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Grade 9 Math Courses - California Curriculum

Discover California's Grade 9 Math courses: Algebra I and Mathematics I. Explore fundamental concepts, problem-solving skills, and prepare for advanced math studies in high school.

CA Algebra I (A1)

CA Mathematics I (M1)

CA Grade 9 Math Curriculum - Algebra I and Math I

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ID
Standard
StudyPug Topic
CA.M1.N.RN.1
Explain rational exponents
Using exponents to describe numbers
CA.M1.N.RN.2
Rewrite expressions with radicals and rational exponents
Exponents: Rational exponents
CA.M1.N.Q.1
Use units to solve problems
Metric systems
Conversions between metric and imperial systems
Imperial systems
CA.M1.N.Q.2
Define appropriate quantities
Upper and lower bound
Cubic and cube roots
Ratios
Rates
Proportions
Squares and square roots
CA.M1.N.Q.3
Choose level of accuracy
Conversions involving squares and cubic
Percents, fractions, and decimals
CA.M1.A.SSE.1
Interpret expressions
Polynomial components
CA.M1.A.CED.1
Create equations and inequalities
Introduction to linear equations
Angles in a circle
Chord properties
Tangent properties
Arcs of a circle
Areas and sectors of circles
CA.M1.A.CED.2
Create equations in two or more variables
Graphing linear functions using table of values
Pythagorean theorem
Classifying triangles
Triangles congruent by ASA and AAS proofs
Isosceles and equilateral triangles
CA.M1.A.CED.3
Represent constraints with equations
Applications of linear relations
Scale diagrams
Similar triangles
Introduction to volume
CA.M1.A.CED.4
Rearrange formulas
Applications of linear equations
Surface area and volume of prisms
Word problems relating ladder in trigonometry
Word problems relating guy wire in trigonometry
Other word problems relating angles in trigonometry
Solving expressions using 45-45-90 special right triangles
Solving expressions using 30-60-90 special right triangles
Applications of pythagorean theorem
CA.M1.A.REI.1
Explain solving steps
Use sine ratio to calculate angles and sides (Sin = o / h)
Use cosine ratio to calculate angles and sides (Cos = a / h)
Combination of SohCahToa questions
Use tangent ratio to calculate angles and sides (Tan = o / a)
CA.M1.A.REI.3
Solve linear equations and inequalities
Law of sines
Law of cosines
Applications of the sine law and cosine law
CA.M1.A.REI.3.1
Solve absolute value equations and inequalities
Solving absolute value equations
Introduction to bearings
Bearings and direction word problems
Angle of elevation and depression
CA.M1.A.REI.5
Prove replacement in systems
Solving systems of linear equations by elimination
Line symmetry
Rotational symmetry and transformations
CA.M1.A.REI.6
Solve systems of equations
Solving systems of linear equations by graphing
Solving multi-step linear inequalities
Solving absolute value inequalities
Compound inequalities
CA.M1.A.REI.10
Understand solutions of equations
Graphing linear functions using x- and y-intercepts
Tessellations using rotations
CA.M1.A.REI.11
Explain solving f(x) = g(x)
Introduction to surface area of 3-dimensional shapes
Nets of 3-dimensional shapes
CA.M1.A.REI.12
Graph inequalities in two variables
Graphing linear inequalities in two variables
Probability of independent events
CA.M1.F.IF.1
Understand function concept
Identifying functions
Fundamental counting principle
Permutations
Problems involving both permutations and combinations
Box-and-whisker plots and scatter plots
Stem and leaf plots
CA.M1.F.IF.2
Use function notation
Function notation
Probability with Venn diagrams
CA.M1.F.IF.3
Recognize sequences as functions
Arithmetic sequences
Inductive reasoning
Statements
Negations
Conjunctions and disjunctions
Truth tables
Conditionals
Inverses, converses, and contrapositives
Biconditionals
Deductive reasoning
Algebraic proofs
CA.M1.F.IF.4
Interpret key features of graphs
Graphing linear functions using a single point and slope
Arithmetic series
Geometric sequences
Sigma notation
Consecutive integers
Number sequences
Finding the missing digit
CA.M1.F.IF.5
Relate domain of a function to its graph
Domain and range of a function
Understand relations between x- and y-intercepts
Set notation
Set builder notation
Intersection and union of 2 sets
Intersection and union of 3 sets
Interval notations
CA.M1.F.IF.6
Calculate and interpret average rate of change
Rate of change
Relationship between two variables
Understanding graphs of linear relationships
Introduction to vectors
Direct variation
Word problems on vectors
CA.M1.F.IF.7
Graph functions
Graphing from slope-intercept form y=mx+b
Magnitude of a vector
Direction angle of a vector
Equivalent vectors
Adding and subtracting vectors in component form
CA.M1.F.BF.1
Write a function for a relationship
Word problems of graphing linear functions
Money related questions in linear equations
Unknown number related questions in linear equations
Distance and time related questions in linear equations
Rectangular shape related questions in linear equations
CA.M1.F.BF.2
Write arithmetic and geometric sequences
Exponents: Power rule: (a^x)^y = a^(xy)
Exponents: Zero exponent: a^0 = 1
Graphing exponential functions
Graphing transformations of exponential functions
CA.M1.F.BF.3
Identify effects on graphs
Transformations of functions: Horizontal translations
Multiplying monomial by monomial
Multiplying monomial by binomial
Multiplying binomial by binomial
Multiplying polynomial by polynomial
Common factors of polynomials
Factoring polynomials by grouping
Factoring polynomials: x^2 + bx + c
Factoring polynomials: ax^2 + bx + c
Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2
Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)
Using algebra tiles to factor polynomials
CA.M1.F.LE.1
Distinguish linear and exponential
Factor theorem
Characteristics of quadratic functions
Transformations of quadratic functions
Converting from general to vertex form by completing the square
Solving quadratic equations by factoring
Solving quadratic equations by completing the square
Using quadratic formula to solve quadratic equations
Nature of roots of quadratic equations: The discriminant
CA.M1.F.LE.2
Construct linear and exponential functions
Polynomial long division
Slant asymptote
Solving rational equations
Vertical asymptote
Horizontal asymptote
Simplifying complex fractions
Partial fraction decomposition
CA.M1.F.LE.3
Observe using graphs
Exponential growth and decay by a factor
Adding and subtracting rational expressions
Multiplying rational expressions
Dividing rational expressions
Evaluating piecewise functions
Graphing piecewise linear functions
Graphing piecewise non-linear functions
CA.M1.G.CO.1
Know precise definitions
Pairs of lines and angles
CA.M1.G.CO.2
Represent transformations
Combinations
Data collection
CA.M1.G.CO.3
Describe rotations and reflections
Combining transformations of functions
Influencing factors in data collection
Probability
CA.M1.G.CO.4
Develop definitions of transformations
Reflection across the y-axis: y = f(-x)
Median and mode
Mean
Range and outliers
Application of averages
CA.M1.G.CO.5
Transform given geometric figure
Quadratic function in general form: y = ax^2 + bx + c
Graphing quadratic functions: General form VS. Vertex form
Finding the quadratic functions for given parabolas
Quadratic function in vertex form: y = a(x-p)^2 + q
Introduction to quadratic functions
CA.M1.G.CO.6
Use geometric descriptions of rigid motions
Congruence and congruent triangles
Conics - Parabola
Conics - Circle
CA.M1.G.CO.7
Use definition of congruence
Triangles congruent by SSS proofs
Notation of matrices
Adding and subtracting matrices
Scalar multiplication of matrices
Matrix multiplication
The three types of matrix row operations
CA.M1.G.CO.8
Explain triangle congruence criteria
Triangles congruent by SAS and HL proofs
Zero matrix
Identity matrix
Properties of matrix addition
Properties of scalar multiplication
CA.M1.G.CO.12
Make formal geometric constructions
Properties of matrix multiplication
The determinant of a 2 x 2 matrix
The determinant of a 3 x 3 matrix (General & Shortcut Method)
The Inverse of a 2 x 2 matrix
The inverse of 3 x 3 matrices with matrix row operations
The inverse of 3 x 3 matrix with determinants and adjugate
CA.M1.G.CO.13
Construct regular polygons inscribed in circles
2 x 2 invertible matrix
Solving linear systems using Cramer's Rule
Solving linear systems using 2 x 2 inverse matrices
CA.M1.G.GPE.4
Use coordinates to prove geometric theorems
Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}d=(x2​−x1​)2+(y2​−y1​)2​
Transforming vectors with matrices
Transforming shapes with matrices
Finding the transformation matrix
CA.M1.G.GPE.5
Prove the slope criteria for parallel and perpendicular lines
Parallel and perpendicular lines in linear functions
Angle in standard position
Coterminal angles
Reference angle
Converting between degrees and radians
CA.M1.G.GPE.7
Use coordinates to compute perimeters and areas
Solving first degree trigonometric equations
Solving trigonometric equations involving multiple angles
Solving trigonometric equations using pythagorean identities
Solving trigonometric equations using sum and difference identities
Solving trigonometric equations using double-angle identities
CA.M1.S.ID.1
Represent data with plots
Organizing data
Unit circle
Determining non-permissible values for trig expressions
CA.M1.S.ID.2
Use statistics to compare center and spread
Reading and drawing bar graphs
Solving second degree trigonometric equations
Find the exact value of trigonometric ratios
ASTC rule in trigonometry (All Students Take Calculus)
CA.M1.S.ID.3
Interpret differences in shape, center, and spread
Reading and drawing histograms
Sine graph: y = sin x
Cosine graph: y = cos x
Tangent graph: y = tan x
Cotangent graph: y = cot x
Secant graph: y = sec x
Cosecant graph: y = csc x
Graphing transformations of trigonometric functions
Determining trigonometric functions given their graphs
CA.M1.S.ID.5
Summarize categorical data
Reading and drawing Venn diagrams
Quotient identities and reciprocal identities
Pythagorean identities
Sum and difference identities
Double-angle identities
CA.M1.S.ID.6
Represent data on two quantitative variables
Reading and drawing line graphs
Geometric series
Infinite geometric series
CA.M1.S.ID.7
Interpret slope and intercept
Slope intercept form: y = mx + b

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