STUDY GUIDE

ALGEBRA

1. Solving quadratic equations by completing the square will NOT be examined.

2. Solving quadratic equations using the substitution method (k-method) is examinable.

3. Equations involving surds that lead to a quadratic equation are examinable.

4. Solution of non-quadratic inequalities should be seen in the context of functions.

5. Nature of the roots will be tested intuitively with the solution of quadratic equations and in all the prescribed functions.

TOPICS

Unit 1: Exponents and surds.

1.The number system.

  1. Working with irrational numbers.

  1. Exponents.

  1. Exponential equations.

  2. Equations with rational exponents.

Unit 2: Algebra.

1. Algebraic expressions.

2.Addition and subtraction.

3. Multiplication and division.

4. Factorizing.

5.Notes on factorizing a trinomial.

6.Quadratic equations.

7. Quadratic inequalities.

8. Simultaneous equations.

9.The nature of the roots.

1.The number system.

1. Natural Numbers

= {1; 2; 3; …} (positive whole numbers)

Its roots are derived from the counting numbers used in everyday life, forming the basis for more complex numerical systems.

2. Whole Numbers

= {0; 1; 2; …} (Natural numbers and 0)

its roots are essential for understanding the structure of mathematics and serve as a foundation for arithmetic operations such as addition and multiplication.

3. Integers

= {… ;–3; –2; –1; 0; 1; 2; 3; …}

4. Rational Numbers

• A rational number is a Real number which can be written in the form   __a b, where a, b ∈ 핑 and b ≠ 0. The rational numbers include all the integers.