Grade 9 Math Exam Study Notes 484x2t

Math Exam Study Notes Linear: When a graph of a relation is a straight line. Direct Variation: has an equation of the y=mx, meaning that the line crosses the y-axis at 0. Fraction in Direct Variation: You must create new x. Y= ½ X New x -2 0 2

X -1 0 1

Y -1 0 1

Partial Variation: has an equation of the form y=mx+b and does not cross the y-axis at 0. Exponential Relationship: ∆2. Quadratic Relationship: ∆3. Parabola: formed when ∆3 occurs. Variable: an expression that can change a relation. Independent Variable: The variable that does not depend on the other (x) Dependent Variable: The variable that depends on the other variable (y). Conditions for linear relationships:

Rate Triangle: can be drawn between any two points. It determines how steep a line is. Definitions of slope: • • • Role of slope: The slop determines certain points on a line. The y-intercept also helps. Steeper line: slope is a higher number, meaning line is closer to y-axis. Vertical Lines: have an undefined slop because they have no y-intercept (b,0), and the equation of the line is x=b. Horizontal lines: have no x-intercept, and are parallel to the x-axis. Slope of 0 (0,a) and the equation of the line is y=a. Parallel lines: have same slope but different y-intercepts. Perpendicular lines: have slopes that are negative reciprocals and different y-intercepts. Non-linear relationship: if a single smooth curve can be drawn through every point.

Weak Relationship: if the data has no obvious pattern either in the table of values, or on the plot of the data points. Correlation coefficient (r): when graphing technology is used, correlation coefficient for a line is given. This measures goodness of fit of the line to the data. If the regression line fits the data exactly, and has a positive slop, then r=1. If the line fit the data exactly and has a negative slope r=-1. Point of Intersection: when two lines are graphed on the same set of axes, they may cross each other. This point identifies where the variables are equal in two different relationships. Linear Regression Equation (how to calculate the equation of a line of best fit):

Displacement: in a problem involving movement, the graph shows this (distance, height. Or depth) versus time. Distance, height or depth is the dependent variable and time is the independent variable. Velocity: is the rate of change in this relationship. V= ∆d = the change in displacement ∆t the change in time - In a linear relationship, the velocity is constant. - In a nonlinear relationship, the velocity changes with time. This means there is non-zero acceleration or deceleration.

Sets of numbers and how to operate in I and Q: see other study page. Exponent Rules:

Rational Exponents: • = (√49)^1 =7 • = (3√-125)^2 =(-5)^2 =25 • =(49/36)^3/2 =(√49/36)^3 =(7/60^3 =243/216

• = -21a ^3/2 + 1/5 = -21a ^15/10 + 2/10 = -21a ^17/10

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Exponential Growth: if the constant multiplier is greater than 1. (nonlinear relationship) Scientific notation: 0.0000000 5 = .5x10^-8 ; 2 000 000 = 2.0 x 10^6

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Multiplying with exponents: add the exponents Dividing with exponents: subtract exponents. Dealing with a negative exponent: put the exponent over 1. When dealing with brackets: multiply exponents. Exponent to a fraction: x^n/y^n Multiplication in brackets to an exponent: multiply each variable or number by the exponent.

Changing non-terminating decimals: x= 0.6666666  10x=6.66666  10x-x=6  9x=6 100x= 27.2727272727 -x = 0.27272727 99x= 27 x= 27/99 = 3/11 Types of Q/Rationals: Fractions (proper and improper) -Mixed Numbers -Integers -Terminating Decimals -Periodic Decimals Ratio: comparing two or more items with the same unit. Percentage: type of ratio. Rate: two equal ratios form this proportion. Quotient: the answer to a division problem. Period: the block over repeating digits. Divisor: the number which is dividend. (42/7...7 is the divisor) Basic type of Ratio word problems: •

Warren Jason and Robert score goals in ratios of 3:7:4. If Robert got 56 goals, how many did the others get?

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Dylan, Mike and Amanda bought a lottery ticket by contributing 2,5,7. They won 560 000$, how much money will each get?

Percentages: 90% of 240 1290 is what % of 750 186 is 60% of?

X 240 * 100 = 90% 1290 750 * 100 = % 186 x * 100 = 60%

154% of what # is 154?

Percentage into fraction: 6%= 0.6 = 6/100 then reduce= 3/50. Transversal: a line that intersects a pair of angles. In a Polygon with n sides: • The sum of the interior angles is 180(n-2)۫ • The sum of the exterior angles is 360 Composite Figures: two dimensional shapes made from a combination of several different shapes. Alternate Interior Angles: congruent angles formed by two parallel lines cut by a transversal; located on opposite sides of the transversal between the parallel lines

Alternate Exterior: When two parallel lines are cut by a transversal, the two pairs of angles on opposite sides of the transversal and outside the parallel lines Supplementary Angles: Two angles for which the sum of their measures is 180 degrees. Vertex: A point where lines, rays, sides of a polygon or edges of a polyhedron meet (corner). Corresponding: Two angles that lie on the same side of the transversal, in corresponding positions with respect to the two lines that the transversal intersects.

-remote interior -remote exterior

Degree of a Polynomial: The highest exponent when there is a situation of addition or subtraction. In the case of multiplication, we add the exponents. Monomial: one single term. Binomial: an expression consisting of the sum or difference of two monomials (see the definition of monomial), such as 4a-8b. Trinomial: Three . Coefficient: the term multiplying. For ex. 3y = 3 is the coefficient. Variables: values that can change a relationship. (often letters) Other Key Words: -Origin -Rate Triangle -Cartesian Plane -Order of Operations -Absolute Value -Prime Number: is a whole number greater than 1 with exactly to factors: 1 and the number itself. -Additive inverse: 3 = -3 -Proportion: two equations form this. -Quotient: the result of dividing one number by another.