General Mathematics: Arithmetic, Algebra and Geometry Fundamentals
Arithmetic
Master percentages, ratio and proportion, average, profit and loss, simple and compound interest, speed-distance-time, and work problems. Learn the standard formulas and when each applies: simple interest is P×r×t/100, while compound interest grows on the accumulated amount. Percentage change is always computed on the original base, a frequent source of error.
Algebra
Revise algebraic identities, factorisation, linear equations, and simultaneous equations. Useful identities: (a+b)² = a²+2ab+b², a²−b² = (a+b)(a−b). For word problems, define the unknown clearly before forming an equation.
Geometry and mensuration
Know the properties of triangles, circles, and quadrilaterals, and the mensuration formulas for area and volume of rectangles, triangles, circles, cylinders, and spheres. Recall that the angles of a triangle sum to 180° and that the Pythagoras relation holds only in right triangles.
Traps and a rule of thumb
Traps include: computing percentage on the new value instead of the original; forgetting unit conversion (km/h to m/s); treating compound interest as simple interest; and misreading 'discount then tax' order, which changes the result. Rule of thumb: write down the units and the base for every percentage before calculating. Worked example: an item costs 500 taka, is discounted 20%, then taxed 10%. Discount gives 400; tax on 400 gives 440 taka. Applying tax first would give a different, wrong answer.