Grade 9 Mathematics Unit 3 Variation Answers

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9-10.AR Arithmetic

9-10.AR.1 Understanding real numbers
- 9-10.AR.1.8 Distinguishes rational numbers from irrational numbers in the set of real numbers
  - Classify numbers ( 9-A.1 )
  - Classify rational and irrational numbers ( 10-A.8 )
- 9-10.AR.1.9 Represents, in different types of notation, various subsets of real numbers (discrete or continuous): interval, list/roster, on a number line
  - Number lines ( 9-A.4 )
- 9-10.AR.1.10 Defines the concept absolute value in context (e.g. difference between two numbers, distance between two points)
  - Absolute value and opposites ( 10-A.11 )
- 9-10.AR.1.11 Represents and writes
  - 9-10.AR.1.11.d numbers in scientific notation
    - Convert between standard and scientific notation ( 9-J.1 )
  - 9-10.AR.1.11.e cubes and cube roots
    - Cube roots ( 10-A.7 )
  - 9-10.AR.1.11.f numbers in exponential notation (fractional exponents)
    - Evaluate rational exponents ( 10-E.1 )
- 9-10.AR.1.12 Estimates the value of the power of an exponential expression with respect to its components: base (between 0 and 1, greater than 1), exponent (positive or negative, integral or fractional)
- 9-10.AR.1.13 Estimates the order of magnitude of a real number in different contexts
- 9-10.AR.1.14 Estimates the order of magnitude of a real number using scientific notation
  - Compare numbers written in scientific notation ( 9-J.2 )
9-10.AR.3 Operations involving real numbers
- 9-10.AR.3.7 Computes, in writing, the four operations with numbers that are easy to work with (including large numbers), using equivalent ways of writing numbers and the properties of operations
  - 9-10.AR.3.7.c numbers written in fractional notation
    - Add and subtract rational numbers ( 9-B.4 )
    - Add and subtract rational numbers: word problems ( 9-B.5 )
    - Multiply and divide rational numbers ( 9-B.6 )
    - Multiply and divide rational numbers: word problems ( 9-B.7 )
    - Evaluate numerical expressions involving rational numbers ( 9-B.8 )
- 9-10.AR.3.14 Manipulates numerical expressions involving
  - 9-10.AR.3.14.a integral exponents (rational base) and fractional exponents
    - Multiplication with exponents - integral bases ( 9-I.5 )
    - Division with exponents - integral bases ( 9-I.6 )
    - Multiplication and division with exponents - integral bases ( 9-I.7 )
    - Power rule - integral bases ( 9-I.8 )
    - Evaluate expressions using properties of exponents ( 9-I.13 )
    - Identify equivalent expressions involving exponents ( 9-I.14 )
9-10.AR.4 Understanding and analyzing proportional situations
- 9-10.AR.4.10 Establishes relationships between first-degree or rational functions and proportional situations (direct or inverse variation)
  - Identify proportional relationships ( 9-R.1 )
  - Find the constant of variation ( 9-R.2 )
  - Graph a proportional relationship ( 9-R.3 )
  - Write direct variation equations ( 9-R.4 )
  - Write and solve direct variation equations ( 9-R.5 )
  - Write inverse variation equations ( 10-K.7 )
  - Write and solve inverse variation equations ( 10-K.8 )

9-10.AL Algebra

9-10.AL.1 Understanding and manipulating algebraic expressions
- 9-10.AL.1.A Algebraic expressions
  - 9-10.AL.1.A.4 Describes the role of components of algebraic expressions:
    - 9-10.AL.1.A.4.c parameter
  - 9-10.AL.1.A.8 Recognizes or constructs
    - 9-10.AL.1.A.8.b inequalities
      - Write inequalities from graphs ( 9-O.2 )
- 9-10.AL.1.B Manipulating algebraic expressions
  - 9-10.AL.1.B.4 Multiplies
    - 9-10.AL.1.B.4.a algebraic expressions of degree less than 3
      - Distributive property ( 9-H.2 )
      - Multiply monomials to find area ( 9-U.3 )
      - Multiply a polynomial by a monomial ( 9-V.6 )
      - Multiply polynomials to find area ( 9-V.7 )
  - 9-10.AL.1.B.5 Divides
    - 9-10.AL.1.B.5.a algebraic expressions by a monomial
      - Divide monomials ( 9-U.4 )
      - Divide a polynomial by a monomial ( 9-V.8 )
  - 9-10.AL.1.B.6 Factors polynomials by
    - 9-10.AL.1.B.6.a finding the common factor
      - GCF of monomials ( 10-P.1 )
      - Factor out a monomial ( 10-P.2 )
- 9-10.AL.1.C Analyzing situations using equations or inequalities
  - 9-10.AL.1.C.1 Recognizes whether a situation can be translated by
    - 9-10.AL.1.C.1.b an inequality
  - 9-10.AL.1.C.2 Recognizes or constructs
    - 9-10.AL.1.C.2.b inequality relations and first-degree inequalities in one variable
      - Write inequalities from graphs ( 9-O.2 )
  - 9-10.AL.1.C.4 Represents a situation using
    - 9-10.AL.1.C.4.b a first-degree inequality with a variable
  - 9-10.AL.1.C.5 Represents
    - 9-10.AL.1.C.5.b an inequality using another register (type) of representation, if necessary
      - Graph inequalities ( 9-O.1 )
  - 9-10.AL.1.C.8 Transforms inequalities to maintain equivalence (properties and rules for transforming inequalities) and justifies the steps followed, if necessary
    - Solve one-step linear inequalities: addition and subtraction ( 9-O.4 )
    - Solve one-step linear inequalities: multiplication and division ( 9-O.5 )
    - Solve one-step linear inequalities ( 9-O.6 )
    - Solve two-step linear inequalities ( 9-O.8 )
    - Solve advanced linear inequalities ( 9-O.10 )
  - 9-10.AL.1.C.10 Solves first-degree inequalities in one variable
    - Solve one-step linear inequalities: addition and subtraction ( 9-O.4 )
    - Solve one-step linear inequalities: multiplication and division ( 9-O.5 )
    - Solve one-step linear inequalities ( 9-O.6 )
    - Graph solutions to one-step linear inequalities ( 9-O.7 )
    - Solve two-step linear inequalities ( 9-O.8 )
    - Graph solutions to two-step linear inequalities ( 9-O.9 )
    - Solve advanced linear inequalities ( 9-O.10 )
    - Graph solutions to advanced linear inequalities ( 9-O.11 )
- 9-10.AL.1.D Analyzing situations using systems of equations or inequalities
  - 9-10.AL.1.D.1 Determines whether a situation may be translated by a system of
    - 9-10.AL.1.D.1.a equations
  - 9-10.AL.1.D.2 Translates a situation algebraically or graphically using a system of
    - 9-10.AL.1.D.2.a equations
      - Solve a system of equations by graphing: word problems ( 9-T.3 )
  - 9-10.AL.1.D.3 Solves a system
    - 9-10.AL.1.D.3.a of first-degree equations in two variables of the form y = ax + b by using tables of values, graphically or algebraically (by comparison), with or without technological tools
      - Solve a system of equations by graphing ( 9-T.2 )
  - 9-10.AL.1.D.5 Validates the solution, with or without technological tools
    - Is (x, y) a solution to the system of equations? ( 9-T.1 )
  - 9-10.AL.1.D.6 Interprets the solution or makes decisions if necessary, depending on the context
    - Solve a system of equations by graphing: word problems ( 9-T.3 )
9-10.AL.2 Understanding dependency relationships
- 9-10.AL.2.A Relations, functions and inverses
  - 9-10.AL.2.A.4 Chooses the dependent variable and the independent variable
    - Identify independent and dependent variables ( 9-Q.2 )
  - 9-10.AL.2.A.5 Recognizes relations, functions and inverses
    - Relations: convert between tables, graphs, mappings and lists of points ( 9-Q.1 )
    - Identify functions ( 9-Q.3 )
    - Identify functions: vertical line test ( 9-Q.4 )
- 9-10.AL.2.B Analyzing situations using real functions
  - 9-10.AL.2.B.1 Models a situation verbally, algebraically, graphically, using a table of values or a scatter plot
    - Scatter plots: line of best fit ( 9-P.7 )
    - Interpret the graph of a function: word problems ( 9-Q.10 )
    - Slope-intercept form: graph an equation ( 9-S.6 )
    - Write linear functions to solve word problems ( 9-S.12 )
    - Complete a table and graph a linear function ( 9-S.13 )
    - Graph a horizontal or vertical line ( 9-S.19 )
  - 9-10.AL.2.B.2 Finds the rule of a function or its inverse, depending on the context
    - Slope-intercept form: write an equation from a graph ( 9-S.7 )
    - Slope-intercept form: write an equation ( 9-S.8 )
    - Slope-intercept form: write an equation from a table ( 9-S.9 )
    - Slope-intercept form: write an equation from a word problem ( 9-S.10 )
    - Equations of horizontal and vertical lines ( 9-S.18 )
    - Write inverse variation equations ( 10-K.7 )
    - Write and solve inverse variation equations ( 10-K.8 )
  - 9-10.AL.2.B.3 Represents and interprets the inverse
  - 9-10.AL.2.B.4 Interprets parameters (multiplicative or additive) and describes the effect of changing their value, if necessary
    - Find the constant of variation ( 9-R.2 )
    - Find the slope of a graph ( 9-S.2 )
    - Find the slope from two points ( 9-S.3 )
    - Find a missing coordinate using slope ( 9-S.4 )
    - Slope-intercept form: find the slope and y-intercept ( 9-S.5 )
    - Transformations of linear functions ( 9-S.25 )
  - 9-10.AL.2.B.5 Describes the properties of real functions: domain, range, interval within which the function is increasing or decreasing, sign, extrema, x-intercept and y-intercept
    - Slope-intercept form: find the slope and y-intercept ( 9-S.5 )
    - Standard form: find x- and y-intercepts ( 9-S.16 )
  - 9-10.AL.2.B.6 Determines values or data by solving equations and inequalities
    - Evaluate a function ( 9-Q.6 )
    - Write linear functions to solve word problems ( 9-S.12 )
  - 9-10.AL.2.B.7 Interpolates and extrapolates data, if applicable
    - Interpret a scatter plot ( 9-P.6 )
  - 9-10.AL.2.B.8 Compares situations or graphical representations
    - Compare linear functions: graphs, tables and equations ( 9-S.14 )
  - 9-10.AL.2.B.9 Makes decisions, if necessary, depending on the context

9-10.P Probability

9-10.P.1 Understanding data from random experiments
- 9-10.P.1.A Processing data from random experiments
  - 9-10.P.1.A.8 Identifies the type of random variable: discrete or continuous
    - Identify discrete and continuous random variables ( 12-Z.1 )
  - 9-10.P.1.A.9 Enumerates the possible outcomes of a random experiment using
    - 9-10.P.1.A.9.c geometric figures
- 9-10.P.1.B Analyzing probability situations
  - 9-10.P.1.B.5 Calculates the probability of outcomes of random experiments related to situations involving arrangements, permutations or combinations
    - Permutations ( 10-GG.5 )
  - 9-10.P.1.B.7 Calculates probabilities, including geometric probabilities, in measurement contexts
    - Geometric probability ( 10-GG.8 )

9-10.S Statistics

9-10.S.1 Analyzing and making decisions about one- or two-variable distributions, using statistical tools
- 9-10.S.1.A One-variable distributions
  - 9-10.S.1.A.1 Conducts a survey or a census
    - 9-10.S.1.A.1.b Chooses a sampling method:
      - 9-10.S.1.A.1.b.ii stratified, cluster
  - 9-10.S.1.A.6 Organizes and presents data using
    - 9-10.S.1.A.6.c a table of condensed data or data grouped into classes, a histogram, or box-and-whisker plot
      - Interpret bar graphs, line graphs and histograms ( 9-P.1 )
      - Create bar graphs, line graphs and histograms ( 9-P.2 )
      - Interpret box-and-whisker plots ( 9-P.5 )
  - 9-10.S.1.A.11 Determines and interprets
    - 9-10.S.1.A.11.a measures of central tendency: mode, median, weighted mean
      - Calculate mean, median, mode and range ( 9-Y.1 )
      - Interpret charts to find mean, median, mode and range ( 9-Y.2 )
      - Mean, median, mode and range: find the missing number ( 9-Y.3 )
    - 9-10.S.1.A.11.b measures of dispersion:
      - 9-10.S.1.A.11.b.ii range of each part of a box-and whisker plot, interquartile range
        
        Interpret box-and-whisker plots ( 9-P.5 )
        
        Quartiles ( 9-Y.4 )
- 9-10.S.1.B Two-variable distributions
  - 9-10.S.1.B.1 Compares experimental and theoretical data

9-10.G Geometry

9-10.G.1 Spatial sense and analyzing situations involving geometric figures
- 9-10.G.1.A Plane figures
  - 9-10.G.1.A.8 Recognizes and draws main segments and lines
    - 9-10.G.1.A.8.b leg, hypotenuse
- 9-10.G.1.B Solids
  - 9-10.G.1.B.6 Recognizes solids that can be split into
    - 9-10.G.1.B.6.b right cones and spheres
  - 9-10.G.1.B.7 Represents three-dimensional figures in the plane, using different procedures:
    - 9-10.G.1.B.7.a net
      - Nets of three-dimensional figures ( 9-E.13 )
    - 9-10.G.1.B.7.b projection and perspective (e.g. orthogonal projections [different views], parallel projections [cavalier and axonometric perspectives] or central projections [with one or two vanishing points])
      - Cross-sections of three-dimensional figures ( 10-Z.13 )
      - Solids of revolution ( 10-Z.14 )
9-10.G.2 Analyzing situations involving measurements
- 9-10.G.2.D Length
  - 9-10.G.2.D.5 Finds the following unknown measurements, using properties of figures and relations
    - 9-10.G.2.D.5.c segments in a solid resulting from an isometry or a similarity transformation
      - Similar solids ( 9-E.20 )
- 9-10.G.2.E Area
  - 9-10.G.2.E.5 Uses relations that can be used to calculate the area of a right cone and a sphere
    - Surface area of cones and cylinders ( 9-E.15 )
    - Surface area of spheres ( 9-E.16 )
  - 9-10.G.2.E.6 Finds unknown measurements, using properties of figures and relations
    - 9-10.G.2.E.6.f area of figures resulting from a similarity transformation
      - Area and perimeter of similar figures ( 9-E.19 )
      - Volume and surface area of similar solids ( 9-E.21 )
      - Perimeter, area and volume: changes in scale ( 9-E.22 )
    - 9-10.G.2.E.6.g area of a sphere, lateral or total area of right cones and decomposable solids
      - Surface area of cones and cylinders ( 9-E.15 )
      - Surface area of spheres ( 9-E.16 )
- 9-10.G.2.F Volume
  - 9-10.G.2.F.3 Establishes relationships between SI units of volume
    - Convert rates and measurements: metric units ( 10-W.2 )
  - 9-10.G.2.F.4 Establishes relationships between
    - 9-10.G.2.F.4.b measures of capacity
    - 9-10.G.2.F.4.c measures of volume and of capacity
      - Convert between cubic metres and litres ( 8-M.4 )
  - 9-10.G.2.F.5 Constructs relations that can be used to calculate volumes: right cylinders, right pyramids, right cones and spheres
  - 9-10.G.2.F.6 Finds unknown measurements using properties of figures and relations
    - 9-10.G.2.F.6.a volume of right prisms, right cylinders, right pyramids, right cones and spheres
      - Volume of prisms and pyramids ( 9-E.10 )
      - Volume of cones and cylinders ( 9-E.11 )
      - Volume of spheres ( 9-E.12 )
    - 9-10.G.2.F.6.b volume of solids that can be split into right prisms, right cylinders, right pyramids, right cones and spheres
    - 9-10.G.2.F.6.c volume solids resulting from an isometry or a similarity transformation
      - Similar solids ( 9-E.20 )
      - Volume and surface area of similar solids ( 9-E.21 )
      - Perimeter, area and volume: changes in scale ( 9-E.22 )
  - 9-10.G.2.F.7 Justifies statements concerning measures of volume or capacity
- 9-10.G.2.G Metric or trigonometric relations
  - 9-10.G.2.G.1 Determines, through exploration or deduction, different metric relations associated with plane figures
  - 9-10.G.2.G.2 Finds unknown measurements in various situations
    - 9-10.G.2.G.2.a in a right triangle rectangle using
      - 9-10.G.2.G.2.a.i Pythagorean relation
        
        Pythagorean theorem ( 9-E.27 )
        
        Pythagorean theorem: word problems ( 9-E.28 )
  - 9-10.G.2.G.5 Justifies statements concerning
    - 9-10.G.2.G.5.a Pythagorean relation
      - Converse of the Pythagorean theorem: is it a right triangle? ( 9-E.29 )

9-10.AG Analytic Geometry

9-10.AG.1 Analyzing situations using analytic geometry
- 9-10.AG.1.B Straight lines and half-planes
  - 9-10.AG.1.B.1 Uses the concept of change to
    - 9-10.AG.1.B.1.a calculate the distance between two points
      - Distance between two points ( 9-G.3 )
    - 9-10.AG.1.B.1.c calculate and interpret a slope
      - Find the slope of a graph ( 9-S.2 )
      - Find the slope from two points ( 9-S.3 )
      - Find a missing coordinate using slope ( 9-S.4 )
  - 9-10.AG.1.B.2 Determines the relative position of two straight lines using their respective slope (intersecting at one point, perpendicular, non-intersecting parallel or coincident)
    - Slopes of parallel and perpendicular lines ( 9-S.23 )
    - Find the number of solutions to a system of equations by graphing ( 9-T.4 )
  - 9-10.AG.1.B.3 Models, with or without technological tools, a situation involving
    - 9-10.AG.1.B.3.a straight lines: graphically and algebraically
      - Slope-intercept form: graph an equation ( 9-S.6 )
      - Slope-intercept form: write an equation from a graph ( 9-S.7 )
      - Slope-intercept form: write an equation ( 9-S.8 )
      - Slope-intercept form: write an equation from a table ( 9-S.9 )
      - Slope-intercept form: write an equation from a word problem ( 9-S.10 )

Grade 9 Mathematics Unit 3 Variation Answers

Source: https://ca.ixl.com/standards/quebec/math/grade-9

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Grade 9 Mathematics Unit 3 Variation Answers

9-10.AR Arithmetic

9-10.AR.1 Understanding real numbers

9-10.AR.1.8 Distinguishes rational numbers from irrational numbers in the set of real numbers

9-10.AR.1.9 Represents, in different types of notation, various subsets of real numbers (discrete or continuous): interval, list/roster, on a number line

9-10.AR.1.10 Defines the concept absolute value in context (e.g. difference between two numbers, distance between two points)

9-10.AR.1.11 Represents and writes

9-10.AR.1.11.d numbers in scientific notation

9-10.AR.1.11.e cubes and cube roots

9-10.AR.1.11.f numbers in exponential notation (fractional exponents)

9-10.AR.1.12 Estimates the value of the power of an exponential expression with respect to its components: base (between 0 and 1, greater than 1), exponent (positive or negative, integral or fractional)

9-10.AR.1.13 Estimates the order of magnitude of a real number in different contexts

9-10.AR.1.14 Estimates the order of magnitude of a real number using scientific notation

9-10.AR.3 Operations involving real numbers

9-10.AR.3.7 Computes, in writing, the four operations with numbers that are easy to work with (including large numbers), using equivalent ways of writing numbers and the properties of operations

9-10.AR.3.7.c numbers written in fractional notation

9-10.AR.3.14 Manipulates numerical expressions involving

9-10.AR.3.14.a integral exponents (rational base) and fractional exponents

9-10.AR.4 Understanding and analyzing proportional situations

9-10.AR.4.10 Establishes relationships between first-degree or rational functions and proportional situations (direct or inverse variation)

9-10.AL Algebra

9-10.AL.1 Understanding and manipulating algebraic expressions

9-10.AL.1.A Algebraic expressions

9-10.AL.1.A.4 Describes the role of components of algebraic expressions:

9-10.AL.1.A.4.c parameter

9-10.AL.1.A.8 Recognizes or constructs

9-10.AL.1.A.8.b inequalities

9-10.AL.1.B Manipulating algebraic expressions

9-10.AL.1.B.4 Multiplies

9-10.AL.1.B.4.a algebraic expressions of degree less than 3

9-10.AL.1.B.5 Divides

9-10.AL.1.B.5.a algebraic expressions by a monomial

9-10.AL.1.B.6 Factors polynomials by

9-10.AL.1.B.6.a finding the common factor

9-10.AL.1.C Analyzing situations using equations or inequalities

9-10.AL.1.C.1 Recognizes whether a situation can be translated by

9-10.AL.1.C.1.b an inequality

9-10.AL.1.C.2 Recognizes or constructs

9-10.AL.1.C.2.b inequality relations and first-degree inequalities in one variable

9-10.AL.1.C.4 Represents a situation using

9-10.AL.1.C.4.b a first-degree inequality with a variable

9-10.AL.1.C.5 Represents

9-10.AL.1.C.5.b an inequality using another register (type) of representation, if necessary

9-10.AL.1.C.8 Transforms inequalities to maintain equivalence (properties and rules for transforming inequalities) and justifies the steps followed, if necessary

9-10.AL.1.C.10 Solves first-degree inequalities in one variable

9-10.AL.1.D Analyzing situations using systems of equations or inequalities

9-10.AL.1.D.1 Determines whether a situation may be translated by a system of

9-10.AL.1.D.1.a equations

9-10.AL.1.D.2 Translates a situation algebraically or graphically using a system of

9-10.AL.1.D.2.a equations

9-10.AL.1.D.3 Solves a system

9-10.AL.1.D.3.a of first-degree equations in two variables of the form y = ax + b by using tables of values, graphically or algebraically (by comparison), with or without technological tools

9-10.AL.1.D.5 Validates the solution, with or without technological tools

9-10.AL.1.D.6 Interprets the solution or makes decisions if necessary, depending on the context

9-10.AL.2 Understanding dependency relationships

9-10.AL.2.A Relations, functions and inverses

9-10.AL.2.A.4 Chooses the dependent variable and the independent variable

9-10.AL.2.A.5 Recognizes relations, functions and inverses

9-10.AL.2.B Analyzing situations using real functions

9-10.AL.2.B.1 Models a situation verbally, algebraically, graphically, using a table of values or a scatter plot

9-10.AL.2.B.2 Finds the rule of a function or its inverse, depending on the context

9-10.AL.2.B.3 Represents and interprets the inverse

9-10.AL.2.B.4 Interprets parameters (multiplicative or additive) and describes the effect of changing their value, if necessary

9-10.AL.2.B.5 Describes the properties of real functions: domain, range, interval within which the function is increasing or decreasing, sign, extrema, x-intercept and y-intercept

9-10.AL.2.B.6 Determines values or data by solving equations and inequalities

9-10.AL.2.B.7 Interpolates and extrapolates data, if applicable

9-10.AL.2.B.8 Compares situations or graphical representations

9-10.AL.2.B.9 Makes decisions, if necessary, depending on the context

9-10.P Probability

9-10.P.1 Understanding data from random experiments

9-10.P.1.A Processing data from random experiments

9-10.P.1.A.8 Identifies the type of random variable: discrete or continuous

9-10.P.1.A.9 Enumerates the possible outcomes of a random experiment using

9-10.P.1.A.9.c geometric figures

9-10.P.1.B Analyzing probability situations

9-10.P.1.B.5 Calculates the probability of outcomes of random experiments related to situations involving arrangements, permutations or combinations

9-10.P.1.B.7 Calculates probabilities, including geometric probabilities, in measurement contexts

9-10.S Statistics

9-10.S.1 Analyzing and making decisions about one- or two-variable distributions, using statistical tools

9-10.S.1.A One-variable distributions