INDIA MATH CLASS XI – EDmama India

A. Introduction to Probability

A.01. Define probability and related terms (event, sample space, outcome).
A.02. Understand the difference between theoretical and experimental probability.
A.03. Calculate theoretical probabilities of simple events.
A.04. Calculate experimental probabilities from data.
A.05. Apply the counting principle to determine the number of outcomes.
A.06. Determine probabilities of compound events
A.07. Apply geometric probability to calculate probabilities.
A.08. Solve probability problems using simulations.

B. Descriptive Statistics

C. Logic and Reasoning

C.01. Identify hypotheses and conclusions in statements.
C.02. Understand and provide counterexamples to disprove statements.
C.03. Construct and interpret truth tables for logical statements.
C.04. Determine truth values of simple and compound statements.
C.05. Recognize and use conditional statements (if-then).
C.06. Formulate negations of statements.
C.07. Relate converses, inverses, and contrapositives of conditional statements.
C.08. Understand and use biconditional statements (if and only if).
C.09. Apply logical reasoning to solve mathematical problems.

D. Consumer Mathematics

E. Single-Variable Inequalities

E.01. Graph linear inequalities on a number line.
E.02. Write linear inequalities from their graphs.
E.03. Identify solutions to linear inequalities.
E.04. Solve one-step linear inequalities using addition and subtraction.
E.05. Solve one-step linear inequalities using multiplication and division, paying attention to sign changes.
E.06. Solve one-step linear inequalities involving multiple operations.
E.07. Graph solutions to one-step linear inequalities on a number line.
E.08. Solve two-step linear inequalities.
E.09. Graph solutions to two-step linear inequalities.
E.10. Solve advanced linear inequalities involving distribution and combining like terms.
E.11. Graph solutions to advanced linear inequalities.
E.12. Graph compound inequalities (AND/OR) on a number line.
E.13. Write compound inequalities from their graphs.
E.14. Solve compound inequalities.
E.15. Graph solutions to compound inequalities.
E.16. Graph solutions to quadratic inequalities.
E.17. Solve quadratic inequalities algebraically.
E.18. Apply inequalities to solve real-world problems involving constraints.

F. Relations and Functions

F.01. Represent relations using tables, graphs, mappings, and lists of points, and convert between these representations.
F.02. Determine the domain and range of a relation from its various representations.
F.03. Identify independent and dependent variables in a relation.
F.04. Define what constitutes a function.
F.05. Identify functions using the vertical line test on a graph.
F.06. Determine function values using function graphs.
F.07. Evaluate a function for a given input value.
F.08. Evaluate a function by substituting an expression for the variable.
F.09. Complete a function table from a graph.
F.10. Complete a function table from an equation.
F.11. Interpret the graph of a function in the context of word problems.
F.12. Identify different types of functions (linear, quadratic, exponential, etc.) from their graphs and equations.

G. Linear Functions

G.01. Determine the slope of a line from its graph.
G.02. Calculate the slope of a line given two points on the line.
G.03. Find a missing coordinate given the slope and another point on the line.
G.04. Identify the slope and y-intercept from the slope-intercept form of a linear equation.
G.05. Graph a linear equation using the slope-intercept form.
G.06. Write the equation of a line in slope-intercept form from its graph.
G.07. Write the equation of a line in slope-intercept form given the slope and a point or two points.
G.08. Write the equation of a line in slope-intercept form from a table of values.
G.09. Write the equation of a line in slope-intercept form from a word problem.
G.10. Write linear functions to solve word problems.
G.11. Complete a table of values and graph a linear function.
G.12. Write equations in standard form (Ax + By = C).
G.13. Find the x- and y-intercepts from the standard form of a linear equation.
G.14. Graph a linear equation using the standard form.
G.15. Recognize and write equations of horizontal and vertical lines.
G.16. Graph horizontal and vertical lines.
G.17. Determine the slopes of parallel and perpendicular lines.
G.18. Write the equation of a line parallel or perpendicular to a given line passing through a specified point.
G.19. Describe and perform transformations of linear functions (translations, reflections, dilations).
G.20. Analyze the impact of changing parameters (slope, y-intercept) on the graph of a linear function.

H. Linear Inequalities

H.01. Determine if a given point (x, y) satisfies a linear inequality.
H.02. Solve a linear inequality for y to express it in slope-intercept form.
H.03. Graph a linear inequality in the coordinate plane.
H.04. Solve linear inequality word problems.
H.05. Determine if a given point (x, y) is a solution to a system of linear inequalities.
H.06. Solve systems of linear inequalities by graphing.
H.07. Solve systems of linear and absolute value inequalities by graphing.
H.08. Model real-world constraints using systems of linear inequalities and find feasible regions.

I. Complex Numbers

I.02. Add and subtract complex numbers.
I.03. Define and find the complex conjugate of a complex number.
I.04. Multiply complex numbers.
I.05. Divide complex numbers.
I.06. Perform all basic arithmetic operations (addition, subtraction, multiplication, and division) with complex numbers.
I.07. Calculate the absolute value (or modulus) of a complex number.
I.08. Simplify powers of i.
I.09. Convert complex numbers between rectangular and polar forms.
I.01. Define the imaginary unit i and understand the concept of complex numbers.

J. Argand Plane

J.01. Introduce the Argand plane (complex plane) and its components.
J.02. Graph complex numbers on the Argand plane.
J.03. Perform addition of complex numbers graphically on the Argand plane.
J.04. Perform subtraction of complex numbers graphically on the Argand plane.
J.05. Graph complex conjugates on the Argand plane and recognize their symmetry.
J.06. Determine the absolute value of a complex number graphically on the Argand plane.
J.07. Find the midpoint of a line segment connecting two complex numbers on the Argand plane.
J.08. Calculate the distance between two complex numbers on the Argand plane.
J.09. Represent geometric transformations of complex numbers on the Argand plane.

K. Factoring

L. Quadratic Functions

L.01. Identify key characteristics of quadratic functions (vertex, axis of symmetry, intercepts).
L.02. Complete a function table for quadratic functions.
L.03. Write a quadratic function given specific points or properties.
L.04. Graph a quadratic function.
L.05. Match quadratic functions to their corresponding graphs.
L.06. Solve a quadratic equation using square roots.
L.07. Solve a quadratic equation using the zero product property.
L.08. Solve a quadratic equation by factoring.
L.09. Complete the square to rewrite a quadratic equation.
L.10. Solve a quadratic equation using the quadratic formula.
L.11. Use the discriminant to determine the nature of the roots of a quadratic equation.
L.12. Apply quadratic functions to model real-world scenarios.

M. Polynomials

M.01. Understand polynomial vocabulary (degree, leading coefficient, terms).
M.02. Add and subtract polynomials.
M.03. Multiply polynomials.
M.04. Divide polynomials using long division.
M.05. Divide polynomials using synthetic division.
M.06. Evaluate polynomials using synthetic division (Remainder Theorem).
M.07. Solve polynomial equations.
M.08. Write a polynomial given its roots.
M.09. Find the roots of factorised polynomials.
M.10. Apply the Rational Root Theorem to find potential rational roots of a polynomial.
M.11. Understand and apply the Complex Conjugate Theorem.
M.12. Understand and apply Conjugate Root Theorems.
M.13. Match polynomials to their corresponding graphs.
M.14. State and understand the Fundamental Theorem of Algebra.
M.15. Construct Pascal’s triangle.
M.16. Relate Pascal’s triangle to the Binomial Theorem.
M.17. Apply the Binomial Theorem to expand binomials (Part I).
M.18. Apply the Binomial Theorem to find specific terms in a binomial expansion (Part II).
M.19. Use polynomial functions to model and solve real-world problems.

N. Parabolas

N.01. Identify the direction a parabola opens (upward or downward).
N.02. Find the vertex of a parabola.
N.03. Find the focus and directrix of a parabola.
N.04. Find the axis of symmetry of a parabola.
N.05. Write equations of parabolas in vertex form from graphs.
N.06. Write equations of parabolas in vertex form using given properties (vertex, focus, directrix).
N.07. Convert equations of parabolas from general to vertex form.
N.08. Find properties of a parabola from equations in general form.
N.09. Graph parabolas.
N.10. Solve application problems involving parabolas.

O. Circles

O.01. Find the center of a circle given its equation or graph.
O.02. Find the radius or diameter of a circle given its equation or graph.
O.03. Write equations of circles in standard form from graphs.
O.04. Write equations of circles in standard form using given properties (center, radius).
O.05. Convert equations of circles from general to standard form.
O.06. Find properties of circles from equations in general form.
O.07. Graph circles.
O.08. Determine the points of intersection between a circle and a line.

P. Ellipses

P.01. Find the center, vertices, and co-vertices of an ellipse.
P.02. Find the length of the major and minor axes of an ellipse.
P.03. Find the foci of an ellipse.
P.04. Write equations of ellipses in standard form from graphs.
P.05. Write equations of ellipses in standard form using given properties (center, vertices, foci).
P.06. Convert equations of ellipses from general to standard form.
P.07. Find properties of ellipses from equations in general form.
P.08. Graph ellipses.
P.09. Apply properties of ellipses to solve real-world problems.

Q. Hyperbolas

Q.01. Find the center of a hyperbola.
Q.02. Find the vertices of a hyperbola.
Q.03. Find the length of the transverse and conjugate axes of a hyperbola.
Q.04. Find the equations of the asymptotes of a hyperbola.
Q.05. Find the foci of a hyperbola.
Q.06. Write equations of hyperbolas in standard form from graphs.
Q.07. Write equations of hyperbolas in standard form using given properties (center, vertices, foci, asymptotes).
Q.08. Convert equations of hyperbolas from general to standard form.
Q.09. Find properties of hyperbolas from equations in general form.
Q.10. Graph hyperbolas.
Q.11. Apply properties of hyperbolas to solve real-world problems.

R. Rational Functions and Expressions

R.01. Identify asymptotes and excluded values of rational functions.
R.02. Evaluate rational expressions for given values of the variable (Part I).
R.03. Evaluate rational expressions for given values of the variable (Part II).
R.04. Simplify rational expressions.
R.05. Multiply and divide rational expressions.
R.06. Add and subtract rational expressions.
R.07. Solve rational equations.
R.08. Graph rational functions, identifying key features like asymptotes and intercepts.

S. Exponential and Logarithmic Functions

T. Function Operations

U. Angle Measures

V. Trigonometry

V.01. Apply Pythagoras’ Theorem and its converse.
V.02. Solve problems involving special right triangles (30-60-90 and 45-45-90).
V.03. Define trigonometric ratios (sin, cos, tan) in right triangles.
V.04. Define reciprocal trigonometric ratios (csc, sec, cot).
V.05. Understand that trigonometric ratios are constant for similar right triangles.
V.06. Find trigonometric ratios using the unit circle.
V.07. Determine the values of sin, cos, and tan for special angles (0, 30, 45, 60, 90 degrees).
V.08. Determine the values of csc, sec, and cot for special angles.
V.09. Find trigonometric function values using a calculator.
V.10. Determine the inverses of sin, cos, and tan.
V.11. Determine the inverses of csc, sec, and cot.
V.12. Solve trigonometric equations (Part I).
V.13. Solve trigonometric equations (Part II).
V.14. Use trigonometric ratios to find a side length in a right triangle.
V.15. Use trigonometric ratios to find an angle measure in a right triangle.
V.16. Solve a right triangle (find all sides and angles).
V.17. Apply the Law of Sines to solve triangles.
V.18. Apply the Law of Cosines to solve triangles.
V.19. Solve a triangle given sufficient information.
V.20. Calculate the area of a triangle using the sine formula.
V.21. Calculate the area of a triangle using the Law of Sines.
V.22. Solve application problems involving trigonometry.

W. Trigonometric Functions

W.01. Find properties of sine functions (amplitude, period, phase shift, vertical shift).
W.02. Write equations of sine functions from graphs.
W.03. Write equations of sine functions using given properties.
W.04. Graph sine functions.
W.05. Find properties of cosine functions.
W.06. Write equations of cosine functions from graphs.
W.07. Write equations of cosine functions using given properties.
W.08. Graph cosine functions.
W.09. Graph both sine and cosine functions on the same axes and compare their properties.
W.10. Model periodic phenomena using trigonometric functions.

X. Trigonometric Identities

Y. Problem Solving

Z. Sequences and Series

Z.01. Classify formulas and sequences as arithmetic, geometric, or neither.
Z.02. Find terms of an arithmetic sequence.
Z.03. Find terms of a geometric sequence.
Z.04. Find terms of a recursive sequence.
Z.05. Evaluate formulas for sequences.
Z.06. Write a formula for an arithmetic sequence.
Z.07. Write a formula for a geometric sequence.
Z.08. Write a formula for a recursive sequence.
Z.09. Solve mixed review problems involving sequences.
Z.10. Understand and use sigma notation to represent series.
Z.11. Identify arithmetic and geometric series.
Z.12. Find the sum of a finite arithmetic or geometric series.
Z.13. Introduce the concept of partial sums.
Z.14. Calculate partial sums of arithmetic series.
Z.15. Calculate partial sums of geometric series.
Z.16. Solve mixed review problems involving partial sums.
Z.17. Determine if a geometric series is convergent or divergent.
Z.18. Find the value of an infinite geometric series.
Z.19. Write a repeating decimal as a fraction using geometric series.
Z.20. Apply sequences and series to solve financial and growth problems.

AA. Introduction to Limits

BB. Calculate Limits

CC. Limits Involving Infinity

DD. Limits and Rational Functions

EE. Continuity

EE.01. Identify graphs of continuous functions.
EE.02. Determine continuity of a function using graphs.
EE.03. Determine one-sided continuity using graphs.
EE.04. Find and analyse points of discontinuity using graphs (removable, jump, infinite).
EE.05. Determine continuity on an interval using graphs.
EE.06. Determine the continuity of a piecewise function at a point.
EE.07. Make a piecewise function continuous by choosing appropriate parameters.
EE.08. Apply the Intermediate Value Theorem.
EE.09. Relate continuity to differentiability.

FF. Introduction to Derivatives

FF.01. Calculate the average rate of change of a function (Part I).
FF.02. Calculate the average rate of change of a function (Part II).
FF.03. Find instantaneous rates of change using limits.
FF.04. Interpret velocity as a rate of change.
FF.05. Find values of derivatives using limits.
FF.06. Find the slope of a tangent line using limits.
FF.07. Find equations of tangent lines using limits.
FF.08. Understand the relationship between the derivative and the slope of a curve.

GG. Calculate Derivatives

GG.01. Apply the sum and difference rules of differentiation.
GG.02. Apply the product rule of differentiation.
GG.03. Apply the quotient rule of differentiation.
GG.04. Apply the power rule of differentiation (Part I).
GG.05. Apply the power rule of differentiation (Part II).
GG.06. Find derivatives of polynomials.
GG.07. Find derivatives of rational functions.
GG.08. Find derivatives of trigonometric functions (Part I).
GG.09. Find derivatives of trigonometric functions (Part II).
GG.10. Apply the chain rule of differentiation.
GG.11. Find derivatives of radical functions.
GG.12. Find derivatives using the product rule.
GG.13. Find derivatives using the quotient rule (Part I).
GG.14. Find derivatives using the quotient rule (Part II).
GG.15. Find derivatives using the chain rule (Part I).
GG.16. Find derivatives using the chain rule (Part II).
GG.17. Use implicit differentiation to find derivatives.

Course Content

A. Introduction to Probability

A.01. Define probability and related terms (event, sample space, outcome).

A.02. Understand the difference between theoretical and experimental probability.

A.03. Calculate theoretical probabilities of simple events.

A.04. Calculate experimental probabilities from data.

A.05. Apply the counting principle to determine the number of outcomes.

A.06. Determine probabilities of compound events

A.07. Apply geometric probability to calculate probabilities.

A.08. Solve probability problems using simulations.

B. Descriptive Statistics

B.01. Calculate and interpret measures of central tendency: mean, median, and mode.

B.02. Determine the range and interquartile range (IQR) of a data set.

B.03. Calculate quartiles and represent data using box plots.

B.04. Understand the concept of biased samples and their effect on statistical results.

B.05. Calculate the mean absolute deviation (MAD) of a data set.

B.06. Calculate variance and standard deviation to measure data dispersion.

B.07. Analyze the effects of outliers on measures of central tendency and dispersion.

C. Logic and Reasoning

C.01. Identify hypotheses and conclusions in statements.

C.02. Understand and provide counterexamples to disprove statements.

C.03. Construct and interpret truth tables for logical statements.

C.04. Determine truth values of simple and compound statements.

C.05. Recognize and use conditional statements (if-then).

C.06. Formulate negations of statements.

C.07. Relate converses, inverses, and contrapositives of conditional statements.

C.08. Understand and use biconditional statements (if and only if).

C.09. Apply logical reasoning to solve mathematical problems.

D. Consumer Mathematics

D.01. Calculate simple interest earned on an investment or loan.

D.02. Compute compound interest and understand its effects over time.

D.03. Calculate continuously compounded interest using the formula A = Pe^(rt).

D.04. Calculate percentage increases and decreases, including VAT, discounts, and markups.

D.05. Determine the original price after a discount or markup when given the final price and percentage.

D.06. Solve multi-step problems involving percentages in real-world contexts.

D.07. Compare different loan options based on interest rates and repayment schedules.

E. Single-Variable Inequalities

E.01. Graph linear inequalities on a number line.

E.02. Write linear inequalities from their graphs.

E.03. Identify solutions to linear inequalities.

E.04. Solve one-step linear inequalities using addition and subtraction.

E.05. Solve one-step linear inequalities using multiplication and division, paying attention to sign changes.

E.06. Solve one-step linear inequalities involving multiple operations.

E.07. Graph solutions to one-step linear inequalities on a number line.

E.08. Solve two-step linear inequalities.

E.09. Graph solutions to two-step linear inequalities.

E.10. Solve advanced linear inequalities involving distribution and combining like terms.

E.11. Graph solutions to advanced linear inequalities.

E.12. Graph compound inequalities (AND/OR) on a number line.

E.13. Write compound inequalities from their graphs.

E.14. Solve compound inequalities.

E.15. Graph solutions to compound inequalities.

E.16. Graph solutions to quadratic inequalities.

E.17. Solve quadratic inequalities algebraically.

E.18. Apply inequalities to solve real-world problems involving constraints.

F. Relations and Functions

F.01. Represent relations using tables, graphs, mappings, and lists of points, and convert between these representations.

F.02. Determine the domain and range of a relation from its various representations.

F.03. Identify independent and dependent variables in a relation.

F.04. Define what constitutes a function.

F.05. Identify functions using the vertical line test on a graph.

F.06. Determine function values using function graphs.

F.07. Evaluate a function for a given input value.

F.08. Evaluate a function by substituting an expression for the variable.

F.09. Complete a function table from a graph.

F.10. Complete a function table from an equation.

F.11. Interpret the graph of a function in the context of word problems.

F.12. Identify different types of functions (linear, quadratic, exponential, etc.) from their graphs and equations.

G. Linear Functions

G.01. Determine the slope of a line from its graph.

G.02. Calculate the slope of a line given two points on the line.

G.03. Find a missing coordinate given the slope and another point on the line.

G.04. Identify the slope and y-intercept from the slope-intercept form of a linear equation.

G.05. Graph a linear equation using the slope-intercept form.

G.06. Write the equation of a line in slope-intercept form from its graph.

G.07. Write the equation of a line in slope-intercept form given the slope and a point or two points.

G.08. Write the equation of a line in slope-intercept form from a table of values.

G.09. Write the equation of a line in slope-intercept form from a word problem.

G.10. Write linear functions to solve word problems.

G.11. Complete a table of values and graph a linear function.