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Binomial theorem and partial fractions quiz: N(A)-Level Additional Mathematics (SEAB 4051) quiz

14questions. Pick an answer and you'll see why right away.

  1. The binomial theorem expands (a+b)n(a + b)^n using coefficients that match:

  2. How many terms are there in the expansion of (a+b)6(a + b)^6?

  3. Expand (1+x)3(1 + x)^3.

  4. In the expansion of (a+b)n(a + b)^n, the general term is:

  5. Find the coefficient of x2x^2 in (1+x)5(1 + x)^5.

  6. Evaluate (60)\binom{6}{0}.

  7. Which power of xx does the term with r=3r = 3 give in the expansion of (1+x)7(1 + x)^7?

  8. Find the constant term (the term in x0x^0) in (2+x)3(2 + x)^3.

  9. A fraction can be split into partial fractions with linear terms when it is proper, meaning:

  10. Set up the partial-fraction form for 7(x2)(x+3)\dfrac{7}{(x - 2)(x + 3)}.

  11. Express 5(x1)(x+4)\dfrac{5}{(x - 1)(x + 4)} in partial fractions.

  12. In 3x(x1)=Ax+Bx1\dfrac{3}{x(x - 1)} = \dfrac{A}{x} + \dfrac{B}{x - 1}, substituting x=0x = 0 gives:

  13. Which value of xx is most convenient to substitute to find the constant over (x+5)(x + 5) in a partial-fraction problem?

  14. The middle coefficient in the expansion of (a+b)4(a + b)^4 is: