Examius
🇮🇳 AP EAMCET / TS EAMCET · flashcards
AP EAMCET / TS EAMCET Mathematics - Algebra and Trigonometry Flashcards
50 question-and-answer cards covering Mathematics - Algebra and Trigonometry as it is examined in AP EAMCET / TS EAMCET. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Mathematics - Algebra and Trigonometry deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
What is the value of a 2×2 determinant |a b; c d|?
ad − bc.
State the rule of Sarrus / cofactor expansion for a 3×3 determinant.
|a₁ b₁ c₁; a₂ b₂ c₂; a₃ b₃ c₃| = a₁(b₂c₃−b₃c₂) − b₁(a₂c₃−a₃c₂) + c₁(a₂b₃−a₃b₂).
State three key properties of determinants.
Swapping two rows (or columns) changes the sign; if two rows/columns are identical the determinant is 0; multiplying a row/column by k multiplies the determinant by k. Also |AB|=|A||B| and |Aᵀ|=|A|.
State Cramer's Rule for solving a system of linear equations.
For AX=B with det A=Δ≠0, each unknown x_i = Δ_i/Δ, where Δ_i is Δ with its i-th column replaced by B. If Δ=0 the system has no unique solution.
What is a complex number, and what are i, i², i³, i⁴?
A number z = a+ib where a, b are real and i=√(−1). i²=−1, i³=−i, i⁴=1; powers of i cycle with period 4.
What is the modulus and argument (amplitude) of z = a+ib?
Modulus |z| = √(a²+b²); argument θ = tan⁻¹(b/a) adjusted for the quadrant of (a,b).
What is the conjugate of z=a+ib, and key conjugate properties?
z̄ = a−ib. z·z̄ = |z|²; (z₁+z₂)‾ = z̄₁+z̄₂; (z₁z₂)‾ = z̄₁·z̄₂; z is real iff z=z̄.
Write the polar (modulus-argument) form of a complex number.
z = r(cosθ + i sinθ), where r=|z| and θ=arg z; in exponential form z = r·e^{iθ}.
State De Moivre's Theorem.
For any rational n, (cosθ + i sinθ)ⁿ = cos(nθ) + i sin(nθ).
How is De Moivre's Theorem used to find the nth roots of a complex number?
The n nth roots of r(cosθ+i sinθ) are r^{1/n}[cos((θ+2kπ)/n) + i sin((θ+2kπ)/n)] for k=0,1,…,n−1; they lie equally spaced on a circle of radius r^{1/n}.
What are the cube roots of unity and their key properties?
1, ω, ω², where ω = (−1+i√3)/2. Properties: 1+ω+ω²=0 and ω³=1.
How do you find the square root of a complex number a+ib?
Find x+iy such that (x+iy)²=a+ib, giving x²−y²=a and 2xy=b; solve using x²+y²=√(a²+b²).
What does multiplying a complex number by i do geometrically?
It rotates the corresponding point about the origin by 90° (π/2) anticlockwise, without changing its modulus.
State the reciprocal trigonometric ratios and quotient identities.
cosec θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ; tan θ = sin θ/cos θ, cot θ = cos θ/sin θ.
State the three Pythagorean trigonometric identities.
sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ.
State the compound angle formulas for sin(A±B) and cos(A±B).
sin(A±B) = sinA cosB ± cosA sinB; cos(A±B) = cosA cosB ∓ sinA sinB.
State the double angle formulas for sin2A, cos2A, and tan2A.
sin2A = 2 sinA cosA; cos2A = cos²A−sin²A = 2cos²A−1 = 1−2sin²A; tan2A = 2tanA/(1−tan²A).
State the product-to-sum transformation 2 sinA cosB.
2 sinA cosB = sin(A+B) + sin(A−B); similarly 2 cosA cosB = cos(A+B)+cos(A−B) and 2 sinA sinB = cos(A−B)−cos(A+B).
State the general solutions of the basic trigonometric equations sinθ=0, cosθ=0, tanθ=0.
sinθ=0 ⇒ θ=nπ; cosθ=0 ⇒ θ=(2n+1)π/2; tanθ=0 ⇒ θ=nπ, for integer n.
State the general solutions of sinθ=sinα, cosθ=cosα, and tanθ=tanα.
sinθ=sinα ⇒ θ=nπ+(−1)ⁿα; cosθ=cosα ⇒ θ=2nπ±α; tanθ=tanα ⇒ θ=nπ+α, for integer n.
What are the principal value ranges of sin⁻¹x, cos⁻¹x, and tan⁻¹x?
sin⁻¹x ∈ [−π/2, π/2]; cos⁻¹x ∈ [0, π]; tan⁻¹x ∈ (−π/2, π/2).
State the inverse-trig identity for sin⁻¹x + cos⁻¹x and tan⁻¹x + cot⁻¹x.
sin⁻¹x + cos⁻¹x = π/2 (for x∈[−1,1]); tan⁻¹x + cot⁻¹x = π/2 (for all real x).
Define the hyperbolic functions sinh x and cosh x, and their fundamental identity.
sinh x = (eˣ − e⁻ˣ)/2; cosh x = (eˣ + e⁻ˣ)/2; identity: cosh²x − sinh²x = 1.
State the Sine Rule and the Cosine Rule for a triangle.
Sine Rule: a/sinA = b/sinB = c/sinC = 2R. Cosine Rule: a² = b² + c² − 2bc cosA (and cyclic forms).
What this deck covers
The Mathematics - Algebra and Trigonometry deck follows the AP EAMCET / TS EAMCET Mathematics - Algebra and Trigonometry syllabus — 4 chapters and 16 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 12.5 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 88 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 - Algebra and Trigonometry flashcards FAQ
How many Mathematics - Algebra and Trigonometry flashcards are in this AP EAMCET / TS EAMCET 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 AP EAMCET / TS EAMCET 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 - Algebra and Trigonometry cards cover?
They follow the AP EAMCET / TS EAMCET Mathematics - Algebra and Trigonometry syllabus — 4 chapters and 16 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.