ICSE Class 12 Mathematics — Flashcards
ICSE Class 12 Mathematics flashcards, chapter by chapter — 388 flashcards across 13 chapters. Follows the ICSE / ISC syllabus.
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- Check the answer — mark the cards you got wrong.
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Chapter-Wise Flashcards — 13 Chapters
Q: Find the Cartesian product: A = {a, b, c} and B = {1, 2}.
A: Step 1: Write all ordered pairs with first element from A and second element from B. Step 2: Pair a with 1, 2; b with 1, 2; c with 1, 2. Step 3: A × B = {(a,1), (a,2), (b,1), (b,2), (c,1), (c,2)}. Ans
Q: How many elements are in A × B if n(A) = 3 and n(B) = 4?
A: Step 1: Use the formula n(A × B) = pq, where p = n(A) and q = n(B). Step 2: Substitute p = 3 and q = 4. Step 3: n(A × B) = 3 × 4 = 12. Answer: 12 elements.
Q: If A or B is empty, what is A × B?
A: Step 1: The Cartesian product contains ordered pairs (a,b) with a in A and b in B. Step 2: If one set has no element, no ordered pair can be formed. Step 3: So A × B = ∅. Answer: The Cartesian product
Q: Check whether R = {(1, a), (2, c), (3, b)} from A = {1, 2, 3} to B = {a, b, c} is a function.
A: Step 1: Check each element of A. 1 maps to a. 2 maps to c. 3 maps to b. Step 2: Every element of the domain has exactly one image. Answer: R is a function.
Q: Check whether R = {(1, a), (1, b), (3, c)} from A = {1, 2, 3} to B = {a, b, c} is a function.
A: Step 1: Look at element 1. It has two images: a and b. Step 2: A function cannot give two images to the same domain element. Answer: R is not a function.
Q: Find the domain, co-domain, and range of f = {(1, 5), (2, 6), (3, 7)} where f: A → B with A = {1, 2, 3} and B = {5, 6, 7, 8}.
A: Step 1: Domain is the set of first elements. Domain = {1, 2, 3} Step 2: Co-domain is the given target set. Co-domain = {5, 6, 7, 8} Step 3: Range is the set of actual images. Range = {5, 6, 7} Answer:
Q: Solve: On R, find 2 * 3 if a * b = a + b.
A: Step 1: Substitute a = 2 and b = 3. Step 2: Compute 2 * 3 = 2 + 3. Step 3: 2 + 3 = 5. Answer: 5 Check: The result is a real number, so the operation is closed on R.
Q: Is a * b = a - b a binary operation on N?
A: Step 1: Test closure on N. Step 2: Take a = 1 and b = 2. Step 3: 1 - 2 = -1. Step 4: -1 is not in N. Answer: No, it is not a binary operation on N.
Q: Find the number of binary operations on a set with 3 elements.
A: Step 1: Use the formula Number of binary operations on A = p^(p^2). Step 2: Here p = 3. Step 3: So the number is 3^(3^2) = 3^9. Answer: 3^9 Meaning: A binary operation is a function from A × A to A, s
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Where can I find ICSE Class 12 Mathematics Flashcards?
This page has flashcards for 13 chapters of ICSE Class 12 Mathematics for the board exams 2027. Each chapter links to its own page with the full set.
How should I prepare for ICSE Class 12 Mathematics board exams?
Go through the syllabus first, then work chapter by chapter: learn the ideas, practise questions, and revise with notes and flashcards. Leave time at the end to revise every chapter once more under timed conditions.
How do I use flashcards for ICSE Class 12 Mathematics?
Read the question side, answer it in your head, then check. Put the cards you got wrong back into the pile and review them again the next day. Short daily sessions work better than long ones.
Browse Flashcards by Chapter
13 chapters
Relations and Functions
Functions
Binary Operations
Inverse Trigonometric Functions
Matrices
Determinants
Applications of Matrices and Determinants
Continuity and Differentiability
Differentiation
Mean Value Theorems
Indeterminate Forms
Applications of Derivatives - I
Applications Of Derivatives - II
More Mathematics Resources
ICSE Class 12
Practice Quiz
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Syllabus
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