Algebra 2 Sem 2 Formula Sheet
𝑎𝑎
Determinant �
𝑐𝑐
Inverse of �
𝑎𝑎
𝑐𝑐
𝑎𝑎
𝑑𝑑
𝑔𝑔
𝑏𝑏
𝑒𝑒
ℎ
𝑏𝑏
� = 𝑎𝑎𝑎𝑎 − 𝑐𝑐𝑐𝑐
𝑑𝑑
𝑐𝑐
𝑓𝑓 = (aei + bfg + cdh) – (gec + hfa + idb)
𝑖𝑖
𝑏𝑏
𝑑𝑑
�= 1/(ad-bc)�
𝑑𝑑
−𝑐𝑐
Pythagorean Theorem a2 + b2 = c2
−𝑏𝑏
�
𝑎𝑎
Distance Formula = √[(x2 – x1)2 + (y2 – y1)2]
Midpoint formula = ( (x1 + x2)/2 , (y1 + y2)/2
Inscribed angle = ½ of the intercepted arc
Parabola
Vertical axis of symmetry
Horizontal axis of symmetry
y = 1/(4p)(x – h)2 + k
x = 1/(4p)(y – k)2 + h
vertex: (h, k)
vertex: (h, k)
focus: (h, k + p)
focus: (h + p, k)
directrix: y = k – p
directrix: x = h - p
Horizontal major axis a > b
Vertical major axis a > b
(x – h)2/a2 + (y – k)2/ b2 = 1
(x – h)2/b2 + (y – k)2/ a2 = 1
Center: (h, k)
Center: (h, k)
Vertices: (h ± a, k)
Vertices: (h, k ± a)
Co-vertices: (h, k ± b)
Co-vertices: (h ± b, k)
Major axis: 2a minor axis: 2b
Major axis: 2a minor axis: 2b
Foci: (h ± c, k)
Foci: (h, k ± c)
c2 = a2 – b2
c2 = a2 – b2
Ellipse
Hyperbola
Horizontal axis of symmetry
Vertical axis of symmetry
(x – h)2/a2 – (y – k)2/b2 = 1
(y – k)2/a2 – (x – h)2/b2 = 1
Vertices: (h ± a, k)
Vertices: (h, k ± a)
Co-vertices: (h, k ± b)
Co-vertices: (h ± b, k)
Foci: (h ± c, k)
Foci: (h, k ± c)
Center: (h, k)
Center: (h, k)
Asymptote slope: ±b/a
Asymptote slope: ±a/b
c2 = a2 + b2
c2 = a2 + b2
Circles: ( x – h)2 + (y – k)2 = r2
center: (h, k)
radius: r
Probability
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•
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P(A and B) = P(A) * P(B)
P(A or B) = P(A) + P(B) – P(A and B)
nPr = n! / (n – r)! where P is a permutation of n things taken r at a time
nCr = n! / [r!(n – r)!] where C is a combination of n things taken r at a time
Convert probabilities to odds: If P = m/n, odds in favor are m: (n – m), odds against =(n – m):m
Binomial Theorem (𝑥𝑥 + 𝑦𝑦)𝑛𝑛 = �
𝑛𝑛
�𝑛𝑛𝑘𝑘�𝑥𝑥 𝑘𝑘 𝑦𝑦 𝑛𝑛−𝑘𝑘
𝑘𝑘=0
nth term in an expansion �𝑛𝑛𝑘𝑘�𝑥𝑥 𝑛𝑛− 𝑘𝑘 𝑦𝑦 𝑘𝑘 where n = exponent, k = term – 1
Variance:
1 𝑛𝑛
∑ (𝑥𝑥𝑥𝑥
𝑛𝑛 𝑖𝑖=1
−
)2
Standard deviation = √(variance)
Arithmetic sequence:
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tn = tn – 1 + d
nth term: tn= t1 + (n – 1)d
sum of first n terms of arithmetic series: Sn = n[(t1 + tn)/2]
Geometric sequence: tn = rtn-1 when n ≥ 2,
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r = tn / tn – 1
nth term: tn = t1 rn – 1 where n ≥ 1
sum of first n terms of geometric series: Sn = t1[(1 – rn) / (1 – r)]
sum of infinite geometric series: S = t1/ (1 – r) if |r|< 1
y = a(x − h)2 + k or x = a(y − k)2 + h
Vertex Form Equation of a Parabola
Standard Form Equation of an Ellipse
Standard Form Equation of a Hyperbola
; c2 =a2-b2
or
(𝑥𝑥−ℎ)2
𝑎𝑎 2
−
(𝑦𝑦−𝑘𝑘)2
𝑏𝑏2
= 1 or
(𝑦𝑦−𝑘𝑘)2
𝑎𝑎 2
−
(𝑥𝑥−ℎ)2
𝑏𝑏2
= 1, c2 =a2+b2