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2 marksAlgebraic Operations

CAPE Pure Mathematics Unit 1 · May/June 2011 · Paper 2 · Question 1(b)(i)

A diagram, not drawn to scale, shows a segment of the graph of the function f(x) = x³ + mx² + nx + p, where m, n and p are constants. The graph passes through (0,4), (1,0) and (2,0).

Find the value of p

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Other parts of this question

  1. 1(a)(i)Find the exact value of (√75 + √12)² - (√75 - √12)²[3 marks]
  2. 1(a)(ii)Find the exact value of 27^(3/4) x 9^(3/8) x 81^(1/8)[3 marks]
  3. 1(b)(ii)Find the values of m and n[4 marks]
  4. 1(b)(iii)Find the x-coordinate of the point Q.[2 marks]
  5. 1(c)(i)By substituting y = log₂x, or otherwise, solve, for x, the equation √log₂x = log₂(√x).[6 marks]
  6. 1(c)(ii)Solve, for real values of x, the inequality x² - |x| - 12 < 0.[5 marks]

More practice: the rest of this paper · more Algebraic Operations questions · all CAPE Pure Mathematics Unit 1 past papers