Questions covered in Standard

Review the question prompts below before starting the timed test. Try each problem independently, then use the interactive test to record your answers and review the worked solutions.

1. The total number of terms in the expansion of $(x+a)^{100} + (x-a)^{100}$ is
2. The coefficient of $x^n$ in the expansion of $(1+x)^{2n}$ is
3. If the coefficients of $x^7$ and $x^8$ in $(2 + \frac{x}{3})^n$ are equal, then $n$ is
4. The middle term in the expansion of $(1 - 2x)^6$ is
5. The value of $^nC_0 + ^nC_2 + ^nC_4 + \dots$ is
6. Find the 4th term in the expansion of $(x - 2y)^{12}$.
7. Find the coefficient of $x^5$ in the expansion of $(x+3)^8$.
8. Using Binomial Theorem, evaluate $(96)^3$.
9. Find the term independent of $x$ in the expansion of $(\frac{3}{2}x^2 - \frac{1}{3x})^6$.
10. If the coefficients of $(r-5)^{th}$ and $(2r-1)^{th}$ terms in the expansion of $(1+x)^{34}$ are equal, find $r$.
11. The coefficients of three consecutive terms in the expansion of $(1+a)^n$ are in the ratio 1:7:42. Find $n$.
12. Case Study: Consider the binomial expansion of $(x^2 + \frac{1}{x})^{10}$.
    (i) Write the general term $T_{r+1}$.
    (ii) How many terms are there in the expansion?
    (iii) Find the middle term of the expansion.