Algebra_Topics_Detailed_Presentation.pptx

presentation

1. Algebra Topics Overview Key concepts and methods in algebra

2. Background algebra Covers the basics: algebraic operations, expressions, and simplification.

3. Factors and bracket expansion Breaking expressions into factors and expanding brackets using distributive law.

4. Changing the subject of a formula Rearranging equations to make a different variable the subject.

5. Linear equations Equations of the form ax + b = 0 and their solutions.

6. Quadratic equations Equations of the form ax² + bx + c = 0.

7. Solving quadratic equations Methods: factorisation, completing the square, quadratic formula.

8. Quadratic factorisation Expressing ax² + bx + c as (px + q)(rx + s).

9. The quadratic formula x = [-b ± √(b² - 4ac)] / 2a.

10. The graphs of quadratic functions Parabola shape, vertex, axis of symmetry, roots.

11. Simultaneous equations Solving systems of linear equations using substitution or elimination.

12. Inequalities Solving and graphing linear/quadratic inequalities.

13. Operations with polynomials Addition, subtraction, multiplication, and division of polynomials.

14. Solution of polynomial equations Finding roots of higher-order polynomials.

15. The modulus function f(x) = |x|, properties and graphs.

16. The remainder theorem If f(x) is divided by (x - a), remainder = f(a).

17. The factor theorem If f(a) = 0, then (x - a) is a factor of f(x).

18. The general binomial expansion (a + b)^n expansion using binomial coefficients.

19. Review of algebraic fractions Simplifying, adding, subtracting, multiplying, and dividing algebraic fractions.

20. Partial fractions Expressing rational expressions as a sum of simpler fractions.

21. Using partial fractions with the binomial expansion Combining partial fractions with binomial series expansion.