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Grades 11 and 12: Key Formulas and Rules

Thirty-two cards with the formulas and rules from senior mathematics, science and English that students use most often.

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Quadratic formula
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1
Quadratic formula
x = (-b ± √(b² − 4ac)) / (2a)
2
Discriminant
b² − 4ac: positive means two real roots, zero means one, negative means none.
3
Vertex form of a parabola
y = a(x − h)² + k, with vertex (h, k).
4
Remainder theorem
The remainder when P(x) is divided by (x − k) is P(k).
5
Factor theorem
(x − k) is a factor of P(x) if and only if P(k) = 0.
6
Sine law
a / sin A = b / sin B = c / sin C
7
Cosine law
c² = a² + b² − 2ab cos C
8
Special angles
sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2; cos 60° = 1/2.
9
Trig identity
sin²θ + cos²θ = 1
10
Radians and degrees
180° = π radians.
11
Arithmetic sequence
t_n = a + (n − 1)d and S_n = n(2a + (n − 1)d)/2.
12
Geometric sequence
t_n = a r^(n−1) and S_n = a(r^n − 1)/(r − 1).
13
Exponential growth and decay
A = A0 (growth factor)^(t / period).
14
Logarithm laws
log(xy) = log x + log y; log(x/y) = log x − log y; log(x^n) = n log x.
15
Power rule for derivatives
d/dx (x^n) = n x^(n−1).
16
Product rule
(fg)' = f'g + fg'.
17
Dot product of vectors
(a, b)·(c, d) = ac + bd.
18
Magnitude of a vector
|(a, b)| = √(a² + b²).
19
Combinations
C(n, r) = n! / (r!(n − r)!).
20
Newton's second law
F = ma
21
Kinematic equation
v² = u² + 2as and s = ut + ½at².
22
Kinetic and potential energy
Ek = ½mv² and Ep = mgh.
23
Wave speed
v = fλ
24
Ohm's law
V = IR; resistors in series add: R = R1 + R2.
25
Boyle's law
P1V1 = P2V2 at constant temperature.
26
Charles's law
V1/T1 = V2/T2 at constant pressure, with T in kelvins.
27
Moles
n = m / M; concentration C = n / V.
28
pH
pH = −log[H+]; pH 7 is neutral at 25 °C.
29
Photosynthesis
CO2 + H2O + light energy → glucose + O2.
30
Cellular respiration
Glucose + O2 → CO2 + H2O + ATP.
31
Oxidation and reduction
Oxidation is loss of electrons (at the anode); reduction is gain of electrons (at the cathode).
32
Three appeals of rhetoric
Ethos (credibility), pathos (emotion) and logos (logic).

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