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UPSC CDS Mathematics Flashcards
53 question-and-answer cards covering Mathematics as it is examined in UPSC CDS. 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 a natural number versus a whole number?
Natural numbers are 1, 2, 3, …; whole numbers add zero: 0, 1, 2, 3, …
What is a rational number?
A number expressible as p/q, where p and q are integers and q ≠ 0.
What is an irrational number? Give an example.
A number that cannot be written as p/q with integers (non-terminating, non-repeating decimal); e.g., √2 or π.
State the BODMAS/order of operations.
Brackets, Orders (powers/roots), Division and Multiplication, then Addition and Subtraction.
What are co-prime numbers?
Two numbers whose only common factor is 1 (their HCF is 1), e.g., 8 and 15.
What is the relationship between HCF and LCM of two numbers a and b?
HCF × LCM = a × b (product of the two numbers).
Classify triangles by their sides.
Equilateral (all sides equal), isosceles (two sides equal), and scalene (all sides different).
Classify triangles by their angles.
Acute (all angles < 90°), right (one angle = 90°), and obtuse (one angle > 90°).
What is the angle sum property of a triangle?
The sum of the interior angles of a triangle is 180°.
What is the exterior angle property of a triangle?
An exterior angle equals the sum of the two opposite (remote) interior angles.
State the Pythagoras theorem.
In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: c² = a² + b².
What is the formula for the area of a triangle with base b and height h?
Area = ½ × base × height = ½ × b × h.
State Heron's formula for the area of a triangle with sides a, b, c.
Area = √[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2 is the semi-perimeter.
What is the criterion for similarity of two triangles (AAA/AA)?
Two triangles are similar if their corresponding angles are equal (AA criterion implies the third angle is also equal).
List the main congruence criteria for triangles.
SSS, SAS, ASA, AAS, and RHS (right angle-hypotenuse-side).
What is the centroid of a triangle?
The point where the three medians meet; it divides each median in a 2:1 ratio from the vertex.
Define a circle.
The set of all points in a plane that are at a fixed distance (the radius) from a fixed point (the centre).
What are the formulas for the circumference and area of a circle of radius r?
Circumference = 2πr; Area = πr².
What is the relationship between a diameter and a radius?
Diameter = 2 × radius; the diameter is the longest chord passing through the centre.
State the angle subtended by a diameter at the circumference (angle in a semicircle).
It is a right angle (90°).
What is the relationship between the angle subtended by an arc at the centre and at the circumference?
The angle at the centre is twice the angle subtended by the same arc at any point on the remaining circumference.
What is the angle between a tangent to a circle and the radius at the point of contact?
They are perpendicular; the angle is 90°.
What is the length of an arc subtending angle θ (in degrees) at the centre of a circle of radius r?
Arc length = (θ/360) × 2πr.
What is the area of a sector with central angle θ (in degrees) and radius r?
Sector area = (θ/360) × πr².
What this deck covers
The Mathematics deck follows the UPSC CDS Mathematics syllabus — 2 chapters and 6 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 26.5 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 72 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 UPSC CDS deck?
53 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these UPSC CDS flashcards free?
Yes. The preview here is free to read with no signup, and the full 53-card deck is free inside the Examius app.
What do the Mathematics cards cover?
They follow the UPSC CDS Mathematics syllabus — 2 chapters and 6 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.