1. Indices: Simplify $2^3 \times 2^4$. 2. Indices: Express $\frac{3^5}{3^2}$ in simplest form. 3. Indices: Evaluate $9^{\frac{1}{2}}$. 4. Indices: Solve for $x$ if $5^{x} = 125$. 5. Logarithms: Find $\log_{10} 1000$. 6. Logarithms: Calculate $\log_2 \frac{1}{8}$. 7. Logarithms: If $\log_a 16 = 2$, find $a$. 8. Logarithms: Simplify $\log_3 27 + \log_3 9$. 9. Quadratic Equation: Solve $x^2 - 5x + 6 = 0$ by factorization. 10. Quadratic Equation: Solve $x^2 + 4x + 4 = 0$ by completing the square. 11. Quadratic Equation: Use the quadratic formula to solve $2x^2 - 3x - 2 = 0$. 12. Quadratic Equation: Find the roots of $x^2 - 4 = 0$. 13. Circle Geometry: Define a chord. 14. Circle Geometry: State the property of angles subtended by the same chord. 15. Circle Geometry: Calculate the length of a chord given radius and angle. 16. Circle Geometry: Find the measure of an arc given central angle. 17. Indices: Simplify $\left(\frac{2}{3}\right)^{-2}$. 18. Indices: Express $16^{\frac{3}{4}}$ in simplest form. 19. Logarithms: Solve for $x$ if $\log_5 x = 3$. 20. Logarithms: Simplify $\log_4 64 - \log_4 16$. 21. Quadratic Equation: Solve $3x^2 + 2x - 1 = 0$ by factorization. 22. Quadratic Equation: Complete the square for $x^2 + 6x + 5$. 23. Quadratic Equation: Use formula to solve $x^2 - 2x - 3 = 0$. 24. Quadratic Equation: Find vertex of $y = x^2 - 4x + 7$. 25. Circle Geometry: Explain the relationship between radius and chord length. 26. Circle Geometry: Calculate angle between two chords intersecting inside a circle. 27. Circle Geometry: Define an arc. 28. Circle Geometry: State the theorem about angle in a semicircle. 29. Indices: Simplify $27^{\frac{2}{3}}$. 30. Indices: Express $8^{-\frac{1}{3}}$ in simplest form. 31. Logarithms: Find $\log_{10} 0.01$. 32. Logarithms: Simplify $\log_2 32 + \log_2 \frac{1}{4}$. 33. Quadratic Equation: Solve $x^2 + x - 6 = 0$ by factorization. 34. Quadratic Equation: Complete the square for $x^2 - 8x + 15$. 35. Quadratic Equation: Use formula to solve $4x^2 - 4x + 1 = 0$. 36. Quadratic Equation: Find discriminant of $x^2 + 2x + 5$. 37. Circle Geometry: Calculate chord length given radius 10cm and angle 60°. 38. Circle Geometry: Find arc length for radius 7cm and central angle 90°. 39. Circle Geometry: State the property of angles subtended by diameter. 40. Circle Geometry: Calculate angle between tangent and chord. Theory Questions with full workings: 1. Solve $x^2 - 7x + 12 = 0$ by factorization. 2. Solve $x^2 + 6x + 9 = 0$ by completing the square. 3. Solve $2x^2 - 4x - 6 = 0$ using quadratic formula. 4. Explain the laws of indices with examples. 5. Discuss properties of logarithms and solve $\log_2 8 + \log_2 4$. 6. Prove that the angle subtended by a diameter of a circle is a right angle. Answer keys with full workings for theory questions are prepared in the document as requested.