1. Let's start with **Simple Interest**. The problem is to find the interest earned on a principal amount over time. 2. The formula for simple interest is: $$I = P \times r \times t$$ where $I$ is the interest, $P$ is the principal, $r$ is the annual interest rate (in decimal), and $t$ is the time in years. 3. For example, if you invest 1000 at 5% for 3 years, the interest is: $$I = 1000 \times 0.05 \times 3 = 150$$ 4. Next, **Compound Interest** involves interest on interest. The formula is: $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where $A$ is the amount, $n$ is the number of compounding periods per year. 5. For monthly compounding ($n=12$), 5% rate, 3 years, and 1000 principal: $$A = 1000 \left(1 + \frac{0.05}{12}\right)^{12 \times 3}$$ Calculate the exponent and simplify to find $A$. 6. Moving to **Quadratic Functions**, the general form is: $$y = ax^2 + bx + c$$ 7. To expand and factorize quadratics, use methods like: - Factoring by grouping - Using the quadratic formula - Completing the square 8. For example, factorize $x^2 + 5x + 6$: $$x^2 + 5x + 6 = (x + 2)(x + 3)$$ 9. The vertex of a parabola $y = ax^2 + bx + c$ is at: $$x = -\frac{b}{2a}$$ Substitute back to find $y$. 10. The axis of symmetry is the vertical line $x = -\frac{b}{2a}$. 11. Intercepts are found by setting $y=0$ (roots) and $x=0$ (y-intercept). 12. Transformations include shifting (adding constants), reflecting (changing signs), and dilating (multiplying by constants). 13. For **Polynomials**, identify degree and leading coefficient to understand shape. 14. **Exponential functions** have the form: $$y = a^x$$ with transformations shifting or scaling the graph. 15. **Circle graphs** represent data proportions; no formulas here. 16. **Reciprocal functions** are of form: $$y = \frac{1}{x}$$ and their graphs are hyperbolas with transformations shifting or reflecting. 17. In **Non-Right Trigonometry**, use the unit circle to find exact values of sine, cosine, and tangent. 18. Convert degrees to radians by: $$\text{radians} = \text{degrees} \times \frac{\pi}{180}$$ 19. Solve trigonometric equations by finding all solutions in the domain. 20. The **Area Rule** for triangles is: $$\text{Area} = \frac{1}{2}ab\sin C$$ 21. The **Sine Rule** is: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ 22. The **Cosine Rule** is: $$c^2 = a^2 + b^2 - 2ab \cos C$$ 23. Graph basic sine and cosine functions by plotting key points and noting amplitude and period. 24. In **Probability**, two-step experiments can be analyzed with tree diagrams, Venn diagrams, or two-way tables. 25. Conditional probability is: $$P(A|B) = \frac{P(A \cap B)}{P(B)}$$ 26. Independent events satisfy: $$P(A \cap B) = P(A) \times P(B)$$ 27. Set notation includes union ($\cup$), intersection ($\cap$), and complements. 28. For **Measurement**, surface area and volume formulas for prisms, cylinders, pyramids, and cones are: - Prism surface area: sum of all faces - Cylinder surface area: $2\pi r(h + r)$ - Pyramid surface area: base area + lateral area - Cone surface area: $\pi r(l + r)$ where $l$ is slant height 29. Volume formulas: - Prism: base area $\times$ height - Cylinder: $\pi r^2 h$ - Pyramid: $\frac{1}{3}$ base area $\times$ height - Cone: $\frac{1}{3} \pi r^2 h$ This overview covers the key formulas and concepts for your revision topics.