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
{a^{n}}/{a^{m}} = a^{n-m}
{a^{n}}/{b^{n}} = left (frac{a}/{b} \right )^{n}
(b^{n})^{m} = b^{(n^{m})}
sqrt[m]{b^{n}} = b^{{n}/{m}}
b^{{1}/{n}} = sqrt[n]{b}
a^{-n} = {1}/{a^{n}}

3. Exponential Powers – Rules of Exponents

{x^{n}}/{x^{m}} = x^{n-m}
x^{n}x^{m} = x^{n+m}
x^{n}y^{n} = (xy)^{n}
({x}/{y})^{n} = {x^{n}}/{y^{n}}
x^{-n} = {1}/{x^{n}}
(x^{y})^{z} = x^{y.z}

4. Roots & Radicals

Basic Concepts like Radical, Radicand, Square and Cube Roots

Rules of Roots & Radicals

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

5. 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.

6. Linear Equations

Example –

5x + 7y = 14

Non-Linear Equations

Example –

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

7. 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

8. Quadratic Equations

The Quadratic Formula –

x={-b (+-) \sqrt{b^{2}-4ac}}/{2a}[/latex]

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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