Geometry & Trig System

The volume/area formulas are handed to you — so the points here are won by knowing the few things that aren't on the sheet and by not eyeballing figures. Geometry & Trigonometry is ~15% of Math. Difficulty stays moderate; trig is right-triangle SOHCAHTOA plus radian conversion, never identities. The losses are radian/degree slips, diameter-for-radius, and trusting "not drawn to scale" figures.

Sources: College Board math types; College Panda, Piqosity. Examples MERIDIAN-original. Point convention: each = 1 of ~44 Math; Module-1 misses are ceiling-risk.

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#WHAT IT TESTS

Area & volume (formulas on the sheet); lines, angles, triangles (angle-chasing, similarity); right triangles & trig (sin/cos/tan, special triangles); circles (equation, arc length, sector area, radians↔degrees).

#THE METHOD

1. PULL the area/volume formula off the sheet; for circles/trig use the Formula Vault (NOT on the sheet).
2. MARK the figure: label everything; for "not drawn to scale," ignore appearance — use given values only.
3. RELATE: angle rules (supplementary 180°, parallel-line transversals, triangle sum 180°),
   similar-triangle ratios, SOHCAHTOA, circle equation.
4. CHECK units & mode: radius vs diameter; radians vs degrees.

Why (mechanism): the test plants figures that look a certain way to bait estimation, and mixes radians with degrees to catch mode errors. Working only from given values and the right formula removes both. Desmos alt: type a circle's equation to read centre/radius; graph to find intercepts.

#TRAP TAXONOMY

• Radius/diameter swap.
• Radian/degree mismatch (and calculator mode).
• Eyeballing a "not drawn to scale" figure.
• Arc length vs sector area mix-up.
• Cofunction miss: forgetting sin(x)=cos(90−x).
• Forgetting the ½ in triangle area.

#SAME ITEM, TWO LEVELS (MERIDIAN-original)

Problem: "A circle has equation x² + y² − 6x + 8y = 0. What is its radius?"

• ~700 (trap): reads coefficients, guesses r = 6 or 8. Trap: didn't complete the square. [−1]
• 800 (precise): complete the square: (x−3)² + (y+4)² = 9+16 = 25 ⇒ r = 5. Or Desmos: type the equation; read the circle's radius directly. Move: used the circle-equation method (Formula Vault), or let Desmos draw it.

#DIAGNOSE YOUR ANSWER

• Off by a factor of 2? Radius/diameter swap. Fix: label which one the problem gives.
• Trig value wrong? Radian/degree mode, or cofunction. Fix: check mode; sin(x)=cos(90−x).
• Circle wrong? Didn't complete the square. Fix: convert general → centre-radius form (or Desmos).
• Trusted the picture? "Not drawn to scale" — use numbers only.

#DRILLS (timed · self-marked · MERIDIAN-original)

Drill 1 — Formula pull (target 8/8, ≤3 min): for 8 prompts, write the exact formula needed (arc length, sector area, circle equation, SOHCAHTOA ratio, cofunction, radian conversion, sphere volume, triangle area). PASS: all correct (gaps → Anki). Drill 2 — Circle equations (target 4/4, ≤6 min): complete the square to find centre + radius for 4 circles; verify in Desmos. PASS: centre + radius correct each. Repetition: fail → repeat next day.

#TRANSFER

Abstract rule: right formula + given values (not appearance) + unit/mode check. Second context: a satellite-orbit arc problem and a pizza-slice sector problem use the same (θ/360) fraction. Constant: method + trap list + Vault formulas. Changes: the shape and story.

#REFERENCE CARD — GEOMETRY & TRIG

Sheet gives areas/volumes/Pythagoras/special triangles. YOU carry:
circle (x−h)²+(y−k)²=r² (complete the square) · arc (θ/360)·2πr · sector (θ/360)·πr² ·
SOHCAHTOA · sin(x)=cos(90−x) · radians = degrees·π/180
CHECK: radius vs diameter · radian vs degree · "not to scale" = use numbers · ½ in triangle area
Desmos draws circles. Each item = 1 of 44 Math Q; Module-1 miss = ceiling risk.

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MERIDIAN · FORGE · GEOMETRY & TRIG SYSTEM | v1.0