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100 Facts - Mrs. Kerr's 7th Grade Math |
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100 FACTS FOR ALGEBRA I
CHAPTER 1 1. A variable is a letter that is used to represent one or more numbers. 2. The numbers are the values of the variables. 3. A variable expression is a collection of numbers, variables, and operations. 4. Replacing each variable in an expression by a number is called evaluating the expression. 5. The distance formula is distance equals rate times time (d=rt). 6. The order of operations are grouping symbols, exponents, multiply and divide (left to right), and add and subtract (left to right). 7. An equation is a statement formed when an equals sign is placed between two expressions. 8. A solution is anything making an equation true. 9. An inequality is a mathematical sentence formed by placing an inequality symbol between to expressions. 10. A function is a rule that establishes a relationship between two quantities. 11. A collection of input values is the domain. 12. A collection of output values is the range. CHAPTER TWO 13. Absolute value is the distance a number is from zero. 14. Two points that are the same distance from the origin are opposites. 15. The speed of an object is the value of its velocity. Velocity indicates both speed and direction. 16. The order in which two numbers are added does not change the sum is called the commutative property. 17. The way you group numbers when adding or multiplying does not change the sum or product explains the associative property. 18. The sum of a number and zero is zero describes the identity property. (Also, the product of a number and one equals the value of the first factor describes the identity property.) 19. A matrix is a rectangular arrangement of numbers into horizontal rows and vertical columns. 20. Each number in a matrix is called an entry or element. 21. The product of a number and zero is zero demonstrates the property of zero. 22. When multiplying or dividing integers with the same sign the answer is always positive. 23. When multiplying or dividing integers with different signs the answer is always negative. 24. a(b+c)=ab+ac demonstrates the distributive property. 25. In a term that is the product of a variable and a number, the number is called a coefficient. 26. Like terms are terms that have the same variables raised to the same power. 27. Constant terms are terms without variable parts. 28. An expression is simplified if it has no grouping symbols and if all the like terms have been combined. 29. The product of a number and its reciprocal is one. 30. The probability of an event is a measure of the likelihood that the event will occur. 31. When you do a probability experiment, the different possible results are called outcomes. CHAPTER 3 32. An inverse operation is an operation that "undoes" another operation. 33. An identity is an equation that is true for all values of the variable. 34. Interest equals principle times rate times time (I=prt). 35. A formula is algebraic equation that relates two or more real-life quantities. 36. A unit rate is a rate per one given unit. 37. When you reach a conclusion, called a generalization, based on observations you are using inductive reasoning. 38. When you use facts, definitions, rules, or properties to reach a conclusion, you are using deductive reasoning. CHAPTER 4 39. A coordinate plane is formed by the intersection of a horizontal and a vertical number line. 40. The horizontal number line of the coordinate plane is called the x-axis and the vertical number line is called the y-axis. 41. Points on a number line can be described by an address called an ordered pair. 42. The first number in an ordered pair is called the x-coordinate. The second number in an ordered pair is called the y-coordinate. 43. The graph of an equation in x and y is the set of all points (solutions) that make an equation true. 44. The graph of x=a is a vertical line. 45. The graph of y=b is a horizontal line. 46. The x-intercept is the x-coordinate where the graph crosses the x-axis. The y-intercept is the y-coordinate where the graph crosses the y-axis. 47. The slope of a line is the number of units a line rises or falls for each unit of horizontal change from left to right. 48. A linear equation in slope-intercept form is y = mx + b. 49. The formula for slope is m = (y2 - y1)/(x2 - x1). You can also find slope by figuring rise/run. 50. A horizontal line has a slope of zero. 51. A vertical line's slope is called undefined. 52. The equation for direct variation is y = kx. 53. Two quantities that vary directly are said to have direct variation. 54. The "m" in slope-intercept form is the slope. 55. The "b" in slope-intercept form is the y-intercept. 56. A set of ordered pairs is called a relation. 57. In a function, each input has only one output. 58. One way to test for functions is a vertical line test. CHAPTER 5 59. The point-slope form of an equation is (y-y1) = m(x-x1). 60. The standard form of an equation is Ax + By = C. CHAPTER 6 61. When dividing an inequality by a negative number, the inequality reverses. 62. A compound inequality consists of two inequalities connected by "and" or "or." 63. The mean of a set of data is the average. 64. The median of a set of data is the middle number or the average of the two middle numbers. 65. The mode of a set of data is the number or item that occurs most often. 66. In a box-and-whisker plot, the second quartile is the median of the given data. 67. The first quartile is the median of the lower half of the data. 68. The third quartile is the median of the upper half of the data. CHAPTER 7 69. The solution of a system of equation is the ordered pair that simultaneously makes all equations true. 70. You can solve a system of equations by using any of the following methods: graphing and checking, substituting, or using linear combinations. 71. If the lines in a system of equations intersect, there is one solution. 72. If the lines in a system of equations are parallel, there are no solutions. 73. If the lines in a system of equations coincide, there are an infinite number of solutions. CHAPTER 8 74. When multiplying two powers that have the same base, you add the exponents. 75. To find the power of a power, multiply the exponents. 76. When a nonzero number is raised to the zero power, the answer is one. 77. a-n is the reciprocal of an. 78. A negative number raised to an odd power will result in a negative number. 79. A negative number raised to an even power will result in a positive number. 80. A number is written in scienctific notation if it is in the form of c X 10n where c is a number between 1 and 10 and n i an integer. CHAPTER 9 81. Numbers whose square roots are integers or quotients of integers are called perfect squares. 82. An irrational number is a number that cannot be written as a quotient of two integers. 83. A quadratic equation is an equation that can be written in the following form: ax2 + bx + c = 0, what a cannot be zero. 84. In standard form, a is the leading coefficient. 85. A quadratic equation has a u-shaped graph called a parabola. 86. The roots of a quadratic equation are the x-intercepts. 87. The quadric formula can be used to solve any quadratic equation and is: x equals negative b, plus or minus the square root of b squared minus 4ac, all over 2a. CHAPTER 10 88. The degree of each term of a polynomial is the exponent of the variable. 89. The degree of a polynomial is the largest degree of its terms. 90. The leading coefficient is the first coefficient in a polynomial written in standard form. 91. A polynomial with only one term is called a monomial. 92. A polynomial with two terms is called a binomial. 93. A polynomial with three terms is called a trinomial. 94. The FOIL pattern for factoring is First, Outside, Inside and Last. 95. A polynomial is in factored form if it is written as the product of two or more linear factors. Geometry 96. The distance around a polygon is called the perimeter. 97. The space inside a polygon is called the area. 98. The space inside a three-dimensional figure is called the volume. 99. The sum of the areas of the polygons that make a three-dimensional figure is called surface area. 100. The formula for the Pythagorean Theory is a2 + b2 = c2 .
100 Facts (Plus One) for Math Course 2 Chapter One 1. The order of operations are grouping symbols, exponents, multiply and divide from left to right, and add and subtract from left to right. 2. An exponent is a number that represent how many times a base is used as a factor in a repeated multiplication. 3. A power consists of a base and an exponent. 4. A variable is a symbol, usually a letter, used to represent an unknown number. 5. A variable expression consists of letters, numbers, and at least one operation. 6. The answer to an addition problem is called the sum. The answer to a subtraction problem is called the difference. The answer to a multiplication problem is called the product. The answer to a division problem is called the quotient. 7. A solution is any value you can substitute for a variable making an equation true. Chapter 13 8. The possible results of an experiment are called outcomes. 9. The measure of the likelihood that an event will occur is called probability. 10. To find the probability of an event, divide the number of favorable outcomes by the total number of outcomes. Chapter 3 11. The mean is the average in a set of data. 12. The median is the middle number in a set of data arranged in increasing order. 13. The mode is the value that occurs the most often in a set of data. Chapter 2 14. The four place values following the decimal are tenths, hundredths, thousandths, and ten-thousandths. 15. The leading digit of a number is the first non-zero digit. 16. Scientific notation is a way of writing large numbers by using a number between one and ten multiplied by a power of ten. (C x 10n) 17. The metric system is a decimal system of measurement. 18. The meter is the basic unit of length in the metric system. The gram is the basic unit of mass in the metric system. The liter is the basic unit of capacity in the metric system. 19. The following pre-fixes associated with the metric system are placed in order by place value: kilo-, hecto-, deka-, liter/meter/gram, deci-, centi-, milli-. Chapter 4 20. A prime number is a whole number greater than one whose only factors are one and itself. 21. A composite number is a whole number greater than one that has more factors than one and itself. 22. Expressing whole numbers as a product of prime numbers is called prime factorization. A way to do this is by using a factor tree. 23. The greatest common factor is the largest number that “goes into” two or more numbers. 24. The least common multiple is the smallest matching product for two or more numbers. 25. Two or more numbers are relatively prime if their greatest common factor is one. 26. A fraction is a number in the form of a/b where b cannot be zero. 27. The numerator is the top number in a fraction. The denominator is the bottom number in a fraction. 28. A fraction is in simplest or reduced form when the GCF of the numerator and denominator is one. 29. An improper fraction is when the numerator is larger than the denominator. Chapter 5 30. Two non-zero numbers whose product is one are reciprocals (or multiplicative inverses). A reciprocal is found quickly by flipping a fraction upside-down. 31. There are 8 ounces (oz) in a cup, 2 cups in a pint (pt), 2 pints in a quart (qt), and 4 quarts in a gallon (gal). 32. There are 12 inches (in) in a foot (ft), 3 feet in a yard (yd), and 5280 feet in a mile (mi). 33. There are 16 ounces in a pound (lb) and 2000 pounds in a ton. Geometry 34. The distance around a polygon is called the perimeter. 35. The space inside a polygon is called area. 36. The sum of the areas of the polygons that make a three-dimensional figure is called surface area. 37. The space inside a three-dimensional figure is called volume. 38. A prism is a three-dimensional figure that has two parallel and congruent bases in the shape of polygons. 39. A cylinder is a three-dimensional figure with two parallel congruent circular bases. 40. To bisect something is to divide something into two congruent parts. 41. Two lines on a plane that will never intersect are said to be parallel. 42. Congruent angles are two angles that have the same measure.. 43. The sum of supplementary angles equal 180°. The sum of complimentary angles equal 90°. 44. Adjacent angles are angles that share one side. 45. The vertex is the common endpoint of the rays forming an angle. 46. Alternate interior angles are angles that are diagonally across from each other in a quadrilateral. 47. An equilateral triangle has three congruent sides and three congruent angles. 48. An isosceles triangle has two congruent sides and two congruent angles. 49. A scalene triangle has no congruent sides or angles. 50. The sum of the interior angles of a triangle equal 180 degrees. 51. The formula for the Pythagorean Theorum is a2 + b2 = c2. 52. In a right triangle, the side opposite the right angle is called the hypotenuse. 53. A translation is a method of sliding a pattern to create the same change on opposite sides of a polygon. 54. Rotation is when a shape is turned clockwise or counter-clockwise. 55. Reflection is when a shape is flipped over or mirrored across a line of symmetry. 56. Degrees are the most common unit of measurement for angles. 57. A tool used for measuring angles is a protractor. 58. A polygon with four sides is a quadrilateral. A polygon with five sides is a pentagon. A polygon with six sides is a hexagon. A polygon with seven sides is a heptagon. A polygon with eight sides is an octagon. A polygon with nine sides is a nonagon. A polygon with ten sides is a decagon. 59. A quadrilateral with two parallel and congruent sides is a parallelogram. 60. A parallelogram with four right angles is a rectangle. 61. A parallelogram with four congruent sides is a rhombus. 62. A rectangle with four congruent sides is a square. A square is also a kind of rhombus. 63. A trapezoid is a quadrilateral with one set of parallel sides. 64. The formula for the perimeter of a square is P = 4s (perimeter equals four times the side length). 65. The formula for the area of a rectangle or parallelogram is A = lw (area equals length times width). 66. The formula for the area of a square is A = s2 (area equals side length squared). 67. The x-axis is the horizontal number line in a coordinate plane. The y-axis is the vertical number line in a coordinate plane. 68. The x and y axis meet at the origin (0, 0). 69. Points on a coordinate plane are represented by ordered pairs (x,y). 70. The first number in an ordered pair is the x-coordinate. The second number in an ordered pair is the y-coordinate. Chapter 6 71. Absolute value is the distance between a number and zero. 72. Opposites are integers that are the same distance from zero. 73. When multiplying and dividing integers that have the same sign, the answer is positive. When multiplying and dividing integers that have different signs, the answer is negative. 74. An algebraic model for the Commutative Property of Addition is a + b = b + a. The Commutative Property of Addition is a rule that says you can add terms in any order and the sum will not change. 75. An algebraic model for the Commutative Property of Multiplication is ab= ba. The Commutative Property of Multiplication is a rule that says you can multiply terms in any order and the sum will not change. 76. An algebraic model for the Associative Property of Addition is (a + b) + c = a + (b + c). The Associative Property of Addition is a rule that says changing the grouping of terms will not change the sum. 77. An algebraic model for the Associative Property of Multiplication is (ab)c = a(bc). The Associative Property of Multiplication is a rule that says changing the grouping of terms will not change the product. 78. The sum of a number and its opposite is zero and demonstrates the Inverse Property of Addition. 79. The product of a number and its reciprocal is one and demonstrates the Inverse Property of Multiplication. 80. The sum of a number and zero is the number and demonstrates the Identity Property of Addition. 81. The product of a number and one is the number and demonstrates the Identity Property of Multiplication. 82. An algebraic model for the Distributive Property is a(b + c) = ab + bc. CHAPTER 7 83. A mathematical sentence formed by setting two expressions equal is called an equation. 84. Parts of an expression are called terms. 85. Terms that have identical variable parts are called like terms. 86. The coefficient of a term that has a variable is the number part of the term. 87. A term that has no variable part is called a constant term. 88. An inverse operation is an operation that "undoes" another operation. 89. The distance formula is distance equals rate times time (d=rt). 90. Whatever you do to one side of an equation, you must do to the other. 91. An inequality is a mathematical sentence formed by placing an inequality symbol between to expressions. 92. The set of all input values is the domain. The set of all output values is the range. CHAPTER 8 93. A solution of an equation is any number(s) making an equation true. 94. A ratio used division to compare two numbers. 95. Two ratios are equivalent ratios when they have the same value. 96. A rate is a ratio measured in two different units. 97. A unit rate is a rate that has a denominator of one unit. To change ratio to a unit rate or to change a fraction to a decimal, divide top by bottom. 98. A proportion is an equation that states two ratios are equivalent. To find an unknown in a proportion, use cross products. CHAPTER 9 99. The word percent means "per hundred." 100. For percent proportion problems, write % over 100 equals "is" over "of." 101. The formula for interest is Interest equals principal times rate times time (I=prt).
100 FACTS FOR PRE-ALGEBRA GEOMETRY 1. The distance around a polygon is called the perimeter. 2. The space inside a polygon is called area. 3. The sum of the areas of the polygons that make a three-dimensional figure is called surface area. 4. The space inside a three-dimensional figure is called volume. 5. A prism is a three-dimensional figure that has two parallel and congruent bases in the shape of polygons. 6. A cylinder is a three-dimensional figure with two parallel congruent circular bases. 7. To bisect something is to divide something into two congruent parts. 8. Two lines on a plane that will never intersect are said to be parallel. 9. Congruent angles are two angles that have the same measure.. 10. The sum of supplementary angles equal 180°. 11. The sum of complimentary angles equal 90°. 12. Adjacent angles are angles that share one side. 13. The vertex is the common endpoint of the rays forming an angle. 14. If you extend the side of a polygon, an exterior angle is formed. 15. Alternate interior angles are angles that are diagonally across from each other in a quadrilateral. 16. An equilateral triangle has three congruent sides and three congruent angles. 17. An isosceles triangle has two congruent sides and two congruent angles. 18. A scalene triangle has no congruent sides or angles. 19. The sum of the interior angles of a triangle equal 180 degrees. 20. The formula for the Pythagorean Theorem is a2 + b2 = c2. 21. In a right triangle, the side opposite the right angle is called the hypotenuse. 22. A translation is a method of sliding a pattern to create the same change on opposite sides of a polygon. 23. Rotation is when a shape is turned clockwise or counter-clockwise. 24. Reflection is when a shape is flipped over or mirrored across a line of symmetry. 25. Degrees are the most commen unit of measurement for angles. 26. A tool used for measuring angles is a protractor. 27. A tool used for constructing given angles and/or circles is a compass. 28. A polygon with four sides is a quadrilateral. A polygon with five sides is a pentagon. A polygon with six sides is a hexagon. A polygon with seven sides is a heptagon. A polygon with eight sides is an octagon. A polygon with nine sides is a nonagon. A polygon with ten sides is a decagon. 29. A quadrilateral with two parallel and congruent sides is a parallelogram. 30. A parallelogram with four right angles is a rectangle. 31. Acute angles are less than 90 degrees. Straight angles are exactly 180 degrees. Obtuse angles are more than 90 degrees. Right angles are exactly 90 degrees.
CHAPTER 1 33. A variable is a letter that is used to represent one or more numbers. 34. The numbers are the values of the variables. 35. A variable expression is a collection of numbers, variables, and operations. 36. Replacing each variable in an expression by a number is called evaluating the expression. 37. The distance formula is distance equals rate times time (d=rt). 38. The order of operations are grouping symbols, exponents, multiply and divide (left to right), and add and subtract left to right). 39. An equation is a statement formed when an equals sign is placed between two expressions. 40. A solution is anything making an equation true. 41. An inequality is a mathematical sentence formed by placing an inequality symbol between to expressions. 42. A function is a rule that establishes a relationship between two quantities. 43. A collection of input values is the domain. 44. A collection of output values is the range. CHAPTER TWO 45. Absolute value is the distance a number is from zero. 46. Two points that are the same distance from the origin are opposites. 47. The speed of an object is the value of its velocity. Velocity indicates both speed and direction. 48. The order in which two numbers are added does not change the sum is called the commutative property. 49. The way you group numbers when adding or multiplying does not change the sum or product explains the sociative property. 50. The sum of a number and zero is zero describes the identity property. (Also, the product of a number and one equals the value of the first factor describes the identity property.) 51. A matrix is a rectangular arrangement of numbers into horizontal rows and vertical columns. 52. Each number in a matrix is called an entry or element. 53. The product of a number and zero is zero demonstrates the property of zero. 54. When multiplying or dividing integers with the same sign the answer is always positive. 55. When multiplying or dividing integers with different signs the answer is always negative. 56. a(b+c)=ab+ac demonstrates the distributive property. 57. In a term that is the product of a variable and a number, the number is called a coefficient. 58. Like terms are terms that have the same variables raised to the same power. 59. Constant terms are terms without variable parts. 60. An expression is simplified if it has no grouping symbols and if all the like terms have been combined. 61. The product of a number and its reciprocal is one. 62. The probability of an event is a measure of the likelihood that the event will occur. 63. When you do a probability experiment, the different possible results are called outcomes. CHAPTER 3 64. An inverse operation is an operation that "undoes" another operation. 65. An identity is an equation that is true for all values of the variable. 66. Interest equals principle times rate times time (I=prt). 67. A formula is algebraic equation that relates two or more real-life quantities. 68. A unit rate is a rate per one given unit. 69. When you reach a conclusion, called a generalization, based on observations you are using inductive reasoning. 70. When you use facts, definitions, rules, or properties to reach a conclusion, you are using deductive reasoning. CHAPTER 4 71. A coordinate plane is formed by the intersection of a horizontal and a vertical number line. 72. The horizontal number line of the coordinate plane is called the x-axis and the vertical number line is called the y-ais. 73. Points on a number line can be described by an address called an ordered pair. 74. The first number in an ordered pair is called the x-coordinate. The second number in an ordered pair is called the y-coordinate. 75. The graph of an equation in x and y is the set of all points (solutions) that make an equation true. 76. The graph of x=a is a vertical line. 77. The graph of y=b is a horizontal line. 78. The x-intercept is the x-coordinate where the graph crosses the x-axis. The y-intercept is the y-coordinate where the graph crosses the y-axis. 79. The slope of a line is the number of units a line rises or falls for each unit of horizontal change from left to right. 80. A linear equation in slope-intercept form is y = mx + b. 81. The formula for slope is m = (y2 - y1)/(x2 - x1). You can also find slope by figuring rise/run. 82. A horizontal line has a slope of zero. 83. A vertical line's slope is called undefined. 84. The equation for direct variation is y = kx. 85. Two quantities that vary directly are said to have direct variation. 86. The "m" in slope-intercept form is the slope. 87. The "b" in slope-intercept form is the y-intercept. 88. A set of ordered pairs is called a relation. 89. In a function, each input has only one output. 90. One way to test for functions is a vertical line test. CHAPTER 5 91. The point-slope form of an equation is (y-y1) = m(x-x1). 92. The standard form of an equation is Ax + By = C. CHAPTER 6 93. When dividing an inequality by a negative number, the inequality reverses. 94. A compound inequality consists of two inequalities connected by "and" or "or." 95. The mean of a set of data is the average. 96. The median of a set of data is the middle number or the average of the two middle numbers. 97. The mode of a set of data is the number or item that occurs most often. 98. In a box-and-whisker plot, the second quartile is the median of the given data. 99. The first quartile is the median of the lower half of the data. 100. The third quartile is the median of the upper half of the data.
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Belle Isle Enterprise Middle School
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