Pure Mathematics · 3rd secondary · First Term

Algebra - Binomial theorem — Ratio between two consecutive terms of the binomial expansion

About this lesson

This unit focuses on the binomial theorem, specifically the ratio between two consecutive terms in a binomial expansion. It teaches how to find the ratio between consecutive terms, the ratio between their coefficients, and how to use these ratios to solve problems such as finding unknown values, proving the absence of a term free of x, and determining the greatest term in an expansion. The unit includes worked examples and exercises that involve expansions like (x + a)^n, (3 + 2y)^12, (x^2 + 2)^8, (x + y)^9, (1 + x)^n, and (x + y)^10, with applications to find specific terms, coefficients, and ratios. By the end, students should be able to compute ratios between consecutive terms and coefficients, solve for unknowns using given ratios, and identify the greatest term in an expansion.

Main topics in this lesson

  • Ratio between two consecutive terms in a binomial expansion
  • Ratio between coefficients of consecutive terms
  • Finding the greatest term in a binomial expansion
  • Solving problems involving ratios of terms and coefficients

Key terms and vocabulary

  • Binomial expansion
  • Consecutive terms
  • Coefficient
  • Greatest term
  • Ratio

Questions and answers on Algebra - Binomial theorem — Ratio between two consecutive terms of the binomial expansion - practice and revision

Multiple choice questions on this lesson in Pure Mathematics for 3rd secondary, First Term, with practice exercises for revision and exam preparation.

1

في مفكوك (x^2 + 2)^8، النسبة بين الحد الثاني والحد الأول تساوي:

  • 1 16/x^2
  • 2 x^2/16
  • 3 8/x^2
  • 4 4/x^2
2

في مفكوك (3 + 2y)^12، النسبة بين الحد الثاني والحد الأول تساوي:

  • 1 8y
  • 2 8y/3
  • 3 24y
  • 4 4y
3

في مفكوك (x + y)^10، النسبة بين معاملي الحد الخامس والحد الرابع تساوي:

  • 1 7/4
  • 2 4/7
  • 3 10/4
  • 4 7/10
4

في مفكوك (x + a)^n، إذا كانت النسبة بين الحد الثالث والحد الثاني تساوي 15/2x، وكان a = 5، فإن قيمة n تساوي:

  • 1 4
  • 2 6
  • 3 8
  • 4 10
5

في مفكوك (1 + x)^n، إذا كانت النسبة بين معاملي الحد الرابع والحد الثالث تساوي 4/3، فإن قيمة n تساوي:

  • 1 6
  • 2 8
  • 3 5
  • 4 7
6

في مفكوك (x + y)^9، النسبة بين الحد الرابع والحد الثالث تساوي:

  • 1 7y/3x
  • 2 3y/7x
  • 3 7x/3y
  • 4 3x/7y

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