Linear equation
ax + b = 0 → x = −b / a
Slope-intercept form: y = mx + b, where m is slope and b is the y-intercept.
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Calculator and science desk for homework
A standard and scientific calculator, a full periodic table, and the formulas students actually look up: algebra, geometry, trig, physics, chemistry, SI prefixes, and unit conversions. History and theme stay on this device.
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Keyboard: numbers, + − * / %, Enter, Backspace, Esc. Period and comma both work as a decimal point.
Periodic table
All 118 elements. Click a cell for name, atomic number, mass, and a short student note. Use mass sends the atomic mass into the calculator.
Select an element to see details.
Formula sheet
The identities and equations that show up most in middle school, high school, and first-year college work.
Algebra
Quadratic formula
x = (−b ± √(b² − 4ac)) / 2a
Discriminant D = b² − 4ac. D > 0 two real roots, D = 0 one root, D < 0 complex roots.
Exponent rules
aᵐ · aⁿ = aᵐ⁺ⁿ (aᵐ)ⁿ = aᵐⁿ a⁻ⁿ = 1/aⁿ
a⁰ = 1 (a ≠ 0). √a = a^(1/2). Change of base: log_b a = ln a / ln b.
Logarithms
log(ab) = log a + log b log(a/b) = log a − log b
log(aⁿ) = n log a. Natural log ln is log base e. Common log is base 10.
Geometry
Areas
Rectangle: lw. Triangle: ½bh. Circle: πr². Trapezoid: ½(a+b)h. Parallelogram: bh.
Volumes
Box: lwh. Cylinder: πr²h. Sphere: ⁴⁄₃πr³. Cone: ⅓πr²h. Pyramid: ⅓Bh.
Pythagorean theorem
a² + b² = c²
Distance between (x₁,y₁) and (x₂,y₂): √((x₂−x₁)² + (y₂−y₁)²).
Circle facts
Circumference C = 2πr. Arc length = θr (θ in radians). Sector area = ½r²θ.
Trigonometry
SOH-CAH-TOA
sin θ = opp/hyp cos θ = adj/hyp tan θ = opp/adj
csc = 1/sin, sec = 1/cos, cot = 1/tan.
Identities
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ. sin(2θ) = 2 sinθ cosθ. cos(2θ) = cos²θ − sin²θ.
Law of sines / cosines
a/sin A = b/sin B = c/sin C
c² = a² + b² − 2ab cos C. Use this for any triangle, not just right triangles.
Radians
180° = π rad. 1 rad ≈ 57.3°. Full circle = 2π rad = 360°. Unit circle: (cos θ, sin θ).
Physics
Motion
v = v₀ + at s = v₀t + ½at² v² = v₀² + 2as
Average speed = distance / time. Velocity is a vector; speed is not.
Newton and energy
F = ma W = Fd cosθ KE = ½mv² PE = mgh
Momentum p = mv. Impulse = Δp = FΔt. Power P = W/t = Fv.
Waves and electricity
v = fλ V = IR P = IV = I²R
Series resistors add. Parallel: 1/R = 1/R₁ + 1/R₂. Coulomb: F = kq₁q₂ / r².
Gases and heat
PV = nRT Q = mcΔT
STP is 0 °C and 1 atm. Specific heat of water is 4.184 J/g·°C.
Chemistry
Moles
n = m / M n = N / NA n = C · V
NA = 6.022 × 10²³ mol⁻¹. Molarity C is moles per liter of solution.
Stoichiometry
Balance the equation. Convert given grams → moles → mole ratio → desired grams. Limiting reactant is the one that runs out first.
pH
pH = −log[H⁺] pOH = −log[OH⁻] pH + pOH = 14
Acids pH < 7, bases pH > 7. Strong acids fully dissociate in water.
Bonding quick read
Ionic: metal + nonmetal, electrons transferred. Covalent: shared electrons. Metallic: delocalized electrons. Polar molecules have uneven charge.
Unit conversions
Exact or commonly used classroom values. Temperature is the one that is not a simple multiply.
Length
| 1 in | 2.54 cm |
| 1 ft | 12 in = 0.3048 m |
| 1 yd | 3 ft = 0.9144 m |
| 1 mi | 1.60934 km |
| 1 Å | 10⁻¹⁰ m |
Mass
| 1 kg | 2.20462 lb |
| 1 lb | 16 oz = 453.592 g |
| 1 t (metric) | 1000 kg |
| 1 u (amu) | 1.66054 × 10⁻²⁷ kg |
Volume
| 1 L | 1000 mL = 0.001 m³ |
| 1 gal (US) | 3.78541 L |
| 1 qt | 0.946353 L |
| 1 cup | 236.588 mL |
Temperature
| °C → °F | F = 1.8C + 32 |
| °F → °C | C = (F − 32) / 1.8 |
| °C → K | K = C + 273.15 |
| 0 K | absolute zero |
Pressure & energy
| 1 atm | 101325 Pa = 760 mmHg |
| 1 bar | 10⁵ Pa |
| 1 cal | 4.184 J |
| 1 eV | 1.602 × 10⁻¹⁹ J |
| 1 kWh | 3.6 × 10⁶ J |
SI prefixes
| giga (G) | 10⁹ |
| mega (M) | 10⁶ |
| kilo (k) | 10³ |
| centi (c) | 10⁻² |
| milli (m) | 10⁻³ |
| micro (µ) | 10⁻⁶ |
| nano (n) | 10⁻⁹ |
| pico (p) | 10⁻¹² |
Constants, Greek letters, and exam notes
Physical constants
| c | 2.99792458 × 10⁸ m/s |
| g | 9.80665 m/s² (standard) |
| G | 6.674 × 10⁻¹¹ N·m²/kg² |
| h | 6.626 × 10⁻³⁴ J·s |
| k | 8.987 × 10⁹ N·m²/C² |
| e | 1.602 × 10⁻¹⁹ C |
| R | 8.314 J/mol·K |
| NA | 6.022 × 10²³ mol⁻¹ |
Math constants
| π | 3.1415926535 |
| e | 2.7182818284 |
| √2 | 1.4142135623 |
| √3 | 1.7320508075 |
| φ (golden) | 1.6180339887 |
Greek alphabet
| α alpha | often angles, alpha particles |
| β beta | beta decay, coefficients |
| γ gamma | photons, Lorentz factor |
| Δ delta | change, discriminant |
| θ theta | angles |
| λ lambda | wavelength, eigenvalues |
| μ mu | micro, friction, mean |
| σ sigma | sum, stress, conductivity |
| ω omega | angular frequency |
Study reminders
| Sig figs | multiply: fewest sig figs; add: fewest decimals |
| Vectors | break into x and y, then add components |
| Units | write them through the whole solution |
| Graphs | slope = rise/run; area under v–t is displacement |
| Lab | % error = |exp − acc| / acc × 100 |
How Helix Desk works
Basic operations
Enter the first number, pick an operator, enter the second number, press equals. You can chain + and − without pressing equals every time.
Memory
MS stores the display. M+ and M− add or subtract. MR recalls. MC clears. The M badge appears when memory is set.
Scientific mode
Adds square root, square, reciprocal, and π. Use the periodic table “Use mass” button to drop an atomic mass into the display.
Privacy
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