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🇮🇳 ICSE Class 10 · flashcards
ICSE Class 10 Mathematics Flashcards
50 question-and-answer cards covering Mathematics as it is examined in ICSE 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.
State the Basic Proportionality Theorem (Thales' Theorem).
If a line is drawn parallel to one side of a triangle to intersect the other two sides, it divides those two sides in the same ratio.
How do the perimeters, areas, and volumes of two similar figures relate to the ratio of corresponding sides k?
Ratio of perimeters (or any corresponding lengths) = k; ratio of areas = k²; ratio of volumes = k³.
State the theorem about the angle subtended by an arc at the centre versus at the circumference.
The angle subtended by an arc at the centre is twice the angle subtended by the same arc at any point on the remaining part of the circumference.
State the cyclic quadrilateral angle theorem.
The opposite angles of a cyclic quadrilateral are supplementary (each pair sums to 180°).
What is the relationship between the tangent to a circle and the radius at the point of contact, and the equal-tangents property?
A tangent is perpendicular to the radius at the point of contact. Two tangents drawn from an external point to a circle are equal in length.
State the alternate segment theorem for a circle.
The angle between a tangent to a circle and a chord drawn from the point of contact equals the angle subtended by that chord in the alternate segment.
State the angle in a semicircle theorem and the equal-chords property.
The angle in a semicircle is a right angle (90°). Equal chords of a circle are equidistant from the centre, and chords equidistant from the centre are equal.
State the relationship sin θ, cos θ, and tan θ have via the basic identity, and give the reciprocal ratios.
tan θ = sin θ / cos θ, and sin²θ + cos²θ = 1. Reciprocals: cosec θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ.
State the two trigonometric identities (besides sin²θ + cos²θ = 1) involving sec and cosec.
sec²θ − tan²θ = 1 (i.e. 1 + tan²θ = sec²θ) and cosec²θ − cot²θ = 1 (i.e. 1 + cot²θ = cosec²θ).
Give the values of sin, cos, and tan for 0°, 30°, 45°, 60°, and 90°.
sin: 0, ½, 1/√2, √3/2, 1. cos: 1, √3/2, 1/√2, ½, 0. tan: 0, 1/√3, 1, √3, undefined (∞).
In heights and distances, define the angle of elevation and the angle of depression.
Angle of elevation is the angle above the horizontal when looking up at an object; angle of depression is the angle below the horizontal when looking down at an object. They are equal (alternate angles).
State the curved (lateral) surface area, total surface area, and volume of a right circular cylinder of radius r and height h.
CSA = 2πrh; TSA = 2πr(h + r); Volume = πr²h.
State the slant height, curved surface area, total surface area, and volume of a right circular cone (radius r, height h, slant l).
l = √(r² + h²); CSA = πrl; TSA = πr(l + r); Volume = (1/3)πr²h.
State the surface area and volume of a sphere and a hemisphere of radius r.
Sphere: surface area = 4πr², volume = (4/3)πr³. Hemisphere: CSA = 2πr², TSA = 3πr², volume = (2/3)πr³.
How do you find the surface area and volume of a combination/solid (e.g. a cone mounted on a cylinder)?
Total surface area = sum of the exposed surface areas of each part (excluding hidden joined faces); total volume = sum of the individual volumes of the component solids.
Give the formula for the length of an arc and the area of a sector of a circle with radius r and central angle θ°.
Arc length = (θ/360) × 2πr; Sector area = (θ/360) × πr².
State the formula for the mean of grouped data using the direct method.
Mean x̄ = Σfᵢxᵢ / Σfᵢ, where xᵢ are class marks (midpoints) and fᵢ are the corresponding frequencies.
What are the two main methods, besides direct, to calculate the mean of grouped data?
Assumed mean (short-cut) method: x̄ = A + Σfd/Σf, where d = x − A. Step-deviation method: x̄ = A + (Σfu/Σf) × h, where u = (x − A)/h and h is the class size.
State the formula for the median of grouped (continuous) data.
Median = l + [(N/2 − cf)/f] × h, where l = lower boundary of median class, N = total frequency, cf = cumulative frequency before median class, f = frequency of median class, h = class size.
State the formula for the mode of grouped data.
Mode = l + [(f₁ − f₀)/(2f₁ − f₀ − f₂)] × h, where l = lower boundary of modal class, f₁ = modal class frequency, f₀ = preceding frequency, f₂ = following frequency, h = class size.
State the empirical relationship between mean, median, and mode.
Mode = 3 × Median − 2 × Mean.
What are an ogive and the two types of cumulative frequency curves, and how is the median found graphically?
An ogive is a cumulative frequency curve: the 'less than' ogive (rising) and 'more than' ogive (falling). The median is the x-coordinate of the point where the two ogives intersect (or where the less-than ogive reaches N/2).
State the classical (theoretical) definition of probability of an event E.
P(E) = (Number of favourable outcomes) / (Total number of equally likely outcomes). It always satisfies 0 ≤ P(E) ≤ 1.
What is the probability of the complement of an event, and the probability of a sure and an impossible event?
P(not E) = 1 − P(E). The sum P(E) + P(not E) = 1. P(sure event) = 1 and P(impossible event) = 0.
What this deck covers
The Mathematics deck follows the ICSE Class 10 Mathematics syllabus — 1 chapters and 5 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 50.0 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 122 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 ICSE Class 10 deck?
50 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these ICSE Class 10 flashcards free?
Yes. The preview here is free to read with no signup, and the full 50-card deck is free inside the Examius app.
What do the Mathematics cards cover?
They follow the ICSE Class 10 Mathematics syllabus — 1 chapters and 5 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.