GMAT Quant Algebra Syllabus

GMAT Quant Algebra Syllabus

GMAT Algebra Syllabus

Sums on algebra for GMAT exam consists of the following primary topics –

  1. Absolute Value
  2. Exponential Equations
  3. Exponential Powers
  4. Roots & Radicals
  5. Inequalities
  6. Adding & Subtracting
  7. Multiplying & Dividing
  8. Absolute Value
  9. Exponents
  10. Linear Equations
  11. Order of Operations
  12. Quadratic Equations
  13. Factoring
  14. Simplifying Equations
  15. Simultaneous Equations

 

Absolute Value

Definition, Solving Equations & Working With Multiple Absolute Values

 

Exponential Equations

  1. Basic Concepts – Base, Exponent, Radical, Exponential Expression, Exponential Equation
  2. Laws of Exponents

 

\(a^{0} = 1\) \(0^{n} = 0 ; n>0\) \(a^{1} = a\) \((-1)^{n} = \left\{\begin{matrix} 1 & , n \; even\\ -1 & n \; odd \end{matrix}\right.\) \(a^{n} . a^{m} = a^{n+m}\) \(a^{n} . b^{n} = (a.b)^n\) \(\frac{a^{n}}{a^{m}} = a^{n-m}\) \(\frac{a^{n}}{b^{n}} = \left ( \frac{a}{b} \right )^{n}\) \((b^{n})^{m} = b^{(n^{m})}\) \(\sqrt[m]{b^{n}} = b^{\frac{n}{m}}\) \(b^{\frac{1}{n}} = \sqrt[n]{b}\) \(a^{-n} = \frac{1}{a^{n}}\)

 

  1. Exponential Powers – Rules of Exponents
\(\frac{x^{n}}{x^{m}} = x^{n-m}\) \(x^{n}x^{m} = x^{n+m}\) \(x^{n}y^{n} = (xy)^{n}\) \(\left ( \frac{x}{y} \right )^{n} = \frac{x^{n}}{y^{n}}\) \(x^{-n} = \frac{1}{x^{n}}\) \((x^{y})^{z} = x^{y.z}\)

 

  1. Roots & Radicals

Basic Concepts like Radical, Radicand, Square and Cube Roots

Rules of Roots & Radicals

\(a^{\frac{x}{y}} = \sqrt[y]{a^{x}}\) \(\sqrt{x}.\sqrt{n} = \sqrt{xn}\) \(\sqrt{\frac{x}{y}} = \frac{\sqrt{x}}{\sqrt{y}}\) \((\sqrt{x})^{n} = \sqrt{x^{n}}\) \(a\sqrt{c} + b\sqrt{c} = (a+b)\sqrt{c})\) \(\sqrt{a} + \sqrt{b} \neq \sqrt{a+b}\)

 

**NOTE – It’s recommended for the aspirants to memorize the types of Radicals –

\(\sqrt{2} \approx 1.41 \; and \; (1.41)^{2} \approx 2\) \(\sqrt{3} \approx 1.73 \; and \; (1.73)^{2} \approx 3\) \(\sqrt{11} = 11 \; and \; (11)^{2} = 121\) \(\sqrt{169} = 13 \; and \; (13)^{2} = 169\) \(\sqrt{225} = 15 \; and \; (15)^{2} = 225\) \(\sqrt{625} = 25 \; and \; (25)^{2} = 625\)

 

  1. Inequalities

Types of Inequalities – Greater Than (>), Less Than (<), Greater Than or Equal to (>), Less Than or Equal to (<) and Not Equal to (≠). Adding & Subtracting, Multiplying & Dividing, Absolute Value, Exponents.

 

  1. Linear Equations

Example –

\(5x + 7y = 14\)

Non-Linear Equations

Example –

\(x^{2} -2x + 1 = 0\) \(x^{-3} + y^{-3} + 9x^{2} + 2= 0\)

 

  1. Order of Operations

To solve a fundamental mathematical operation, the order of operations must be followed, which is –

P – Parentheses
E – Exponents
M – Multiplication
D – Division
A – Addition
S – Subtraction

 

  1. Quadratic Equations

The Quadratic Formula –

\(x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\)

Factoring Quadratic Equations –

\(a^{2} – b^{2} = (a+b)(a-b)\) \(a^{2} + 2ab + b^{2} = (a+b)^{2}\) \(a^{2} – 2ab + b^{2} = (a-b)^{2}\)

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