Mathematics 2U (HSC) Resources
← All SubjectsPrimitive, by first-principle, fundamental theorem, properties of definite integral, indefinite integral applications of integration, compound areas, trapezoidal approximation
geometric application, stationary points, second derivative, max & min
calculus including: limits, differentiation - 1st principle, chain, product, quotient
Math A in-class: quadratic identity, sum & products of roots, discriminant, polynomials, logarithm and law
Math A in-class: Functions including notation, domain & range, composition, even & odd, sketching, region, transformation
These are some notes on vectors covering the theory of vectors , No examples. Also people who know vectors well please fact check me. Good Luck!
Induction Proof is a 3-step method: 1. Prove the Base Case (Multiple may be needed situationally). 2. Prove the Inductive Step. In other words: Assume that the N case is true, to prove that the N+1 case is true. 3. By the Principle of Mathematical Induction, this equation (or relevant information) is true for N [where N is in some subset of numbers]. Example Proof: Prove that 1 + 2 + 3 + ... + n = 1/2 * n (n + 1), for all positive integers n. 1. Prove the Base Case (n = 1) LHS = 1 RHS = 1/2 * 1 * (1 + 1) = 1/2 * 1 * 2 = 1 = LHS Therefore the Base Case has been proved. 2. Prove the Inductive Step Assume that 1 + 2 + 3 + ... + k = 1/2 * k (k + 1), where n = k and k is a positive integer ...........................( 1 ) To prove that 1 + 2 + 3 + ... + k + (k + 1) = 1/2 * (k + 1) (k + 2) ...........................( 2 ) LHS of ( 2 ) = 1/2 * k (k + 1) + (k + 1) = 1/2 * [k (k + 1) + 2 (k + 1)] = 1/2 * (k + 1) (k + 2) = RHS of (2) 3. Writing the essay (* for must write this statement) Because we have proved the Base Case n = 1, And we have proved that n = k + 1 is true IF n = k is true, Therefore it must be true for n = 1 + 1 = 2, n = 2 + 1 = 3, n = 3 + 1 = 4, and so on. *Therefore by the Principle of Mathematical Induction, the statement is true for all positive integers n.
Notes for the concept of Final Values and Present values in financial mathematics. All credit to Ricky
In-class work for topic Sequence and Series