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Mathematical Tools is not a chapter NEET(UG) asks about directly, and that is exactly why it is skipped — and exactly why marks leak out of every other chapter. A student who is slow at differentiating, or unsure what the area under a graph means, pays for it in kinematics, in electricity, and in every numerical that follows. Spend one afternoon here and the whole year gets easier. Ten questions below. Give them ten honest minutes.
What this chapter carries in NEET(UG)
- NEET(UG) does not ask this chapter on its own. It asks it inside every other chapter.
- Differentiation and integration appear in kinematics, work and energy, and current electricity.
- Graph slopes, graph areas and the two vector products are used throughout the paper.
What the syllabus says
In the syllabus (part of Unit 2, Kinematics): Scalars and vectors, addition and subtraction of vectors, scalar and vector products, unit vector, resolution of a vector.
Taken out in 2024: elementary concepts of differentiation and integration for describing motion.
Taken from the NMC syllabus for NEET (UG) 2026, the latest one published. See the full syllabus, unit by unit.
Formulas you must know by heart
| Power rule | d/dx (xn) = n xn−1 |
| Trigonometric derivatives | d/dx (sin x) = cos x, d/dx (cos x) = −sin x |
| Basic integral | ∫ xn dx = xn+1/(n+1) + C |
| Standard sines | sin 30° = ½, sin 45° = 1/√2, sin 60° = √3/2 |
| Identity | sin2θ + cos2θ = 1 |
| Scalar product | A·B = AB cosθ |
| Vector product | |A × B| = AB sinθ |
| Slope of a graph | slope = dy/dx |
| Area under a curve | area = ∫ y dx |
| Logarithms | log(ab) = log a + log b, log(a/b) = log a − log b |
The two graph lines are the ones to hold on to. Slope and area are how physics reads a graph: the slope of a position–time graph is velocity, and the area under a velocity–time graph is displacement. The same pair comes back for charge, work and impulse.
Ten questions. Give yourself ten minutes.
Write your answers down before you scroll. A question you looked up is a question you have not answered.
Q1. The derivative of x3 with respect to x is
- (a) 3x2
- (b) x2/3
- (c) 3x
- (d) x4/4
Q2. ∫ x2 dx is equal to
- (a) 2x
- (b) x3/3 + C
- (c) x3 + C
- (d) 3x3
Q3. The value of sin 30° is
- (a) ½
- (b) √3/2
- (c) 1
- (d) 1/√2
Q4. The derivative of sin x with respect to x is
- (a) cos x
- (b) −cos x
- (c) −sin x
- (d) tan x
Q5. If y = 5x2 + 3x, the value of dy/dx at x = 2 is
- (a) 13
- (b) 20
- (c) 23
- (d) 26
Q6. The slope of a position–time graph gives the
- (a) displacement
- (b) velocity
- (c) acceleration
- (d) force
Q7. The area under a velocity–time graph gives the
- (a) acceleration
- (b) displacement
- (c) speed
- (d) force
Q8. If two vectors are perpendicular, their scalar product is
- (a) AB
- (b) zero
- (c) AB sinθ
- (d) −AB
Q9. The magnitude of the vector product of two parallel vectors is
- (a) AB
- (b) zero
- (c) AB cosθ
- (d) 1
Q10. log(ab) is equal to
- (a) log a × log b
- (b) log a + log b
- (c) log a − log b
- (d) (log a)/(log b)
Answer key, with a hint for each
| Q1 | (a) | Bring the power down and reduce it by one: 3x3−1. |
| Q2 | (b) | Raise the power by one and divide by the new power. Never forget the constant. |
| Q3 | (a) | One of the three values worth knowing cold, along with 45° and 60°. |
| Q4 | (a) | And the derivative of cos x carries a minus sign. Students drop that minus more often than anything else here. |
| Q5 | (c) | dy/dx = 10x + 3, so at x = 2 it is 20 + 3. |
| Q6 | (b) | Slope is the rate of change of position, which is exactly what velocity means. |
| Q7 | (b) | Velocity multiplied by time is displacement, and that product is what the area under the graph adds up. |
| Q8 | (b) | A·B = AB cosθ, and cos 90° = 0. |
| Q9 | (b) | |A × B| = AB sinθ, and sin 0° = 0. Parallel vectors have no cross product. |
| Q10 | (b) | Multiplication inside a log turns into addition outside it. |
Now mark yourself honestly
NEET(UG) marks the way it marks. Use the same rule here:
- +4 for a right answer
- −1 for a wrong one
- 0 for a blank
So ten questions here are out of 40. In the real paper, 45 Physics questions are out of 180.
If you scored 32 or more, the basics of this chapter are secure. Move to harder questions, not more of these.
If you scored below 24, do not feel bad about it. You have just found out something useful before the exam did. Go back to the formula table above, learn it properly, and sit these ten again tomorrow.
And if you guessed a few and they landed, count those as wrong. A guess that works once will not work in May.
The full chapter, on a clock
Ten questions tell you a little. Forty-five tell you the truth.
The Beginner paper for Mathematical Tools is waiting for you on the portal: 45 questions, 45 minutes, marked out of 180, with the answer key and a hint for every question. Sit it tonight and you will know exactly where this chapter stands.
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