MHT CET Mathematics Syllabus: Check the Latest Syllabus

1. For any two angles A and B, cos (A -B) = cos A cos B + sin A sin B

2. For any two angles A and B, cos (A + B) = cos A cos B − sin A sin B

3. For any two angles A and B, sin (A − B) = sin A cos B − cos A sin B

4. For any two angles A and B, sin (A + B) = sin A cos B + cos A sin B

5. For any two angles A and B, tan (A + B) =` (tan A + tan B)/(1 –tan A tan B)`

6. For any two angles A and B, tan (A -B) = `(tan A -tan B)/(1 + tan A tan B)`

• Definition:  Line of Sight
• Definition: Angles of Elevation
• Definition: Angle of Depression

• Equation of a locus

• Slope of a Line Or Gradient of a Line.
• Parallelism of Line
• Perpendicularity of Line in Term of Slope
• Collinearity of Points
• Slope of a line when coordinates of any two points on the line are given
• Conditions for parallelism and perpendicularity of lines in terms of their slopes
• Angle between two lines
• Collinearity of three points

• Introduction of Distance of a Point from a Line
• Distance between two parallel lines

• Locus
• Equation of Locus
• Shift of Origin

• Inclination of a line
• Slope of a line
• Perpendicular Lines
• Angle between intersecting lines
• Different Forms of an equation of a straight line
• General form to other forms

• Point-slope Form
• Slope-Intercept form
• Two-points Form
• Double-Intercept form
• Normal Form

• Standard form
• Centre-radius form
• Diameter Form

The general equation of a circle is of the form x² + y² + 2gx + 2fy + c = 0, if g² + f² − e > 0.

• Introduction
• Definition: Secant
• Definition: Tangent
• Key Points Summary

1. Variance and Standard Deviation for raw data
2. Variance and Standard Deviation for ungrouped frequency distribution
3. Variance and Standard Deviation for grouped frequency distribution

• Mean deviation for grouped data
• Mean deviation for ungrouped data

• Random Experiment
• Outcome
• Sample space
• Favourable Outcome

1. Using the definition of probability
2. Using Venn diagram

• Independent Events

• Partition of a sample space
• Theorem of total probability

• Imaginary number
• Complex Number

• Equality of two Complex Numbers 
• Conjugate of a Complex Number 
• Properties of `barz`
• Addition of complex numbers - Properties of addition, Scalar Multiplication
• Subtraction of complex numbers - Properties of Subtraction
• Multiplication of complex numbers - Properties of Multiplication
• Powers of i in the complex number
• Division of complex number - Properties of Division
• The square roots of a negative real number
• Identities

• Geometrical representation of conjugate of a complex number
• Properties of Complex Conjugates

• Solution of a Quadratic Equation in complex number system

• Properties of Modulus of a complex number
• Square roots of a complex number 

• Modulus of z
• Argument of z
• Argument of z in different quadrants/axes - Properties of modulus of complex numbers, Properties of arguments 
• Polar & Exponential form of C.N.

• Properties of 1, w, w²

• Tree Diagram 
• Addition Principle 
• Multiplication principle

• Properties of the factorial notation:
  For any positive integers m, n.,
  1) n! = n × (n - 1)!
  2) n > 1, n! = n × (n - 1) × (n - 2)!
  3) n > 2, n! = n × (n - 1) × (n - 2) × (n - 3)!
  4) (m + n)! is always divisible by m! as well as by n!
  5) (m × n)! ≠ m! × n!
  6) (m + n)! ≠ m! + n!
  7) m > n, (m - n)! ≠ m! - n! but m! is divisible by n!
  8) (m ÷ n)! ≠ m! ÷ n

• Permutation
• Permutation of repeated things
• Permutations when all the objects are not distinct
• Number of Permutations Under Certain Restricted Conditions
• Circular Permutations

• ⁿC_r , ⁿC_n =1, ⁿC₀ = 1, ⁿC_r = ⁿC_n–r, ⁿC_x = ⁿC_y, then x + y = n or x = y, ⁿ⁺¹C_r = ⁿC_r-1 + ⁿC_r
• When all things are different
• When all things are not different.
• Mixed problems on permutation and combinations.

• Properties of Combinations:
  1. Consider ⁿC_{n - r} = ⁿC_r for 0 ≤ r ≤ n.
  2. ⁿC₀ = `(n!)/(0!(n - 0)!) = (n!)/(n!) = 1, because 0! = 1` as has been stated earlier.
  3. If ⁿC_r = ⁿC_s, then either s = r or s = n - r.
  4. `"" ^nC_r = (""^nP_r)/(r!)`
  5. ⁿC_r + ⁿC_{r - 1} = ^{n + 1}C_r
  6. ⁿC₀ + ⁿC₁ + ......... ⁿC_n = 2ⁿ 
  7. ⁿC₀ + ⁿC₂ + ⁿC₄ + ...... = ⁿC₁ + ⁿC₃ + ⁿC₅ + ....... = 2^{(n - 1)}
  8. ⁿC_r = `"" (n/r) ^(n - 1)C_(r- 1) = (n/r)((n - 1)/(r - 1)) ^(n - 2)C_(r - 2) = ....`
  9. ⁿC_r has maximum value if (a) r = `n/2 "when n is even (b)" r = (n - 1)/2 or (n + 1)/2` when n is odd.

• Composition of Functions
• Inverse functions
• Piecewise Defined Functions
  1) Signum function
  2) Absolute value function (Modulus function)
  3) Greatest Integer Function (Step Function)
  4) Fractional part function

• Definition of Limit
• One-Sided Limit
• Left-hand Limit
• Right-hand Limit
• Existence of a limit of a function at a point x = a
• Algebra of limits:
  Let f(x) and g(x) be two functions such that
  `lim_(x→a) f(x) = l and lim_(x → a) g(x) = m, then`
  1. `lim_(x → a) [f(x) ± g(x)] = lim_(x → a) f(x) ± lim_(x → a) g(x) = l ± m`
  2. `lim_(x → a) [f(x) xx g(x)] = lim_(x→ a) f(x) xx lim_(x→ a) g(x) = l xx m`
  3. `lim_(x → a) [kf(x)] = k xx lim_(x→ a) f(x) = kl, "where" ‘k’ "is a constant"`
  4. `lim_(x → a) f(x)/g(x) = (lim_(x → a) f(x))/(lim_(x → a) g(x)) = l/m "where" m≠ 0`.

1. `lim_(x → 0) ((e^x - 1)/x) = log e = 1`

2. `lim_(x → 0) ((a^x - 1)/x) = log a (a > 0, a ≠ 0)`

3. `lim_(x → 0) [ 1 + x]^(1/x) = e`

4. `lim_(x → 0) (log(1 + x)/x) = 1`

5. `lim_(x → 0) ((e^(px) - 1)/(px)) = 1`, (p constant)

6. `lim_(x → 0) ((a^(px) - 1)/(px)) = log a`, (p constant)

7. `lim_(x → 0) (log(1 + px)/(px)) = 1`, (p constant)

8. `lim_(x → 0) [ 1 + px]^(1/(px)) = e`, (p constant)

• Limit at infinity
• Infinite Limits

• Continuity of a function at a point
• Definition of Continuity
• Continuity from the right and from the left
• Examples of Continuous Functions
• Properties of continuous functions
• Types of Discontinuities
• Jump Discontinuity
• Removable Discontinuity
• Infinite Discontinuity
• Continuity over an interval
• The intermediate value theorem for continuous functions

Discontinuous Function

• Geometric description of conic section
• Degenerate Forms
•  Identifying the conics from the general equation of the conic 

• Introduction
• Definition: Sets
• Well-defined and Not Well-defined Sets
• Elements of a Set and Notation
• Properties of Sets
• Examples
• Real-Life Applications
• Key Points Summary

• N^th Term of Geometric Progression (G.P.)
• General Term of a Geometric Progression (G.P.)
• Sum of First N Terms of a Geometric Progression (G.P.)
• Sum of infinite terms of a G.P.
• Geometric Mean (G.M.)

• Sum to infinite terms of a G.P.

• Arithmetic mean (A. M.)
• Geometric mean (G. M.) 
• Harmonic mean (H. M.)

• n^th term of A.G.P.
• Sum of n terms of A.G.P.
• Properties of Summation

• Concept of Statements

1. Conjunction (∧)
2. Disjunction (∨)
3. Conditional statement (Implication) (→)
4. Biconditional (Double implication) (↔) or (⇔)
5. Negation (∼)

• Universal quantifier (∀)
• Existential quantifier (∃)

• Negation of conjunction
• Negation of disjunction
• Negation of implication
• Negation of biconditional

• Idempotent law
• Associative law
• Commutative law
• Distributive law
• Identity law
• Complement law
• Involution law
• DeMorgan’s laws

• Two switches in series
• Two switches in parallel

• Interchange of any two rows or any two columns
• Multiplication of the elements of any row or column by a non-zero scalar
• Adding the scalar multiples of all the elements of any row (column) to corresponding elements of any other row (column)

• Method of Inversion
• Method of Reduction

• Trigonometric equation
• Solution of Trigonometric equation
• Principal Solutions
• The General Solution

• Polar co-ordinates
• Relation between the polar co-ordinates and the Cartesian co-ordinates
• Solving a Triangle
• The Sine rule
• The Projection rule
• Applications of the Sine rule, the Cosine rule and the Projection rule

• Introduction of Inverse Trigonometric Functions

• Degree of a term
• Homogeneous Equation

• The necessary conditions for a general second degree equation
  ax² + 2hxy + by² + 2gx + 2fy + c = 0

1. abc + 2fgh - af² - bg² - ch² = 0
2. h² - ab ≥ 0

• Equation of a line through a given point and parallel to a given vector `vec b`
• Equation of a line passing through two given points

• Addition of Two Vectors
  - Parallelogram Law
  - Triangle Law of addition of two vectors
• Subtraction of two vectors
• Scalar multiplication of a vector

• Co-ordinates of a point in space
• Co-ordinates of points on co-ordinate axes
• Co-ordinates of points on co-ordinate planes
• Distance of P(x, y, z) from co-ordinate planes
• Distance of any point from origin
• Distance between any two points in space
• Distance of a point P(x, y, z) from coordinate axes

• Vector addition using components
• Components of a vector in two dimensions space
• Components of a vector in three-dimensional space

• Formula
• Division of Line Segment
• Proof
• Examples

• Equation of a line passing through a given point and parallel to given vector
• Equation of a line passing through given two points

• Introduction of Distance of a Point from a Line
• Distance between two parallel lines

• Distance between skew lines
• Distance between parallel lines

• Passing through a point and perpendicular to a vector
• Passing through a point and parallel to two vectors
• Passing through three non-collinear points
• In normal form
• Passing through the intersection of two planes

• Angle between two planes
• Angle between a line and a plane

• Convex Sets
• Graphical representation of linear inequations in two variables
• Graphical solution of linear inequation

• Meaning of Linear Programming Problem
• Mathematical formulation of a linear programming problem
• Familiarize with terms related to Linear Programming Problem

• Graphical method of solution for problems in two variables
• Feasible and infeasible regions and bounded regions
• Feasible and infeasible solutions
• Optimum feasible solution

• Rule of Differentiation
• Introduction

• First and Second Derivative test
• Determine critical points of the function
• Find the point(s) of local maxima and local minima and corresponding local maximum and local minimum values
• Find the absolute maximum and absolute minimum value of a function

1. `int1/(x^2 + a^2) dx = 1/a tan^-1 (x/a) + c`
2. `int1/(x^2 - a^2) dx = 1/(2a) log ((x - a)/(x + a)) + c`
3. `int1/(a^2 - x^2) dx = 1/(2a) log ((a + x)/(a - x)) + c`
4. `int1/sqrt(a^2 - x^2) dx = sin^-1 (x/a) + c`
5. `int1/sqrt(x^2 - a^2) dx = log ( x + sqrt(x^2 - a^2))+ c`
6. `int1/sqrt(x^2 + a^2) dx = log ( x + sqrt(x^2 + a^2))+ c`
7. `int1/(xsqrt(x^2 - a^2)) dx = 1/a sec^-1(x/a) + c`

• `int(u.v) dx = u intv dx - int((du)/(dx)).(intvdx) dx`

• Simple curves: lines, parabolas, polynomial functions

• Formation of Differential equations from Physical Situations
• Formation of Differential Equations from Geometrical Problems

• Population Growth and Growth of bacteria
• Ratio active Decay
• Newton's Law of Cooling
• Surface Area

• Discrete random variable
• Continuous random variable
• Probability Mass Function
• Cumulative Distribution Function or Distribution Function
• Cumulative Distribution Function from Probability Mass function
• Probability Mass Function from Cumulative Distribution Function