# CBSE Class 10 Math Important Questions & Revision Key Notes

#### UNIT I : Number Systems

1. REAL NUMBERS

Euclid’s division lemma, Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of 2, 3, 5 . Decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.

#### UNIT II : Algebra

1. POLYNOMIALS

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real coefficients.

2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency.Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically – by substitution, by elimination and by cross multiplication method. Simple situational problems. Simple problems on equations reducible to linear equations.

Standard form of a quadratic equation ax2 + bx + c = 0, (a 0). Solutions of quadratic equations (only real roots) by factorization, by completing the square and by using quadratic formula. Relationship between discriminant and nature of roots.
Situational problems based on quadratic equations related to day to day activities to be incorporated.

4. ARITHMETIC PROGRESSIONS
Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P. and their application in solving daily life problems.

#### UNIT III : Coordinate Geometry

1. LINES (In two-dimensions)

Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division). Area of a triangle.

#### UNIT IV : Geometry

1. TRIANGLES

Definitions, examples, counter examples of similar triangles.

• (Prove) If a line is drawn parallel to one side
of a triangle to intersect the other two sides
in distinct points, the other two sides are divided
in the same ratio.
• (Motivate) If a line divides two sides of a triangle
in the same ratio, the line is parallel to the third side.
• (Motivate) If in two triangles, the corresponding angles
arc equal, their corresponding sides are proportional and
the triangles are similar.
• (Motivate) If the corresponding sides of two triangles are
proportional, their corresponding angles are equal and the
two triangles are similar.
• (Motivate) If one angle of a triangle is equal to one angle
of another triangle and the sides including these angles
are proportional, the two triangles are similar.
• (Motivate) If a perpendicular is drawn from the vertex of
the right angle of a right triangle to the hypotenuse,the
triangles on each side of the perpendicular are similar to
the whole triangle and to each other.
• (Prove) The ratio of the areas of two similar triangles is
equal to the ratio of the squares of their corresponding
sides.
• 8. (Prove) In a right triangle, the square on the hypotenuse
is equal to the sum of the squares on the other two sides.
• 9. (Prove) In a triangle, if the square on one side is equal to
sum of the squares on the other two sides, the angles
opposite to the first side is a right angle.

2. CIRCLES

Tangent to a circle at, point of contact

• (Prove) The tangent at any point of a circle is
perpendicular to the radius through the point of contact.
• (Prove) The lengths of tangents drawn from an external point to a circle are equal.

3. CONSTRUCTIONS

• 1. Division of a line segment in a given ratio (internally).
• 2. Tangents to a circle from a point outside it.
• 3. Construction of a triangle similar to a given triangle.

#### UNIT V : Trigonometry

1. INTRODUCTION TO TRIGONOMETRY
Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios whichever arc defined at 0° and 90°. Values (with proofs) of the trigonometric ratios of 30°, 45° and 60°. Relationships between the ratios.

2. TRIGONOMETRIC IDENTITIES
Proof and applications of the identity sin2A + cos2 A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.

3. HEIGHTS AND DISTANCES: Angle of elevation, Angle of Depression
Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30°. 45°, 60°.

#### UNIT VI: Mensuration

1. AREAS RELATED TO CIRCLES
Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restricted to central angle of 60°, 90° and 120° only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.)

2. SURFACE AREAS AND VOLUMES
Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones. Frustum of a cone.Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with combination of not more than two different solids be taken).

#### UNIT VII : Statistics and Probability

1. STATISTICS
Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.

2. PROBABILITY
Classical definition of probability. Simple problems on single events (not using set notation).

One of the major step in mastering maths subject is to Understand the basic concepts, learn all the important formulae, apply formula according to the concept and crack the most difficult question.Advanced mathematics can only be learnt with the solid foundation of Class 10 maths formulas.Ribblu provides 10th standard maths formulas for free download in the PDF format. These have been uploaded by various users on ribblu.com

#### CBSE Class 10 Maths Important Formulas

Class 10 Maths Formulas – Chapter 15

Class 10 Maths Formulas – Chapter 14

Class 10 Maths Formulas – Chapter 13

Class 10 Maths Formulas – Chapter 12

Class 10 Maths Formulas – Chapter 11

Class 10 Maths Formulas – Chapter 10

Class 10 Maths Formulas – Chapter 8 and 9

Class 10 Maths Formulas – Chapter 7

Class 10 Maths Formulas – Chapter 6

Class 10 Maths Formulas – Chapter 5

Class 10 Maths Formulas – Chapter 4

Class 10 Maths Formulas – Chapter 3

Class 10 Maths Formulas – Chapter 2

Class 10 Maths Formulas – Chapter 1

#### 1   Trigonometric ratio : In Δ ABC, ΔB = 90°. For Angle A,

sin A = Perpendicular / Hypotenuse = Opposite side / Hypotenuse

cos A = Base / Hypotenuse = adjacent side / Hypotenuse

tan A = Perpendicular / Base = Opposite side / adjacent side

cot A = Base / Perpendicular = adjacent side / opposite side

sec A = Hypotenuse / Base = Hypotenuse / adjacent side

cosec A = Hypotenuse / Perpendicular = Hypotenuse / Opposite side

#### 2. Opposites

sin θ = 1 /cosec θ , cosec = 1 / sinθ

cos θ = 1 / sec θ , sec = 1/ cos θ

tan θ= 1 / cot θ , cot = 1/ tan θ

tan θ = sinθ / cos θ , cot θ = cos θ / sin θ

#### 3. Identities

sin² θ + cos² θ = 1 ⇒ sin² θ = 1 – cos² θ and cos² θ= 1 – sin² θ

1 + tan² θ= sec² θ ⇒  tan² θ= sec² θ – 1 and  sec² θ – tan² θ = 1

1 + cot² θ = cosec² θ ⇒ cot² θ= cosec² θ– 1 and cosec² θ– cot² θ = 1

4. Trigonometric ratios of some specific angles

#### 5. Trigonometric ratios of complementary angles

sin (90° – θ) = cos θ

cos (90° –θ) = Sin θ

tan (90° –θ) = cot θ

cot (90° –θ) = tan θ

sec (90° –θ) = cosec θ

cosec (90° –θ) = sec θ

On Ribblu.com you may find numerous CBSE sample papers for class 10 Maths related to board exams 2020 as well as for the previous years exams. These sample papers have been uploaded by various users and surely will be able to help students acquaint with the examination pattern and type of questions expected to be asked in board exams.
To prepare better for CBSE Class 10 as this is the first board exam year, effective practice is necessary. One needs to practice all Important Questions for Class 10 Maths Board Exam 2020. These Sample Papers and Practice Tests along with some worksheets act as a practical guide for students to help them score more as well as for effectively preparing for the final examination.

#### Latest Class 10 Maths Sample Papers

Sample papers for class 10 Maths – 10

Sample papers for class 10 Maths – 9

Sample papers for class 10 Maths – 8

Sample papers for class 10 Maths – 7

Sample papers for class 10 Maths – 6

Sample papers for class 10 Maths – 5

Sample papers for class 10 Maths – 4

Sample papers for class 10 Maths – 3

Sample papers for class 10 Maths – 2

Sample papers for class 10 Maths – 1

#### Chapter wise Test Papers for Class 10 Maths

Similar Triangles Test Papers for Class 10 Maths

Pair of Linear Equation in Two variables Test Papers for Class 10 Maths

Areas Related to Circle Test Papers for Class 10 Maths

Class 10 Maths Practice Test – Arithmetic Progression

Circles Test Papers for Class 10 Maths

Construction Test Papers for Class 10 Maths

Coordinate Geometry Test Papers for Class 10 Maths

Class 10 Maths Practice Test – Heights and Distance

Class 10 Maths Practice Test – Polynomials

Class 10 Maths Practice Test – Probability

Class 10 Maths Practice Test – Quadratic Equations

Class 10 Maths Practice Test – Real Numbers

Class 10 Maths Practice Test – Statistics

Class 10 Maths Practice Test – Surface Areas and Volumes

Class 10 Maths Practice Test – Trigonometry

#### Maths Worksheets for Class 10 ( Chapter Wise)

Surface Areas and Volumes Class 10 Worksheet

Probability Class 10 Worksheet

Coordinate Geometry Class 10 Worksheet

Class 10 Maths Worksheet – Some Applications of Trigonometry

Areas Related to Circles Class 10 Worksheet

Class 10 Maths Worksheet – Statistics

Class 10 Maths Worksheet – Chapter Circles

Class 10 Maths Practice Worksheet (2) – Probability

Pair of Linear Equations in two Variables Class 10 Worksheet

Class 10 Maths Practice Worksheet (1) – Arithmetic Progression

Class 10 Maths Practice Worksheet (1) – Quadratic Equations

Class 10 Maths Practice Worksheet (2) – Arithmetic Progression

Class 10 Maths Practice Worksheet (2) – Coordinate Geometry

Class 10 Maths Practice Worksheet (2) – Quadratic Equations

Class 10 Maths Practice Worksheet (3) – Coordinate Geometry

#### Multiple Choice Questions Worksheets – Class 10 Maths

Class 10 Maths MCQ Worksheet (5) – Probability

Class 10 Maths MCQ Worksheet (4) – Probability

Class 10 Maths MCQ Worksheet (3) – Probability

Class 10 Maths MCQ Worksheet (2) – Probability

Class 10 Maths MCQ Worksheet (1) – Probability

Class 10 Maths MCQ Worksheet (4 ) – Pair of Linear Equations in two Variables

Class 10 Maths MCQ Worksheet (4 ) – Pair of Linear Equations in two Variables

Class 10 Maths MCQ Worksheet (4 ) – Polynomials

Class 10 Maths MCQ Worksheet (4 ) – Quadratic Equations

Class 10 Maths MCQ Worksheet (4) – Areas Related to Circles

Class 10 Maths MCQ Worksheet (4) – Areas Related to Circles

Class 10 Maths MCQ Worksheet (4) – Arithmetic Progression

Class 10 Maths MCQ Worksheet (4) – Coordinate Geometry

Class 10 Maths MCQ Worksheet (4) – Introduction to Trigonometry

Class 10 Maths MCQ Worksheet (4) – Real Numbers

Class 10 Maths MCQ Worksheet (4) – Statistics

Class 10 Maths MCQ Worksheet (4) – Surface Areas and Volumes

Class 10 Maths MCQ Worksheet (4) – Triangles

Class 10 Maths MCQ Worksheet (5) – Real Numbers

Class 10 Maths MCQ Worksheet (5) – Surface Areas and Volumes

Class 10 Maths MCQ Worksheet (6) – Surface Areas and Volumes

Class 10 Maths MCQ Worksheet (7) – Surface Areas and Volumes

Class 10 Maths MCQ Worksheet (3) – Triangles

Class 10 Maths MCQ Worksheet (3) – Surface Areas and Volumes

Class 10 Maths MCQ Worksheet (3) – Statistics

Class 10 Maths MCQ Worksheet (3) – Some Applications to Trigonometry

Class 10 Maths MCQ Worksheet (3) – Real Numbers

Class 10 Maths MCQ Worksheet (3) – Polynomials

Class 10 Maths MCQ Worksheet (3) – Introduction to Trigonometry

Class 10 Maths MCQ Worksheet (3) – Introduction to Trigonometry

Class 10 Maths MCQ Worksheet (3) – Coordinate Geometry

Class 10 Maths MCQ Worksheet (3) – Circles

Class 10 Maths MCQ Worksheet (3 ) – Quadratic Equations

Class 10 Maths MCQ Worksheet (3 ) – Pair of Linear Equations in two Variables

Class 10 Maths MCQ Worksheet (2) – Triangles

Class 10 Maths MCQ Worksheet (2) – Surface Areas and Volumes

Class 10 Maths MCQ Worksheet (2) – Statistics

Class 10 Maths MCQ Worksheet (2) – Some Applications to Trigonometry

Class 10 Maths MCQ Worksheet (2) – Real Numbers

Class 10 Maths MCQ Worksheet (2) – Quadratic Equations

Class 10 Maths MCQ Worksheet (2) – Polynomials

Class 10 Maths MCQ Worksheet (2) – Introduction to Trigonometry

Class 10 Maths MCQ Worksheet (2) – Coordinate Geometry

Class 10 Maths MCQ Worksheet (2) – Circles

Class 10 Maths MCQ Worksheet (2) – Arithmetic Progression

Class 10 Maths MCQ Worksheet (2) – Areas Related to Circles

Class 10 Maths MCQ Worksheet (2 ) – Quadratic Equations

Class 10 Maths MCQ Worksheet (2) – Pair of Linear Equations in two Variables

MCQ Questions for Class 10 Maths Triangles(1)

Class 10 Maths MCQ Worksheet (1) – Surface Areas and Volumes

Class 10 Maths MCQ Worksheet (1) – Statistics

Class 10 Maths MCQ Worksheet (1) – Some Applications to Trigonometry

Class 10 Maths MCQ Worksheet (1) – Real Numbers

MCQ Questions for Class 10 Maths Quadratic Equations

MCQ Questions for Class 10 Maths Polynomials (1)

Class 10 Maths MCQ Worksheet (1) – Pair of Linear Equations in two Variables

Class 10 Maths MCQ Worksheet (1) – Introduction to Trigonometry

MCQ Questions for Class 10 Maths Coordinate Geometry (1)

MCQ Questions for Class 10 Maths Constructions(1)

MCQ Questions for Class 10 Maths Circles (1)

MCQ Questions for Class 10 Maths Arithmetic Progression (1)

MCQ Questions for Class 10 Maths Areas Related to Circles (1)