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5 marksMatrices and Systems of Equations

CAPE Integrated Mathematics · 2017 · Paper 2 · Question 2(c)

Given that A = \begin{pmatrix} 1 & 2 & 3 \\ 0 & 4 & 5 \\ p & 0 & 0 \end{pmatrix} and \det(A) = -4, find the value of p.

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  1. 2(a)(i)Show that the expansion 2\log 2 - \frac{1}{2}\log 9 + 4\log 3, when expressed as a single logarithm is \log 108.[6 marks]
  2. 2(a)(ii)Solve \log (x + 3) = 1.[3 marks]
  3. 2(b)Let f(x) = x^3 - 6x^2 + ax - 6. If (x - 2) is a factor of f(x), find the value of a.[5 marks]
  4. 2(d)The graph shows f(x) = \sin x and g(x) = a + b\sin x. Determine the values of a and b and write the equation of g(x).[3 marks]
  5. 2(e)The first term and the second term of a geometric series are 120 and 60 respectively. Find the sum to infinity.[3 marks]

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