Mathematics: Algebra, Trigonometry, Calculus, Vectors and Matrices
Mathematics on the ETEA engineering test covers FSc-level algebra, trigonometry, sequences, calculus, vectors and matrices. Items are short and designed for a two-minute solution, so recognize the standard form, apply the rule, and move on.
Core rules to hold
- For ax² + bx + c = 0, x = [−b ± √(b² − 4ac)]/2a, and the discriminant b² − 4ac decides whether roots are real, equal, or complex.
- Differentiation: product rule (uv)′ = u′v + uv′, quotient rule (u/v)′ = (u′v − uv′)/v², and chain rule for composite functions.
- Standard limit: lim(x→0) sin x / x = 1, working in radians.
- Pythagorean identity sin²θ + cos²θ = 1 links the trigonometric ratios to a right triangle.
- For vectors, a·b = |a||b|cosθ gives the angle, and a×b is perpendicular to both.
Worked example
Differentiate y = x² sin x and evaluate the slope at x = π/2. Apply the product rule with u = x² and v = sin x: u′ = 2x, v′ = cos x, so dy/dx = 2x sin x + x² cos x. At x = π/2, sin(π/2) = 1 and cos(π/2) = 0, giving dy/dx = 2(π/2)(1) + 0 = π.
Traps that cost marks
- Forgetting the chain rule on sin(3x) or (2x + 1)⁵.
- Using degrees where calculus requires radians.
- Reading the discriminant sign backwards, or dropping the ± in the quadratic formula.
- Multiplying vectors as if a·b and a×b were the same operation; only the dot product gives a scalar.