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1 markAlgebraic Operations

CAPE Pure Mathematics Unit 1 · May/June 2012 · Paper 2 · Question 1(a)

The expression f(x) = 2x³ – px² + qx – 10 is divisible by x – 1 and has a remainder -6 when divided by x + 1.

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Other parts of this question

  1. 1(a)(i)the values of the constants p and q[7 marks]
  2. 1(a)(ii)the factors of f(x).[3 marks]
  3. 1(b)Find positive integers x and y such that (√x + √y)² = 16 + √240.[8 marks]
  4. 1(c)(i)Solve, for real values of x, the inequality |3x-7|≤5.[5 marks]
  5. 1(c)(ii)Show that no real solution, x, exists for the inequality |3x-7|+5≤0.[2 marks]

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