Mathematics Short Tricks Notes | Super 40 Tricks

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Number System: The number system is the foundation of mathematics. It includes various types of numbers such as natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.

Algebra: Algebra deals with symbols and the rules for manipulating these symbols. It includes concepts like variables, equations, expressions, polynomials, and solving linear and quadratic equations.

Geometry: Geometry focuses on the study of shapes, sizes, and properties of figures and their relationships. It includes concepts like points, lines, angles, triangles, polygons, circles, and three-dimensional figures.

Trigonometry: Trigonometry deals with the relationships and properties of triangles, particularly right triangles. It includes trigonometric functions such as sine, cosine, and tangent, and their applications in solving angles and distances.

Calculus: Calculus is the branch of mathematics that deals with rates of change and the accumulation of quantities. It includes concepts like limits, derivatives, and integrals, which are used to study functions and their properties.

Probability: Probability deals with the likelihood of events occurring. It involves concepts such as sample space, events, probability of an event, and conditional probability. Probability is used to analyze and predict outcomes in various situations.

Statistics: Statistics involves the collection, analysis, interpretation, presentation, and organization of data. It includes concepts such as mean, median, mode, range, standard deviation, and probability distributions. Statistics is used to make informed decisions and draw conclusions from data.

Measurement: Measurement involves the quantification of physical quantities such as length, area, volume, time, and mass. It includes units of measurement, conversion between units, and the application of formulas for calculating measurements.

Arithmetic: Arithmetic is the basic branch of mathematics that deals with the properties and operations of numbers. It includes concepts like addition, subtraction, multiplication, division, fractions, decimals, and percentages.

Coordinate Geometry: Coordinate geometry combines the concepts of algebra and geometry. It involves plotting points on a coordinate plane and studying the relationship between these points using equations and graphs.

Matrices and Vectors: Matrices are rectangular arrays of numbers, and vectors are mathematical objects that have both magnitude and direction. They are used in various branches of mathematics and have applications in fields like physics and computer science.

Logical Reasoning: Logical reasoning involves using logic and reasoning skills to analyze and solve problems. It includes concepts such as deductive reasoning, inductive reasoning, and logical operations like conjunction, disjunction, and implication.

These are some important points and concepts in mathematics. Mathematics is a vast subject with numerous applications in various fields, and these concepts form the building blocks for further learning and problem-solving.

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Important Question And Answer Maths 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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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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Mathematics Short Tricks Notes | Super 40 Tricks