Binomial Theorem practice questions

Secondary 3 topics from the Additional Mathematics 4049 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise binomial theorem free

What this topic covers

Worked examples

Example 1

Find the value of nn given that (n2)=153\binom{n}{2} = 153.
Show the worked solution
  • $\binom{n}{2} = \frac{n(n-1)}{2}$
  • $\frac{n(n-1)}{2} = 153$
  • $n(n-1) = 306$
  • $n^2 - n - 306 = 0$
  • $(n - 18)(n + 17) = 0$
  • $n = 18 \quad \scriptsize\textit{since }n > 0$

Answer: 1818

Example 2

Find the coefficient of x2x^{2} in the expansion of (3−x)6(3 - x)^{6}.
Show the worked solution
  • $T_{3} = \binom{6}{2} \cdot 3^{4} \cdot (-x)^{2} \quad \scriptsize\textit{general term}$
  • $= 15 \times 81 \times x^{2}$
  • $= 1215x^{2}$
  • Coefficient of $x^{2} = 1215$

Answer: 12151215

Example 3

Find the coefficient of x−8x^{-8} in the expansion of (2x2+2x2)6\left(2x^{2} + \frac{2}{x^{2}}\right)^{6}.
Show the worked solution
  • General term: $T_{6} = \binom{6}{5}(2x^{2})^{1}\left(\frac{2}{x^{2}}\right)^{5}$
  • Power of $x = 2(6 - 5) - 2(5)$
  • $= 2 - 10$
  • $= -8$
  • Coefficient $= 6 \times 2 \times 32$
  • Coefficient $= 384$

Answer: 384384

Questions parents ask

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Which syllabus does this follow?

Additional Mathematics (4049), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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