Unit 1 Basic Skills Review BEDMAS a way of remembering order of operations: Brackets, Exponents, Division, Multiplication, Addition, Subtraction Collect like terms gather all like terms and simplify as per operators (+ / -) Common factor a number that divides evenly into all the numbers in a set Equation a mathematical statement that says that two expressions are equal Evaluate to determine a value for an expression or formula Power of a Power Rule a power of a power can be written as a single power by multiplying the exponents: (x a ) b = x ab Product result of multiplying terms Product Rule to multiply powers of the same base, add the exponents: x a x b = x a+b Pythagorean Theorem in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the two shorter lengths: a 2 + b 2 = c 2 Quotient result of dividing terms Quotient Rule to divide powers of the same base, subtract the exponents: x a x b = x a b Simplify find a simpler or shorter equivalent expression Sum result of adding terms
Unit 2 Powers and Polynomials Algebraic expression a mathematical phrase made up of numbers and variables, connected by addition or subtraction operators Base (of a power) the number used as a factor for repeated multiplication Binomial a polynomial made up of two terms Coefficient the number by which a variable is multiplied Degree of a polynomial the degree of the greatest-degree term Degree of a term the sum of the exponents on the variables in a term Distributive property multiplying all terms inside a bracket by the coefficient of the bracket: a(x + y) = ax + ay Exponent a raised number to denote repeated multiplication of a base Like terms terms that have the same variable(s) raised to the same exponent Like terms terms that have the same variable(s) raised to the same exponent Monomial a polynomial made up of one term Polynomial an algebraic expression formed by adding or subtracting terms Power a base (number, variable, or combination of the two) raised to an exponent Term a number or variable, or the product of numbers and variables Trinomial a polynomial made up of three terms Variable a letter used to represent a value that can change or vary
Unit 3 - Solving Equations and Modelling Word Problems Balance Method a way to rearrange variables using opposite operations; what is done to one side of the equation must be done on the other side of the equation. Constant term a term that contains no variables; its value does not change Equation a mathematical statement that says two expressions are equal Equivalent Expressions algebraic expressions that are equal for all values of the variable Formal Check separating the left side of the equation from the right side of the equation and checking the solution; if LS = RS, then solution is correct, if not, check for errors Formula an algebraic relationship between two or more variables Isolating a term / variable use opposite operations to move all other terms in the expression to the other side of the equations Opposite Operations used in solving for unknowns or isolating variables; opposite of add is subtract, opposite of multiply is divide, opposite of squaring a value is taking the square root of a value Roots another name for the solution to an equation Solution the value of the variable that makes an equation true Solve find the solution Substitute replace a variable with a value or term
UNIT 4 Modelling With Graphs Constant of variation in a direct variation, the ratio of corresponding values of the variables Dependent variable the variable whose value depends on the independent variable; on a coordinate grid, the values of the dependent variable are on the vertical axis Direct variation a relationship between two variables in which one variable is a constant multiple of the other First differences differences between consecutive y-values in tables with evenly spaced x-values Independent variable in a relation, the variable you need to know first; it determines the value of the dependent variable; on a coordinate grid, the values of the independent variable are on the horizontal axis Linear relation a relationship between two variables that appears as a straight line when graphed on the coordinate plane Negative slope the ratio of the rise to the run of a line that rises to the left Non-linear relation a relationship between two variables that is not a straight line when graphed Partial Variation a relationship between two variables in which one variable equals a constant multiple of the other, plus a constant value Positive slope the ratio of the rise to the run of a line that rises to the right Rate of Change a change in one quantity relative to the change in another quantity Rise the vertical distance between two points Run the horizontal distance between two points Slope a measure of the steepness of a line: slope = rise run
Unit 5 Analyze Linear Relations Horizontal line a line with a slope of 0; has the equation y = (any number) Linear system a set or two or more linear equations that are considered at the same time Negative reciprocals two numbers whose product is 1; 3 and 4 are negative reciprocals 4 3 ( 3 4 = 12 = 1 ) 4 3 12 Parallel lines lines on the same plane that never meet; parallel lines have the same slope Perpendicular lines lines that cross at 90 ; perpendicular lines have slopes which are negative reciprocals (their product is 1) Point of intersection the point where two lines cross Slope a measurement of the steepness of a line; slope = rise Vertical line a line with an undefined slope; has the equation x = (any number) x-intercept the coordinate of the point where a line or curve crosses the x-axis; at this point, y = 0 y-intercept the coordinate of the point where a line or curve crosses the y-axis; at this point, x = 0 run
Unit 6 Relations Correlation the relationship between or how things change between two variables Dependent variable the variable whose value depends on the independent variable; on a coordinate grid, the values of the dependent variable are on the vertical axis Extrapolate estimate a value beyond the range of a set of data Independent variable in a relation, the variable you need to know first; it determines the value of the dependent variable; on a coordinate grid, the values of the independent variable are on the horizontal axis Inference conclusion based on reasoning and data Interpolate estimate a value between two measurements in a set of data Line of Best Fit the straight line that passes through or near as possible to the points on a scatter plot Linear Regression a mathematical process used by graphing calculators to find the line of best fit Outlier a data point that does not fit the pattern of the other data Scatter Plot a graphs showing two-variable data as points plotted on a coordinate grid Trend a pattern seen in a graph of a set of data
Unit 7 - Geometric Relationships Acute angle an angle that measures less than 90 Alternate angles pairs of equal angles formed on either side of a transversal crossing a pair of parallel lines Bisect to divide into two equal parts Complementary angles angles whose sum is 90 Congruent identical in shape and size Corresponding angle pairs of equal angles in corresponding positions formed by a transversal crossing a pair of parallel lines Equilateral trinalge a triangle with all three sides equal Exterior angle an angle contained between one side of a polygon and the extension of an adjacent side Interior angle an angle that is formed inside a polygon by two sides meeting at a vertex Isosceles triangle a triangle with exactly two equal sides Median a line segment that joins a vertex of a triangle to the midpoint of the opposite side Midpoint the point that divides a line segment into two equal segments Obtuse angle an angle that measures more than 90 but less than 180. Opposite angles when two lines cross, the pairs of angles formed on either side Polygon a two dimensional closed figure whose sides are line segments Quadrilateral a four sided polygon Ray a part of a line with one endpoint Right angle an angle that measures 90 Right bisector a line that is perpendicular to a line segment and divides the line segment into two equal parts Scalene triangle a triangle with no equal sides Similar polygons in which corresponding sides lengths are proportional Supplementary angles angles whose sum is 180 Transversal a line that crosses or intersects two or more lines Triangle a three sided polygon Vertex a point at which two sides of a polygon meet
Unit 8 Measurement 2-Dimensional Shapes a shape that has only two dimensions; e.g. length and width 3-Dimensional Objects a shape with three dimensions; e.g. length, width, height Area the number of square units contained in a two-dimensional region Composite Shapes a figure made up of two or more simple shapes Cones a three-dimensional object with a circular base and a curved lateral surface that extends from the base to a point called the vertex Diameter a line segment, joining two points on the circumference, which passes through the center of a circle Hypotenuse the longest side of a right triangle Lateral faces the faces of a prism or pyramid that are not bases Length a measurement of a side of a figure Maximum the greatest value in a set of data Minimum the least value in a set of data Optimization the process of finding values that make a given quantity the greatest (or least) possible under certain conditions Perimeter the distance around the outside of a shape Prism a three dimensional object with two parallel congruent polygonal bases; prisms are named by the shape of their bases Pyramids a polyhedron whose base is a polygon and other faces are triangles that meet at a common vertex Pythagorean Theorem in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two shorter side lengths c 2 = a 2 + b 2 Radius a line segment joining the center of a circle to a point on the circumference, or the length of this line segment Slant height the height of a triangular face or side of a cone Spheres a round ball-shaped object Surface area the number of square units needed to cover the surface of a three-dimensional object, measured in square units Volume the amount of space that an object occupies, measured in cubic units Width - a measurement of a side of a figure