomials, find the sum of the products of the first terms, the outer terms, the inner terms, and the last terms.
9. Quadratic Expression- An expression in one variable with a degree of 2 written in the form ax2+bx+c.
8-4 None
8-5
10. Factoring- To express a polynomial as the product of monomials and polynomials.
11. Factoring by Grouping- The use of the Distributive Property to factor some polynomials having four or more terms.
12. Zero Product Property- If the product of two factors is 0, then at least one of the factors must be 0.
8-6
13. Quadratic Equation- An equation of the form ax2+bx+c=0, where a≠0.
8-7
14. Prime Polynomial- A polynomial that cannot be written as a product of two polynomials with integral coefficients.
8-8
15. Difference of Two Squares- Two perfect squares separated by a subtraction sign.
8-9
16. Perfect Square Trinomials- A trinomial that is the square of a binomial.
Test #9
9-1
1. Quadratic Functions- An equation of the form ax2+bx+c, where a≠0.
2. Standard Form of a Quadratic Function- The standard form of a linear equation is f(x)=ax2+by+c, where a≠0.
3. Parabola- The graph of a quadratic function.
4. Axis of Symmetry- The vertical line containing the vertex of a parabola.
5. Vertex- The maximum or minimum point of a parabola.
6. Minimum- The lowest point on the graph of a curve.
7. Maximum- The highest point on the graph of a curve.
9-2
8. Double Root- The roots of a quadratic function that are the same number.
9-3
9. Transformation- A movement of a geometric figure.
10. Translation- A transformation where a figure is slid from one position to another without being turned.
11. Dilation- A transformation that alters the size of a figure, but not its shape.
12. Reflection- A transformation where a figure, line, or curve, is flipped across a line.
13. Vertex Form- A quadratic function in the form f(x)=a(x-h)2+k.
9-4
14. Completing the Square- Too add a constant term to a binomial of the form x2+bx so that the resulting trinomial is a perfect square.
9-5
15. Quadratic Formula- The solutions of a quadratic equation in the form , where a≠0, are given by the formula .
16. Discriminant- In the Quadratic Formula, the expression under the radical sign, b2-4ac.
9-6 None
9-7
17. Step Function- A function with a graph that is a series of horizontal line segments.
18. Piecewise-Linear Function- A function written using two or more linear expressions.
19. Greatest Integer Function- A step function, written as , where f(x) is the greatest integers less than or equal to x.
20. Absolute Value Function- A function written as f(x)=|x|, in which f(x)≥0 for all values of x.
21. Piecewise-Defined Function- A function that is using two or more expressions.
Test #10
10-1
1. Square Root Function- Function that contains the square root of a variable.
2. Radical Function- A function that contains radicals with variable in the radicand.
3. Radicand- The expression that is under the radical sign.
10-2
4. Radical Expression- An expression that contains a square root.
5. Rationalize the Denominator- A method used to eliminate radicals from the denominator of a function.
6. Conjugates- Binomials of the form and .
10-3 None
10-4
7. Radical Equations- Equations that contain radicals with variables in the radicand.
8. Extraneous Solutions- Results that are not solutions to the original equation.
10-5
9. Hypotenuse- The side opposite the right angle in a right triangle.
10. Legs- The sides of a right triangle that form the right angle.
11. Converse- The statement formed by exchanging the phrases after if and then of in if-then statement.
12. Pythagorean Triple- Counting numbers that satisfy the Pythagorean Theorem.
10-6
13. Trigonometry- The study of the properties of triangles and trigonometric functions and their applications.
14. Trigonometric Ratio- A ration of the lengths of sides of a right triangle.
15. Sine- For an acute angle of a right triangle, the ratio of the measure of the leg opposite the acute angle to the measure of the hypotenuse.
16. Cosine- For an acute angle of a right triangle, the ratio of the measure of the leg adjacent of the acute angle to the measure of the hypotenuse.
17. Tangent- For an acute angle of a right triangle. The ratio of the measure of the leg opposite the acute angle to the measure of the leg adjacent to the acute angle.
18. Solving the Triangle- Finding the measures of all the angles and sides of a triangle.
19. Inverse Sine- If is an acute angle and the sine of A is x, then the in inverse sine of is the measure of
20. Inverse Cosine- If is an acute angle and the cosine of A is x, then the inverse cosine of x is the measure of .
21. Inverse Tangent- If is an acute angle and the tangent of A is x, then the inverse tangent of x is the measure of .
Test #11
11-1
1. Inverse Variation- An equation in the form xy=k, where k≠0.
2. Product Rule- If (x1, y1) and (x2, y2) are solutions to an inverse variation, then y1x1=y2x2
11-2
3. Rational Function- An equation in the form f(x)=p(x)/q(x), where p(x) and q(x) are polynomial functions and q(x) ≠0
4. Excluded Values- Any valunes of a variable that result in a denominator of 0 must be excluded from the domain of that variable.
5. Asymptote- A line that a graph approaches.
11-3
6. Rational Expression- An algebraic fraction with a numerator and denominator that re polynomials.
11-4 None
11-5 None
11-6
7. Least Common Multiple (LCM)- The least number that is a common multiple of two or more numbers.
8. Least Common Denominator (LCD)- The least common multiple of two or more numbers.
11-7
9. Mixed Expression- An expression that contains the sum of a monomial and a rational expression.
10. Complex Fraction- A fraction that has one or more fractions in the numerator or denominator.
11-8
11. Rational Equation- Equations that contain rational expressions.
12. Extraneous Solutions- Results that are not solutions to the original equation.
13. Work Problems- Rational equations are used to solve problems involving work rates.
14. Rate Problems- Problems in which an object moves at a certain speed or rate.
Test #12
Test #13