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🇵🇰 PIEAS Admission Test · flashcards
PIEAS Admission Test Mathematics Flashcards
50 question-and-answer cards covering Mathematics as it is examined in PIEAS 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.
What does it mean for a system of linear equations to be consistent versus inconsistent?
Consistent: has at least one solution. Inconsistent: has no solution. A consistent system may have a unique solution or infinitely many.
Using determinants, what is Cramer's Rule for solving a system of linear equations?
For AX = B, each unknown xᵢ = Dᵢ / D, where D is the determinant of the coefficient matrix and Dᵢ replaces the i-th column of A with B (requires D ≠ 0).
What does the value of the coefficient determinant D tell you about a system's solutions?
If D ≠ 0: unique solution. If D = 0: either no solution (inconsistent) or infinitely many solutions (dependent).
What is the general (nth) term of an arithmetic progression with first term a and common difference d?
aₙ = a + (n − 1)d.
State the formula for 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 (A.M.) between two numbers a and b?
A.M. = (a + b)/2.
What is the general (nth) term of a geometric progression with first term a and common ratio r?
aₙ = a·rⁿ⁻¹.
State the formula for the sum of the first n terms of a geometric progression (r ≠ 1).
Sₙ = a(1 − rⁿ)/(1 − r) for r < 1, or a(rⁿ − 1)/(r − 1) for r > 1.
What is the geometric mean (G.M.) between two positive numbers a and b?
G.M. = √(ab).
What is a harmonic progression, and how is its nth term found?
A sequence whose reciprocals form an arithmetic progression. To find the nth term, take the reciprocal of the corresponding A.P. term: 1/[a + (n−1)d].
What is the harmonic mean (H.M.) between two numbers a and b?
H.M. = 2ab/(a + b).
State the relationship (and inequality) between A.M., G.M., and H.M. of two positive numbers.
G.M.² = A.M. × H.M., and A.M. ≥ G.M. ≥ H.M. (equality when the numbers are equal).
Under what condition does an infinite geometric series converge, and what is its sum to infinity?
It converges when |r| < 1; then S∞ = a/(1 − r).
What happens to the sum of an infinite geometric series when |r| ≥ 1?
The series diverges — it has no finite sum to infinity.
Define the six trigonometric functions of an angle in a right triangle.
sin = opp/hyp, cos = adj/hyp, tan = opp/adj, csc = hyp/opp, sec = hyp/adj, cot = adj/opp.
State the three Pythagorean trigonometric identities.
sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = csc²θ.
State the sine and cosine addition formulas.
sin(A + B) = sinA cosB + cosA sinB; cos(A + B) = cosA cosB − sinA sinB.
State the double-angle formula for sin 2θ and the three forms for cos 2θ.
sin 2θ = 2 sinθ cosθ; cos 2θ = cos²θ − sin²θ = 1 − 2sin²θ = 2cos²θ − 1.
State the tangent addition formula tan(A + B).
tan(A + B) = (tanA + tanB)/(1 − tanA tanB).
What are the periods of sin θ, cos θ, and tan θ?
sin and cos have period 2π (360°); tan and cot have period π (180°).
How do you convert between degrees and radians?
π radians = 180°. To convert degrees to radians multiply by π/180; radians to degrees multiply by 180/π.
State the Law of Sines and the Law of Cosines for a triangle.
Law of Sines: a/sinA = b/sinB = c/sinC. Law of Cosines: c² = a² + b² − 2ab cosC.
State the half-angle formulas for sin(θ/2) and cos(θ/2).
sin(θ/2) = ±√[(1 − cosθ)/2]; cos(θ/2) = ±√[(1 + cosθ)/2], sign depending on the quadrant of θ/2.
In which quadrants are sin, cos, and tan positive (the 'All, Sin, Tan, Cos' rule)?
Quadrant I: all positive. Quadrant II: only sin (and csc) positive. Quadrant III: only tan (and cot) positive. Quadrant IV: only cos (and sec) positive.
What this deck covers
The Mathematics deck follows the PIEAS Admission Test Mathematics syllabus — 10 chapters and 34 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 5.0 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 74 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 PIEAS 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 PIEAS 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 PIEAS Admission Test Mathematics syllabus — 10 chapters and 34 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.