This resource will cover common concepts that you should know to attempt the SAT Math section. If anything was missed in this resource, feel free to contact me @scripted_mari0 on discord or join the StudyHaven discord server.

Quadratics

Sometimes you'll be asked to solve for the sum or the product of the roots of a quadratic equation. You can use the quadratic formula and then add or multiply the results, but it's quicker to just memorize these two expressions.

sum of the roots: $-\frac{b}{a}-\backslash frac\{b\}\{a\}$
product of the roots: $\frac{c}{a}\backslash frac\{c\}\{a\}$

The discriminant, $DD$, of a quadratic in the standard form $a{x}^2+bx+c=0ax^2\; +\; bx\; +\; c\; =\; 0$ is $b^2-4acb^2\; -\; 4ac$

• If the discriminant is positive, the quadratic has 2 real solutions.
• If the discriminant equals 0, the quadratic has 1 real solution.
• If the discriminant equals negative, the quadratic has no real solutions.
  
  

Logarithms (Exponential growth and decay)

General equation of exponential growth or decay:
$c=a{b}^{t}c\; =\; ab^t$
Where:

• $cc$ = final amount
• $aa$ = original amount
• $bb$ = multiplier
• $tt$ = number of changes
  
  

Linear Algebra

The equation of a line can take two forms. In either form, $(x,y)(x,\; y)$ is a point on the line.

• In slope-intercept form, $y=mx+by\; =\; mx+b$, the slope is $mm$ and the $yy$-intercept is $bb$.
• In standard form, $Ax+By=CAx+By\; =\; C$, the slope is $-\frac{A}{B}-\backslash frac\{A\}\{B\}$ and the $yy$-intercept is $\frac{C}{B}\backslash frac\{C\}\{B\}$
  
  

Another equation for a line is $y-y_1=m(x-x_1)y\; -\; y\_1\; =\; m(x\; -\; x\_1)$

Given two points on a line, $(x_1,y_1)(x\_1,\; y\_1)$ and $(x_2,y_2)(x\_2,\; y\_2)$, the slope is $\frac{(y_2-y_1)}{(x_2-x_1)}\backslash frac\{(y\_2\; -\; y\_1)\}\{(x\_2\; -\; x\_1)\}$

Coordinate Geometry

There are 4 different forms for a circle equation:

• The standard form
• The general form
• The polar form
• The parametric form
  
  

The SAT only considers the standard form and the general form.

The standard form of a circle equation is $(x-h{)}^2+(y-k{)}^2=r^2(x-h)^2\; +\; (y-k)^2\; =\; r^2$, where $(h,k)(h,\; k)$ is the center and $rr$ is the radius.

The general form of a circle equation is $x^2+y^2+2gx+2fy+c=0x^2\; +\; y^2\; +\; 2gx\; +\; 2fy\; +\; c\; =\; 0$ where $gg$, $ff$ and $cc$ are constants.

To convert the general form equation to the standard form equation, remember that the center is $(-g,-f)(-g,\; -f)$ and the radius is $\sqrt{g^2+f^2-c}\backslash sqrt\{g^2\; +\; f^2\; -\; c\}$

Geometry and Trigonometry

Basic trigonometric rules:

The sine rule:

The cosine rule:

Heron's formula:

Area of a triangle:

Where (For area of a triangle and Heron's formula):

• $AA$ = area of the triangle
• $ss$ = half perimeter of the triangle
• $aa$, $bb$, $cc$ = sides of the triangle
• $\theta \backslash theta$ = angle
  
  

A Simple Guide

❗Some points in this post are from the princeton review guide❗

Credits for some points in this post goes to @vpurnitha on discord