SAT/AMC · Free math lesson
SAT / Olympiad Prep
After this lesson, you will be able to use smart shortcuts to solve SAT math problems faster and more accurately.
Practice SAT / Olympiad Prep freeSkills in this unit
Pick a skill to try three free questions on just that.
- SAT linear equations and inequalities in context
- SAT systems of equations
- SAT nonlinear equations and functions
- SAT ratios, rates, and percentages
- SAT data interpretation
- SAT probability and statistics
- SAT geometry and trigonometry
- Number theory puzzles
- Counting and probability puzzles
- Clever algebra
Plug In Numbers First
When a problem has variables, pick a simple number like 2 or 5 and test it. This turns abstract algebra into real arithmetic you can actually check.
Example: The question says '3x + 6 is how much more than 3x?' Pick x = 2. Then 3(2)+6 = 12 and 3(2) = 6. The answer is 12 - 6 = 6. Every time, the answer is just 6.
Remember: When you see 'in terms of x,' plug in x = 2 first!
Work Backwards from Choices
SAT gives you 4 answer choices — use them! Start with the middle value, plug it into the problem, and see if it works. If it's too big, try a smaller one.
Example: Solve: 2x + 3 = 11. Choices: A) 2 B) 4 C) 6 D) 8. Try B) 4: 2(4)+3 = 11. ✓ Done — no algebra needed!
Remember: On number answer choices, always try the middle value first to cut your work in half.
Draw It, Label It, Trust It
SAT geometry problems become easy when you draw the figure yourself and label every number you know. Your eyes catch things your brain misses.
Example: A triangle has sides 5 and 12. What is the hypotenuse? Draw it, label 5 and 12 on the two legs, then use 5²+12² = 25+144 = 169, so the hypotenuse = 13.
Remember: Write every given number ON your drawing — never leave info floating in the question text.
Worked example
If 4(x + 3) = 28, what is the value of x + 3?
- 1Notice the question asks for (x + 3), not just x — that's a hint!
- 2Divide both sides by 4: (x + 3) = 28 ÷ 4 = 7.
- 3You never even need to find x alone. The answer is right there.
Answer: x + 3 = 7
The #1 mistake to avoid
Students solve for x first, then add 3 — wasting time. Always read what the question ACTUALLY asks for before you start solving.
Key takeaways
- Plug in simple numbers to test variable expressions instead of doing pure algebra.
- Work backwards from answer choices — start in the middle to save time.
- Draw and label every geometry problem so you can see the answer clearly.
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