SAT Math Prep: Common Math Tricks

To prepare for the SAT, students should learn common math tricks. Common math tricks include ways of getting an answer other than the typical way that students solve math question in school.

1. Picking Numbers to Substitute in for Variables

The “picking numbers” strategy is another useful trick explained in the Caddell Prep math book (Digital SAT Math Secrets), and it can help simplify algebraic problems — especially when you’re dealing with abstract expressions or unknown variables.

When to Pick Numbers for Variables

Use picking numbers when:

The question contains variables (like $a, b, r, t, x, y$ ) but no equation to solve.
The answer choices also contain variables.
You’re asked to simplify an expression or compare values.
The question says something like “for any number x” or gives no specific value.

How to Use the Picking Numbers Trick

Pick numbers for the variables.
- Use easy numbers like 3, 4, 5.
- Avoid 0, 1, or 2 unless the question involves multiplying/dividing or squaring — those values can create special cases.
Plug your numbers into the original expression to find its value.
Plug the same numbers into the answer choices to see which one matches the value from Step 2.
Choose the matching answer.

2. Try the Answer Choices

Using the answer choices is an efficient way to solve certain algebra and word problems when solving algebraically might take longer or be confusing.

When to Try to Answer Choices

Use this method when:

The question is multiple choice
You’re asked to find the value of a variable (like “What is the value of x?”)
The equation is hard to rearrange algebraically
Or you feel more confident checking than solving

How to Try the Answer Choices

Start with the middle answer (usually Choice B or C). This helps narrow down whether you need to go higher or lower.
Plug the answer into the problem. Replace the variable in the original equation or situation with the choice you’re testing.
Check if it works. Does it make the equation true or the situation work?
Adjust accordingly:
- If it’s too high, eliminate it and any answers higher than it.
- If it’s too low, eliminate it and any answers lower than it.
Repeat until you find the one that works.

3. Use the Factors

It’s especially useful for factoring expressions and simplifying problems involving multiplication and grouping.

This trick involves identifying and using common factors in expressions to help you combine or simplify terms, especially when you’re dealing with symmetric expressions or forms like:

$x^2+2xy+y^2$
or
$a^2-b^2$

It can help you:

Recognize patterns (like perfect squares, difference of squares, factoring by grouping)
Rearrange terms to factor and simplify
Quickly solve for expressions like $x+y$ or $x-y$

How to Use the Using Factors Trick

Look for structure in the expression — can you group or factor it?
Check if the terms share a common factor or resemble a known identity (like $(x+y)^2$ or $(x - y)^2$
Factor the expression, if possible.
Plug in known values, if any, or simplify to solve.

4. Estimate Lengths & Angles

For geometry questions that ask for a missing length or the measure of an angle, estimating lengths and angles is a helpful trick.

When to Use Estimating Lengths & Angles

This trick can be used when:

You’re asked to find the length of a missing side
You’re asked to find the measure of a missing angle
The figure is drawn to scale (If it doesn’t state “Not drawn to scale”, then it is drawn to scale)

How to Use This Trick

Identify lengths or angles that are given in the diagram
Use the provided information to make estimates for the missing information
For example, you can compare the length you are looking for is to a provided length. Is the missing side half of the given side? Is it 3/4 of the given side? etc.