BCS Written Mathematics study guide
BCS Written Mathematics · Work through your exam, one topic at a time.
The BCS Written Mathematics paper is the written arithmetic and problem-solving component of the Bangladesh Civil Service (BCS) examination, taken by candidates competing for cadre posts in the Bangladesh government. It is intended for graduates who can work accurately under time pressure and show clean, step-by-step solutions rather than lucky final answers. The BCS Written Mathematics study guide has 7 sections and about 2,385 words.
01Arithmetic: Ratio, Percentage, Averages and Number Work
Arithmetic in a written paper rewards disciplined method more than speed. You need fluency with fractions, decimals and percentages and the ability to move between them; ratio and proportion, including dividing a quantity in a given ratio and scaling recipes or maps; averages, including the mean of a combined group; simple and compound interest; profit and loss with cost price versus selling price; speed, distance and time with unit conversion; and the rules of divisibility, factors, multiples, HCF and LCM.
351 words, about 2 min02Algebra: Manipulation, Equations and Inequalities
Algebra questions test whether you can manipulate expressions cleanly and justify each step. Be secure with expanding brackets, including double brackets; factorising by common factors, difference of two squares and simple quadratics; simplifying algebraic fractions; solving linear equations and simultaneous equations by elimination and substitution; solving quadratics by factorising or the formula; rearranging formulae to change the subject; laws of indices; and solving linear inequalities, remembering to reverse the sign when multiplying or dividing by a negative number.
342 words, about 2 min03Geometry: Angles, Triangles, Circles and Solids
Geometry rewards precise vocabulary and a habit of stating reasons. You should know angle facts for straight lines, around a point, in triangles and quadrilaterals, and for parallel lines cut by a transversal: corresponding, alternate and co-interior angles.
341 words, about 2 min04Trigonometry: Ratios, Rules and Identities
Trigonometry questions mix right-angled triangles with general triangles. For right-angled work, know sine, cosine and tangent as ratios of sides, and choose the ratio by which sides are involved.
366 words, about 2 min05Calculus: Differentiation, Integration and Applications
Introductory calculus questions test rules and interpretation. For differentiation, know the power rule, constant and sum rules, and how to differentiate polynomials; understand gradient of a curve, tangents and normals, stationary points and their classification by the second derivative or by sign change; and apply calculus to rates of change and simple optimisation.
342 words, about 2 min06Statistics and Probability: Data, Averages and Chance
You need to summarise data and reason about chance. Know the mean, median, mode and range, and when each is appropriate; understand quartiles, interquartile range and box plots; read and interpret bar charts, histograms and cumulative frequency curves.
320 words, about 2 min07Matrices and Determinants: Operations and Linear Systems
Matrix questions test careful bookkeeping. Know matrix notation and order, and when addition, subtraction and multiplication are defined.
323 words, about 2 min