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Grade 11 Math — Functions & Applications — formula sheet

Quadratics, growth and decay, periodic motion, trigonometry and money · 43 formulas · metric edition 1

The full booklet — learning zone, problems, answer key
Vertex x-Coordinate of a Parabola
h=−b2ah = -\frac{b}{2a}
Discriminant of a Quadratic
Δ=b2−4ac\Delta = b^2 - 4ac
Vertex y-Coordinate of a Parabola
k=c−b24ak = c - \frac{b^2}{4a}
Completing the Square: the Constant Needed
k=(b2)2k = \left( \frac{b}{2} \right)^{2}
Quadratic Formula (Positive Root)
x=−b+b2−4ac2ax = \frac{-b + \sqrt{b^2 - 4ac}}{2a}
Quadratic Formula (Negative Root)
x=−b−b2−4ac2ax = \frac{-b - \sqrt{b^2 - 4ac}}{2a}
Sum of the Roots of a Quadratic
S=−baS = -\frac{b}{a}
Product of the Roots of a Quadratic
P=caP = \frac{c}{a}
Displacement (Uniform Acceleration)
d=v0t+12at2d = v_0 t + \tfrac{1}{2} a t^2
Projectile Maximum Height
H=v02sin⁡2θ2gH = \frac{v_0^{2} \sin^{2}\theta}{2g}
Projectile Time of Flight
T=2v0sin⁡θgT = \frac{2 v_0 \sin\theta}{g}
Exponential Growth
A=A0(1+r)tA = A_0 (1 + r)^{t}
Exponential Decay
A=A0(1−r)tA = A_0 (1 - r)^{t}
Percent Change
c=xnew−xoldxoldc = \frac{x_{\text{new}} - x_{\text{old}}}{x_{\text{old}}}
Declining-Balance Depreciation (Book Value)
B=C (1−d)kB = C\,(1 - d)^k
Half-Life Decay
N=N0(12)t/t1/2N = N_0 \left(\frac{1}{2}\right)^{t/t_{1/2}}
Half-Life and Decay Constant
t1/2=ln⁡2λt_{1/2} = \frac{\ln 2}{\lambda}
Exponential Growth by Doubling Time
N=N0⋅2t/TN = N_0 \cdot 2^{t/T}
Rule of 72 (Doubling Time)
n≈0.72in \approx \frac{0.72}{i}
Solve an Exponential Equation for the Exponent
x=ln⁡(y/a)ln⁡bx = \frac{\ln (y / a)}{\ln b}
Logarithm Change of Base
log⁡bx=ln⁡xln⁡b\log_b x = \frac{\ln x}{\ln b}
Period-Frequency Relation
T=1fT = \frac{1}{f}
Wave Speed (v = fλ)
v=fλv = f \lambda
Simple Pendulum Period
T=2πLgT = 2\pi \sqrt{\frac{L}{g}}
Speed in Circular Motion (v = 2πr/T)
v=2πrTv = \frac{2\pi r}{T}
SHM Displacement at Time t
x=Acos⁡(ωt)x = A \cos\left(\omega t\right)
Period of a Spring-Mass Oscillator
T=2πmkT = 2\pi \sqrt{\tfrac{m}{k}}
Right-Triangle Sine Ratio (SOH)
sin⁡θ=oh\sin\theta = \frac{o}{h}
Right-Triangle Cosine Ratio (CAH)
cos⁡θ=ah\cos\theta = \frac{a}{h}
Right-Triangle Tangent Ratio (TOA)
tan⁡θ=oa\tan\theta = \frac{o}{a}
Pythagorean Theorem
a2+b2=c2a^{2} + b^{2} = c^{2}
Law of Sines
asin⁡A=bsin⁡B\frac{a}{\sin A} = \frac{b}{\sin B}
Law of Cosines
c2=a2+b2−2abcos⁡Cc^2 = a^2 + b^2 - 2ab\cos C
Triangle Area (Two Sides and Included Angle)
A=12 absin⁡CA = \tfrac{1}{2}\,ab\sin C
Arithmetic Sequence nth Term
an=a1+(n−1)da_n = a_1 + (n - 1) d
Geometric Sequence nth Term
an=a1 r n−1a_n = a_1 \, r^{\,n-1}
Arithmetic Series Sum
Sn=n2(2a1+(n−1)d)S_n = \frac{n}{2} \left( 2 a_1 + (n - 1) d \right)
Geometric Series Sum
Sn=a1(1−rn)1−rS_n = \frac{a_1 (1 - r^{n})}{1 - r}
Simple Interest
I=P r tI = P \, r \, t
Compound Interest (Periodic)
A=P(1+rn)ntA = P \left( 1 + \frac{r}{n} \right)^{n t}
Present Value
PV=FV(1+r)t\mathit{PV} = \frac{\mathit{FV}}{(1 + r)^{t}}
Future Value of an Annuity (Regular Deposits)
FV=D (1+i)n−1i\mathit{FV} = D\,\frac{(1+i)^n - 1}{i}
Loan Payment (Amortized Loan or Mortgage)
M=P i1−(1+i)−nM = \frac{P\,i}{1 - (1+i)^{-n}}