Recognition Signals:
Fractions, parentheses, parameters (k, a, t), messy expressions, or two linear sides.

Goal:
Simplify first → solve second. DSAT tests structure, not computation.

Step-by-Step Framework:
1) Distribute everything
2) Combine like terms
3) Move variable terms to one side
4) Handle parameters → check for restrictions

Shortcut: If both sides are linear → the solution always takes 2–3 moves.

Common Pitfalls:
– Negative distribution errors
– Forgetting to multiply all terms when clearing fractions
– Ignoring undefined values for parameters

Pattern Example:
“Which value of k makes the equation have no solution?”

Recognition:
Two variables, two relationships, or comparing two plans/people.

The Three Paths:
1) Elimination → best for ax + by = c forms
2) Substitution → best when one variable is isolated
3) Graphing → best when comparing models

Trap:
DSAT often asks for x+y, 2x–3y, or final cost—not x or y.

Recognition:
Words like “per”, “each”, “initial”, “starting value”, “rate”.

Modeling Framework:
1) Identify two changing quantities
2) Assign variables
3) Build the relationship from context
4) Identify starting value (intercept) and growth rate (slope)

Golden Rule:
“Starts at” = intercept
“Every / per / each” = slope

Top Pitfall:
Confusing “initial value” with a later value mentioned in the text.

Choose the right form:
Vertex form → max/min problems
Factored form → roots/zeros
Standard form → direction, shape, axis

Rule:
Use the form that directly answers the question.

Common Pitfall:
Solving the entire quadratic when the question only needs vertex/leading coefficient info.

Recognition:
Constant ratio, table patterns, doubling time, half-life.

Key Insight:
Constant difference → linear
Constant ratio → exponential

Pitfall:
Mixing up % increase (×1+r) with raw percent values.

Core Method:
Increase by r% → ×(1 + r)
Decrease by r% → ×(1 – r)

Pitfall:
“Increased by 20% twice” ≠ 40%
Correct multiplier = 1.2 × 1.2

Framework:
1) totalA = avgA × countA
2) totalB = avgB × countB
3) Combined Avg = (totalA + totalB) ÷ (countA + countB)

Pitfall:
Using simple average instead of weighted.

Steps:
1) Check angle equality
2) Check proportional sides
3) Identify scale factor

Pitfall:
Hidden right angle or parallel lines inside the wording.

Use trig only when:
– One angle is given
– One side is known
– Another side is required

Pitfall:
Using trig when simple algebra solves the question faster.

Purpose:
30% of DSAT mistakes come from answering the wrong quantity.

Rule:
Always read the final line again: Does it ask for x? 2x? x+3? Final value?

Why?
Module timing is strict. Hard questions should not be solved first attempt.

Rule:
After 90 seconds → flag → move on.

Use Desmos for:
– Intersections
– Quadratic comparisons
– Exponential modeling

Avoid graphing:
– Simple linear equations
– Basic percentages
– Unit conversions