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Quant02. Equations
Quant02. Equations
Quant02. Equations
Quant02. Equations
Quant02. Equations
Quant02. Equations
Quant02. Equations
Quant02. Equations
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Quant02. Equations

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Revision Notes for CPT …

Revision Notes for CPT
Chapter: Equations
Subject: Quantitative Aptitude

Published in: Education
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  • 1. CPTSuccess
    Revision Notes – Quantitative Aptitude
    Chapter 2. Equations
  • 2. Chapter 2. Equations
    • An equation is defined to be a mathematical statement of equality.
    • 3. Simple equation
    • 4. A simple equation in one unknown x is in the form
    • 5. ax + b = 0, where a, b are known as constants and a ≠ 0
    • 6. A simple equation has only one root
    • 7.  Simultaneous linear equations in two unknown
    The general form of a linear equation in two unknowns x and y is ax + by + c = 0 where a and b are non-zero coefficients.
    Two equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 form a pair of simultaneous equations in x and y. A value for each unknown which satisfies both equations at the same time gives the roots / solution of the equation.
    •  
    ©
    Revision Notes – Quantitative Aptitude
    CPTSuccess
    www.cptsuccess.com
  • 8. Chapter 2. Equations
    • Methods to Solve Simultaneous linear equations
    Elimination method: In this method one unknown is eliminated, thus reducing two linear equations to a linear equation in one unknown. This unknown is solved and its value substituted in the equation to find the other unknown.
    ©
    Revision Notes – Quantitative Aptitude
    CPTSuccess
    www.cptsuccess.com
  • 9. Chapter 2. Equations
    • Methods to Solve Simultaneous linear equations
    Cross-multiplication method
    For two equation, a1x + b1y + c1 = 0, and a2x + b2y + c2 = 0
    Coefficients of x and y and constant term are arranged as:
      
    which gives: x / (b1 c2 – b2 c1) = y / (c1 a2 – c2 a1) = 1 / (a1 b2 – a2 b1)
    Hence, x = (b1 c2 – b2 c1) / (a1 b2 – a2 b1)
    y = (c1 a2 – c2 a1) / (a1 b2 – a2 b1)
     Equations in three variables can also be solved using the above two methods
    ©
    Revision Notes – Quantitative Aptitude
    CPTSuccess
    www.cptsuccess.com
  • 10. Chapter 2. Equations
    • Quadratic Equations
    An equation in the form ax2 + bx + c = 0, where x is a variable and a, b and c are constants with a ≠ 0 is called a quadratic equation. When b = 0 the equation is called a pure quadratic equation and when b ≠ 0 the equation is called an affected quadratic.
     
    • Roots of a Quadratic Equation
    x = [- b ±  (b2 – 4ac)] / 2a
    Sum of roots = - b / a = - (coefficient of x / coefficient of x2)
    Product of roots = c / a = (constant term / coefficient of x2)
    Construction of a Quadratic Equation
    x2 – (sum of roots) x + (product of roots) = 0
    ©
    Revision Notes – Quantitative Aptitude
    CPTSuccess
    www.cptsuccess.com
  • 11. Chapter 2. Equations
    • Roots of a Quadratic Equation
    b2 – 4ac is known as the discriminant in the equation as it discriminates the nature of roots of the equation
     
    If b2 – 4ac = 0, the roots are real and equal
    If b2 – 4ac > 0, the roots are real and distinct (unequal)
    If b2 – 4ac < 0, the roots are imaginary
    If b2 – 4ac is a perfect square the roots are real rational and distinct
    If b2 – 4ac > 0 but not a perfect square the roots are real irrational and distinct
     
    Other properties
    Irrational roots occur in pairs. If p+ q is one root, then the other root p - q
    If a = c then one root is reciprocal to the other
    If b = 0 the roots are equal but of opposite signs
    ©
    Revision Notes – Quantitative Aptitude
    CPTSuccess
    www.cptsuccess.com
  • 12. Chapter 2. Equations
    • Application of Equations to Coordinate Geometry
     
    Distance of a point P (x, y) from Origin (0, 0) is  (x2 + y2)
    Distance between two points P (x1, y1) and Q (x2, y2) is  [(x1 – x2)2 + (y1 – y2)2]
    Equation of a straight line is written as y = mx + c, where m is the slope and c is the constant
    The Slope of the line is given by, m = (y2 – y1) / (x2 – x1)
    ©
    Revision Notes – Quantitative Aptitude
    CPTSuccess
    www.cptsuccess.com
  • 13. CPTSuccess

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