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AMUEEE Mathematics - Algebra And Trigonometry Flashcards
50 question-and-answer cards covering Mathematics - Algebra And Trigonometry as it is examined in AMUEEE. 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.
State the identity relating nC_r and nC_(r-1) (Pascal's rule).
nC_r + nC_(r-1) = (n+1)C_r. Also nC_r = nC_(n-r).
What is the order of a matrix, and when can two matrices be multiplied?
Order is m x n (rows x columns). Matrices A (m x n) and B (p x q) can be multiplied (AB) only if n = p; the product has order m x q.
Define a symmetric and a skew-symmetric matrix.
Symmetric: A^T = A (a_ij = a_ji). Skew-symmetric: A^T = -A (a_ij = -a_ji), with all diagonal entries zero.
State the formula for the inverse of a square matrix A.
A^(-1) = (1/|A|) · adj(A), valid only when |A| ≠ 0 (A is non-singular).
What is the value of a 2x2 determinant |a b; c d|?
ad - bc.
State Cramer's Rule for solving a system of linear equations.
For AX = B with D = |A| ≠ 0, each variable x_i = D_i / D, where D_i is D with the ith column replaced by the constants B.
What does it mean for a system of linear equations to be consistent vs inconsistent in terms of determinants?
If D ≠ 0: unique solution (consistent). If D = 0 and all D_i = 0: infinitely many solutions (consistent). If D = 0 and some D_i ≠ 0: no solution (inconsistent).
State the key property of determinants regarding row/column operations.
Adding a multiple of one row (or column) to another does not change the determinant; interchanging two rows changes its sign; multiplying a row by k multiplies the determinant by k.
How does the inequality sign behave when multiplying or dividing both sides by a negative number?
The inequality sign reverses (e.g., if a < b and c < 0, then ac > bc).
How do you represent the solution of a linear inequality in one variable on a number line vs in two variables on a graph?
One variable: a ray/interval on the number line (open circle for strict <, >; closed for ≤, ≥). Two variables: a half-plane bounded by the line (dashed line for strict, solid for inclusive).
State the three fundamental Pythagorean trigonometric identities.
sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ.
State the sine and cosine addition 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 sin 2A, cos 2A, and tan 2A.
sin 2A = 2 sinA cosA; cos 2A = cos²A - sin²A = 2cos²A - 1 = 1 - 2sin²A; tan 2A = 2tanA/(1 - tan²A).
State the formula for tan(A+B).
tan(A+B) = (tanA + tanB) / (1 - tanA tanB).
List the values of sin θ for θ = 0°, 30°, 45°, 60°, 90°.
sin 0° = 0, sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2, sin 90° = 1.
State the general solution of sin θ = sin α.
θ = nπ + (-1)^n α, where n is any integer.
State the general solutions of cos θ = cos α and tan θ = tan α.
cos θ = cos α: θ = 2nπ ± α. tan θ = tan α: θ = nπ + α, where n is any integer.
State the principal value ranges (codomains) 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 identity for sin⁻¹x + cos⁻¹x and tan⁻¹x + cot⁻¹x.
sin⁻¹x + cos⁻¹x = π/2 (for x in [-1,1]); tan⁻¹x + cot⁻¹x = π/2 (for all real x).
State the formula for tan⁻¹x + tan⁻¹y (when xy < 1).
tan⁻¹x + tan⁻¹y = tan⁻¹[(x+y)/(1 - xy)], valid when xy < 1.
State the Law of Sines (Sine Rule) for a triangle.
a/sinA = b/sinB = c/sinC = 2R, where R is the circumradius.
State the Law of Cosines (Cosine Rule) for side a of a triangle.
a² = b² + c² - 2bc·cosA. Equivalently, cosA = (b² + c² - a²)/(2bc).
State two formulas for the area of a triangle in terms of its sides/angles.
Area = (1/2)·ab·sinC (two sides and included angle); and Heron's formula: Area = sqrt[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2.
State the formula relating the area, sides, and circumradius/inradius of a triangle.
Area Δ = abc/(4R) = r·s, where R is circumradius, r is inradius, and s is the semi-perimeter.
What this deck covers
This deck covers the Mathematics - Algebra And Trigonometry portion of the AMUEEE syllabus in question-and-answer form. Browse the full AMUEEE syllabus to see how it fits with the rest.
Answers are written to be recallable, not just readable — averaging about 87 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 AMUEEE 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 AMUEEE 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 Mathematics - Algebra And Trigonometry portion of the AMUEEE syllabus, in question-and-answer form.
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.