Mathematics: Algebra, Geometry and Problem Solving
Core concepts
Revise algebraic identities, factorization, simple and simultaneous equations, and exponents. In geometry, know the theorems on triangles, circles and parallel lines, and be able to construct and prove. Arithmetic topics include ratio, percentage, profit and loss, simple and compound interest, and averages. Mensuration requires formulas for area and volume of standard figures. Statistics covers mean, median and mode from grouped and ungrouped data.
Traps to expect
- Sign errors when expanding identities such as (a − b)².
- Using diameter where radius is required, or forgetting unit conversion.
- Mixing simple and compound interest formulas.
- Giving a numerical answer without the required unit or statement.
Rule of thumb
Write the formula first, substitute values second, and simplify last. Check the answer against the question's units and rough magnitude before finalizing.
Worked example
Find compound interest on 5,000 taka at 10% for 2 years. Amount = 5000 × (1.1)² = 6,050; interest = 6,050 − 5,000 = 1,050 taka.