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WAEC Further Mathematics questions: The binomial theorem

15 questions with answers and explanations. Tap an option to check yourself.

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All topicsCoordinate geometry and conic sections · 16Differentiation · 18Dynamics · 15Functions and rational functions · 15Integration · 16Matrices and determinants · 16Permutations and combinations · 15Polynomials and the remainder theorem · 16Probability · 16Sequences and series · 16Sets, binary operations and logic · 16Statics · 14Statistics · 15Surds, indices and logarithms · 16The binomial theorem · 15Trigonometry · 16Vectors · 16

  1. Question 1· The binomial theorem· WAEC

    How many terms are there in the expansion of (a + b)⁸?

    Explanation and discussion

  2. Question 2· The binomial theorem· WAEC

    Find the sum of the coefficients in the expansion of (1 + x)⁵.

    Explanation and discussion

  3. Question 3· The binomial theorem· WAEC

    Use the binomial expansion to evaluate (1.01)⁵ correct to three decimal places.

    Explanation and discussion

  4. Question 4· The binomial theorem· WAEC

    The first three terms of the expansion of (1 + x)⁶ in ascending powers of x are

    Explanation and discussion

  5. Question 5· The binomial theorem· WAEC

    Find the coefficient of x² in the expansion of (1 + 2x)⁵.

    Explanation and discussion

  6. Question 6· The binomial theorem· WAEC

    In the binomial expansion of (1 + x)⁷ in ascending powers of x, what is the coefficient of the fourth term?

    Explanation and discussion

  7. Question 7· The binomial theorem· WAEC

    Using (1 + x)ⁿ ≈ 1 + nx for small x, (1.02)⁵ is approximately

    Explanation and discussion

  8. Question 8· The binomial theorem· WAEC

    The third term in the expansion of (2 + x)⁴ is

    Explanation and discussion

  9. Question 9· The binomial theorem· WAEC

    Find the term independent of x in the expansion of (x + 1/x)⁴.

    Explanation and discussion

  10. Question 10· The binomial theorem· WAEC

    The number of terms in the expansion of (a + b)⁷ is

    Explanation and discussion

  11. Question 11· The binomial theorem· WAEC

    The coefficient of x² in the expansion of (1 + x)⁵ is

    Explanation and discussion

  12. Question 12· The binomial theorem· WAEC

    Find the middle term in the expansion of (a + b)⁶.

    Explanation and discussion

  13. Question 13· The binomial theorem· WAEC

    When (2 − x)⁴ is expanded, the term in x² has coefficient

    Explanation and discussion

  14. Question 14· The binomial theorem· WAEC

    The constant term in the expansion of (x + 1/x)⁴ is

    Explanation and discussion

  15. Question 15· The binomial theorem· WAEC

    The sum of the binomial coefficients in the expansion of (1 + x)⁶ is

    Explanation and discussion

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