New Mathematics Short Tricks Notes for CGPSC

Hello Aspirants,

Mathematics Notes Outline:

Number Systems and Basic Operations:

Natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, complex numbers.
Addition, subtraction, multiplication, division.
Algebra:

Equations and Inequalities.
Polynomials and Factoring.
Exponents and Radicals.
Functions and Graphs.
Geometry:

Euclidean Geometry: Lines, angles, triangles, quadrilaterals, circles.
Coordinate Geometry: Distance, midpoint, slope, equations of lines and conic sections.
Trigonometry:

Trigonometric functions: sine, cosine, tangent, cotangent, secant, cosecant.
Trigonometric identities and equations.
Applications of trigonometry.
Calculus:

Limits and Continuity.
Differentiation: Derivatives, rules of differentiation.
Integration: Definite and indefinite integrals, techniques of integration.
Applications of calculus: Optimization, related rates, area under curves.
Linear Algebra:

Vectors: Vector operations, dot product, cross product.
Matrices: Matrix operations, determinants, inverse.
Systems of Linear Equations.
Differential Equations:

First-order differential equations.
Second-order differential equations: Homogeneous and non-homogeneous.
Systems of differential equations.
Probability and Statistics:

Probability theory: Basic concepts, conditional probability, Bayes’ theorem.
Descriptive statistics: Mean, median, mode, variance, standard deviation.
Probability distributions: Normal distribution, binomial distribution.
Discrete Mathematics:

Set theory: Sets, subsets, unions, intersections.
Logic: Propositional and predicate logic, truth tables.
Combinatorics: Permutations, combinations, counting principles.
Number Theory:

Prime numbers, divisibility, greatest common divisor, least common multiple.
Modular arithmetic and congruences.
Complex Analysis:

Complex functions, complex differentiation, complex integration, residues.
Topology:

Concepts of open and closed sets, continuity, compactness.
Abstract Algebra:

Groups, rings, fields, algebraic structures.
Mathematical Logic:

Propositional logic, first-order logic, formal proofs.
Remember that these are just outlines of the various topics you might encounter in mathematics. If you’re looking for more detailed notes on any specific topic or have specific questions, feel free to ask!

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Important Question & Answer Mathematics Formula

प्राकृतिक संख्या (Natural Numbers) – an – bn = (a – b)(an-1 + an-2 +…+ bn-2a + bn-1)
सम संख्या (Even) – (n = 2k), an + bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1)
विषम संख्या (Odd) – (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +…- bn-2a + bn-1)
(a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + ….
घातांक के नियम (Low Of Formula Exponents)
1. (am)(an) = am+n
2. (ab)m = ambm
3. (am)n = amn
a2 – b2 = (a – b)(a + b)
(a+b)2 = a2 + 2ab + b2
a2 + b2 = (a – b)2 + 2ab
(a – b)2 = a2 – 2ab + b2
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
(a – b – c)2 = a2 + b2 + c2 – 2ab – 2ac + 2bc
(a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
(a – b)3 = a3 – 3a2b + 3ab2 – b3
a3 – b3 = (a – b)(a2 + ab + b2)
a3 + b3 = (a + b)(a2 – ab + b2)
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(a – b)3 = a3 – 3a2b + 3ab2 – b3
(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4)
(a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4)
a4 – b4 = (a – b)(a + b)(a2 + b2)
a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)

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ये भी देखे – सामन्य विज्ञानं के सर्वश्रेष्ठ नोट्स

Maths QUESTION ANSWER

1. The average of first 50 natural numbers is …………..

Answer- _A. ¹/55

3. The number of 3-digit numbers divisible by 6, is ………….. .

Answer- B. 502

5. A clock strikes once at 1 o’clock, twice at 2 o’clock, thrice at 3 o’clock and so on. How many times will it strike in 24 hours?

8. The simplest form of 1.5 : 2.5 is …………… .

Answer- D. 3 : 5

9. 125 gallons of a mixture contains 20% water. What amount of additional water should be added such that water content be raised to 25%?

A. ¹⁵/₂ gallons.

B. ¹⁷/₂ gallons.

C. ¹⁹/₂ gallons.

D. 8¹/₃ gallons.

Answer- D. 8¹/₃ gallons.

Answer- A. 1

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New Mathematics Short Tricks Notes for CGPSC