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Standard form
A way to represent numbers as ax10^k where a is between 1 and 10, and k is an integer indicating how many times a is multiplied or divided by 10.
Laws of indices
Rules to simplify expressions with exponents, including laws for multiplication, division, addition, subtraction, and powers of powers.
Partial fractions
A method to simplify rational expressions into the sum of fractions with constant numerators, aiding in integration of rational functions.
Logarithms
The inverse of exponents, where loga b = x if a^x = b, with key laws like loga xy = loga x + loga y.
Arithmetic Sequences & Series
Sequences with a constant difference between terms, with nth term formula An = a + (n-1)d and series sum formula Sn = n/2(2a + (n-1)d).
Geometric Sequences & Series
Sequences with a common ratio between terms, with nth term formula An = ar^(n-1) and series sum formula Sn = a(1-r^n)/(1-r).
Proof by Deduction
Showing a result is true for all integers, consecutive integers, or even/odd numbers.
Proof by Induction
Proving a result for a set of integers by showing it's true for one integer and the next.
Proof by Contradiction
Proving a result by showing the negation of the result is false.
Binomial Theorem
A method to expand a two-term expression raised to a power using the formula (a + b)^n = ÎŁ(n choose k) a^(n-k) b^k.
Permutations
Number of possible arrangements when order matters, calculated using nPr = n!/(n-r)!.
Combinations
Number of possible arrangements when order doesn't matter, calculated using nCr = n!/(r!(n-r)!).
Complex Numbers
Numbers represented in the complex plane, with Cartesian form z = a + bi, and operations like addition, subtraction, multiplication, and division.
Note 
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