Edexcel C2 — Question 2

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
TopicBinomial Theorem (positive integer n)
TypeSingle binomial expansion
  1. find the first 4 terms, simplifying each term.
  2. Find, in its simplest form, the term independent of \(x\) in this expansion.
    [0pt] [P2 June 2004 Question 3] \item The curve \(C\) has equation \(y = \cos \left( x + \frac { \pi } { 4 } \right) , 0 \leq x \leq 2 \pi\).
  3. Sketch \(C\).
  4. Write down the exact coordinates of the points at which \(C\) meets the coordinate axes.
  5. Solve, for \(x\) in the interval \(0 \leq x \leq 2 \pi , \cos \left( x + \frac { \pi } { 4 } \right) = 0.5\), giving your answers in terms of \(\pi\). \item Given that \(\log _ { 2 } x = a\), find, in terms of \(a\), the simplest form of
  6. \(\log _ { 2 } ( 16 x )\),
  7. \(\log _ { 2 } \left( \frac { x ^ { 4 } } { 2 } \right)\).
  8. Hence, or otherwise, solve \(\log _ { 2 } ( 16 x ) - \log _ { 2 } \left( \frac { x ^ { 4 } } { 2 } \right) = \frac { 1 } { 2 }\), giving your answer in its simplest surd form. \item (a) Given that \(3 \sin x = 8 \cos x\), find the value of \(\tan x\).
  9. Find, to 1 decimal place, all the solutions of \(3 \sin x - 8 \cos x = 0\) in the interval \(0 \leq x < 360 ^ { \circ }\).
  10. Find, to 1 decimal place, all the solutions of \(3 \sin ^ { 2 } y - 8 \cos y = 0\) in the interval \(0 \leq y < 360 ^ { \circ }\). \item \end{enumerate} $$f ( x ) = \frac { \left( x ^ { 2 } - 3 \right) ^ { 2 } } { x ^ { 3 } } , x \neq 0$$
  11. Show that \(\mathrm { f } ( x ) \equiv x - 6 x ^ { - 1 } + 9 x ^ { - 3 }\).
  12. Hence, or otherwise, differentiate \(\mathrm { f } ( x )\) with respect to \(x\).
  13. Verify that the graph of \(y = \mathrm { f } ( x )\) has stationary points at \(x = \pm \sqrt { } 3\).
  14. Determine whether the stationary value at \(x = \sqrt { } 3\) is a maximum or a minimum.
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