Before diving into a problem, spend a few seconds classifying it: what topic is this really testing, and which of your tools does that topic call for? This quick routing step prevents the common trap of starting down one approach for several minutes before realizing a completely different technique would have been immediate.
Keyword-to-technique map
- Algebra — “solve,” “function,” “equation”: try substitution, factoring, or backsolving from the answer choices.
- Number theory — “divisible,” “remainder,” “last digit”: think modular arithmetic first.
- Geometry — shapes, angles, distances: consider coordinate geometry or similarity/congruence relationships.
- Counting — “how many ways,” “arrangements”: think casework, complementary counting, or a direct formula (permutations/combinations).
The quick loop
Read the problem once for the overall shape. Spot any topic-signaling keywords. Glance at the answer choices — their format (integers, fractions, radicals) often confirms which topic you’re in. Pick a starting strategy based on that classification. Begin solving, and be ready to switch strategies if the first one stalls.
Applying it
Scenario: A problem asks: “What is the remainder when is divided by 5?”
Response: The word “remainder” is an immediate number-theory signal — reach for modular arithmetic (specifically, finding the cycle of powers of 7 mod 5) rather than attempting to compute directly.
Practice problems
1.A problem mentions 'divisible by 6' in its statement. What topic and technique does this signal?
2.A problem asks 'in how many ways can 5 people be seated...' What topic and technique does this signal?
3.A problem gives coordinates for three points and asks for the area of the triangle they form. What's the fastest likely technique?
4.Why is it worth spending a few seconds classifying a problem's topic before diving into computation?