Day 2 — Wednesday, May 13, 2026
Yesterday's exam: 10 / 18, 14 minutes.
Real notes, real thinking. The writeups you left on the GCF questions were excellent — even the ones you got wrong showed your reasoning. Three things from yesterday are baked into today's plan, so read this before you start studying.
GCF — 4 / 8. The errors weren't conceptual. You understand "the biggest number that divides both". The breakdown was in listing factors. On (15, 25) you wrote
1, 3, 5, 10, 15as factors of 15 — but 10 isn't a factor of 15. On (14, 35) you wrote1, 3, 5, 10, 15, 20, 25, 30, 35for 35 — those are multiples of 5, not factors of 35 (the actual factors of 35 are 1, 5, 7, 35). You missed 7, so you said the GCF was 1 instead of 7.Today's GCF refresh repeats those exact problem types — (24, 18), (14, 35), (15, 25). You will see them again. Convert them. Read the GCF lesson again — try Euclid's algorithm (the second method on the page) if listing keeps tripping you up. It works in your head and it doesn't care about your factor lists.
Wars 1-4 — 0 / 3. You wrote "I don't really remember these" and moved on. Honest, but the wars aren't going away — you are now responsible for wars 1-8. One of today's three war questions is from yesterday's set. Open the wars lesson.
Periodic table — 4 / 4. Evolution — 2 / 3. Solid. The one evolution miss looked like the end-of-exam rush — you wrote
3700in the note, but the answer field was blank. Two fields, two purposes. The score reads only the answer field. Notes are for your reasoning, for us to read after.
The deal stays the same: 9:00 – 13:30, no phone, no PC outside this window. Plan on 3 to 4 hours of focused work. You can take one or both versions before 13:30 — each version is single-attempt.
Today's exam covers
- Math — GCF refresh (3 questions, repeat of yesterday's failure modes).
- Math — LCM of two numbers (each 1-99) — new today.
- Math — Adding fractions with small numerators and denominators — new today.
- Periodic table — rows 1 and 2 (H, He, Li, Be, B, C, N, O, F, Ne).
- History — 1 question from wars 1-4 + 2 from wars 5-8.
- Biology — Cambrian, first fish, first land plants.
About 18 questions. Two versions — you can take both today.
What good thinking looks like
GCF — the rescue path
If your factor lists keep breaking, stop listing. Use Euclid's algorithm instead. It's three lines.
GCF(24, 18):
24 ÷ 18 = 1 remainder 6
18 ÷ 6 = 3 remainder 0 ← stop
GCF = 6
GCF(14, 35):
35 ÷ 14 = 2 remainder 7
14 ÷ 7 = 2 remainder 0 ← stop
GCF = 7
GCF(15, 25):
25 ÷ 15 = 1 remainder 10
15 ÷ 10 = 1 remainder 5
10 ÷ 5 = 2 remainder 0 ← stop
GCF = 5
The last non-zero remainder is your answer. That's the whole rule. No factor lists, no chance to confuse factors with multiples.
If you do prefer listing, here's the discipline you missed yesterday: every number on a "factors of N" list must divide N exactly. Test each candidate. If the test fails, cross it off.
LCM
Find the LCM of 6 and 8.
Multiples of 6: 6, 12, 18, 24, 30... Multiples of 8: 8, 16, 24, 32... First common multiple: 24.
Or, using the formula:
GCF(6, 8) = 2. LCM = (6 × 8) / 2 = 48 / 2 = 24.
Full lesson: lessons/lcm.
Fraction addition
Add 2/3 + 1/4.
LCM(3, 4) = 12. 2/3 = 8/12. 1/4 = 3/12. 8/12 + 3/12 = 11/12. Already in lowest terms.
Add 1/6 + 5/6.
Same denominator. 1 + 5 = 6, so 6/6 = 1.
Full lesson: lessons/fraction-add. For visual practice, /fractions has an Add mode.
Periodic table — today's full active list
You're now responsible for all of row 1 and row 2 — 10 elements.
| Symbol | Name | P | N | e |
|---|---|---|---|---|
| H | Hydrogen | 1 | 0 | 1 |
| He | Helium | 2 | 2 | 2 |
| Li | Lithium | 3 | 4 | 3 |
| Be | Beryllium | 4 | 5 | 4 |
| B | Boron | 5 | 6 | 5 |
| C | Carbon | 6 | 6 | 6 |
| N | Nitrogen | 7 | 7 | 7 |
| O | Oxygen | 8 | 8 | 8 |
| F | Fluorine | 9 | 10 | 9 |
| Ne | Neon | 10 | 10 | 10 |
In a neutral atom, e = P always. Memorize P and N; e is free.
History — full active list (wars 1-8)
Yesterday's wars are still fair game — one of today's three war questions is from this top half of the table.
| War | Started |
|---|---|
| American Revolutionary | 1775 |
| War of 1812 | 1812 |
| Mexican-American | 1846 |
| American Civil | 1861 |
| Franco-Prussian | 1870 |
| Spanish-American | 1898 |
| Russo-Japanese | 1904 |
| World War I | 1914 |
Tolerance ±1 year.
Biology — new evolution events
Active list is now 6 events (yesterday's 3 + today's 3):
| Event | Approx. mya |
|---|---|
| Big Bang | 13800 |
| Earth forms | 4540 |
| First life | 3700 |
| Cambrian explosion | 540 |
| First fish | 520 |
| First land plants | 470 |
Tolerance ±10%.
Suggested study path
Total time: 3 to 4 hours.
- ~25 min — GCF refresh. Re-read the GCF lesson, focusing on Euclid's algorithm. Practice on yesterday's three failures: (24, 18), (14, 35), (15, 25). Verify each answer by hand.
- ~25 min — Read the LCM lesson and practice with paper.
- ~30 min — Read the fraction-addition lesson. Do every worked example yourself without looking at the answer first. Open /fractions, Add mode, drill 10+ problems until smooth.
- ~15 min — Wars 1-4. Memorize the four dates you skipped yesterday. One war question today is from here.
- ~15 min — Wars 5-8. Add to your list.
- ~25 min — Memorize the eight new elements. Notice that for C, N, O, neutrons equals protons. F, Ne, Be, B, Li have one or two extra.
- ~10 min — Add the three new evolution events.
- break — ~30 min off-screen.
- ~30 min — Take one (or both) versions of the exam.
Reminder for the exam: the score only sees the answer field, not the note. If you write a number in the note, also type it in the answer. Notes are for your reasoning.
Begin the exam
Pick A or B. After you submit, you can choose to take the other version too.