Precalc

Partial fractions

A + B, A + B + C, A + ( Bx + C), (Ax + B) + (Cx + D)

How to find the determinant

Times the number diagonally then subtract them

Multiplicative inverse

Multiply them, row then column. You will get [1, 0/ 0, 1) . They’re inverse because you switch the top left with bottom right and make switch the signs of the rest of the members

Cramers rule

1- a1 + b1 = c1 / a2 + b2 = c2. 2- D = A1 B1/ A2 B2 then find determinant of D 3- DX = C1 , Y1 / C2 , Y2 4- DY = X1, C1 / X2 , C2 5- X = DX/D , Y= DY/D

Ellipse

Positive in between, c² = a² - b², horizontal if bigger number under x, a is bigger

Hyperbola

Negative in between, c² = a² + b², horizontal if x positive, a is first

Parabola

Y² = 4px is horizontal, x² = 4px is vertical

Arithmetic formula

An = a1 + (n-1)d

Arithmetic sum

An = n/2(a1+an)

Geometric sequence

An = a1xr^(n-1)

Geometric sum

Sn = a1(1-r^n)/1-r

Binomial theorem and combinations

N!/r!(n-r)!

Permutation

N!/(n-r)!

How to expand binomial

Use Pascal’s triangle for the coefficients

Finding center

Under x = h term, under y = k term, be careful

Where do you draw the rectangle in hyperbola

Around the endpoint b and the vertices