Algebra and Quadratic Equations

System of Linear Equations in Two Variables

• A system of linear equations in two variables involves two or more equations that must be solved simultaneously
• The algebraic method is used to solve these equations

Solution of Linear Equations in Two Variables

• Linear equations in two variables have applications in solving simple problems, such as:
  • Finding the cost of items
  • Calculating the number of items that can be purchased

Quadratic Equations

• Quadratic equations are polynomial equations of degree two
• Solutions to quadratic equations can be found by:
  • Factorisation
  • Quadratic formula

Applications of Quadratic Equations

• Quadratic equations have applications in solving simple problems, such as:
  • Finding the maximum or minimum value of a quadratic function
  • Solving problems involving area and perimeter of rectangles

Arithmetic Progressions (A.P.)

• An Arithmetic Progression (A.P.) is a sequence of numbers in which each term after the first is obtained by adding a fixed constant to the previous term
• General terms of an A.P. can be represented by an = a + (n-1)d, where a is the first term and d is the common difference
• The sum to n-terms of an A.P. can be calculated using the formula Sn = n/2(2a + (n-1)d)

Applications of A.P.

• A.P. has applications in instalment payment and instalment buying
• Instalment payment involves paying a fixed amount at regular intervals
• Instalment buying involves buying a product by paying a fixed amount at regular intervals