1. Arithmetic Sequence (AS): An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. Formula for the nth term: $$a_n = a_1 + (n-1)d$$ where $a_1$ is the first term, $d$ is the common difference, and $n$ is the term number. 2. Geometric Sequence (GS): A geometric sequence is a sequence where each term is found by multiplying the previous term by a constant ratio. Formula for the nth term: $$a_n = a_1 \times r^{n-1}$$ where $a_1$ is the first term, $r$ is the common ratio. 3. Index Laws: - $$a^m \times a^n = a^{m+n}$$ - $$\frac{a^m}{a^n} = a^{m-n}$$ - $$(a^m)^n = a^{mn}$$ - $$a^0 = 1$$ (if $a \neq 0$) - $$a^{-n} = \frac{1}{a^n}$$ 4. Change of Subject: To change the subject of a formula means to solve the formula for a different variable. Example: For $$y = mx + c$$, to make $x$ the subject: $$y - c = mx$$ $$x = \frac{y - c}{m}$$ 5. Factorization: Factorization is expressing an expression as a product of its factors. Example: $$x^2 - 5x + 6 = (x - 2)(x - 3)$$ Common methods include: - Taking out common factors - Difference of squares: $$a^2 - b^2 = (a - b)(a + b)$$ - Quadratic trinomials 6. Percentage: Percentage means "per hundred". To find percentage of a number: $$\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100$$ To increase/decrease a number by a percentage: - Increase: $$\text{New value} = \text{Original} \times \left(1 + \frac{\text{percentage}}{100}\right)$$ - Decrease: $$\text{New value} = \text{Original} \times \left(1 - \frac{\text{percentage}}{100}\right)$$ These are the key concepts you need to revise for your test. Practice problems on each topic to strengthen your understanding.