Questions covered in Advanced

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. If $\alpha$ and $\beta$ are different complex numbers with $|\beta|=1$, then $|\frac{\beta-\alpha}{1-\bar{\alpha}\beta}|$ is equal to
2. The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even places is
3. If the coefficients of 2nd, 3rd and 4th terms in the expansion of $(1+x)^n$ are in A.P., then the value of $n$ is
4. If 9 times the 9th term of an A.P. is equal to 13 times the 13th term, then the 22nd term of the A.P. is
5. The solution set of the system of inequalities $3x - 7 < 5 + x$ and $11 - 5x \le 1$ is
6. If $x + iy = \frac{a+ib}{a-ib}$, prove that $x^2 + y^2 = 1$.
7. How many numbers greater than 1,000,000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?
8. Find the sum of all natural numbers between 200 and 400 which are divisible by 7.
9. Find the coefficient of $x^5$ in the product $(1+2x)^6 (1-x)^7$ using binomial expansion.
10. Solve the following system of inequalities graphically: $x + 2y \le 10, x + y \ge 1, x - y \le 0, x \ge 0, y \ge 0$.
11. The sum of two numbers is 6 times their geometric mean, show that the numbers are in the ratio $(3+2\sqrt{2}) : (3-2\sqrt{2})$.
12. Case Study: Dr. Strange has 6 different flags. He wants to generate signals by arranging at least 2 flags in order one below the other on a vertical staff.
    (i) How many signals can be generated with exactly 2 flags?
    (ii) How many signals with exactly 3 flags?
    (iii) Find the total number of signals possible.