{"id":9256,"date":"2024-01-06T16:33:08","date_gmt":"2024-01-06T11:03:08","guid":{"rendered":"https:\/\/krmangalamvaishali.com\/?p=9256"},"modified":"2024-01-06T16:33:08","modified_gmt":"2024-01-06T11:03:08","slug":"essential-maths-formulas-for-class-10","status":"publish","type":"post","link":"https:\/\/krmangalamvaishali.com\/new\/essential-maths-formulas-for-class-10\/","title":{"rendered":"Essential Maths Formulas for Class 10"},"content":{"rendered":"\n\n\n<p class=\"wp-block-paragraph\">As a Class 10 student, you&#8217;re on the brink of a significant academic milestone. Mathematics at this stage plays a pivotal role, not just in your exams but in shaping analytical and problem-solving skills. Mathematics in Class 10 is not just a subject, but a crucial skill that lays the foundation for various concepts and problem-solving techniques used in higher studies and everyday life. Understanding and memorizing mathematical formulas at this level is essential for scoring well in exams and for future academic pursuits. This blog aims to provide a comprehensive guide to all the important Maths Formulas for Class 10 students need to know.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Essential Maths Formulas for Class 10 Chapter Wise<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Chapter 1: Real Numbers<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Euclid&#8217;s Division Lemma: <\/strong>For any two positive integers a and b, there exist unique integers q and r such that a = bq + r, where 0 \u2264 r &lt; b. This lemma is a basis for many proofs and problems in this chapter.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Irrational Numbers:<\/strong> An irrational number is a number that cannot be expressed as a ratio of two integers. Their decimal expansions are non-terminating and non-repeating. For example, \u221a2 is an irrational number.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Rational Numbers: <\/strong>A rational number is a number that can be expressed as a ratio of two integers (i.e., in the form p\/q, where q is not zero).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Chapter 2: Polynomials&nbsp;<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">For a quadratic polynomial ax<sup>2<\/sup>+ bx+ c, the sum of its zeros \u03b1 + \u03b2 is &nbsp;-b&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">and the product \u03b1\u03b2 of its zeros is C.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For a cubic polynomial ax<sup>3<\/sup>+bx<sup>2<\/sup>+cx + d, if \u03b1,\u03b2, and \u03b3 are its zeros, then&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u03b1+\u03b2+\u03b3 = -b ,&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u03b1\u03b2+\u03b2\u03b3+\u03b3\u03b1= c<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u03b1\u03b2\u03b3= -d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Chapter 3: Pair Of Linear Equations In Two Variables&nbsp;<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">General Form of Linear Equations:<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">A linear equation in two variables x and y can be expressed in the form ax+by+c=0, where a, b, and c are real numbers, and a and b are not both zero.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Pair of Linear Equations:<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">a1x+b1y+c1=0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a2x+b2y+c2=0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Conditions for Consistency:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A pair of linear equations is consistent if they have a solution.<\/li>\n\n\n\n<li>The equations are consistent and have a unique solution if a<sub>1<\/sub><sub> \u2260 <\/sub>b<sub>1<\/sub><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<sub>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/sub>a<sub>2<\/sub><sub> &nbsp; &nbsp; <\/sub>b<sub>2<\/sub><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The equations are consistent and have infinitely many solutions if a<sub>1<\/sub><sub> =&nbsp; <\/sub>b<sub>1&nbsp; <\/sub><sub>=&nbsp; <\/sub>c<sub>1<\/sub><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<sub>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/sub>a<sub>2<\/sub><sub> &nbsp; &nbsp; <\/sub>b<sub>2 &nbsp; &nbsp; <\/sub>c<sub>2<\/sub><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The equations are inconsistent (have no solution) if a<sub>1<\/sub><sub> =&nbsp; <\/sub>b<sub>1 <\/sub><sub>&nbsp;<\/sub><sub>&nbsp;but<\/sub><sub>&nbsp; <\/sub>c<sub>1&nbsp; <\/sub><sub>\u2260 <\/sub>b<sub>1<\/sub><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<sub>&nbsp;&nbsp;&nbsp;&nbsp;<\/sub>a<sub>2<\/sub><sub> &nbsp; &nbsp; <\/sub>b<sub>2 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <\/sub>c<sub>2&nbsp; &nbsp; &nbsp; <\/sub>b<sub>2<\/sub><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Chapter 4: QUADRATIC EQUATIONS &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Standard Form of a Quadratic Equation:<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">A quadratic equation in the variable x is of the form ax<sup>2<\/sup> +bx+c=0, where<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a,b, and c are constants, and a<sub>\u2260 <\/sub>0.&nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Quadratic Formula:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The roots of the quadratic equation ax<sup>2<\/sup>+bx+c=0 can be found using the formula:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><em>x<\/em>= -b+(-) \u221ab<sup>2<\/sup>-4ac&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The term b<sup>2<\/sup>\u22124ac is known as the discriminant.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Chapter 5: Arithmetic Progressions&nbsp;<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Definition of an Arithmetic Progression:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is always the same. This difference is called the common difference, denoted as<strong> <\/strong><strong><em>d<\/em><\/strong><strong>.<\/strong><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Arithmetic Progressions (AP):<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Nth term of an AP: a<sub>n<\/sub>=a + ( n &#8211; 1 ) d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sum of the first n terms: S<sub>n<\/sub> = n&nbsp; &nbsp;\u29972a + (n &#8211; 1)d \u2998<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Chapter 6:&nbsp; Triangles&nbsp;<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Similar Triangles:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Two triangles are similar if their corresponding angles are equal <a href=\"https:\/\/krmangalamvaishali.com\/new\/\">and<\/a> their corresponding sides are in the same ratio.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Basic Proportionality Theorem (or Thales&#8217; Theorem):<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Criteria for Similarity of Triangles:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>AA (Angle-Angle) Similarity Criterion: Two triangles are similar if two pairs of corresponding angles are equal.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>SSS (Side-Side-Side) Similarity Criterion: Two triangles are similar if the corresponding sides are in the same ratio.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>SAS (Side-Angle-Side) Similarity Criterion: Two triangles are similar if one pair of corresponding sides are in the same ratio and the angles included between these sides are equal.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Pythagoras Theorem:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. Mathematically, c<sup>2<\/sup>=a<sup>2<\/sup>+b<sup>2<\/sup> for a right triangle with a hypotenuse c and legs a and b.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Converse of Pythagoras Theorem:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is right-angled.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Area of Similar Triangles:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Mid-point Theorem:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The line segment joining the mid-points of two sides of a triangle is parallel to the third side and is half of it.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Chapter 7: Coordinate Geometry<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Distance Formula:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The distance between two points(x<sub>1<\/sub>,y<sub>1<\/sub>) and(x<sub>2<\/sub>,y<sub>2<\/sub>) in the coordinate plane is given by:<\/li>\n\n\n\n<li>Distance= \u221a(x<sub>2<\/sub> -x<sub>1<\/sub>)<sup>2<\/sup> + (y<sub>2<\/sub>-y<sub>1<\/sub>) <sup>2<\/sup><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Area of a Triangle:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The area of a triangle formed by three points (<em>x<\/em><sub>1<\/sub>,<em>y<\/em><sub>1<\/sub>),(<em>x<\/em><sub>2<\/sub>,<em>y<\/em><sub>2<\/sub>), and(<em>x<\/em><sub>3<\/sub>,<em>y<\/em><sub>3<\/sub>) is given by:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Area= 1 &nbsp; &nbsp;\u2997 x<sub>1 <\/sub>(y<sub>2 <\/sub>&#8211; y<sub>3<\/sub>) + x<sub>2<\/sub> (y<sub>3<\/sub> &#8211; y<sub>1<\/sub>) +x <sub>3<\/sub>(y<sub>1<\/sub> &#8211; y<sub>2<\/sub>) \u2998<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2 &nbsp; \u2997&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2998<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Chapter 8: Introduction To Trigonometry<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Trigonometric Ratios:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In a right triangle, if \u03b8 is one of the acute angles, then the three main trigonometric ratios are defined as follows:\n<ul class=\"wp-block-list\">\n<li>Sine (sin \u03b8) = Opposite side \/ Hypotenuse<\/li>\n\n\n\n<li>Cosine (cos \u03b8) = Adjacent side \/ Hypotenuse<\/li>\n\n\n\n<li>Tangent (tan \u03b8) = Opposite side \/ Adjacent side&nbsp;<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Reciprocal Trigonometric Ratios:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Cosecant (csc \u03b8) = 1 \/ sin \u03b8<\/li>\n\n\n\n<li>Secant (sec \u03b8) = 1 \/ cos \u03b8<\/li>\n\n\n\n<li>Cotangent (cot \u03b8) = 1 \/ tan \u03b8<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Pythagorean Trigonometric Identity:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>sin^2 \u03b8 + cos^2 \u03b8 = 1<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Trigonometric Ratios of Complementary Angles:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>sin(90\u00b0 &#8211; \u03b8) = cos \u03b8<\/li>\n\n\n\n<li>cos(90\u00b0 &#8211; \u03b8) = sin \u03b8<\/li>\n\n\n\n<li>tan(90\u00b0 &#8211; \u03b8) = 1 \/ tan \u03b8<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Trigonometric Ratios of Special Angles:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>sin 30\u00b0 = 1\/2, cos 30\u00b0 = \u221a3\/2, tan 30\u00b0 = 1\/\u221a3<\/li>\n\n\n\n<li>sin 45\u00b0 = cos 45\u00b0 = 1\/\u221a2, tan 45\u00b0 = 1<\/li>\n\n\n\n<li>sin 60\u00b0 = \u221a3\/2, cos 60\u00b0 = 1\/2, tan 60\u00b0 = \u221a3<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Trigonometric Ratios of Negative Angles:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>sin(-\u03b8) = -sin \u03b8<\/li>\n\n\n\n<li>cos(-\u03b8) = cos \u03b8<\/li>\n\n\n\n<li>tan(-\u03b8) = -tan \u03b8<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Chapter 9: Some Applications Of Trigonometry&nbsp;<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Important Formulas:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Distance between two objects (AB) = (BC) \/ (tan \u03b8), where BC is the vertical height.<\/li>\n\n\n\n<li>Height of an object (BC) = (AB) \u00d7 (tan \u03b8), where AB is the horizontal distance.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Chapter 10:&nbsp; Circles<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Circle: A circle is a set of all points in a plane that are equidistant from a fixed point called the center.<\/li>\n\n\n\n<li>Radius (r): The distance from the center of the circle to any point on the circle.<\/li>\n\n\n\n<li>Diameter (d): The longest chord of a circle that passes through the center, and it is equal to 2 times the radius (d = 2r).<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Circumference of a Circle (C):<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>C = 2\u03c0r, where \u03c0 (pi) is approximately 3.14159.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Area of a Circle (A):<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">A = \u03c0r\u00b2<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Chapter 11: Areas Related To Circles<\/h2>\n\n\n\n<h4 class=\"wp-block-heading\">Circumference of a Circle (C):<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">C = 2\u03c0r, where \u03c0 (pi) is approximately 3.14159, and r is the radius of the circle.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Area of a Circle (A):<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">A = \u03c0r\u00b2<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Arc Length (L):<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">L = (\u03b8\/360) * 2\u03c0r, where \u03b8 is the angle in degrees formed at the center of the circle by the arc.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Area of a Sector (A_sector):<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">A_sector = (\u03b8\/360) * \u03c0r\u00b2, where \u03b8 is the angle in degrees formed at the center of the circle by the sector.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Length of an Arc:<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">The length of an arc (S) can be calculated as: S = (\u03b8\/360) * 2\u03c0r, where \u03b8 is the angle in degrees formed at the center of the circle by the arc.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Length of a Major Arc:<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">For a major arc (angle &gt; 180 degrees), the length of the arc can be calculated as: S_major = 2\u03c0r &#8211; S_minor, where S_minor is the length of the corresponding minor arc.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Length of a Minor Arc:<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">For a minor arc (angle &lt; 180 degrees), the length of the arc can be calculated as S_minor = (\u03b8\/360) * 2\u03c0r.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Chapter 12: Surface Areas And Volumes<\/h2>\n\n\n\n<h4 class=\"wp-block-heading\">Surface Area of a Cuboid:<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Surface Area (S) = 2(lw + lh + wh)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>l is the length of the cuboid.<\/li>\n\n\n\n<li>w is the width of the cuboid.<\/li>\n\n\n\n<li>h is the height of the cuboid.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Lateral Surface Area of a Cuboid:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Lateral Surface Area (LSA) = 2h(l + w)<\/li>\n\n\n\n<li>It represents the total area of the four sides of the cuboid, excluding the top and bottom faces.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Total Surface Area of a Cube:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total Surface Area (S) = 4a\u00b2<\/li>\n\n\n\n<li>Where &#8220;a&#8221; is the length of the side of the cube.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Surface Area of a Right Circular Cylinder:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Curved Surface Area (CSA) = 2\u03c0rh<\/li>\n\n\n\n<li>Total Surface Area (TSA) = 2\u03c0rh + 2\u03c0r\u00b2<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>r is the radius of the base.<\/li>\n\n\n\n<li>h is the height of the cylinder.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Surface Area of a Right Circular Cone:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Curved Surface Area (CSA) = \u03c0rl<\/li>\n\n\n\n<li>Total Surface Area (TSA) = \u03c0rl + \u03c0r\u00b2<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>r is the radius of the base.<\/li>\n\n\n\n<li>l is the slant height of the cone.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Surface Area of a Sphere:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Surface Area (S) = 4\u03c0r\u00b2<\/li>\n\n\n\n<li>Where &#8220;r&#8221; is the radius of the sphere.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Volume of a Cuboid:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Volume (V) = lwh<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>l is the length of the cuboid.<\/li>\n\n\n\n<li>w is the width of the cuboid.<\/li>\n\n\n\n<li>h is the height of the cuboid.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Volume of a Cube:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Volume (V) = a\u00b3<\/li>\n\n\n\n<li>Where &#8220;a&#8221; is the length of the side of the cube.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Volume of a Right Circular Cylinder:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Volume (V) = \u03c0r\u00b2h<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>r is the radius of the base.<\/li>\n\n\n\n<li>h is the height of the cylinder.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Volume of a Right Circular Cone:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Volume (V) = (1\/3)\u03c0r\u00b2h<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>r is the radius of the base.<\/li>\n\n\n\n<li>h is the height of the cone.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Volume of a Sphere:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Volume (V) = (4\/3)\u03c0r\u00b3<\/li>\n\n\n\n<li>Where &#8220;r&#8221; is the radius of the sphere.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Frustum of a Cone:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The frustum of a cone is the portion that remains after cutting off the top portion of a cone with a smaller cone.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Volume of a Frustum of a Cone:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Volume (V) = (1\/3)\u03c0h(h\u2081\u00b2 + h\u2082\u00b2 + h\u2081h\u2082)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>h is the height of the frustum.<\/li>\n\n\n\n<li>h\u2081 and h\u2082 are the heights of the smaller and larger cones, respectively.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Chapter 13: Statistics<\/h2>\n\n\n\n<h4 class=\"wp-block-heading\">Mean (Average):<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Mean (\u03bc) = (Sum of all observations) \/ (Total number of observations)<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Median:<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Median is the middle value of a data set when the data is arranged in ascending or descending order. If there is an even number of data points, the median is the average of the two middle values.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Mode:<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Mode is the value that appears most frequently in a data set.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Range:<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Range = (Maximum value) &#8211; (Minimum value)<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Quartiles:<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Quartiles divide a data set into four equal parts. The three quartiles are Q1 (25th percentile), Q2 (50th percentile or median), and Q3 (75th percentile).<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Interquartile Range (IQR):<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">IQR = Q3 &#8211; Q1<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Variance:<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Variance (\u03c3\u00b2) = [(\u03a3(xi &#8211; \u03bc)\u00b2) \/ N], where \u03bc is the mean, xi is each individual data point, and N is the total number of data points.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Standard Deviation:<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Standard Deviation (\u03c3) = \u221a\u03c3\u00b2<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Chapter 14: Probability&nbsp;<\/h2>\n\n\n\n<h4 class=\"wp-block-heading\">Probability of an Event (P(E)):<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Probability is a measure of the likelihood of an event occurring.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">P(E) is a number between 0 (impossible) and 1 (certain).<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Probability of Complementary Events:<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">P(not E) = 1 &#8211; P(E)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The probability of an event not occurring is equal to 1 minus the probability of the event occurring.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Probability of the Union of Two Events (P(A \u222a B)):<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">P(A \u222a B) = P(A) + P(B) &#8211; P(A \u2229 B)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The probability of either event A or event B occurring (or both) is <a href=\"https:\/\/www.krmangalamgurgaon.com\/blogs\/understanding-the-grading-system-in-cbse-class-12\/.\">calculated<\/a> as the sum of their individual probabilities minus the probability of their intersection.<\/p>\n\n    <div class=\"xs_social_share_widget xs_share_url after_content \t\tmain_content  wslu-style-1 wslu-share-box-shaped wslu-fill-colored wslu-none wslu-share-horizontal wslu-theme-font-no wslu-main_content\">\n\n\t\t\n        <ul>\n\t\t\t        <\/ul>\n    <\/div> \n","protected":false},"excerpt":{"rendered":"<p>As a Class 10 student, you&#8217;re on the brink of a significant academic milestone. Mathematics at this stage plays a pivotal role, not just in your exams but in shaping analytical and problem-solving skills. Mathematics in Class 10 is not just a subject, but a crucial skill that lays the foundation for various concepts and problem-solving techniques used in higher studies and everyday life. Understanding and memorizing mathematical formulas at this level is essential for scoring well in exams and for future academic pursuits. This blog aims to provide a comprehensive guide to all the important Maths Formulas for Class 10 students need to know. Essential Maths Formulas for Class 10 Chapter Wise Chapter 1: Real Numbers Euclid&#8217;s Division Lemma: For any two positive integers a and b, there exist unique integers q and r such that a = bq + r, where 0 \u2264 r &lt; b. This lemma is a basis for many proofs and problems in this chapter.&nbsp; Irrational Numbers: An irrational number is a number that cannot be expressed as a ratio of two integers. Their decimal expansions are non-terminating and non-repeating. For example, \u221a2 is an irrational number. Rational Numbers: A rational number is a number that can be expressed as a ratio of two integers (i.e., in the form p\/q, where q is not zero). Chapter 2: Polynomials&nbsp; For a quadratic polynomial ax2+ bx+ c, the sum of its zeros \u03b1 + \u03b2 is &nbsp;-b&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a and the product \u03b1\u03b2 of its zeros is C. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a For a cubic polynomial ax3+bx2+cx + d, if \u03b1,\u03b2, and \u03b3 are its zeros, then&nbsp; \u03b1+\u03b2+\u03b3 = -b ,&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a&nbsp; \u03b1\u03b2+\u03b2\u03b3+\u03b3\u03b1= c &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a \u03b1\u03b2\u03b3= -d &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a Chapter 3: Pair Of Linear Equations In Two Variables&nbsp; General Form of Linear Equations: A linear equation in two variables x and y can be expressed in the form ax+by+c=0, where a, b, and c are real numbers, and a and b are not both zero. Pair of Linear Equations: a1x+b1y+c1=0 a2x+b2y+c2=0 Conditions for Consistency: &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a2 &nbsp; &nbsp; b2 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a2 &nbsp; &nbsp; b2 &nbsp; &nbsp; c2 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a2 &nbsp; &nbsp; b2 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; c2&nbsp; &nbsp; &nbsp; b2 Chapter 4: QUADRATIC EQUATIONS &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Standard Form of a Quadratic Equation: A quadratic equation in the variable x is of the form ax2 +bx+c=0, where a,b, and c are constants, and a\u2260 0.&nbsp; Quadratic Formula: x= -b+(-) \u221ab2-4ac&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2a Chapter 5: Arithmetic Progressions&nbsp; Definition of an Arithmetic Progression: Arithmetic Progressions (AP): Nth term of an AP: an=a + ( n &#8211; 1 ) d Sum of the first n terms: Sn = n&nbsp; &nbsp;\u29972a + (n &#8211; 1)d \u2998 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp; Chapter 6:&nbsp; Triangles&nbsp; Similar Triangles: Basic Proportionality Theorem (or Thales&#8217; Theorem): Criteria for Similarity of Triangles: Pythagoras Theorem: Converse of Pythagoras Theorem: Area of Similar Triangles: Mid-point Theorem: Chapter 7: Coordinate Geometry Distance Formula: Area of a Triangle: Area= 1 &nbsp; &nbsp;\u2997 x1 (y2 &#8211; y3) + x2 (y3 &#8211; y1) +x 3(y1 &#8211; y2) \u2998 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2 &nbsp; \u2997&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2998 Chapter 8: Introduction To Trigonometry Trigonometric Ratios: Reciprocal Trigonometric Ratios: Pythagorean Trigonometric Identity: Trigonometric Ratios of Complementary Angles: Trigonometric Ratios of Special Angles: Trigonometric Ratios of Negative Angles: Chapter 9: Some Applications Of Trigonometry&nbsp; Important Formulas: Chapter 10:&nbsp; Circles Circumference of a Circle (C): Area of a Circle (A): A = \u03c0r\u00b2 Chapter 11: Areas Related To Circles Circumference of a Circle (C): C = 2\u03c0r, where \u03c0 (pi) is approximately 3.14159, and r is the radius of the circle. Area of a Circle (A): A = \u03c0r\u00b2 Arc Length (L): L = (\u03b8\/360) * 2\u03c0r, where \u03b8 is the angle in degrees formed at the center of the circle by the arc. Area of a Sector (A_sector): A_sector = (\u03b8\/360) * \u03c0r\u00b2, where \u03b8 is the angle in degrees formed at the center of the circle by the sector. Length of an Arc: The length of an arc (S) can be calculated as: S = (\u03b8\/360) * 2\u03c0r, where \u03b8 is the angle in degrees formed at the center of the circle by the arc. Length of a Major Arc: For a major arc (angle &gt; 180 degrees), the length of the arc can be calculated as: S_major = 2\u03c0r &#8211; S_minor, where S_minor is the length of the corresponding minor arc. Length of a Minor Arc: For a minor arc (angle &lt; 180 degrees), the length of the arc can be calculated as S_minor = (\u03b8\/360) * 2\u03c0r. Chapter 12: Surface Areas And Volumes Surface Area of a Cuboid: Surface Area (S) = 2(lw + lh + wh) Where: Lateral Surface Area of a Cuboid: Total Surface Area of a Cube: Surface Area of a Right Circular Cylinder: Where: Surface Area of a Right Circular Cone: Where: Surface Area of a Sphere: Volume of a Cuboid: Where: Volume of a Cube: Volume of a Right Circular Cylinder: Where: Volume of a Right Circular Cone: Where: Volume of a Sphere: Frustum of a Cone: Volume of a Frustum of a Cone: Where: Chapter 13: Statistics Mean (Average): Mean (\u03bc) = (Sum of all observations) \/ (Total number of observations) Median: Median is the middle value of a data set when the data is arranged in ascending or descending order. If there is an even number of data points, the median is the average of the two middle values. Mode: Mode is the value that appears most frequently in a data set. Range: Range = (Maximum value) &#8211; (Minimum value) Quartiles: Quartiles divide a data set into four equal parts. The three quartiles are Q1 (25th percentile), Q2 (50th percentile or median), and Q3 (75th percentile). Interquartile Range (IQR): IQR = Q3 &#8211; Q1 Variance: Variance (\u03c3\u00b2) = [(\u03a3(xi &#8211; \u03bc)\u00b2) \/ N], where \u03bc is the mean, xi is each individual data point, and N is the 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