FORMULA LIST (MATHS - STD.10TH)

 

ARITHMETIC PROGRESSION

 Sequence – The arrangement of the numbers according to some rule.

Arithmetic Progression – The sequence in which the difference between any two consecutive numbers is constant.

The difference between the numbers is called as “Common Difference”.

The c.d. can be zero, positive or negative.

The succeeding number is AP is obtained by adding c.d. to the preceding number.

 n^th term of an AP à a_n = a + (n-1)d

a_n – nth term of an AP                                    a – first term of an AP

d – c.d.                                                           n – number of terms

Sum of the n term of an AP (Sn)

S_n = n/2[2a + (n-1)d]                       S_n = n/2(a + l)         l – last term of AP

TRIANGLES

 Similar Figures – Two figures having same shape are called as “Similar Figures”.

Congruent Figures – Two figures having same shape and size are called “Congruent Figures”.

Note : All congruent figures are similar but all similar figures are not congruent.

 Two Polygons of the same number of sides are similar if

i) their corresponding angle are equal.

ii) their corresponding sides are in the same ratio (or proportion)

 Two triangles are similar if 

i) their corresponding angles are equal and

ii) their corresponding sides are in the same ratio (or proportion)

If a line is drawn parallel to one side of the triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

In DABC, DE ǁ BC

AD = AE

DB    EC

Criteria for Similarity of Triangles

AAA à If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar.

AA à If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.

SSS à If in two triangles, sides of one triangle are proportional to the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar.

SAS à If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.

 Areas of Similar Triangles – The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides

Pythagoras Theorem – In a right angles triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides

 

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

 General form of linear equation in two variables: ax + by + c = 0

 If a pair of lines have unique or infinitely many solutions then the lines are consistent. (Intersecting and coincident lines)

 If the pair of lines has no solution then the lines are inconsistent. (Parallel lines)

CIRCLES

Secant – The line passing through two points on the circumference of the circle.

Tangent – The line touching the circle at one and only one point.

The common point of the tangent and the circle is called the “The point of contact.”

Only one tangent can be drawn to the circle through the point on the circle.

Two tangents can be drawn from the point lying outside the circle.

Theorems

4.1 – The tangent at any point of a circle is perpendicular to the radius through the point of contact.

 4.2 – The length of the tangents drawn from the external point to the circle are equal.

COORDINATE GEOMETRY

QUADRATIC EQUATION

Standard Form à ax² + bx + c = 0

Roots of quadratic equation

X = – b ± √ b² – 4ac

               2a

 Discriminant = b² – 4ac

Discriminant	Nature of roots
b2 – 4ac > 0	Roots are real and distinct
b2 – 4ac = 0	Roots are equal
b2 – 4ac < 0	Roots are not real.

INTRODUCTION TO TRIGONOMETRY

Trigonometric Ratios of the angles – Ratios of the sides of the right triangle with respect to its acute angles are called Trigonometric Ratios of the angles.

 Trigonometric Ratios

Sin q = Opp side /hypotenuse       Cosec q = hypotenuse /opp side = 1/sin q

Cos q = Adj side /hypotenuse       Sec q = hypotenuse /adj side = 1/cos q

Tan q = Opp side /adj side             Cot q = adj side/opp side = 1/tan q

Trigonometric Ratios of Complimentary Angles

Sin (90⁰ – A) = Cos A                      Cosec (90⁰ – A) = Sec A

Cos (90⁰ – A) = Sin A                      Sec (90⁰ – A) = Cosec A

Tan (90⁰ – A) = Cot A                     Cot (90⁰ – A) = Tan A

 Trigonometric Identities

Cos² A + Sin² A = 1

1 + Tan² A = Sec² A

Cot² A + 1 = Cosec² A

SOME APPLICATIONS OF TRIGONOMETRY

Line of Sight – The line drawn from the eye of an observer to the point in the object viewed by the observer.

Angle of Elevation – Angle formed by the line of sight with the horizontal when the object is above the horizontal level.

Angle of Depression – Angle formed by the line of sight with the horizontal when the object is below the horizontal level.

STATISTICS

MEDIAN

                                                                            MEAN

3 Median = Mode + 2 Mean

  Ogive or Cumulative Frequency Curve – Representation of Cumulative Frequency Curve graphically is called Ogive.

For Less Than Type Ogive – Take Upper Limit and add frequency from top to bottom.

For More Than Type Ogive – Take Lower Limit and add frequency from bottom to top.

NOTE : This formula list is based on 30% reduced syllabus for the year 2020-21

Follow our youtube channel "VrushuRaj Classes" for the important educational and motivational videos