Mathematics for the BTEB Admission Test
What the exam actually tests
Polytechnic admission mathematics leans on arithmetic fluency and algebraic manipulation rather than long proofs. Prioritise: ratio and proportion, percentage and profit-loss, simple and compound interest, averages, time-speed-distance, time and work, sets, exponents and logarithms, polynomials and factorization, simple equations, geometry of triangles and circles, and basic trigonometry (ratios, identities, heights and distances).
Concepts to master
Know the difference between simple interest (SI = PRT/100) and compound interest (CI = P(1+R/100)^T − P), and be able to move between the two. In percentage problems, fix a base value before computing change. In ratio problems, convert ratios to a common unit by introducing a multiplier k. In sets, use n(A∪B) = n(A) + n(B) − n(A∩B) and extend to three sets. Memorise standard identities: a² − b², (a±b)², and the factorization patterns for x² + (a+b)x + ab.
Traps examiners plant
Mixing up marked price with cost price; forgetting that successive percentage changes do not add; treating average speed as the arithmetic mean of two speeds when distances are equal (it is the harmonic mean); and misreading 'in how many years will a sum double' style questions. In trigonometry, always check which quadrant the angle lies in before assigning signs.
Worked example
A shopkeeper marks an item 40% above cost and offers a 25% discount. What is the profit percent? Let cost = 100. Marked price = 140. Selling price = 140 × 0.75 = 105. Profit = 5, so profit percent = 5%. Rule of thumb: for successive changes of +a% and −b%, net change = a − b − ab/100 percent.
Practice habit
Time yourself on 20 mixed items; log every wrong answer by topic, and redo only those topics the next day.