Algebra - BSEB Inter Study Guide
Algebra
In BSEB Inter Mathematics, algebra questions cover complex numbers, quadratic equations, permutations and combinations, binomial expansion and sequences. The exam tests formula recognition and careful index work.
Core rules
- For az²+bz+c=0, roots are (−b±√(b²−4ac))/(2a); sum=−b/a, product=c/a.
- Complex modulus: |z1z2|=|z1||z2|; conjugate of z=a+ib is a−ib; z·z̄=a²+b².
- nPr=n!/(n−r)!, nCr=n!/(r!(n−r)!), and nCr=nC(n−r).
- Binomial theorem: (a+b)^n=sum from r=0 to n of nCr a^(n−r)b^r; general term T_(r+1)=nCr a^(n−r)b^r.
- AP: a_n=a+(n−1)d, S_n=n/2[2a+(n−1)d]; GP: a_n=ar^(n−1), S_n=a(1−r^n)/(1−r), r not equal to 1.
Worked example
Find the term independent of x in (2x+1/x²)^6. T_(r+1)=6Cr(2x)^(6−r)(x⁻²)^r=6Cr 2^(6−r)x^(6−3r). For no x, 6−3r=0, so r=2. The term is 6C2·2⁴=15·16=240.
Traps
- Starting the binomial general term at r=1 instead of r=0.
- Confusing nCr with nPr; order matters only in permutations.
- Dropping the modulus when simplifying complex numbers.
- Using the GP sum formula when r=1.
- Forgetting that a quadratic with real coefficients has non-real roots in conjugate pairs.