Mathematics: Algebra, Calculus, and Probability
Mathematics on SITEEE tests algebra, trigonometry, coordinate geometry, calculus, vectors, matrices, and probability. The section rewards clean setup: most marks are lost before the final calculation, through a wrong sign, a missed root, or an unstated domain restriction.
Core rules and concepts
- Quadratic ax^2 + bx + c = 0: discriminant D = b^2 - 4ac; real distinct roots if D > 0, equal if D = 0.
- Trigonometry: use identities such as sin^2 θ + cos^2 θ = 1 and the range/domain of inverse functions.
- Coordinate geometry: distance, section formula, slope; for a circle, (x - h)^2 + (y - k)^2 = r^2.
- Calculus: derivative as slope; definite integral as signed area; substitution reverses the chain rule.
- Probability: P(A|B) = P(A ∩ B)/P(B); independent events satisfy P(A ∩ B) = P(A)P(B).
- Matrices: AB ≠ BA in general; determinant zero means no unique inverse.
Worked example
Evaluate ∫_0^1 x e^(x^2) dx. Let u = x^2, so du = 2x dx, hence x dx = du/2. When x = 0, u = 0; when x = 1, u = 1. The integral becomes (1/2)∫_0^1 e^u du = (1/2)(e^1 - e^0) = (e - 1)/2. The substitution changes both the integrand and the limits; forgetting the factor 1/2 is the usual error.
Traps
Dropping the +C for indefinite integrals; cancelling before noting x ≠ 0; using the wrong denominator in conditional probability; reversing matrix multiplication order; ignoring domain restrictions for inverse trig functions.