Preparing for the CBSE Class 10 Mathematics exam on March 10, 2025, involves focusing on key topics and practicing frequently asked questions. Based on an analysis of previous years’ papers. For the CBSE Class 10 Mathematics exam in 2025, the Question paper is divided into two main parts:
Table of Contents
CBSE Class 10 Maths Weightage 2025 exam
- Theory Examination: This carries 80 marks and is structured as follows:
- Section A: 20 Multiple Choice Questions (MCQs), each worth 1 mark, total 20 marks.
- Section B: 5 Very Short Answer (VSA) questions, each worth 2 marks, total 10 marks.
- Section C: 6 Short Answer (SA) questions, each worth 3 marks, total 18 marks.
- Section D: 4 Long Answer (LA) questions, each worth 5 marks, total 20 marks.
- Section E: 3 Case-Based questions, each worth 4 marks, total 12 marks.
- Internal Assessment: This accounts for 20 marks, distributed as follows:
- Periodic Tests and Multiple Assessments: 10 marks.
- Portfolio: 5 marks.
- Lab Practical Work: 5 marks.
The unit-wise weightage for the theory paper is as follows:
- Number Systems: 6 marks.
- Algebra: 20 marks.
- Coordinate Geometry: 6 marks.
- Geometry: 15 marks.
- Trigonometry: 12 marks.
- Mensuration: 10 marks.
- Statistics and Probability: 11 marks.
Here is the CBSE Class 10 Maths Syllabus 2025 with topic-wise breakdown:
Unit I: Number Systems (6 Marks)
- Real Numbers (Euclid’s division lemma, Fundamental Theorem of Arithmetic, Rational & Irrational numbers)
Unit II: Algebra (20 Marks)
- Polynomials
- Pair of Linear Equations in Two Variables
- Quadratic Equations
- Arithmetic Progressions
Unit III: Coordinate Geometry (6 Marks)
- Distance formula, Section formula
Unit IV: Geometry (15 Marks)
- Triangles (Similarity theorems & applications)
- Circles (Tangent properties)
Unit V: Trigonometry (12 Marks)
- Introduction to Trigonometry
- Trigonometric Identities
- Heights and Distances
Unit VI: Mensuration (10 Marks)
- Areas related to Circles
- Surface Areas and Volumes
Unit VII: Statistics and Probability (11 Marks)
- Statistics (Mean, Median, Mode, Graphs)
- Probability
This is based on the latest CBSE syllabus for 2025. Would you like a study plan or important questions for these topics?
here are some important questions and topics that have a high probability of appearing in the exam:
1. Probability:
- From a standard deck of 52 cards, if the King, Queen, and Jack of clubs are removed, calculate the probability of drawing:
- A spade
- A black King
- A club
- A Jack
2. Triangles:
- In ΔABC, altitudes AD and CE intersect at point P. Prove the following relationships:
- ΔAPE ~ ΔCPD
- ΔADB ~ ΔCЕB
- AP × PD = CP × PE
- AB × CE = BC × AD
3. Linear Equations:
- Solve the pair of linear equations graphically:
- x + 3y = 6
- 2x – 3y = 12 Also, find the area of the triangle formed by these lines with the y-axis.
4. Quadratic Equations:
- A passenger’s injury during boarding causes a 30-minute delay. To reach a destination 1500 km away on time, the plane’s speed is increased by 250 km/h. Determine the plane’s usual speed.
5. Surface Areas and Volumes:
- A solid consists of a cone mounted on a hemisphere, each with a radius of 3.5 cm. The total height of the solid is 9.5 cm. Calculate the volume of the solid.
6. Arithmetic Progressions:
- A thief runs at a constant speed of 100 m/min. A policeman starts chasing him at the same speed but increases his speed by 10 m/min every minute. After how many minutes will the policeman catch the thief?
7. Statistics:
- Given a data set with a median of 525 and a total frequency of 100, find the missing frequencies x and y in the frequency distribution table.
8. Real Numbers:
- In a school, 104 students from Class X and 96 from Class IX are to be seated in parallel rows such that no two adjacent rows are from the same class. Determine the maximum number of parallel rows for each class and the number of students per row.
9. Trigonometry:
- From the top of a 100 m high lighthouse, the angles of depression to two ships are 30° and 45°. If one ship is behind the other on the same side, calculate the distance between the two ships.
10. Trigonometric Identities:
- Prove the identity: (1 + cot A + tan A)(sin A – cos A) = (sec³ A – csc³ A) / (sec² A * csc² A)
Focusing on these topics and practicing similar problems will enhance your preparation for the upcoming exam.
Preparing for the CBSE Class 10 Mathematics exam requires a thorough understanding of key concepts and consistent practice. Building upon the previous set of important questions, here are additional questions categorized by chapter to further aid your preparation:
Questions that comes in the CBSE Math Exam 2025
1. Real Numbers:
- Prove that √2 is irrational.
- Show that any positive odd integer is of the form 6q + 1 or 6q + 3 or 6q + 5, where q is some integer.
2. Polynomials:
- If α and β are the zeros of the polynomial 2x² – 4x + 5, find a quadratic polynomial whose zeros are (α + 2) and (β + 2).
- For the polynomial p(x) = x³ – 3x² + x + 1, verify that the sum of the products of its zeros taken two at a time is equal to the coefficient of x term.
3. Pair of Linear Equations in Two Variables:
- Solve the following system of equations using the substitution method:
- 2x + 3y = 9
- 4x – y = 1
- Determine the value of k for which the following system of equations has infinitely many solutions:
- (k + 1)x + 3y = 2k + 1
- (k – 1)x + (k + 1)y = k + 3
4. Quadratic Equations:
- Solve the quadratic equation: 3x² – 2√6x + 2 = 0.
- The sum of the reciprocals of Reena’s ages, 3 years ago and 5 years from now, is 1/3. Find her present age.
5. Arithmetic Progressions:
- The 7th term of an AP is 20, and the 15th term is 44. Find the AP.
- If the sum of the first n terms of an AP is 4n – n², find the nth term.
6. Triangles:
- Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
- In ΔABC, D and E are points on AB and AC respectively such that DE || BC. Prove that AD/DB = AE/EC.
7. Coordinate Geometry:
- Find the coordinates of the point which divides the line segment joining (4, -3) and (8, 5) in the ratio 3:1 internally.
- Determine the area of the quadrilateral formed by the points (1, 2), (4, 5), (7, 8), and (2, 6).
8. Introduction to Trigonometry:
- Prove that: (1 + tan²A)/(1 + cot²A) = tan²A.
- If sinA + sin²A = 1, find the value of cos²A + cos⁴A.
9. Some Applications of Trigonometry:
- From the top of a 50 m high building, the angle of depression to a car on the ground is 30°. Find the distance of the car from the base of the building.
- Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.
10. Circles:
- Prove that the tangents drawn from an external point to a circle are equal in length.
- A circle is inscribed in a ΔABC, touching AB, BC, and CA at P, Q, and R respectively. Prove that AP + BQ + CR = BP + CQ + AR.
11. Constructions:
- Construct a triangle similar to a given triangle ABC with a scale factor of 3/4.
- Draw a pair of tangents to a circle of radius 4 cm from a point 6 cm away from its center.
12. Areas Related to Circles:
- Find the area of the shaded region in a circle of radius 10 cm, if the central angle is 60°.
- A square is inscribed in a circle of diameter 8 cm. Find the area of the square.
13. Surface Areas and Volumes:
- A cylinder and a cone have the same base radius and height. Find the ratio of their volumes.
- A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.
14. Statistics:
- Calculate the mean, median, and mode for the following data:
- Class intervals: 0-10, 10-20, 20-30, 30-40, 40-50
- Frequencies: 5, 8, 12, 7, 3
- For a given data set, the mean is 50, and the sum of the deviations of the data points from the mean is 0. Verify this property.
15. Probability:
- A bag contains 5 red, 7 blue, and 8 green balls. If a ball is drawn at random, what is the probability that it is:
- Red
- Not blue
- Two dice are thrown simultaneously. What is the probability of getting a sum of 9?
Consistent practice of these questions, along with a clear understanding of your own choice. You can choose to practice set.