Day 4 — Friday, May 15, 2026
Last day of the trial. Today is fraction division, formal inverse, and a wrap-up of every subject from the week.
The deal, one last time: 9:00 – 13:30, no phone, no PC outside this window. Plan on 3 to 4 hours of focused work. After today's exam the trial is officially over.
Today's exam covers
- Math — Fraction division. Each numerator/denominator < 10.
- Math — Formal inverse. Reciprocal of a fraction; 1/n of an integer.
- Math — Reviews: GCF, LCM, fraction add/subtract/multiply.
- Periodic table — rows 1, 2, 3 review (any of the 18 elements).
- History — wars 13-15 plus a couple of review questions pulled from any of the 15 wars.
- Biology — three final evolution events (mammals, hominids, Homo sapiens).
About 18 questions. Two versions — pick one.
What good thinking looks like
Fraction division (Keep–Change–Flip)
Compute 2/3 ÷ 4/5.
Keep 2/3. Change ÷ to ×. Flip 4/5 to 5/4. 2/3 × 5/4 = 10/12 = 5/6.
Compute 6 ÷ 2/3.
6 = 6/1. Flip 2/3 to 3/2. 6/1 × 3/2 = 18/2 = 9. Larger than 6 — that's correct, dividing by less than 1 makes things bigger.
Full lesson: lessons/fraction-div.
Formal inverse
Inverse of 3/8 = 8/3 (flip). Inverse of 5 = 1/5 (put 1 over it). Inverse of −2/7 = −7/2 (sign stays). Inverse of 0 = undefined.
Full lesson: lessons/fraction-inverse.
In the exam, the inverse questions show a number and ask you to type the inverse as a fraction (numerator and denominator). For an integer like 5, type 1/5.
Periodic table — full review
You're now responsible for all 18 elements, rows 1-3. The full table is in lessons/periodic-table-rows-1-3.
Spend a few minutes scanning. Look for places where you're least sure.
History — today's wars
New today:
| War | Started |
|---|---|
| Vietnam War | 1955 |
| Gulf War | 1990 |
| Iraq War | 2003 |
Plus a couple of review questions drawn from any of the 15 wars from the whole week. Tolerance ±1 year.
Biology — final three evolution events
| Event | Approx. mya |
|---|---|
| First mammals | 210 |
| First hominids | 7 |
| Homo sapiens | 0.3 |
Tolerance ±10% (with a minimum of 1 mya for very recent events). For Homo sapiens, anything from about 0.1 to 1 should be accepted.
Suggested study path
Total time: 3 to 4 hours.
- ~30 min — Fraction division lesson. The whole rule is "flip the second one." Do the practice problems on paper. /fractions, Divide mode.
- ~15 min — Inverse lesson. There are only two cases (integer → 1/n; fraction → flip). Quick.
- ~30 min — Skim the periodic table once and note any element where you have to stop and think. Drill those.
- ~20 min — Fifteen wars on a single page. Read them in order, then in reverse, then by century.
- ~15 min — Eleven evolution events on a single page. Read them in order from 13800 mya down to 0.3 mya.
- ~30 min — Mixed review of the week's math (GCF, LCM, all four fraction operations).
- break — ~30 min off-screen.
- ~40 min — Take one version of the exam. This one is bigger; pace yourself.
Begin the exam
Pick A or B. Take one. Submit when done. After this, the trial is complete — you've earned the right to read your own notes back.