Tamil Nadu HSE First Year Business Mathematics and Statistics common mistakes
Tamil Nadu HSE First Year Business Mathematics and Statistics · Understand the traps and how to avoid them.
In a 3×3 determinant, expands along a row but keeps all minor signs positive instead of applying the alternating cofactor signs, so the final value is wrong even when each 2×2 minor is correct.
The cofactor is (−1)^(i+j) times the minor; under time pressure candidates copy minor values straight into the expansion and forget the checkerboard pattern.
What to do instead
Write the sign pattern for the chosen row or column above the entries before expanding, replace each minor with its signed cofactor, and verify by expanding along a different row/column or checking det(A)=det(A^T).
When decomposing a rational function with a repeated linear factor such as (x+2)^2, writes only B/(x+2) and omits the C/(x+2)^2 term.
Candidates memorise the simple linear-factor form and do not count the multiplicity of the factor in the denominator.
What to do instead
First compare degrees and divide if the fraction is improper; then write one partial-fraction term for every power of a repeated factor, clear denominators, and verify by substituting convenient x-values or comparing coefficients.
For an infinite geometric series, substitutes into S∞=a/(1−r) without checking |r|<1, or writes the n-th term as ar^n instead of ar^(n−1).
The formulas are recalled as strings rather than as conditions on the first term, common ratio, and index.
What to do instead
Identify a as the first term and r=T2/T1; state |r|<1 before using S∞; for the n-th term use ar^(n−1). Test with n=1 to confirm the formula gives the first term.
Solving sin θ=1/2 gives only θ=30° and misses 150° and the general solution, or takes an inverse-trig calculator value without placing it in the correct quadrant.
Inverse trigonometric functions return a principal value only, while the equation usually has multiple solutions in the required interval.
What to do instead
Find the reference angle first, use the quadrant sign rules to locate all solutions in the given range, and add the correct period: 360°k for sine/cosine and 180°k for tangent.
In the section formula, uses m1x1+m2x2 over m1+m2 without checking which ratio part belongs to which endpoint, or uses a plus sign in the denominator for external division.
The formula is applied mechanically without a diagram, and internal versus external division is confused.
What to do instead
Sketch the segment, label the ratio from the starting point, use the plus sign for internal and the difference for external division, then check that the computed point lies on the line and satisfies the required distance ratio.
Differentiates y=(3x^2+1)^5 as 5(3x^2+1)^4 and omits the inner derivative 6x, or applies the quotient rule but drops the v^2 denominator.
The chain rule and quotient rule are partially memorised, so the outer derivative is written but the inner function or denominator is forgotten.
What to do instead
Name the outer and inner functions explicitly, write dy/dx=outer′(inner)·inner′, and for a quotient write (u′v−uv′)/v^2 before simplifying. Differentiate the final answer numerically or structurally as a quick check.
Evaluates a definite integral by substitution but keeps the original x-limits, or omits +C after an indefinite integration.
The limits belong to the original variable, and the constant is treated as optional notation rather than part of the antiderivative family.
What to do instead
Either change the limits to the new variable when substituting, or substitute back to x before applying the original limits; always write +C for indefinite integrals and check by differentiating the result.
Uses simple-interest formulas for a compound-interest problem, or values an annuity due as an ordinary annuity by omitting the extra (1+i) factor.
Formula selection is based on keywords rather than on the timing of cash flows and the compounding convention.
What to do instead
Draw a short timeline, mark whether payments occur at the beginning or end of each period, identify the compounding frequency, and convert nominal to effective rates when needed. Check that the number of periods and the rate period match.
For grouped data, uses class limits instead of class midpoints in the mean, or divides by the number of classes instead of N=Σf when computing variance or standard deviation.
The frequency table is read as a list of individual values, so the midpoint column and total frequency are not used consistently.
What to do instead
Build columns for f, midpoint x, fx, and fx^2; use N=Σf throughout; compute mean=Σfx/N and SD from sqrt(Σfx^2/N−(Σfx/N)^2) or the assumed-mean method. Check that the mean lies inside the data range and that SD is non-negative.
Adds P(A)+P(B) for events that can occur together, or treats independent events as mutually exclusive and adds their probabilities instead of multiplying.
The words 'or' and 'and' are matched to addition and multiplication without checking whether the events overlap or are independent.
What to do instead
Decide first whether the events are mutually exclusive, independent, or neither; use P(A∪B)=P(A)+P(B)−P(A∩B) for overlapping events, multiply for independent joint events, and draw a Venn diagram or contingency table to check the overlap.