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🇵🇰 GIKI Admission Test · flashcards
GIKI Admission Test Mathematics Flashcards
50 question-and-answer cards covering Mathematics as it is examined in GIKI Admission Test. 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.
How is the determinant of a 3×3 matrix found by expansion along the first row?
For [[a,b,c],[d,e,f],[g,h,i]]: det = a(ei − fh) − b(di − fg) + c(dh − eg), expanding by cofactors along the first row with the +,−,+ sign pattern.
State two key properties of determinants relating to row operations.
Interchanging two rows (or columns) multiplies the determinant by −1. If two rows (or columns) are identical or proportional, the determinant is 0. Adding a multiple of one row to another leaves the determinant unchanged.
What is the determinant of a product of matrices, and of a transpose?
det(AB) = det(A)·det(B), and det(Aᵀ) = det(A).
When does a square matrix have an inverse (is non-singular)?
A square matrix A is invertible (non-singular) if and only if its determinant is non-zero, det(A) ≠ 0. If det(A) = 0 the matrix is singular and has no inverse.
What is the formula for the inverse of a matrix A using the adjoint?
A⁻¹ = (1/det(A)) · adj(A), where adj(A) is the adjoint (the transpose of the cofactor matrix), valid when det(A) ≠ 0.
How do you find the inverse of a 2×2 matrix [[a, b],[c, d]]?
A⁻¹ = (1/(ad − bc)) · [[d, −b],[−c, a]], provided ad − bc ≠ 0.
What is Cramer's Rule for solving simultaneous linear equations?
For a system AX = B with det(A) = D ≠ 0, each unknown xᵢ = Dᵢ / D, where Dᵢ is the determinant of A with its i-th column replaced by the constants column B.
In a system of linear equations AX = B, how does the determinant of A classify the solution?
If det(A) ≠ 0, there is a unique solution. If det(A) = 0, the system has either no solution (inconsistent) or infinitely many solutions (dependent).
What is the quadratic formula for ax² + bx + c = 0?
x = [−b ± √(b² − 4ac)] / (2a), where a ≠ 0.
What is the discriminant of a quadratic equation and what does it represent?
The discriminant is D = b² − 4ac. It determines the nature of the roots of ax² + bx + c = 0.
How does the discriminant determine the nature of the roots of ax² + bx + c = 0?
If D > 0: two distinct real roots. If D = 0: two equal (repeated) real roots. If D < 0: two complex conjugate roots. If D > 0 and is a perfect square (with rational coefficients): roots are rational.
For ax² + bx + c = 0 with roots α and β, what are the sum and product of the roots?
Sum of roots α + β = −b/a, and product of roots αβ = c/a.
How do you form a quadratic equation given the sum S and product P of its roots?
x² − Sx + P = 0, i.e., x² − (α+β)x + αβ = 0.
How are equations reducible to quadratic form, such as ax⁴ + bx² + c = 0, solved?
Substitute y = x² to convert it into ay² + by + c = 0, solve for y, then back-substitute and solve x² = y for x. The same substitution technique handles other equations expressible as a quadratic in some expression.
Define an arithmetic progression (AP) and its common difference.
An AP is a sequence in which each term differs from the previous by a constant called the common difference d, where d = aₙ − aₙ₋₁. Example: a, a+d, a+2d, ...
What is the formula for the nth term of an arithmetic progression?
aₙ = a + (n − 1)d, where a is the first term and d is the common difference.
What is the sum of the first n terms of an arithmetic progression?
Sₙ = (n/2)[2a + (n − 1)d] = (n/2)(a + l), where l is the last term.
What is the arithmetic mean between two numbers a and b?
The arithmetic mean is (a + b)/2. It is the term inserted between a and b so the three form an AP.
Define a geometric progression (GP) and give the formula for its nth term.
A GP is a sequence where each term is the previous term multiplied by a constant ratio r (r = aₙ/aₙ₋₁). The nth term is aₙ = a·rⁿ⁻¹.
What is the sum of the first n terms of a geometric progression?
Sₙ = a(rⁿ − 1)/(r − 1) for r ≠ 1 (equivalently a(1 − rⁿ)/(1 − r)). If r = 1, Sₙ = na.
What is the formula for the sum to infinity of a geometric series, and when does it apply?
S∞ = a/(1 − r), valid only when |r| < 1. If |r| ≥ 1 the infinite series diverges and has no finite sum.
What is the geometric mean between two positive numbers a and b?
The geometric mean is √(ab). It is the term inserted between a and b so the three form a GP.
Define a harmonic progression (HP) and how it relates to an AP.
A harmonic progression is a sequence whose reciprocals form an arithmetic progression. To find an HP term, take the corresponding AP of reciprocals, find its term, then take the reciprocal. The harmonic mean of a and b is 2ab/(a + b).
What is the formula for permutations of n distinct objects taken r at a time, and how do permutations differ from combinations?
ⁿPᵣ = n!/(n − r)! while ⁿCᵣ = n!/[r!(n − r)!]. Permutations count arrangements where order matters; combinations count selections where order does not matter, so ⁿPᵣ = ⁿCᵣ · r!.
What this deck covers
The Mathematics deck follows the GIKI Admission Test Mathematics syllabus — 11 chapters and 44 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 4.5 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 GIKI Admission Test 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 GIKI Admission Test 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 GIKI Admission Test Mathematics syllabus — 11 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.