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The names on the Wall of Fame are displayed based on the Composite score achieved by the students over the past 7 days.

The composite score is calculated based on their weighted performance in Activities, Smart sheets, Assessments and Question of the Day and Discussion forum posts.

A student needs to have attempted at least one smart sheet or assessment over the past 7 days in order to qualify for the Wall of Fame.

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Arithmetic Series
$u_n = a + (n – 1)d$
$S_n = 1/2n(a + l) = 1/2n[2a + (n – 1)d]$

Geometric Series
$u_n = ar^{(n – 1)}$
$S_n = {a{(1-r^n)}}/{1-r}$
$S_∞ = a/{1-r}$ for |r| < 1

Trigonometric identities
$sin(A±B) ≡ sin A cos B ± cos A sin B$
$cos(A±B) ≡ cos A cos B ∓ sin A sin B$
$tan(A±B) ≡ {tan A + tan B}/{1 ∓ tanA tanB}$
$sin A + sin B ≡ 2 sin {A + B}/2 cos{A - B}/2$
$sin A - sin B ≡ 2 cos {A + B}/2 sin{A - B}/2$
$cos A + cos B ≡ 2 cos {A + B}/2 cos{A - B}/2$
$cos A - cos B ≡ -2 sin {A + B}/2 sin{A - B}/2$

Statistics - Probability
$P(A∪B) = P(A) + P(B) − P(A∩B)$
$P(A∩B) = P(A) P(B|A)$
$P(A|B) = {P(B|A) P(A)}/P(B|A)P(A) + P(B|A')P(A')$

Quadratic equation
$ax^2 + bx +c = 0$ has either one or two solutions
$$x = {-b±√{(b^2 − 4ac)}/{2a} $$
Points and lines
Given two points in a plane P = $(x_1, y_1), Q = (x_2, y_2)$, you can find the following information
1. Distance between the two points $$d(P,Q) = √{{(x_2-x_1)}^2 + {(y_2-y_1)}^2}$$
2. The coordinates of the midpoint between them,$$ M =({x_1+x_2}/2, {y_1+y_2}/2)$$
3. The slope of the line through them, $$m = {(y_2 - y_1)}/{(x_2 - x_1)} = {rise}/{run} $$
Lines can be represented in three different ways,
1. Standard form = $ax + by = c$, where a, b and c are real numbers
2. Slope-intercept form = $y = mx + b$, where m is the slope and b is the y-intercept
3. Point-Slope form = $y-y_1= m (x-x_1)$, where (x_1, y_1) is any fixed point on the line
Area
Parallelogram = bh where b = base and h = height
Trapezoid = ${h/2}(b_1 + b_2)$
Ellipse = $πr_1r_2$
Triangle = $1/2bh$
Equilateral Triangle = ${√3/4}a^2$
Triangle given a,b,c = $√{s(s-a)(s-b)(s-c)}$ when s = $(a+b+c)/2$ (Heron's formula)

Volume
Cylinder = $πr^2h$
Cone = $1/3πr^2h$
Sphere = $4/3πr^3$
Ellipsoid = $4/3πr_1r_2r_3$

Surface Area
Surface area of sphere = $4πr^2$
Area of curved surface of cone = $πr x $ slant height

Algebraic Identities
${(x + y)}^2 = x^2 + 2xy + y^2$, Square of a sum
${(x - y)}^2 = x^2 - 2xy + y^2$, Square of a difference
${(x + y)}^3 = x^3 + 3x^2y + 3xy^2 + y^3$, Cube of a sum
${(x - y)}^3 = x^3 - 3x^2y + 3xy^2 - y^3$, Cube of a difference
${(x + y)}^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4$, To the power four of a sum
${(x - y)}^4 = x^4 - 4x^3y + 6x^2y^2 - 4xy^3 + y^4$, To the power four of a difference

Factoring Formulas
$x^2 - y^2 = (x + y)(x - y)$, Difference of squares
$x^3 - y^3 = (x - y)(x^2 + xy + y^2)$, Difference of cubes
$x^3 + y^3 = (x + y)(x^2 - xy + y^2)$, Sum of cubes



Exponentiation rules
For any real numbers a and b, and any rational numbers $p/q$ and $r/s$, $a^{p/q}a^{r/s} = a^{{p/q}+{r/s}} = a ^{ps+qr}/{qs}$, Product rule
$a^{p/q} / a^{r/s} = a^{{p/q}-{r/s}} = a ^{ps-qr}/{qs}$, Quotient rule
${(a^{p/q})}^{r/s} = a^{{pr}/{qs}}$, Power of power rule
${(ab)}^{p/q} = a^{p/q}b^{p/q}$, Power of product rule
${(a/b)}^{p/q} = a^{p/q}/b^{p/q}$, Power of quotient rule
${a^0} = 1$, Zero exponent
${a^{−{(p/q)}}} = 1/{a^{(p/q)}}$, Negative exponents
${1/{a^{−{(p/q)}}}} = {a^{(p/q)}}$, Negative exponents
$√^q{a} = a^{1/q}$
$√^q{a^p} = a^{p/q} = {(a^{1/q})}^p$