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. If the sum of $n$ terms of an A.P. is $3n^2 + n$, then its common difference is
2. The 5th term of a G.P. is 2. The product of its first 9 terms is
3. If AM and GM of two positive numbers $a$ and $b$ are 10 and 8 respectively, then the numbers are
4. The sum of the series $1^2 + 2^2 + 3^2 + \dots + n^2$ is
5. Which term of the sequence $\sqrt{3}, 3, 3\sqrt{3}, \dots$ is 729?
6. Insert 3 numbers between 1 and 256 so that the resulting sequence is a G.P.
7. Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
8. If $\frac{a^n + b^n}{a^{n-1} + b^{n-1}}$ is the A.M. between $a$ and $b$, then find the value of $n$.
9. The sum of the first three terms of a G.P. is 13/12 and their product is -1. Find the common ratio and the terms.
10. Find the sum to $n$ terms of the series: $5 + 55 + 555 + \dots$
11. If $a$ and $b$ are the roots of $x^2 - 3x + p = 0$ and $c, d$ are roots of $x^2 - 12x + q = 0$, where $a, b, c, d$ form a G.P. Prove that $(q+p):(q-p) = 17:15$.
12. Case Study: A man saves Rs 32 during the first year, Rs 36 in the second year and in this way he increases his savings by Rs 4 every year.
    (i) Find the amount saved in the 10th year.
    (ii) Find the total amount saved in 10 years.
    (iii) Find the time in which his saving will be Rs 2000.