SAT Prep – Math: Advanced Math

DSAT Math Content: Advanced Math Domain

This domain covers linear equations, inequalities, and systems. Students analyze relationships between variables, manipulate algebraic expressions, and solve equations efficiently.

Core Skills

  • Solve quadratic equations (factored, vertex, or standard form)
  • Work with exponential models
  • Perform polynomial operations (add, subtract, multiply)
  • Solve rational equations and analyze restrictions
  • Interpret function graphs and key features
  • Understand function notation and composition

Example

If the roots of a quadratic equation $ax^2+bx+c=0$ are reciprocal to each other, which of the following is necessarily true? (Without calculator)

  1. $a=b$
  2. $a=c$
  3. $b=0$
  4. $c=-a$

Solution

We know that the product of the roots of a quadratic equation $ax^2 + bx + c=0$ is equal to $\frac{c}{a}$.

Given: the roots are reciprocal to each other.

Let's assume that the roots are $\alpha$ and $\frac{1}{\alpha}$.

So, product of the roots = $\alpha \times \frac{1}{\alpha}=\frac{c}{a}$

$=>1=\frac{c}{a}$

$=>c=a$

The correct answer is option B.

Applications

  • Growth and decay models
  • Projectile motion
  • Revenue, profit, and optimization
  • Chemical reaction rate modeling

Tools on DSAT

  • Graph visualization for nonlinear behavior
  • Ability to check solutions by graphing lines