Arithmetic and financial maths
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Be familiar with the following terms and how to find them: order of magnitude, accumulate error, percentage error, tolerance, cost price, selling price, loss, discount, mark up (profit as a % of cost price), margin (profit as a % of selling price).
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Be able to complete calculations involving income tax and net pay.
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Be able to calculate compound interest and depreciation (reducing balance method)
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It’s very important that students can change interest rates, depending on the time intervals.
Example: Find the AER that is equivalent to a monthly interest rate of 0.25%.
Let i = annual interest rate. Therefore the annual rate is 3%.
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You should be able to use the sum of a geometric series to complete calculations
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Be able to derive the formula for a mortgage repayment.
Proof by induction: There are three types of proof by induction that can be asked. A proof involving inequalities has never been examined. Students can also be asked to prove De Moivre’s theorem by induction.
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Simple identities
Example: Prove, by induction, that the sum of the first n natural numbers,
⋯
1+2+3+ + n is . Example: Prove by induction that ● Simple inequalities
Example: Prove by induction that
∈
n!>2n for all n N,n ≥4
Example: Prove by induction that n∈
2n ≥ n2 for all N,n ≥4
Example: Prove by induction that, for x > –1, ∈N
(1+ x)n ≥1+ nx for all n
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Factorisation/divisibility proofs
Example: Prove by induction that 3 is a ∈N factor of 4n – 1 for all n involving present and future values. Remember to use future value when investing money and present values for loans.