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5 marksSeries

CAPE Pure Mathematics Unit 2 · May/June 2007 · Paper 2 · Question 4(b)(i)

John's father gave him a loan of 10\,800 to buy a car, repaid by 12 unequal monthly instalments starting with an initial payment of P in the first month. There is no interest charged, but instalments increase by $60 per month.

Show that P = 570.

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Other parts of this question

  1. 4(a)(i)Show that f(x) = 0 has a root \alpha in the interval (0, 1).[4 marks]
  2. 4(a)(ii)If x_1 is a first approximation to \alpha of f(x) = 0 in (0, 1), show that the Newton-Raphson method gives a second approximation x_2 in (0, 1)…[5 marks]
  3. 4(b)(ii)Find, in terms of n, 1 \le n \le 12, an expression for the remaining debt on the loan after John has paid the n-th instalment.[6 marks]

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