CBSE Important Questions for Class 10 Maths Board Exam 2021-22 are intended to help students get hold over each and every chapter of the mathematics of Class 10 and eventually score higher marks in board exams. After solving exercises from Class NCERT Book of Class 10, Students can also analyse all the important concepts or chapters which needs lot of focus and attention after going through Important Questions for Class 10 Maths. Below you will find previous year board questions and 10 years Important Questions chapter wise which have been shared by various users on ribblu.com. These questions can act as practice tests or worksheets for Class 10 maths.
CBSE Class 10 Math Important Questions
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
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.
3. QUADRATIC 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
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
- 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.
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.
- 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
Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.
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
CBSE Class 10 Maths – Introduction to Trigonometry Formula
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
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
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
- Class 10 Maths Practice Test – Trigonometry
- Class 10 Maths – Notes , Important Questions and Solutions – Trigonometry
- Class 10 Maths Worksheet ( Some Applications of Trigonometry )
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.