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7 marksAlgebraic Operations

CAPE Pure Mathematics Unit 1 · 2021 · Paper 2 · Question 1(c)

The function f(x) = ax³ + 3x² - b is divisible by 2x - 1 and has a remainder of -5 when divided by x + 2.

Calculate the values of a and b.

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Other parts of this question

  1. 1(a)(i)Complete the truth table below.[4 marks]
  2. 1(a)(ii)Hence, state whether the statements ~(p ∨ q) and ~p ∧ ~q are logically equivalent. Justify your response.[2 marks]
  3. 1(b)(i)Write the converse of the statement "n is an integer ⇒ n² is an integer".[1 mark]
  4. 1(b)(ii)Prove that * is closed in ℝ.[3 marks]
  5. 1(b)(iii)Determine whether the operation * is commutative.[2 marks]
  6. 1(d)Solve the logarithmic equation log₂ x + log₄ x + log₁₆ x = 7.[6 marks]

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