# Algebra Quiz

## Make sure to try these on a piece of paper first

#1-1 Paper 2 Difficulty: Easy

In an arithmetic sequence, the first term is 2, and the fourth term is 14.

a) Find the common difference, d.

b) Calculate the sum of the first 14 terms, $S_{14}$.

#1-2 Paper 1 Difficulty: Easy

Let $log_{b}\, 2=u$, and $log_{b}\, 5=v$. Find an expression in terms of u and v for:

a) $log_{b}\, 10$.

b) $log_{b}\, 25$.

#1-3 Paper 2 Difficulty: Medium

Find the $x^{3}$ term in the expansion of $\left ( x-\frac{2}{x} \right )^{5}$.

#1-4 Paper 1 Difficulty: Medium

The first 3 terms in a geometric sequence are: $k^{2}, \: -k, \: k-2$.

a) Find the value of k.

b) Find the sum of the terms to infinity.

#1-5 Paper 2 Difficulty: Medium

In an arithmetic series, $S_{20}=670$, and $u_{20}=62$.

a) What is the first term, $u_{1}$?

b) What is the common difference, d?

#1-6 Paper 1 Difficulty: Easy

Solve the following sum:

$\sum_{n=1}^{100}2n+3$

#1-8 Paper 1 Difficulty: Easy

Simplify $\frac{\left (-6 x^{-2}y^{2} \right ) \left (-8x^{-5}y^{-3} \right )}{4x^{2}y^{-4}}$.

#1-7 Paper 2 Difficulty: Medium

The sum of the first 6 terms of a sequence is 39.75. Also, the 7th term is $\frac{6}{5}$ times the 2nd term. Find the first term and the common difference of the sequence.

#1-9 Paper 1 Difficulty: Medium

Let $log_{8}A=x, \, log_{8}B=y, \, log_{8}C=z$. Express $log_{8}\left ( \frac{A^{2}}{B^{3}C} \right )^{4}$ in terms of x, y and z.

#1-10 Paper 2 Difficulty: Medium

Consider the expansion of $\left ( \frac{1}{3}x – 2 \right ) ^{7}$. Find the coefficient of $x^{3}$.