Table of Contents

## Syllabus – Class 10 Maths

One of the most important things to master in any examination is to be thoroughly versed in the prescribed syllabus. For all the doubts that a student has regarding the syllabus, here’s everything that you need to study for** the class 10 Maths **examination:

**NUMBER SYSTEMS – 06 Marks**

**Real Numbers **** **

Fundamental Theorem of Arithmetic – statements after reviewing the work done earlier and after illustrating and motivating through examples; Proofs of the irrationality of. The decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.

**ALGEBRA – 20 Marks**

**Polynomials**

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.

2. **Pair of Linear Equations in Two Variables**

Pair of linear equations in two variables and graphical methods of their solution, consistency/ inconsistency.

Algebraic conditions for a number of solutions. The solution of a pair of linear equations in two variables algebraically – by substitution, by elimination. Simple situational problems. Simple problems on equations reducible to linear equations.

3.** Quadratic Equations **

Standard form of a quadratic equation *ax*2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization and by using the quadratic formula. Relationship between discriminant and nature of roots.

4.** Arithmetic Progressions **

The motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of an A.P.

**COORDINATE GEOMETRY – 06 Marks**

**Lines (In two-dimensions)**

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

**GEOMETRY – 15 Marks**

a. **Triangles**

Definitions, examples, counterexamples 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 the corresponding angles are equal in two triangles, 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, and 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) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.

b. **Circles **

Tangent to a circle at the 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.

c. **Constructions **

- Division of a line segment in a given ratio (internally).
- 2. Tangents to a circle from a point outside it.

**TRIGONOMETRY – 12 Marks**

a.** Introduction to Trigonometry **

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined). Values (with proofs) of the trigonometric ratios of 30o, 45o, and 60o. Relationships between the ratios.

b. **Trigonometric Identities **

Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be given.

c. **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 30o, 45o, 60o.

**MENSURATION – 10 Marks**

a. **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 the area of a segment of a circle, problems should be restricted to the central angle of 60°, 90° only. Plane figures involving triangles, simple quadrilaterals, and circles should be taken.)

b. **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.
- 2. Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with combinations of not more than two different solids can be taken).

**STATISTICS AND PROBABILITY – 11 Marks**

a. **Statistic**

Mean, median, and mode of grouped data (bimodal situation to be avoided).

b.** Probability**

The classical definition of probability. Simple problems on finding the probability of an event.

## Class 10 Maths – Paper Pattern, Tips, and Tricks

The question paper pattern for this exam is:

**Section A:**Objective Type Questions that are 20 in a number containing 1 mark each.**Section B:**Short Answer Type Questions – I, 6 questions of marks each.**Section C:**Short Answer Type Questions – II, 8 questions of 3 marks each.**Section D:**Long Answer Type Questions, 6 questions containing 4 marks each.

Some tips and tricks during preparation and exam time to score full marks would be to understand each unit and solve sums by yourself, find your strengths and weaknesses, complete the syllabus on time and start a thorough revision. During the exam, start with the section that you are most familiar with, keep your paper as clean as possible, solve in steps as step marking is essential and draw as many diagrams and graphs as time permits.

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**FAQs**

##### What are the total marks in the written examination for class 10 Maths?

There are 80 marks in total, along with an internal evaluation that contains 20 marks (making 100).

##### Which is the most difficult section in the paper?

Section C is reportedly the most challenging section as it tests more of your understanding than practice.

##### How many mock tests should one take to be completely ready?

Solving more and more questions will always help to grasp the concepts better, but this can vary depending on individual needs. Around 8-10 tests would be great.

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