Last Updated on October 17, 2026 by XAM CONTENT
This Class 9 to Class 10 bridge diagnostic checks whether the core Maths and Science skills needed for Class 10 are ready for use. It is an original XAM CONTENT diagnostic, not an official CBSE examination. Because the Class 9 curriculum has changed for 2026–27, this test maps skills and concepts rather than relying on old chapter numbers.
M1. Is √11 rational or irrational? Give one reason.
Answer: Irrational. Since 11 is not a perfect square, √11 cannot be expressed as a ratio of two integers.
M2. Expand and simplify: (2x − 3)(x + 4).
Answer: 2x² + 5x − 12. Multiply term by term: 2x² + 8x − 3x − 12.
M3. Solve: 5x − 7 = 3x + 9.
Answer: x = 8. Rearranging gives 2x = 16.
M4. In which quadrant does the point (−4, 5) lie?
Answer: Quadrant II, because x is negative and y is positive.
M5. Find the 12th term of the sequence 7, 11, 15, 19, …
Answer: 51. Here a = 7 and d = 4, so a₁₂ = 7 + 11×4 = 51.
M6. A right triangle has legs 6 cm and 8 cm. Find its hypotenuse.
Answer: 10 cm. By the Pythagorean theorem, c² = 6² + 8² = 100.
M7. A bag contains 3 red and 5 blue balls. One ball is chosen at random. What is the probability of choosing red?
Answer: 3/8. There are 3 favourable outcomes among 8 equally likely balls.
M8. A rectangular floor is 7.5 m long and 4 m wide. Find its area.
Answer: 30 m². Area = length × breadth = 7.5 × 4.
S1. What is the difference between an element and a compound?
Answer: An element contains only one type of atom, while a compound contains two or more elements chemically combined in a fixed proportion.
S2. Why can a mixture of sand and water be separated physically?
Answer: The substances are not chemically bonded into a new substance, so their physical-property differences can be used for separation.
S3. A cyclist increases speed from 4 m/s to 10 m/s in 3 s. Find the average acceleration.
Answer: 2 m/s². Acceleration = (10 − 4)/3 = 2 m/s².
S4. What happens to momentum if mass stays constant and velocity becomes three times as large?
Answer: Momentum becomes three times as large because p = mv.
S5. A force of 20 N moves an object 5 m in the direction of the force. How much work is done?
Answer: 100 J. Work = force × displacement = 20 × 5.
S6. Which cell structure controls movement of substances into and out of the cell?
Answer: The plasma membrane.
S7. Why are organisms classified into groups?
Answer: Classification organises biological diversity using shared characteristics, making organisms easier to study and compare and helping reveal relationships.
S8. A distance–time graph is a straight line with constant slope. What does this indicate?
Answer: Uniform motion at constant speed.
| Question(s) | Skill to Review | Revision Route |
|---|---|---|
| M1 | Number sense: rational / irrational numbers | Class 9 Maths Hub → then Class 10 Maths Hub |
| M2–M3 | Algebraic manipulation and equations | Class 9 Maths Hub → Linear-Equation Practice |
| M4 | Coordinate representation | Class 9 Maths Hub → Coordinate Geometry in Class 10 Hub |
| M5 | Sequences and arithmetic progressions | Class 9 Maths Hub → Arithmetic Progressions in Class 10 |
| M6 | Right-triangle reasoning and geometry | Class 9 Maths Hub → Triangles / Trigonometry in Class 10 |
| M7 | Basic probability | Class 9 Maths Hub → Class 10 Probability |
| M8 | Mensuration and units | Class 9 Maths Hub → Class 10 Mensuration |
| S1–S2 | Matter, elements, compounds and mixtures | Class 9 Science Hub → Class 10 Science Hub |
| S3 | Motion, formula use and units | Motion Numericals |
| S4 | Force, momentum and proportional reasoning | Force & Motion Numericals |
| S5 | Work and energy calculations | Work & Energy Practice |
| S6 | Cell structure and function | Cell MCQs → Class 10 Science Hub |
| S7 | Biological classification and comparison | Class 9 Science Hub |
| S8 | Graphs and interpretation of motion | Motion Revision |
R1. Factorise: x² + 7x + 12.
Answer: (x + 3)(x + 4).
R2. Find the 20th term of the AP 3, 8, 13, 18, …
Answer: 98. a = 3, d = 5, so a₂₀ = 3 + 19×5.
R3. A fair die is rolled once. What is the probability of obtaining a number greater than 4?
Answer: 2/6 = 1/3, because the favourable outcomes are 5 and 6.
R4. A square has side 6.5 cm. Find its area.
Answer: 42.25 cm².
R5. A car changes velocity from 6 m/s to 18 m/s in 4 s. Find the average acceleration.
Answer: 3 m/s².
R6. Why is filtration suitable for separating insoluble sand from water?
Answer: Sand particles are insoluble and larger than the pores of the filter medium, so they are retained while water passes through.
R7. What is the work done when a 15 N force moves an object 4 m in the direction of the force?
Answer: 60 J.
R8. Why is the plasma membrane described as selectively permeable?
Answer: Because it allows some substances to pass through while restricting others, thereby regulating exchange between the cell and its surroundings.
Is this an official CBSE bridge test?
No. It is an original XAM CONTENT diagnostic designed around transferable prerequisite skills. Use official CBSE curriculum documents for syllabus requirements.
Why does the diagnostic not follow old Class 9 chapter numbers?
Class IX Mathematics and other secondary-stage materials have changed for 2026–27. Skill mapping avoids incorrectly treating previous textbook numbering as the current structure.
Should I revise every Class 9 topic before starting Class 10?
Not necessarily. Use the diagnostic to identify prerequisite gaps, repair those gaps, and then continue into Class 10 while revisiting Class 9 concepts when needed.
How long should I spend on the bridge plan?
A focused week can be enough for a first pass, but the actual time should depend on which skills need review. The goal is stable understanding, not finishing on a fixed date.
When should I attempt Class 10 sample papers?
After you have studied a substantial part of the Class 10 syllabus. At the bridge stage, subject-hub practice is more useful than attempting a full board paper too early.
