Most of Class 10 Science is words and diagrams, so students are often caught off guard by how much of the paper is numerical in the few chapters where numbers appear. Those chapters are predictable. Within each of them, the same handful of problem types keep returning in different clothes: a new object distance, a different resistor combination, a different defect of vision. If you know the types, you stop meeting each numerical as a surprise.
This article walks through the chapters in order, names the types that recur, and solves one of each with the arithmetic checked. It is a list of patterns drawn from how the chapters are built, not a prediction of any one year’s paper, so read it alongside the previous year question papers to see how your own board frames them.
First, Which Chapters Actually Have Numericals
Three chapters carry almost all the calculation: light (reflection and refraction), the human eye and the colourful world, and electricity. A fourth, heredity, has ratio-style questions that are numerical in spirit. Magnetic effects of electric current, chemical reactions, acids and bases, and the biology chapters are mostly conceptual, although chemical equations demand a quiet kind of arithmetic that we return to at the end.
Syllabus numbering differs between boards. In the current CBSE Class 10 Science book, Light is Chapter 9, the Human Eye is Chapter 10, Electricity is Chapter 11 and Heredity is Chapter 8. In the Karnataka SSLC textbook, Light is Chapter 10, the Human Eye is Chapter 11, Electricity is Chapter 12 and Heredity and Evolution is Chapter 9. Some of Deeksha’s chapter pages use the older numbering, so match the topic name, not the number, and confirm the current numbering with your own board.
Light: Mirror and Lens Calculations
The chapter on light, reflection and refraction produces the most formula-heavy numericals of the year. The recurring types are:
- Finding image distance and nature using the mirror formula, 1/v + 1/u = 1/f.
- Finding magnification, m = minus v / u for mirrors and m = v / u for lenses, and image height.
- Using the lens formula, 1/v minus 1/u = 1/f, and the power of a lens, P = 1/f with f in metres.
- Refractive index from speed of light, n = c / v, or from angles, n = sin i / sin r.
- Combinations of lenses, where powers add.
The sign convention is where most marks are lost. Distances are measured from the pole or optical centre, with the direction of the incident light taken as positive. For a concave mirror, f is negative; for a convex lens, f is positive. Write the signs next to every given value before substituting.
Solved: concave mirror. An object is placed 20 cm in front of a concave mirror of focal length 15 cm. Here u = minus 20 and f = minus 15. Then 1/v = 1/f minus 1/u = minus 1/15 + 1/20 = (minus 4 + 3)/60 = minus 1/60, so v = minus 60 cm. Magnification m = minus v/u = minus (minus 60)/(minus 20) = minus 3. The image is real, inverted, enlarged three times and formed 60 cm in front of the mirror.
Solved: convex lens. An object is 30 cm from a convex lens of focal length 10 cm. u = minus 30, f = plus 10. 1/v = 1/f + 1/u = 1/10 minus 1/30 = 2/30 = 1/15, so v = plus 15 cm and m = v/u = 15/(minus 30) = minus 0.5. The image is real, inverted and half the size of the object.
Solved: refractive index. The speed of light in glass is 2 x 10 to the power 8 metres per second. n = 3 x 10 to the power 8 divided by 2 x 10 to the power 8 = 1.5.
For more practice on mirrors specifically, the page on spherical mirrors and the important questions for the chapter are good places to go next.
The Human Eye: Power of Corrective Lenses
The numericals here are a narrow, repeated type: find the power of the lens that corrects a defect. The method is always the same. Decide what the lens must do, which is to take an object at the normal distance and form its image at the person’s far point or near point. Then use the lens formula, convert focal length to metres, and take the reciprocal.
Solved: myopia. A person’s far point is at 80 cm. The corrective lens must form an image at 80 cm of a very distant object, so u is at infinity and v = minus 80 cm. Then f = minus 80 cm = minus 0.8 m, and P = 1/f = minus 1.25 D. The lens is concave.
Solved: hypermetropia. A person’s near point is 1 m, and the normal near point is 25 cm. The lens must make an object at 25 cm appear at 100 cm: u = minus 25, v = minus 100. 1/f = 1/v minus 1/u = minus 1/100 + 1/25 = 3/100, so f = 33.3 cm and P = plus 3.0 D. The lens is convex.
The typical errors are forgetting to convert centimetres to metres, and mixing up which defect needs which type of lens. Remember that a negative power means a diverging lens. The pages on human eye numericals with solutions collect more of these in one place.
Electricity: Where Most of the Numericals Live
Electricity is the chapter with the widest range of numerical types, and the one with the highest chance of appearing in more than one question. The recurring types are:
- Ohm’s law, V = IR, in direct form and in graph form.
- Resistance and resistivity: R = rho l / A, including the effect of changing length or area.
- Series and parallel combinations, and the equivalent resistance of mixed circuits.
- Electric power, P = VI = I squared R = V squared / R.
- Electrical energy and its cost in kilowatt hours.
- Heating effect, H = I squared R t.
Solved: stretching a wire. A wire of resistance 4 ohm is stretched to double its length. Its volume is constant, so doubling the length halves the area. R is proportional to length divided by area, so the resistance becomes 2 x 2 = 4 times larger, which is 16 ohm.
Solved: parallel combination. Resistors of 2, 3 and 6 ohm are connected in parallel. 1/R = 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 1, so R = 1 ohm. Notice that the answer is smaller than the smallest resistor, as it must be in parallel.
Solved: energy and cost. A 100 W bulb is used for 5 hours a day for 30 days. Energy = 0.1 kW x 5 h x 30 = 15 kWh, which is 15 units. At an assumed rate of Rs 7 per unit, the cost is Rs 105.
Solved: heating effect. A current of 2 A flows through a 10 ohm resistor for 10 seconds. H = I squared R t = 4 x 10 x 10 = 400 J.
For more on these, electricity numericals with solutions, the page on the resistance of a system of resistors and the page on electric power give worked problems, and the page on where students lose marks in Ohm’s law numericals names the slips directly.
Heredity: Ratio Questions
Heredity does not need a calculator, but it does ask for ratio arithmetic. A cross between two plants differing in one trait gives a 3 to 1 ratio of dominant to recessive in the second generation. If there are 400 plants in the second generation, then 300 show the dominant trait and 100 the recessive. The genotype ratio is 1 : 2 : 1, so 100 are homozygous dominant, 200 heterozygous and 100 homozygous recessive.
For a cross involving two traits, the phenotype ratio is 9 : 3 : 3 : 1. Out of 160 plants, that is 90, 30, 30 and 10, since 160 divided by 16 is 10. Whether the dihybrid cross is part of your current syllabus is worth confirming with your board, as the heredity chapter has been revised in recent years. The important questions for heredity and evolution show the typical forms.
Chapters That Look Numerical but Mostly Are Not
The chapter on magnetic effects of electric current is mostly rules and reasoning: direction of force, direction of field, the working of motors and generators. A few boards include simple questions on field strength or force, so check yours. Chemical equations and acids and bases are not numerical in the usual sense, but balancing an equation is arithmetic with atoms: count each element on both sides and adjust coefficients. That skill is worth practising on its own, and the chemical reactions and equations notes are a good start.
A Habit That Works for Every Numerical
Write given quantities with units and signs. Write the formula. Substitute. Check units and plausibility. That last step catches many errors: the image from a convex mirror must be virtual and smaller, the parallel resistance must be smaller than the smallest resistor, and a power of a corrective lens must have the sign that fits the defect.
Frequently Asked Questions
Q1. Which Class 10 Science chapters have the most numericals?
Light, the human eye and electricity carry most of the numerical questions. Heredity has ratio-based questions, and the remaining chapters are largely conceptual.
Q2. What are the most important formulas to remember?
The mirror and lens formulas, magnification, power of a lens, Ohm’s law, resistivity, the series and parallel rules, electric power, energy in kilowatt hours, and the heating formula H = I squared R t.
Q3. Why do I lose marks even when I use the right formula?
Usually because of sign convention, a missing unit conversion such as centimetres to metres, or a missing final statement about the nature of the image or the type of lens.
Q4. How should I practise numericals?
Practise by type rather than by chapter order. Solve three or four examples of each type, then check against previous year papers to see how your board frames them.
Q5. Do numericals differ between CBSE and Karnataka SSLC?
The core types are the same, but chapter numbering, the depth of some topics and the marking pattern can differ. Confirm with your own board’s syllabus and sample papers.
Conclusion: Learn the Types, Not Just the Formulas
Class 10 Science numericals repeat in families. Learn each family once, practise with the sign convention and units written down, and check the answer against what the physics says it should look like.
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