 11 and 12 Grade Math Topics, Lessons, Problems and Answers, Worksheets, Practice Tests

Students are expected to be acquainted with Grade 11 & 12 Math Concepts and must be able to apply them. Whichever course you opt in your High School you can get comprehensive knowledge of core math skills needed for further studies. Become a Pro in 11th Grade & 12th Grade Math Lessons through the plenty of opportunities provided for Math Practice here. Assess your strengths and weaknesses taking the help of the 11th & 12th Grade Math Problems and Answers, Worksheets, Practice Tests, etc.

All the Grade 11 and Grade 12 Math Topics explained are as per the latest textbooks and are given by subject experts. Sufficient Problems are inserted in Worksheets so that you can choose them depending on levels such as beginner, advanced, hard, etc. Look no further and take your preparation to the next level.

Grade 11th & 12th Math Topics, Problems, Worksheets, Textbook Solutions

Grade 11 and 12 Math Topics cover the lessons belonging to absolute value, systems of equations, systems of inequalities, radicals & square roots, quadratic equations, graphing parabolas & quadratic functions, polynomials, factoring trinomials, etc. You just need to click on the quick links available for the corresponding topics so that you can learn them completely.

Ace up your preparation by having a quick look at the complete concepts of Grade 11 and Grade 12. Solve the Grade 11 and 12 Worked out Problems available on a frequent basis and attempt the exam with confidence and clear with flying colors.

Algebra

In 11 and 12 Grade Math these are the topics that are covered in Algebra.

• Variation
• Arithmetic Progression
• Geometric Progression
• Surds
• Laws of Indices
• Logarithms
• Complex Numbers
• Permutations
• Combinations
• Binomial Theorem for Positive Integral Index
• Infinite Series

Trigonometry

In 11 and 12-grade math, these are the topics that are covered in Trigonometry.

• The Negative and Associated angles
• Trigonometrical Ratios of Compound Angles
• Trigonometrical Ratios
• General Solutions of Trigonometrical Equations
• Multiple and Sub-multiple Angles
• Graphs of Trigonometrical Functions
• Properties of Triangles

Plane Analytical Geometry, Mensuration & Solid Geometry

In 11 and 12-grade math, these are the topics that are covered in Plane Analytical Geometry, Mensuration & Solid Geometry.

• Rectangular Cartesian Co-ordinates
• Polar Co-ordinates
• Transformation
• Distance between Two Points
• Division of a Line Segment
• Area of the Triangle Formed by Three co-ordinate Points
• Medians of a Triangle are Concurrent
• Apollonius’ Theorem
• Locus
• Locus of a Moving Point
• Equation of a Straight Line
• Angle between Two Lines
• Distance of a Point from a Given Line
• Equations of Circles
• Conic Section
• Parabola
• Ellipse and Hyperbola
• Diameters of Conic
• Solid Geometry

Theorems

• Theorems on Solid Geometry
• Theorems on Straight Lines and Plane
• Theorem on Co-planar
• Theorem on Parallel Lines and Plane
• Theorem of Three Perpendiculars

Mensuration

• Formulas for 3D Shapes
• Prism
• Pyramid

Formula

• Basic Math Formulas
• Math Formula Sheet on Co-Ordinate Geometry
• All Math Formula on Mensuration
• Simple Math Formula on Trigonometry

Mathematical Induction

• Mathematical Induction
• Problems on Principle of Mathematical Induction
• Proof by Mathematical Induction
• Induction Proof

Surds

• Definitions of Surds
• Order of a Surd
• Pure and Mixed Surds
• Simple and Compound Surds
• Similar and Dissimilar Surds
• Comparison of Surds
• Addition and Subtraction of Surds
• Multiplication of Surds
• Division of Surds
• Rationalization of Surds
• Conjugate Surds
• Product of two unlike Quadratic Surds
• Express of a Simple Quadratic Surd
• Properties of Surds
• Rules of Surds
• Problems on Surds

Complex Numbers

• Introduction of Complex Numbers
• Equality of Complex Numbers
• Addition of Two Complex Numbers
• Subtraction of Complex Numbers
• Multiplication of Two Complex Numbers
• Commutative Property of Multiplication of Complex Numbers
• Associative Property of Multiplication of Complex Numbers
• Division of Complex Numbers
• Integral Powers of a Complex Number
• Conjugate Complex Numbers
• Reciprocal of a Complex Number
• Complex Number in the Standard Form
• Modulus of a Complex Number
• Amplitude or Argument of a Complex Number
• Roots of a Complex Number
• Properties of Complex Numbers
• The Cube Roots of Unity
• Problems on Complex Numbers

Arithmetic Progression

• Definition of Arithmetic Progression
• General Form of an Arithmetic Progress
• Arithmetic Mean
• Sum of the First n Terms of an Arithmetic Progression
• Sum of the Cubes of First n Natural Numbers
• Sum of First n Natural Numbers
• Sum of the Squares of First n Natural Numbers
• Properties of Arithmetic Progression
• Selection of Terms in an Arithmetic Progression
• Arithmetic Progression Formulae
• Problems on Arithmetic Progression
• Problems on Sum of ‘n’ Terms of Arithmetic Progression

Geometric Progression

• Definition of Geometric Progression
• General Form and General Term of a Geometric Progression
• Sum of n terms of a Geometric Progression
• Definition of Geometric Mean
• Position of a term in a Geometric Progression
• Selection of Terms in Geometric Progression
• Sum of an infinite Geometric Progression
• Geometric Progression Formulae
• Properties of Geometric Progression
• Relation between Arithmetic Means and Geometric Means
• Problems on Geometric Progression

• Quadratic Equation has Only Two Roots
• Relation between Roots and Coefficients of a Quadratic Equation
• Quadratic Equation cannot have more than Two Roots
• Formation of the Quadratic Equation whose Roots are Given
• Nature of the Roots of a Quadratic Equation
• Complex Roots of a Quadratic Equation
• Irrational Roots of a Quadratic Equation
• Symmetric Functions of Roots of a Quadratic Equation
• Condition for Common Root or Roots of Quadratic Equations
• Theory of Quadratic Equation Formulae
• Sign of the Quadratic Expression
• Maximum and Minimum Values of the Quadratic Expression

Logarithm

• Mathematics Logarithms
• Convert Exponentials and Logarithms
• Logarithm Rules or Log Rules
• Solved Problems on Logarithm
• Common Logarithm and Natural Logarithm
• Antilogarithm

Trigonometry

Measurement of Angles

• Sign of Angles
• Trigonometric Angles
• Measure of Angles in Trigonometry
• Systems of Measuring Angles
• Important Properties on Circle
• S is Equal to R Theta
• Sexagesimal, Centesimal and Circular Systems
• Convert the Systems of Measuring Angles
• Convert Circular Measure
• Problems Based on Systems of Measuring Angles
• Length of an Arc
• Problems based on S R Theta Formula

Trigonometric Functions

• Basic Trigonometric Ratios and Their Names
• Restrictions of Trigonometrical Ratios
• Reciprocal Relations of Trigonometric Ratios
• Quotient Relations of Trigonometric Ratios
• Limit of Trigonometric Ratios
• Trigonometrical Identity
• Problems on Trigonometric Identities
• Elimination of Trigonometric Ratios
• Eliminate Theta between the equations
• Problems on Eliminate Theta
• Trig Ratio Problems
• Proving Trigonometric Ratios
• Trig Ratios Proving Problems
• Verify Trigonometric Identities
• Trigonometrical Ratios of 0°
• Trigonometrical Ratios of 30°
• Trigonometrical Ratios of 45°
• Trigonometrical Ratios of 60°
• Trigonometrical Ratios of 90°
• Trigonometrical Ratios Table
• Problems on Trigonometric Ratio of Standard Angle
• Trigonometrical Ratios of Complementary Angles
• Rules of Trigonometric Signs
• Signs of Trigonometrical Ratios
• All Sin Tan Cos Rule
• Trigonometrical Ratios of (- θ)
• Trigonometrical Ratios of (90° + θ)
• Trigonometrical Ratios of (90° – θ)
• Trigonometrical Ratios of (180° + θ)
• Trigonometrical Ratios of (180° – θ)
• Trigonometrical Ratios of (270° + θ)
• Trigonometrical Ratios of (270° – θ)
• Trigonometrical Ratios of (360° + θ)
• Trigonometrical Ratios of (360° – θ)
• Trigonometrical Ratios of any Angle
• Trigonometrical Ratios of some Particular Angles
• Trigonometric Ratios of an Angle
• Trigonometric Functions of any Angles
• Problems on Trigonometric Ratios of an Angle
• Problems on Signs of Trigonometrical Ratios

Compound Angle

• Proof of Compound Angle Formula sin (α + β)
• Proof of Compound Angle Formula sin (α – β)
• Proof of Compound Angle Formula cos (α + β)
• Proof of Compound Angle Formula cos (α – β)
• Proof of Compound Angle Formula Sin2(α – β)
• Proof of Compound Angle Formula Cos2 α – Sin2β
• Proof of Tangent Formula tan (α + β)
• Proof of Tangent Formula tan (α – β)
• Proof of Cotangent Formula cot (α + β)
• Proof of Cotangent Formula cot (α – β)
• Expansion of sin (A + B + C)
• Expansion of sin (A – B + C)
• Expansion of cos (A + B + C)
• Expansion of tan (A + B + C)
• Compound Angle Formulae
• Problems using Compound Angle Formulae
• Problems on Compound Angles

Converting Product into Sum/Difference and Vice Versa

• Converting Product into Sum or Difference
• Formulae for Converting Product into Sum or Difference
• Converting Sum or Difference into Product
• Formulae for Converting Sum or Difference into Product
• Express the Sum or Difference as a Product
• Express the Product as a Sum or Difference

Multiple Angles

• sin 2A in Terms of A
• cos 2A in Terms of A
• tan 2A in Terms of A
• sin 2A in Terms of tan A
• cos 2A in Terms of tan A
• Trigonometric Functions of A in Terms of cos 2A
• sin 3A in Terms of A
• cos 3A in Terms of A
• tan 3A in Terms of A
• Multiple Angle Formulae

Submultiple Angles

• Trigonometric Ratios of Angle A/2
• Trigonometric Ratios of Angle A/3
• Trigonometric Ratios of Angle A/2 in terms of Cos A
• Tan A/2 in terms of Tan A
• Exact value of sin 7½°
• Exact value of cos 7½°
• Exact value of tan 7½°
• Exact Value of cot 7½°
• Exact Value of tan 11¼°
• Exact Value of sin 15°
• Exact Value of cos 15°
• Exact Value of tan 15°
• Exact Value of sin 18°
• Exact Value of cos 18°
• Exact Value of sin 22½°
• Exact Value of cos 22½°
• Exact Value of tan 22½°
• Exact Value of sin 27°
• Exact Value of cos 27°
• Exact Value of tan 27°
• Exact Value of sin 36°
• Exact Value of cos 36°
• Exact Value of sin 54°
• Exact Value of cos 54°
• Exact Value of tan 54°
• Exact Value of sin 72°
• Exact Value of cos 72°
• Exact Value of tan 72°
• Exact Value of tan 142½°
• Submultiple Angle Formulae
• Problems on Submultiple Angles

Conditional Trigonometric Identities

• Identities Involving Sines and Cosines
• Sines and Cosines of Multiples or Submultiples
• Identities Involving Squares of Sines and Cosines
• Square of Identities Involving Squares of Sines and Cosines
• Identities Involving Tangents and Cotangents
• Tangents and Cotangents of Multiples or Submultiples

Graphs of Trigonometrical Functions

• Graph of y = sin x
• Graph of y = cos x
• Graph of y = tan x
• Graph of y = csc x
• Graph of y = sec x
• Graph of y = cot x

Trigonometric Equations

• General solution of the equation sin x = ½
• General solution of the equation cos x = 1/√2
• General solution of the equation tan x = √3
• General Solution of the Equation sin θ = 0
• General Solution of the Equation cos θ = 0
• General Solution of the Equation tan θ = 0
• General Solution of the Equation sin θ = sin ∝
• General Solution of the Equation sin θ = 1
• General Solution of the Equation sin θ = -1
• General Solution of the Equation cos θ = cos ∝
• General Solution of the Equation cos θ = 1
• General Solution of the Equation cos θ = -1
• General Solution of the Equation tan θ = tan ∝
• General Solution of a cos θ + b sin θ = c
• Trigonometric Equation Formula
• Trigonometric Equation using Formula
• General solution of Trigonometric Equation
• Problems on Trigonometric Equation

Inverse Trigonometric Functions

• General and Principal Values of sin-1x
• General and Principal Values of cos-1x
• General and Principal Values of tan-1x
• General and Principal Values of csc-1x
• General and Principal Values of sec-1x
• General and Principal Values of cot-1x
• Principal Values of Inverse Trigonometric Functions
• General Values of Inverse Trigonometric Functions
• arcsin(x) + arccos(x) =  π/2
• arctan(x) + arccot(x) = π/2
• arctan(x) + arctan(y) = arctan$$\frac { x+y }{1-xy}$$
• arctan(x) – arctan(y) = arctan$$\frac { x-y }{1+xy}$$
• arctan(x) + arctan(y) + arctan(z)= arctan$$\frac { x+y+z-xyz }{1-xy-yz-xz}$$
• arccot(x) + arccot(y) = arccot$$\frac { xy-1 }{y+x}$$
• arccot(x) – arccot(y) = arccot$$\frac { xy+1 }{y-x}$$
• arcsin(x) + arcsin(y) = arcsin(x√1-y2±y√1-x2)
• arcsin (x) – arcsin(y) = arcsin(x√1-y2–y√1-x2)
• arccos (x) + arccos(y) = arccos(xy-√1-x2.√1-y2)
• arccos(x) – arccos(y) = arccos(xy+√1-x2.√1-y2)
• 2 arcsin(x) = arcsin(2x.√1-x2)
• 2 arccos(x) = arccos(2x2-1)
• 2 arctan(x) = arctan( 2x/1-x2) = arcsin(2x/1+x2) = arccos((1-x2)/(1+x2)
• 3 arcsin(x) = arcsin(3x – 4x3)
• 3 arccos(x) = arccos(4x3 -3x)
• 3 arctan(x) = arctan{3x – 4x3}/{1-3x2}
• Inverse Trigonometric Function Formula
• Principal Values of Inverse Trigonometric Functions
• Problems on Inverse Trigonometric Function

Properties of Triangles

• The Law of Sines or The Sine Rule
• Theorem on Properties of Triangle
• Projection Formulae
• Proof of Projection Formulae
• The Law of Cosines or The Cosine Rule
• Area of a Triangle
• Law of Tangents
• Properties of Triangle Formulae
• Problems on Properties of Triangle

Trigonometrical Table

• Finding sin Value from Trigonometric Table
• Finding cos Value from Trigonometric Table
• Finding tan Value from Trigonometric Table
• Table of Sines and Cosines
• Table of Tangents and Cotangents

Coordinate Geometry

• What is Co-ordinate Geometry?
• Rectangular Cartesian Co-ordinates
• Polar Co-ordinates
• Relation between Cartesian and Polar Co-Ordinates
• Distance between Two given Points
• Distance between Two Points in Polar Co-ordinates
• Division of Line Segment: Internal & External
• Area of the Triangle Formed by Three co-ordinate Points
• Condition of Collinearity of Three Points
• Medians of a Triangle are Concurrent
• Apollonius’ Theorem
• Problems on Distance Between Two Points
• Area of a Triangle Given 3 Points
• Worksheet on Rectangular – Polar Conversion
• Worksheet on Line-Segment Joining the Points
• Worksheet on Distance Between Two Points
• Worksheet on Distance Between the Polar Co-ordinates
• Worksheet on Finding Mid-Point
• Worksheet on Division of Line-Segment
• Worksheet on Centroid of a Triangle
• Worksheet on Area of Co-ordinate Triangle
• Worksheet on Collinear Triangle
• Worksheet on Area of Polygon
• Worksheet on Cartesian Triangle

Locus

• Concept of Locus
• Concept of Locus of a Moving Point
• Locus of a Moving Point
• Worked-out Problems on Locus of a Moving Point
• Worksheet on Locus of a Moving Point
• Worksheet on Locus

The Straight Line

• Straight Line
• Slope of a Straight Line
• Slope of a Line through Two Given Points
• Collinearity of Three Points
• Equation of a Line Parallel to x-axis
• Equation of a Line Parallel to y-axis
• Slope-intercept Form
• Point-slope Form
• Straight line in Two-point Form
• Straight Line in Intercept Form
• Straight Line in Normal Form
• General Form into Slope-intercept Form
• General Form into Intercept Form
• General Form into Normal Form
• Point of Intersection of Two Lines
• Concurrency of Three Lines
• Angle between Two Straight Lines
• Condition of Parallelism of Lines
• Equation of a Line Parallel to a Line
• Condition of Perpendicularity of Two Lines
• Equation of a Line Perpendicular to a Line
• Identical Straight Lines
• Position of a Point Relative to a Line
• Distance of a Point from a Straight Line
• Equations of the Bisectors of the Angles between Two Straight Lines
• Bisector of the Angle which Contains the Origin
• Straight Line Formulae
• Problems on Straight Lines
• Word Problems on Straight Lines
• Problems on Slope and Intercept

The Circle

• Definition of Circle
• Equation of a Circle
• General Form of the Equation of a Circle
• General Equation of Second Degree Represents a Circle
• Centre of the Circle Coincides with the Origin
• Circle Passes through the Origin
• Circle Touches x-axis
• Circle Touches y-axis
• Circle Touches both x-axis and y-axis
• Centre of the Circle on x-axis
• Centre of the Circle on y-axis
• Circle Passes through the Origin and Centre Lies on x-axis
• Circle Passes through the Origin and Centre Lies on y-axis
• Equation of a Circle when Line Segment Joining Two Given Points is a Diameter
• Equations of Concentric Circles
• Circle Passing Through Three Given Points
• Circle Through the Intersection of Two Circles
• Equation of the Common Chord of Two Circles
• Position of a Point with Respect to a Circle
• Intercepts on the Axes made by a Circle
• Circle Formulae
• Problems on Circle

The Parabola

• Concept of Parabola
• Standard Equation of a Parabola
• Standard form of Parabola y2 =-4ax
• Standard form of Parabola x2=4ay
• Standard form of Parabola x2=-4ay
• Parabola whose Vertex at a given Point and Axis is Parallel to x-axis
• Parabola whose Vertex at a given Point and Axis is Parallel to y-axis
• Position of a Point with respect to a Parabola
• Parametric Equations of a Parabola
• Parabola Formulae
• Problems on Parabola

The Ellipse

• Definition of Ellipse
• Standard Equation of an Ellipse
• Two Foci and Two Directrices of the Ellipse
• Vertex of the Ellipse
• Centre of the Ellipse
• Major and Minor Axes of the Ellipse
• Latus Rectum of the Ellipse
• Position of a Point with respect to the Ellipse
• Ellipse Formulae
• Focal Distance of a Point on the Ellipse
• Problems on Ellipse

The Hyperbola

• Definition of Hyperbola
• Standard Equation of an Hyperbola
• Vertex of the Hyperbola
• Centre of the Hyperbola
• Transverse and Conjugate Axis of the Hyperbola
• Two Foci and Two Directrices of the Hyperbola
• Latus Rectum of the Hyperbola
• Position of a Point with Respect to the Hyperbola
• Conjugate Hyperbola
• Rectangular Hyperbola
• Parametric Equation of the Hyperbola
• Hyperbola Formulae
• Problems on Hyperbola

Solid Geometry

• Solid Geometry
• Worksheet on Solid Geometry
• Theorems on Solid Geometry
• Theorems on Straight Lines and Plane
• Theorem on Co-planar
• Theorem on Parallel Lines and Plane
• Theorem of Three Perpendiculars
• Worksheet on Theorems of Solid Geometry

Mensuration

• Formulas for 3D Shapes
• Volume and Surface Area of the Prism
• Worksheet on Volume and Surface Area of Prism
• Volume and Whole Surface Area of Right Pyramid
• Volume and Whole Surface Area of Tetrahedron
• Volume of a Pyramid
• Volume and Surface Area of a Pyramid
• Problems on Pyramid
• Worksheet on Volume and Surface Area of a Pyramid
• Worksheet on Volume of a Pyramid

Math Objectives for 11th & 12th Grade Curriculum

Depending on the 11th & 12th Grade Math Curriculums you have to meet certain guidelines and they are as follows

• To be able to Solve One Variable Linear Inequalities including Compound Inequalities, represent solutions set both algebraically and graphically.
• Find the Solutions of Quadratic Equations by completing the square.
• Analyze and factor the Polynomials completely.
• Convert between degree and radian measures.
• Identify and Analyze the Graphs of Logarithmic Functions.

Why one should learn from Grade 11 & 12 Math Lessons?

Go through the following steps to learn about the advantages of Grade 11 & 12 Math Topics listed here. They are as such

• Student Paced Learning Promotes effective learning alongside reduces anxiety in students.
• Master the 11th Grade & 12th Grade Topics by retaking the quizzes and tests.
• You can access the Learning Materials irrespective of your busy schedules.
• Interactive Lesson Activities provided help to learn the concepts in an efficient manner.
• Builds prior knowledge and skills through interactive lessons, exercises, practice opportunities.

Summary

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