1. Let's start with Arithmetic Sequences (AS). An arithmetic sequence is a list of numbers with a constant difference between consecutive terms. 2. The formula for the $n$th term of an arithmetic sequence is $$a_n = a_1 + (n-1)d$$ where $a_1$ is the first term and $d$ is the common difference. 3. For Geometric Sequences (GS), each term is found by multiplying the previous term by a constant ratio $r$. 4. The formula for the $n$th term of a geometric sequence is $$a_n = a_1 \times r^{n-1}$$ where $a_1$ is the first term and $r$ is the common ratio. 5. Index laws help simplify expressions with powers. Key rules include: - $$a^m \times a^n = a^{m+n}$$ - $$\frac{a^m}{a^n} = a^{m-n}$$ - $$(a^m)^n = a^{mn}$$ - $$a^0 = 1$$ (if $a \neq 0$) 6. Change of subject means rearranging a formula to make a different variable the subject. For example, from $$y = mx + c$$ to $$x = \frac{y - c}{m}$$. 7. Factorization involves expressing an expression as a product of its factors. For example, $$x^2 - 9 = (x-3)(x+3)$$. 8. Percentages represent parts per hundred. To find a percentage of a number, multiply the number by the percentage divided by 100. Example: Find 20% of 50: $$20\% \times 50 = \frac{20}{100} \times 50 = 10$$. This covers the basics of AS, GS, index laws, change of subject, factorization, and percentages to help you revise for your test.