Mathematics for the BUET Written Paper
Scope of the paper
BUET mathematics rewards precise technique across algebra, trigonometry, coordinate geometry, differential and integral calculus, vectors, and matrices. Expect problems that combine topics: a conic geometry question needing calculus, or a trigonometric identity feeding an integral. Accuracy and clean presentation matter as much as insight.
Concepts to command
Know the standard forms of lines, circles, parabolas, ellipses, and hyperbolas, and how to convert between general and standard forms. In calculus, understand limits, continuity, differentiation rules, maxima-minima, definite integrals as areas, and basic techniques of substitution and parts. In trigonometry, master sum, product, and multiple-angle identities. In matrices, know determinants, inverses, and the conditions for a system to have unique, infinite, or no solutions.
Traps to watch
- Losing solutions when dividing by an expression that could be zero.
- Forgetting the constant of integration in indefinite integrals.
- Reversing the inequality direction when multiplying by a negative number.
- Applying L'Hopital's rule without first confirming an indeterminate form.
- Ignoring domain restrictions in logarithmic and inverse trigonometric problems.
Worked example
Find the maximum of f(x) = x³ − 3x on [−2, 2]. f'(x) = 3x² − 3 = 0 gives x = ±1. Evaluate: f(1) = −2, f(−1) = 2, and endpoints f(2) = 2, f(−2) = −2. Maximum is 2. Rule of thumb: always check endpoints, not just critical points, when the domain is closed.
Strategy
Rewrite expressions into standard forms before differentiating or integrating, sketch curves to sanity-check answers, and verify solutions by substitution. When a problem looks long, look for a substitution that collapses it.