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🇮🇳 CBSE Class 10 · flashcards
CBSE Class 10 Mathematics Flashcards
78 question-and-answer cards covering Mathematics as it is examined in CBSE Class 10. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Mathematics deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
What is the curved surface area and total surface area of a cone with radius r, height h and slant height l (l = √(r²+h²))?
Curved surface area = πrl; Total surface area = πr(l + r).
What are the surface area formulas for a sphere of radius r and a hemisphere of radius r?
Sphere surface area = 4πr²; Hemisphere curved surface area = 2πr²; Hemisphere total surface area = 3πr².
State the volume formulas for a cylinder, cone and sphere.
Cylinder = πr²h; Cone = (1/3)πr²h; Sphere = (4/3)πr³.
What principle is used when a solid is converted (recast/melted) from one shape into another?
The volume remains constant (volume is conserved), so the volume of the original solid equals the volume of the new solid.
What is a frustum of a cone?
A frustum is the solid obtained when a cone is cut by a plane parallel to its base, removing the smaller cone on top; it has two circular ends of different radii.
State the volume of a frustum of a cone with radii r₁ and r₂ and height h.
Volume = (1/3)πh(r₁² + r₂² + r₁r₂).
State the curved surface area and total surface area of a frustum with radii r₁, r₂ and slant height l.
Curved surface area = π(r₁ + r₂)l; Total surface area = π(r₁ + r₂)l + πr₁² + πr₂², where l = √[h² + (r₁ − r₂)²].
State the direct method formula for the mean of grouped data.
Mean x̄ = Σf_i x_i / Σf_i, where x_i are the class marks and f_i the corresponding frequencies.
State the assumed mean (deviation) method formula for the mean of grouped data.
Mean x̄ = a + (Σf_i d_i / Σf_i), where a is the assumed mean and d_i = x_i − a.
State the step-deviation method formula for the mean of grouped data.
Mean x̄ = a + h × (Σf_i u_i / Σf_i), where u_i = (x_i − a)/h and h is the class size.
State the formula for the mode of grouped data.
Mode = l + [(f₁ − f₀)/(2f₁ − f₀ − f₂)] × h, where l is the lower limit of the modal class, f₁ its frequency, f₀ and f₂ the frequencies of the preceding and succeeding classes, and h the class size.
State the formula for the median of grouped data.
Median = l + [(n/2 − cf)/f] × h, where l is the lower limit of the median class, n = Σf_i, cf the cumulative frequency before the median class, f the frequency of the median class, and h the class size.
State the empirical relationship between mean, median and mode.
3 Median = Mode + 2 Mean (equivalently, Mode = 3 Median − 2 Mean).
What are the two types of ogives used to graphically represent a cumulative frequency distribution?
The 'less than' ogive and the 'more than' ogive (both are cumulative frequency curves).
How can the median be obtained graphically from ogives?
It is the x-coordinate of the point of intersection of the 'less than' and 'more than' ogives (or the x-value corresponding to cumulative frequency n/2 on a single ogive).
State the classical (theoretical) definition of the probability of an event E.
P(E) = (Number of outcomes favourable to E) / (Total number of equally likely outcomes), assuming all outcomes are equally likely.
What is the range of the probability of any event E?
0 ≤ P(E) ≤ 1.
What are a sure (certain) event and an impossible event, and what are their probabilities?
A sure event is certain to happen with probability 1; an impossible event cannot happen and has probability 0.
What are complementary events, and what is the relation between their probabilities?
E and 'not E' are complementary events; P(E) + P(not E) = 1, so P(not E) = 1 − P(E).
What is an elementary event in probability?
An event having only one (single) outcome of the experiment; the sum of the probabilities of all elementary events of an experiment is 1.
How does the SSS similarity criterion differ from the SSS congruence criterion?
SSS similarity requires corresponding sides to be in the same ratio (proportional), giving same shape; SSS congruence requires corresponding sides to be exactly equal, giving same shape and size.
Compare consistent and inconsistent pairs of linear equations.
A consistent pair has at least one solution (intersecting lines give one solution; coincident lines give infinitely many); an inconsistent pair has no solution (parallel lines).
Outline the steps to construct a tangent to a circle from an external point P.
Join P to centre O, find midpoint M of OP, draw a circle with centre M and radius MO; this circle cuts the given circle at two points; lines from P to these points are the required tangents.
How do you find the area of a combination of plane figures (e.g., a shape made of a rectangle and semicircles)?
Decompose the figure into known basic shapes, calculate each area separately, then add or subtract these areas as appropriate to get the total area.
What this deck covers
The Mathematics deck follows the CBSE Class 10 Mathematics syllabus — 15 chapters and 44 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 5.2 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 117 characters, which is long enough to carry the reasoning and short enough to say out loud.
A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.
Mathematics flashcards FAQ
How many Mathematics flashcards are in this CBSE Class 10 deck?
78 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these CBSE Class 10 flashcards free?
Yes. The preview here is free to read with no signup, and the full 78-card deck is free inside the Examius app.
What do the Mathematics cards cover?
They follow the CBSE Class 10 Mathematics syllabus — 15 chapters and 44 topics — so the questions track what is actually examinable.
How should I use these flashcards?
Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.