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Air University Entry Test Mathematics Flashcards
50 question-and-answer cards covering Mathematics as it is examined in Air University Entry 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.
State the condition for matrix multiplication AB and the order of the resulting matrix.
The number of columns of A must equal the number of rows of B. If A is m×n and B is n×p, then AB is m×p.
Is matrix multiplication commutative? State the key property.
No; in general AB ≠ BA. Matrix multiplication is associative and distributive but not commutative.
What is the identity matrix, and what is its effect under multiplication?
The identity matrix I is a square matrix with 1's on the main diagonal and 0's elsewhere. For any compatible matrix A: AI = IA = A.
What is the transpose of a matrix, and what is (AB)ᵀ?
The transpose Aᵀ is formed by interchanging rows and columns. (AB)ᵀ = BᵀAᵀ.
Define a symmetric matrix and a skew-symmetric matrix.
Symmetric: Aᵀ = A. Skew-symmetric: Aᵀ = −A (its diagonal entries are all zero).
How do you compute the determinant of a 2×2 matrix [[a, b], [c, d]]?
det = ad − bc.
What does it mean when det(A) = 0?
The matrix is singular: it has no inverse, and a related system of equations has either no unique solution (no solution or infinitely many).
State the formula for the inverse of a 2×2 matrix A = [[a, b], [c, d]].
A⁻¹ = (1/det A) [[d, −b], [−c, a]], provided det A = ad − bc ≠ 0.
State the property det(AB) and det(Aᵀ) in terms of determinants.
det(AB) = det(A)·det(B); det(Aᵀ) = det(A).
What is the cofactor expansion method for a 3×3 determinant?
Expand along a row or column: det = Σ aᵢⱼ·Cᵢⱼ, where Cᵢⱼ = (−1)^(i+j)·Mᵢⱼ and Mᵢⱼ is the minor (determinant of the matrix with row i and column j deleted).
State Cramer's Rule for solving a system Ax = b.
Each variable xᵢ = det(Aᵢ)/det(A), where Aᵢ is A with its ith column replaced by b, provided det(A) ≠ 0.
In the matrix method, how is the solution to AX = B found?
X = A⁻¹B, provided A is invertible (det A ≠ 0).
Classify the consistency of a linear system by its number of solutions.
Consistent with a unique solution; consistent with infinitely many solutions; or inconsistent (no solution).
What are the three elementary row operations used in Gaussian elimination?
1) Swap two rows; 2) Multiply a row by a nonzero scalar; 3) Add a multiple of one row to another row.
Define the six trigonometric ratios in a right triangle for angle θ.
sin θ = opp/hyp; cos θ = adj/hyp; tan θ = opp/adj; csc θ = 1/sin θ; sec θ = 1/cos θ; cot θ = 1/tan θ.
State the three Pythagorean identities.
sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = csc²θ.
State the sine and cosine addition formulas.
sin(A + B) = sin A cos B + cos A sin B; cos(A + B) = cos A cos B − sin A sin B.
State the double angle formulas for sin 2θ and cos 2θ.
sin 2θ = 2 sin θ cos θ; cos 2θ = cos²θ − sin²θ = 1 − 2sin²θ = 2cos²θ − 1.
State the Law of Sines for a triangle with sides a, b, c opposite angles A, B, C.
a/sin A = b/sin B = c/sin C = 2R, where R is the circumradius.
State the Law of Cosines for side a.
a² = b² + c² − 2bc·cos A.
Give two formulas for the area of a triangle using its sides/angles.
Area = ½·ab·sin C (two sides and included angle); or Heron's formula: √[s(s−a)(s−b)(s−c)] where s = (a+b+c)/2.
State the domain and range of the inverse function y = sin⁻¹x (arcsin).
Domain: −1 ≤ x ≤ 1; Range (principal values): −π/2 ≤ y ≤ π/2.
State the slope formula and the slope-intercept form of a straight line.
Slope m = (y₂ − y₁)/(x₂ − x₁); slope-intercept form: y = mx + c, where c is the y-intercept.
State the point-slope form of a line and the conditions for two lines to be parallel or perpendicular.
Point-slope: y − y₁ = m(x − x₁). Parallel lines have equal slopes (m₁ = m₂); perpendicular lines satisfy m₁·m₂ = −1.
What this deck covers
The Mathematics deck follows the Air University Entry Test Mathematics syllabus — 6 chapters and 20 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 85 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 Air University Entry 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 Air University Entry 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 Air University Entry Test Mathematics syllabus — 6 chapters and 20 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.