YOUR EDGE

Tips & Reference

Most of your lost points aren't bad math — they're grabbing the wrong tool. This page is the top of your cheat sheet.

Tap through it

Which Type Is This?

Name the type first, then reach for the formula. Answer a question or two and this points you at the type and your first move.

What kind of problem is it?

Look at the squared terms. How many, and what are the signs?

Does the order matter?

From one term to the next — do you add the same amount or multiply by the same amount?

Parabola

First move: only one variable is squared. The positive term names the axis it opens along. Complete the square on the squared variable to find the vertex.

Circle

First move: both squared, same sign, equal coefficients. Complete the square in both x and y to read off the center and radius.

Not a circle if the coefficients differ — that's an ellipse.

Ellipse

First move: both squared, same sign, different coefficients. Get it to standard form, then for the foci use c² = a² − b².

Ellipse subtracts: c² = a² − b².

Hyperbola

First move: squared terms have opposite signs. The positive term names the axis it opens along. For the foci use c² = a² + b².

Hyperbola adds: c² = a² + b². This is the one people flip — hyperbola = add.

Permutation — nPr

First move: order matters, so it's a permutation. Plug n and r into nPr.

Combination — nCr

First move: order doesn't matter, so it's a combination. Plug n and r into nCr.

Arithmetic sequence

First move: a common difference — you add the same each time. Read the stem twice: a sum uses Sₙ, one specific term uses aₙ.

Counting terms from a₃ to a₇? It's last − first + 1 = 5. Always +1.

Geometric sequence

First move: a common ratio — you multiply by the same each time. Read the stem twice: a sum uses Sₙ, one specific term uses aₙ.

Counting terms from a₃ to a₇? It's last − first + 1 = 5. Always +1.

No JavaScript? The same decision trees are written out just below — they work either way.

The Decision Trees, Written Out

The same calls the tapper makes — here in full so they work with the page open to any problem.

Conic? Look at x² and y².

→ only one squared → parabola
→ both squared, same sign & equal coeff → circle
→ both squared, same sign, different coeff → ellipse
→ squared terms have opposite signs → hyperbola

Opens which way?

the positive term names the axis it opens along.

Foci — don't mix these up:

ellipse c² = a² − b² · hyperbola c² = a² + b² (hyperbola = add).

Counting: does order matter?

→ order matters (podium, ranked) → Permutation nPr
→ order doesn't (a committee, a group) → Combination nCr

Sequence: difference or ratio?

→ add the same each time → arithmetic
→ multiply the same each time → geometric

"Find the sum" vs "find the 30th term"?

sum → use Sₙ; one term → use aₙ. Read the stem twice.

How many terms from a₃ to a₇?

last − first + 1 = 5. Always +1.

Multiple-Choice Strategy

Predict your answer before you look at the options. Work the problem as if it were open-response, get to an answer, then find it in the list. The options are there to pull you off course — don't shop them.

Eliminate the twin. When two options differ by one tiny feature — ³√ vs √, + vs −, a² vs b² — that feature is the question. The test writer built the trap on exactly that detail. Slow down and verify exactly that one thing.

The 5 Accuracy Habits

Your errors live on the steps that feel easy. These five make the easy steps safe.

1 · Keep an error log ›

After each session, jot every miss: what happened · type · the correct step. Types: sign drop, middle term, arithmetic, notation. Weekly, count them and find your Top 3 — those become your personal Check list.

2 · Circle every destination before you distribute ›

See a minus in front of parentheses? Circle every term inside first, then distribute. Say it: "minus hits every term" — especially the last one. Say "negative eleven," never "eleven negative."

3 · Write every sub-step (full FOIL) ›

Never write (x+3)² and expand in one jump. Write it as (x+3)(x+3) and do all four products. A square gives THREE terms. If you only have two, you dropped the middle.

4 · 10 min of daily drills ›

Zetamac (multiplication, accuracy over speed) + a short Khan set. Build automatic arithmetic so it stops eating your focus mid-problem.

5 · The 3-point scan (your personal Check) ›

After each problem, 20 seconds, only three things — your Top 3 from the error log. Keep it to 3; more than that collapses under exam stress. Check early (by line 2), before a wrong sign poisons the rest.

Read This Before Any Test

When you get it rightYou got it because you slowed the easy step and checked. That's your method — and the method is yours to repeat.

When you slipThat's the rush tax, not "bad luck" and not "I'm bad at math." The method would've caught it. Re-run it with the check.

The 4-step pre-exam reset ›

Breathe — one slow breath. The buzz means it matters, not that you'll fail.
"My method travels with me." The sheet's in your hand. You're not alone in there.
Do the 3 easiest problems first — bank early wins, settle your body.
Check every easy line — that's where your points hide, not the hard ones.

Your Cheat Sheet — The Weapon

Everything here orbits one thing: your cheat sheet. You're allowed to bring it into the exam, so you build it a little every day — and writing it is the studying. Build a line, then practice without it face-down, then re-sheet whatever you peeked at. By July you'll barely need it, which is exactly when it works best.

Page 1 is your workbench. For each concept, break it into three things: the rule or formula, a worked example in your own words, and the specific mistake you tend to make with that type. Don't delete items as you get confident — just update the dot and track your progress.

Page 2 is what you bring to the exam. After each session, decide what earns a spot — don't copy Page 1, compress it. Three zones, in the order you work a problem: Identify, Solve, then Check against your personal error list. That last zone is the one most students skip, and it's exactly where points get recovered.

Before every exam, rewrite Page 2 from scratch. Don't reuse the old one — that rewrite is a review session.

Open the cheat-sheet template →