April 14, 2024

Table of contents & cheatsheet (ALGEBRA)

1.1 Sequences

Arithmetic: +/− common difference

Arithmetic: +/− common difference

with u1 = a = 1st term, d = common difference.

Geometric: ×/÷ common ratio

Geometric: ×/÷ common ratio

with u1 = a = 1st term, r = common ratio.

Sigma notation

A shorthand to show the sum of a number of terms in a sequence.

sigma notation

1.2 Exponents and logarithms

Exponents

Exponents

Logarithms

    loga ax = x

    aloga b = b

Let ax = b, isolate x from the exponent: loga ax = x = loga b

Let loga x = b, isolate x from the logarithm: aloga x = x = ab

Laws of logarithms

Laws of logarithms

1.3. Binomial Expansion

In an expansion of a binomial in the form (a + b)n . Each term can be described as nCran−rbr, where nCr is the coefficient.

The full expansion can be written thus

Binomial Expansion

Find the coefficient using either pascals triangle

Binomial Expansion 1

Or the nCr function on your calculator