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Real Numbers

Key notes for class X Maths chapter 01 Real Numbers it includes revision notes such as Theorem: If {tex}a{/tex} and {tex}b{/tex} are non-zero integers, the least positive integer which is expressible as a linear combination of {tex}a{/tex} and {tex}b{/tex} is the HCF of {tex}a{/tex} and {tex}b{/tex}, i.e., if {tex}d{/tex} is the HCF of {tex}a{/tex} and {tex}b{/tex}, then these exist integers {tex}x_1{/tex} and {tex}y_1{/tex}, such that {tex}d = a{x_1} + b{y_1}{/tex} and {tex}d{/tex} is the smallest positive integer which is expressible in this form.

Polynomials

Key notes for class X Maths chapter 02 Polynomials it includes revision notes such as The zeroes of a polynomial p(x) are precisely the x–coordinates of the points where the graph of y = p(x) intersects the x-axis i.e. x = a is a zero of polynomial p(x) if p(a) = 0. A quadratic polynomial in x with real coefficient is of the form {tex}{\text{a}}{{\text{x}}^2}{\text{ }} + {\text{ bx }} + {\text{ c}}{/tex},where a, b, c are real numbers with {tex}{\text{a }} \ne 0{/tex}.

Pairs in Linear Equations in Two Variables

Key notes for class X Maths chapter 03 Pairs in Linear Equations in Two Variables it includes revision notes such as A pair of linear equations in two variables is said to form a system of simultaneous linear equations in two variables. A pair of values of x and y satisfying each of the equations in the given system of two simultaneous equations in x and y is called a solution of the system.

Quadratic Equations

Key notes for class X Maths chapter 04 Quadratic Equations it includes revision notes such as A real number {tex}\alpha {/tex}  is said to be a root of the quadratic equation {tex}a{x^2} + bx + c = 0,a \ne 0{/tex} , {tex}{ a } \ne 0{/tex}. If {tex}a{\alpha ^2} + b\alpha + c = 0,{/tex} the zeroes of quadratic polynomial {tex}{\text{a}}{{\text{x}}^2}{\text{ }} + {\text{ bx }} + {\text{ c }}{/tex} and the roots of the the quadratic equation  ax2 + bx + c = 0 are the same.

Arithmetic Progressions

Key notes for class X Maths chapter 05 Arithmetic Progressions it includes revision notes such as Sequence: A set of numbers arranged in some definite order and formed according to some rules is called a sequence. Arithmetic Progression: A sequence in which the difference obtained by subtracting any term from its preceding term is constant throughout, is called an arithmetic sequence or arithmetic progression (A.P.).

Triangles

Key notes for class X Maths chapter 06 Triangles it includes revision notes such as Similar Figures: Similar figures have the same shape (but not necessarily the same size). In geometry, two squares are similar, two equilateral triangles are similar, two circles are similar and two line segments are similar.

Coordinate Geometry

Key notes for class X Maths chapter 07 Coordinate Geometry it includes revision notes such as Section Formula: The co-ordinates of the points p(x, y) which divides the line segment joining the points {tex}A({x_1}, {y_1}){/tex} and {tex}B({x_{2\;,\;}}{y_2}){/tex} in the ratio {tex}{m_{1\;}}:\;{m_2}{/tex} are {tex}\left( {{{{m_1}{x_2} + {m_2}{x_1}} \over {{m_1} + {m_2}}},{{{m_1}{y_2} + {m_2}{y_1}} \over {{m_1} + {m_2}}}} \right){/tex} we can take ratio as {tex}k\;:\;1,\;\;k = \frac{{{m_1}}}{{{m_2}}}{/tex}

Introduction to Trigonmetry

Key notes for class X Maths chapter 08 Introduction to Trigonmetry it includes revision notes such as Positive and Negative angles: Angles in anti-clockwise direction are taken as positive angles and angles in clockwise direction are taken as negative angles. If one of the trigonometric ratios of an acute angle is known, the remaining trigonometric ratios of the angle can be easily determined.

Some Applications Of Trigonometry

Key notes for class X Maths chapter 09 Some Applications Of Trigonometry it includes revision notes such as Angle of Elevation : The angle of elevation is the angle formed by the line of sight with the horizontal, when it is above the horizontal level i.e., the case when we raise our head to look at the object. Angle of Depression : The angle of depression is the angle formed by the line of sight with the horizontal when it is below the horizontal i.e., case when we lower our head to look at the object.

Circles

Key notes for class X Maths chapter 10 Circles it includes revision notes such as There is only one tangent at a point of the circle. No tangent can be drawn from a point inside the circle.The tangent at any point of a circle is perpendicular to the radius through the point of contact.

Constructions

Key notes for class X Maths chapter 11 Constructions it includes revision notes such as Construction of a Triangle similar to a given triangle: By the knowledge of similar triangles and division of a line segment in a given ratio, we can construct a triangle similar to a given triangle. Construction of Tangents to a circle: By the knowledge of tangents to a circle (learnt in chapter 'Circles'), we can construct the tangents to the circle.

Areas Related to Circles

Key notes for class X Maths chapter 12 Areas Related to Circles it includes revision notes such as Perimeter or Circumference of the circle = {tex}2\pi r,{/tex} where {tex}r{/tex} is the radius of the circle. Or Circumference of the circle = {tex}\pi d,{/tex} where {tex}d{/tex} is the diameter of the circle. Area of circle = {tex}\pi {r^2}{/tex} where ‘r’ is the radius of the circle.

Surface Areas and Volumes

Key notes for class X Maths chapter 13 Surface Areas and Volumes it includes revision notes such as Curved surface area of cylinder of radius r and height {tex}h = 2\pi rh{/tex} square units.Total surface area of cylinder of radius r and height {tex}{\text{h }} = {\text{ 2}}\pi {\text{r }}\left( {{\text{r }} + {\text{ h}}} \right){/tex}square units.Volume of cylinder of radius r and height {tex}h = \pi {r^2}h{/tex}  cubic units.

Statistics

Key notes for class X Maths chapter 14 Statistics it includes revision notes such as To obtain the median of frequency distribution from the graph Locate point of intersection of less than type Ogive and more than type Ogive :Draw a perpendicular from this point on x-axis.The point at which it cuts the x-axis gives us the median.

Probability

Key notes for class X Maths chapter 15 Probability it includes revision notes such as Trial: Performing an experiment once is called a trial. Event: The possible outcomes of a trial is called an event. Sure event: An event whose occurence is certain is called a sure event. The sum of the probability of all the elementary events of an experiment is 1.The probability of a sure event is 1 and probability of an impossible event is 0.



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