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Grade 10 Math Courses - California Curriculum

Discover CA Grade 10 Math courses: Geometry and Mathematics II. Explore key concepts, problem-solving techniques, and prepare for advanced mathematical studies in line with California standards.

CA Geometry (G)

CA Mathematics II (M2)

CA Grade 10 Math Curriculum - Geometry & Mathematics II

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ID
Standard
StudyPug Topic
CA.M2.N.RN.1
Explain rational exponents
Exponents: Rational exponents
Convert between radicals and rational exponents
CA.M2.N.RN.2
Rewrite expressions with radicals and rational exponents
Evaluating and simplifying radicals
Conversion between entire radicals and mixed radicals
Adding and subtracting radicals
Multiplying radicals
Operations with radicals
CA.M2.N.RN.3
Explain properties of rational and irrational numbers
Rational vs. Irrational numbers
CA.M2.N.CN.1
Know there is a complex number i
What is an integer
Introduction to imaginary numbers
Complex numbers and complex planes
CA.M2.N.CN.2
Use the relation i² = −1
Adding and subtracting complex numbers
Complex conjugates
Multiplying and dividing complex numbers
CA.M2.N.CN.7
Solve quadratic equations with complex solutions
Using quadratic formula to solve quadratic equations
Nature of roots of quadratic equations: The discriminant
CA.M2.N.CN.8
Extend polynomial identities to complex numbers
Distance and midpoint of complex numbers
Angle and absolute value of complex numbers
CA.M2.N.CN.9
Know the Fundamental Theorem of Algebra
Fundamental theorem of algebra
CA.M2.A.SSE.1
Interpret expressions
Characteristics of quadratic functions
What is a polynomial?
Polynomial components
CA.M2.A.SSE.2
Recognize structure in expressions
Factor by taking out the greatest common factor
Multiplying monomial by monomial
Multiplying monomial by binomial
Multiplying binomial by binomial
CA.M2.A.SSE.3
Choose and produce equivalent forms of expressions
Factoring trinomials
CA.M2.A.APR.1
Perform arithmetic operations on polynomials
Multiplying polynomial by polynomial
Adding and subtracting polynomials
CA.M2.A.CED.1
Create equations and inequalities
Introduction to quadratic functions
Introduction to linear equations
Introduction to nonlinear equations
CA.M2.A.CED.2
Create equations in two or more variables
Finding the quadratic functions for given parabolas
Graphing linear functions using table of values
Graphing linear functions using x- and y-intercepts
Graphing from slope-intercept form y=mx+b
Graphing linear functions using a single point and slope
CA.M2.A.CED.4
Rearrange formulas
Converting from general to vertex form by completing the square
Solving literal equations
CA.M2.A.REI.4
Solve quadratic equations
Solving quadratic equations by factoring
Solving quadratic equations by completing the square
CA.M2.A.REI.7
Solve a simple system of a linear and quadratic equation
System of linear-quadratic equations
CA.M2.F.IF.4
Interpret key features of graphs and tables
Graphing quadratic functions: General form VS. Vertex form
CA.M2.F.IF.5
Relate the domain of a function to its graph
Domain and range of a function
CA.M2.F.IF.6
Calculate and interpret the average rate of change
Rate of change
CA.M2.F.IF.7
Graph functions
Quadratic function in general form: y = ax^2 + bx + c
Quadratic function in vertex form: y = a(x-p)^2 + q
CA.M2.F.IF.8
Write functions in different but equivalent forms
Shortcut: Vertex formula
CA.M2.F.IF.9
Compare properties of two functions
Applications of quadratic functions
Operations with functions
CA.M2.F.BF.1
Write a function that describes a relationship
Function notation (advanced)
One to one functions
CA.M2.F.BF.3
Identify the effect of transformations on graphs
Transformations of quadratic functions
Transformations of functions: Horizontal translations
Transformations of functions: Vertical translations
Reflection across the y-axis: y = f(-x)
Reflection across the x-axis: y = -f(x)
Transformations of functions: Horizontal stretches
Transformations of functions: Vertical stretches
CA.M2.F.BF.4
Find inverse functions
Inverse functions
CA.M2.F.LE.3
Observe exponential functions using graphs and tables
Exponential growth and decay by a factor
Exponential growth and decay by percentage
CA.M2.F.TF.8
Prove the Pythagorean identity
Unit circle
Pythagorean identities
CA.M2.G.CO.9
Prove theorems about lines and angles
Parallel line proofs
Pairs of lines and angles
Parallel lines and transversals
Perpendicular line proofs
CA.M2.G.CO.10
Prove theorems about triangles
Triangles congruent by ASA and AAS proofs
CA.M2.G.CO.11
Prove theorems about parallelograms
Area and perimeter of parallelograms
CA.M2.G.SRT.1
Verify properties of dilations
Enlargements and reductions with scale factors
CA.M2.G.SRT.2
Given similarity transformations, explain similarity
Similar polygons
Scale diagrams
CA.M2.G.SRT.3
Use the AA criterion for similar triangles
Similar triangles
CA.M2.G.SRT.5
Use congruence and similarity criteria for triangles
Congruence and congruent triangles
Triangles congruent by SSS proofs
Triangles congruent by SAS and HL proofs
CA.M2.G.SRT.6
Understand trigonometric ratios
Use sine ratio to calculate angles and sides (Sin = o / h)
Use cosine ratio to calculate angles and sides (Cos = a / h)
CA.M2.G.SRT.7
Explain and use the relationship between sine and cosine of complementary angles
Combination of SohCahToa questions
Cofunction identities
CA.M2.G.SRT.8
Solve right triangles
Use tangent ratio to calculate angles and sides (Tan = o / a)
Pythagorean theorem
CA.M2.G.SRT.8.1
Derive and use trigonometric ratios for special right triangles
Solving expressions using 45-45-90 special right triangles
Solving expressions using 30-60-90 special right triangles
CA.M2.G.C.1
Prove that all circles are similar
Circles and circumference
CA.M2.G.C.2
Identify and describe relationships among angles, radii, and chords
Central and inscribed angles in circles
Angles in a circle
Chord properties
Tangent properties
CA.M2.G.C.3
Construct inscribed and circumscribed circles of a triangle
Circle chord, tangent, and inscribed angles proofs
CA.M2.G.C.5
Derive and use the formula for the area of a sector
Areas and sectors of circles
Arcs of a circle
CA.M2.G.GPE.1
Derive the equation of a circle
Conics - Circle
CA.M2.G.GPE.2
Derive the equation of a parabola
Conics - Parabola
CA.M2.G.GPE.4
Use coordinates to prove simple 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​
Slope equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}m=x2​−x1​y2​−y1​​
CA.M2.G.GPE.6
Find the point that partitions a directed line segment in a given ratio
Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)M=(2x1​+x2​​,2y1​+y2​​)
CA.M2.G.GMD.1
Give informal arguments for geometric formulas
Surface area and volume of pyramids
Surface area and volume of cylinders
Surface area and volume of cones
CA.M2.G.GMD.3
Use volume formulas
Surface area and volume of prisms
Surface area and volume of spheres
CA.M2.G.GMD.6
Verify the properties of triangles and apply them to solve problems
Isosceles and equilateral triangles
CA.M2.S.CP.1
Describe events as subsets of a sample space
Introduction to probability
CA.M2.S.CP.2
Understand independence and conditional probability
Probability of independent events
CA.M2.S.CP.3
Interpret independence of events
Determining probabilities using tree diagrams and tables
CA.M2.S.CP.4
Construct and interpret two-way frequency tables
Intersection and union of 2 sets
Reading and drawing Venn diagrams
CA.M2.S.CP.5
Recognize and explain concepts of conditional probability
Organizing outcomes
Probability of independent events
CA.M2.S.CP.6
Find conditional probability
Probability with Venn diagrams
CA.M2.S.CP.8
Apply multiplication rule of probability
Addition rule for "OR"
CA.M2.S.CP.9
Use permutations and combinations to compute probabilities
Problems involving both permutations and combinations
Permutations
Combinations
CA.M2.S.MD.6
Use probabilities to make fair decisions
Comparing experimental and theoretical probability

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