Mathematical Induction and Binomial Theorem

Maths, HSSC-KPK First Year. This chapter is split into 35 topics and has 915 practice questions. The topics covered are listed below, followed by 10 free sample questions from the chapter.

Topics in this chapter

1. Expanding Binomials of Small Power 28 questions
2. Approximation when x is Small (Neglecting x Squared) 29 questions
3. Induction Formulas for Arithmetic Progressions (Exercise 7.1) 28 questions
4. Validity of the Expansion of (a + bx) to a Non-integer Power 30 questions
5. Finding a Specified Term of an Expansion 30 questions
6. Finding n, r or a from Conditions on Terms 28 questions
7. Pascal's Triangle 25 questions
8. Expansions from Exercise 7.2 (Powers 4, 5 and 7) 26 questions
9. Applying Sum Formulas 1 + 2 + ... + n 23 questions
10. Induction Formulas: Factorials, Geometric and Product Sums (Exercise 7.1) 23 questions
11. Middle Terms of an Expansion 21 questions
12. Sums and Differences of Binomial Expansions 30 questions
13. Inequalities Proved by Induction 25 questions
14. Summation of Infinite Series by the Binomial Series 30 questions
15. Sum of Binomial Coefficients 25 questions
16. Values of Binomial Coefficients 30 questions
17. Term Independent of x 28 questions
18. Divisibility and Factor Proofs by Induction 23 questions
19. Induction on Sums of Binomial Coefficients (Exercise 7.1) 22 questions
20. Binomial Theorem: Statement and Proof 22 questions
21. Expansions of (1 + x) and (1 - x) to a Negative Integer Power 26 questions
22. Principle of Mathematical Induction 27 questions
23. Properties of the Binomial Expansion 30 questions
24. First Four Terms of a Binomial Series 30 questions
25. Sums of Squares and Cubes 21 questions
26. Numerically Greatest Term 26 questions
27. Coefficient of a Power of x in Rational Expressions 26 questions
28. Weighted Sums of Binomial Coefficients (Exercise 7.2 Q11) 21 questions
29. Algebra of the Inductive Step 23 questions
30. Coefficients in the Expansion with Fractional Index 30 questions
31. Smallest n for which an Inequality Holds (Extended Induction) 26 questions
32. Approximate Values using the Binomial Series 30 questions
33. Binomial Series for Negative or Fractional Index 21 questions
34. Coefficient of a Given Power of x 22 questions
35. Divisibility Checks with Numbers 30 questions