The last-night sheet
Every constant, unit and number that keeps coming up in Tahsili, on one page. Read it the night before and the morning of the test.
Every constant, unit and number that keeps coming up in Tahsili, on one page. Read it the night before and the morning of the test.
🧠 Constants
| Constant | Value | Where you need it |
|---|---|---|
| Gravity | g = 9.8 m/s² ≈ 10 | falling, weight, potential energy |
| Speed of light | c = 3 × 10⁸ m/s | EM waves, refraction, E = mc² |
| Speed of sound in air | ≈ 343 m/s | echoes, resonance |
| Gravitational constant | G = 6.67 × 10⁻¹¹ N·m²/kg² | universal gravitation |
| Coulomb’s constant | k = 9 × 10⁹ N·m²/C² | force between charges |
| Electron charge | e = 1.6 × 10⁻¹⁹ C | counting electrons, the electron-volt |
| Electron mass | 9.11 × 10⁻³¹ kg | de Broglie |
| Planck’s constant | h = 6.63 × 10⁻³⁴ J·s | photon energy |
| Electron-volt | 1 eV = 1.6 × 10⁻¹⁹ J | atomic physics |
| Avogadro’s number | 6.02 × 10²³ mol⁻¹ | the mole |
| Molar volume (STP) | 22.4 L/mol | gases |
| Gas constant | R = 0.0821 L·atm/(mol·K) = 8.31 J/(mol·K) | PV = nRT |
| Specific heat of water | 4180 J/(kg·K) | Q = mcΔT |
| Atmospheric pressure | 1 atm = 101.3 kPa = 760 mmHg | gases and fluids |
| Water ionization constant | K w = 1 × 10⁻¹⁴ | pH + pOH = 14 |
| Absolute zero | 0 K = −273 °C | heat and gases |
🧠 Derived units
| Unit | Equals | Why |
|---|---|---|
| newton (N) | kg·m/s² | F = ma |
| joule (J) | N·m = kg·m²/s² | W = Fd |
| watt (W) | J/s | P = W/t |
| pascal (Pa) | N/m² | P = F/A |
| coulomb (C) | A·s | q = It |
| volt (V) | J/C | ΔV = W/q |
| ohm (Ω) | V/A | R = V/I |
| hertz (Hz) | 1/s | f = 1/T |
| tesla (T) | N/(A·m) | F = BIL |
| farad (F) | C/V | C = q/V |
Biology and chemistry numbers that keep coming up
- Humans: 2n = 46, gametes n = 23, 206 bones, a 4-chamber heart, 64 codons, 20 amino acids.
- The 10% rule: only about a tenth of the energy reaches the next food level.
- Cellular respiration: about 36–38 ATP per glucose; glycolysis alone nets 2.
- Shape angles: 180° linear, 120° trigonal planar, 109.5° tetrahedral, 107° pyramidal, 104.5° bent.
- Electronegativity gap: below 0.4 nonpolar, 0.4–1.7 polar, above 1.7 ionic.
- pH: below 7 acid, 7 neutral (pure water), above 7 base. Blood ≈ 7.4, stomach ≈ 2.
For quick sums use g = 10 unless the choices are very close, and when choices differ by powers of ten, work out the power first.
A way of memorizing that sticks
- Understand before you memorize: read “in plain words” for each formula and say out loud what it measures and why each quantity is multiplied or divided. A formula you understand takes a minute to learn.
- Active recall: cover the formula column and write it from memory, then check. Writing from memory beats rereading by far.
- Spaced repetition: review the same sheet after 1 day, 3 days, a week and two weeks. Four short reviews lock it in until test day.
- Your own formula page: write every formula of a book on one page by hand. If it does not fit, you are writing things you can derive, so cut them.
- Teach it: explain the formula to a friend, or to yourself in a mirror, in two sentences. If you cannot explain it, you do not know it yet.
- Use it at once: after each group, press “Try one” in the patterns below. Memory sets when you use it.