NIMCET Mathematics
Mathematics is the highest-weight section of NIMCET: in the recent 120-question, 300-mark pattern it carries 50 questions and 120 marks, with +3 for a correct answer and −1 for a wrong one. Questions test speed and accuracy across algebra, trigonometry, coordinate geometry, calculus, probability and statistics, vectors, matrices, sets and relations, logarithms and number properties. Most items are single-correct MCQs; a few need two or three steps rather than a long proof.
Core rules to keep live
- Quadratic ax²+bx+c=0: roots sum −b/a, product c/a; discriminant D=b²−4ac decides real, equal or complex roots.
- For AP, nth term a+(n−1)d, sum n/2[2a+(n−1)d]; for GP, nth term ar^(n−1), sum a(r^n−1)/(r−1) when r≠1.
- Coordinate geometry: distance √[(x2−x1)²+(y2−y1)²]; slope (y2−y1)/(x2−x1); parallel slopes equal, perpendicular product −1.
- Probability: P(A∪B)=P(A)+P(B)−P(A∩B); independent events multiply.
- Matrix: (AB)ᵀ=BᵀAᵀ; determinant of 2×2 [[a,b],[c,d]]=ad−bc.
Worked example
If log₁₀2=0.3010, find log₁₀50. 50=100/2, so log50=log100−log2=2−0.3010=1.6990. The key is to factor 50 into powers of 10 and 2, then use log(ab)=log a+log b and log(a/b)=log a−log b. Do not approximate 50 as 5×10 and separately guess log5; that adds an extra unknown.
Traps
- Losing the negative root of a square-root equation; always check in the original.
- Using n rather than n−1 in AP/GP formulas.
- Forgetting the −1 penalty when guessing; eliminate at least two options before marking.
- Mixing degree and radian mode in trigonometry.
- Applying a matrix inverse when the determinant is zero.