Plugging in Numbers on the SAT
A Smart Strategy for Algebra
Build equations from context, spot patterns fast, and practice with intent.
Why the SAT Emphasizes Plugging in Numbers
Plugging in numbers is a strategic shortcut when the SAT gives you variables but no values. Instead of doing abstract algebra, you choose simple numbers and test the answer choices.
This lesson shows how to pick values that avoid traps, like $0$ or $1$ when they create special cases. You will also learn how to keep the same values across all expressions so your comparison is fair.
A Simple Definition Unlocks Plugging in Numbers
Choose numbers that make the arithmetic easy but still valid for the problem. If there is a denominator, avoid values that make it zero. If the problem involves even or odd, choose numbers that respect that condition.
After you plug in, compute the original expression and then each answer choice. The correct answer is the one that matches the original value for the numbers you chose.
Work Through Plugging in Numbers Step by Step
If $x = 3$, what is $2x + 5$?
Start with a simple value like $x = 3$ so you can see how plugging in works.
Substitute $x = 3$ to evaluate the expression.
Compute the result to simplify the expression.
Use Desmos to Check Plugging in Numbers
If $x = 3$, what is $2x + 5$?
Desmos can speed up plugging in by letting you define a variable and evaluate expressions. It is useful when answer choices are long.
x = 3
2x + 5
Use Desmos for arithmetic, but the core strategy is still picking a smart number.
Desmos is faster when the arithmetic is messy or when you must test several choices. Algebra is faster when the expression simplifies quickly.
Expert move: After you translate the problem, graph left and right sides or test candidate values quickly in Desmos; keep only values that fit the context.
When to skip Desmos: If a quick algebra step or estimation settles it, solve by hand and use Desmos only to verify.
- Desmos features used: variable assignment.
- Common mistake: choosing $0$ or $1$ and getting ambiguous results.
Practice Plugging in Numbers with SAT-Style Questions
Use plugging in numbers to test answer choices.
If , which expression equals ?
If , which expression equals ?
If , which expression equals ?
If , which expression equals ?
Key Takeaways to Remember for Plugging in Numbers
- Pick a simple number and test answer choices quickly.
- Avoid $0$ and $1$ when they make answers identical.
- Desmos helps with arithmetic, but the strategy is still yours.
About the Instructor
