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🇵🇰 NTS NAT-IGS · flashcards
NTS NAT-IGS Mathematics Flashcards
50 question-and-answer cards covering Mathematics as it is examined in NTS NAT-IGS. 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 discriminant and what does it determine?
D = b² − 4ac; it determines the nature of the roots: D > 0 two distinct real roots, D = 0 one repeated real root, D < 0 complex roots.
For ax² + bx + c = 0, what is the sum and product of the roots?
Sum of roots = −b/a; product of roots = c/a.
What is partial fraction decomposition used for?
To express a proper rational function as a sum of simpler fractions with linear or quadratic denominators.
For a repeated linear factor (x − a)² in the denominator, what partial fraction form is used?
A/(x − a) + B/(x − a)².
For an irreducible quadratic factor (ax² + bx + c) in the denominator, what numerator form is used?
A linear numerator: (Ax + B)/(ax² + bx + c).
What is an arithmetic sequence (A.P.)?
A sequence in which each term differs from the previous by a constant common difference d.
State the nth term formula of an arithmetic progression.
a_n = a + (n − 1)d, where a is the first term and d the common difference.
State the formula for the sum of the first n terms of an A.P.
S_n = (n/2)[2a + (n − 1)d] or S_n = (n/2)(a + l), where l is the last term.
What is a geometric sequence (G.P.)?
A sequence in which each term is obtained by multiplying the previous term by a constant common ratio r.
State the nth term formula of a geometric progression.
a_n = a·r^(n−1), where a is the first term and r the common ratio.
State the formula for the sum to infinity of a geometric series.
S∞ = a/(1 − r), valid when |r| < 1.
State the formula for n factorial (n!).
n! = n × (n − 1) × (n − 2) × ... × 2 × 1, with 0! = 1.
What is the formula for permutations nPr?
nPr = n! / (n − r)!
What is the formula for combinations nCr?
nCr = n! / [r!(n − r)!]
What is the key difference between permutations and combinations?
Permutations count arrangements where order matters; combinations count selections where order does not matter.
State the general (binomial) theorem for (a + b)^n.
(a + b)^n = Σ from r=0 to n of nCr · a^(n−r) · b^r.
What is the general term in the expansion of (a + b)^n?
T_(r+1) = nCr · a^(n−r) · b^r.
How many terms are there in the expansion of (a + b)^n?
n + 1 terms.
Define the six trigonometric ratios in a right triangle.
sin = opp/hyp, cos = adj/hyp, tan = opp/adj, csc = hyp/opp, sec = hyp/adj, cot = adj/opp.
State the fundamental Pythagorean trigonometric identity.
sin²θ + cos²θ = 1.
State the other two Pythagorean identities.
1 + tan²θ = sec²θ and 1 + cot²θ = csc²θ.
State the relationship between radians and degrees.
π radians = 180 degrees, so 1 radian = 180/π ≈ 57.296°.
State the formula relating arc length, radius, and central angle in radians.
s = rθ, where s is arc length, r the radius, and θ the angle in radians.
What are the period and range of the sine and cosine functions?
Both have period 2π and range [−1, 1].
What this deck covers
The Mathematics deck follows the NTS NAT-IGS Mathematics syllabus — 6 chapters and 22 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 8.3 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 59 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 NTS NAT-IGS 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 NTS NAT-IGS 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 NTS NAT-IGS Mathematics syllabus — 6 chapters and 22 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.