Questions — Edexcel P2 (157 questions)

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All questions AEA AS Paper 1 AS Paper 2 AS Pure C1 C12 C2 C3 C34 C4 CP AS CP1 CP2 D1 D2 F1 F2 F3 FD1 FD1 AS FD2 FD2 AS FM1 FM1 AS FM2 FM2 AS FP1 FP1 AS FP2 FP2 AS FP3 FS1 FS1 AS FS2 FS2 AS Further AS Paper 1 Further AS Paper 2 Discrete Further AS Paper 2 Mechanics Further AS Paper 2 Statistics Further Additional Pure Further Additional Pure AS Further Discrete Further Discrete AS Further Extra Pure Further Mechanics Further Mechanics A AS Further Mechanics AS Further Mechanics B AS Further Mechanics Major Further Mechanics Minor Further Numerical Methods Further Paper 1 Further Paper 2 Further Paper 3 Further Paper 3 Discrete Further Paper 3 Mechanics Further Paper 3 Statistics Further Paper 4 Further Pure Core Further Pure Core 1 Further Pure Core 2 Further Pure Core AS Further Pure with Technology Further Statistics Further Statistics A AS Further Statistics AS Further Statistics B AS Further Statistics Major Further Statistics Minor Further Unit 1 Further Unit 2 Further Unit 3 Further Unit 4 Further Unit 5 Further Unit 6 H240/01 H240/02 H240/03 M1 M2 M3 M4 M5 Mechanics 1 P1 P2 P3 P4 PMT Mocks PURE Paper 1 Paper 2 Paper 3 Pure 1 S1 S2 S3 S4 SPS ASFM SPS ASFM Mechanics SPS ASFM Pure SPS ASFM Statistics SPS FM SPS FM Mechanics SPS FM Pure SPS FM Statistics SPS SM SPS SM Mechanics SPS SM Pure SPS SM Statistics Stats 1 Unit 1 Unit 2 Unit 3 Unit 4
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AQA AS Paper 1 AS Paper 2 C1 C2 C3 C4 D1 D2 FP1 FP2 FP3 Further AS Paper 1 Further AS Paper 2 Discrete Further AS Paper 2 Mechanics Further AS Paper 2 Statistics Further Paper 1 Further Paper 2 Further Paper 3 Discrete Further Paper 3 Mechanics Further Paper 3 Statistics M1 M2 M3 Paper 1 Paper 2 Paper 3 S1 S2 S3 CAIE FP1 FP2 Further Paper 1 Further Paper 2 Further Paper 3 Further Paper 4 M1 M2 P1 P2 P3 S1 S2 Edexcel AEA AS Paper 1 AS Paper 2 C1 C12 C2 C3 C34 C4 CP AS CP1 CP2 D1 D2 F1 F2 F3 FD1 FD1 AS FD2 FD2 AS FM1 FM1 AS FM2 FM2 AS FP1 FP1 AS FP2 FP2 AS FP3 FS1 FS1 AS FS2 FS2 AS M1 M2 M3 M4 M5 P1 P2 P3 P4 PMT Mocks Paper 1 Paper 2 Paper 3 S1 S2 S3 S4 OCR AS Pure C1 C2 C3 C4 D1 D2 FD1 AS FM1 AS FP1 FP1 AS FP2 FP3 FS1 AS Further Additional Pure Further Additional Pure AS Further Discrete Further Discrete AS Further Mechanics Further Mechanics AS Further Pure Core 1 Further Pure Core 2 Further Pure Core AS Further Statistics Further Statistics AS H240/01 H240/02 H240/03 M1 M2 M3 M4 Mechanics 1 PURE Pure 1 S1 S2 S3 S4 Stats 1 OCR MEI AS Paper 1 AS Paper 2 C1 C2 C3 C4 D1 D2 FP1 FP2 FP3 Further Extra Pure Further Mechanics A AS Further Mechanics B AS Further Mechanics Major Further Mechanics Minor Further Numerical Methods Further Pure Core Further Pure Core AS Further Pure with Technology Further Statistics A AS Further Statistics B AS Further Statistics Major Further Statistics Minor M1 M2 M3 M4 Paper 1 Paper 2 Paper 3 S1 S2 S3 S4 SPS SPS ASFM SPS ASFM Mechanics SPS ASFM Pure SPS ASFM Statistics SPS FM SPS FM Mechanics SPS FM Pure SPS FM Statistics SPS SM SPS SM Mechanics SPS SM Pure SPS SM Statistics WJEC Further Unit 1 Further Unit 2 Further Unit 3 Further Unit 4 Further Unit 5 Further Unit 6 Unit 1 Unit 2 Unit 3 Unit 4
Edexcel P2 2018 Specimen Q3
3. $$y = \sqrt { \left( 3 ^ { x } + x \right) }$$
  1. Complete the table below, giving the values of \(y\) to 3 decimal places.
    \(x\)00.250.50.751
    \(y\)11.2512
  2. Use the trapezium rule with all the values of \(y\) from your table to find an approximation for the value of $$\int _ { 0 } ^ { 1 } \sqrt { \left( 3 ^ { x } + x \right) } \mathrm { d } x$$ You must show clearly how you obtained your answer.
  3. Explain how the trapezium rule could be used to obtain a more accurate estimate for the value of $$\int _ { 0 } ^ { 1 } \sqrt { \left( 3 ^ { x } + x \right) } d x$$
    \includegraphics[max width=\textwidth, alt={}]{0aafa21b-25f4-4f36-b914-bbaf6cae7a66-10_2673_1948_107_118}
Edexcel P2 2018 Specimen Q4
Given \(n \in \mathbb { N }\), prove, by exhaustion, that \(n ^ { 2 } + 2\) is not divisible by 4 .
\includegraphics[max width=\textwidth, alt={}, center]{0aafa21b-25f4-4f36-b914-bbaf6cae7a66-12_2658_1943_111_118}
Edexcel P2 2018 Specimen Q6
6. (i) Find the exact value of \(x\) for which $$\log _ { 2 } ( 2 x ) = \log _ { 2 } ( 5 x + 4 ) - 3$$ (ii) Given that $$\log _ { a } y + 3 \log _ { a } 2 = 5$$ express \(y\) in terms of \(a\). Give your answer in its simplest form.
\includegraphics[max width=\textwidth, alt={}, center]{0aafa21b-25f4-4f36-b914-bbaf6cae7a66-18_2674_1948_107_118}
Edexcel P2 2018 Specimen Q7
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0aafa21b-25f4-4f36-b914-bbaf6cae7a66-19_739_871_260_532} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} The circle with equation $$x ^ { 2 } + y ^ { 2 } - 20 x - 16 y + 139 = 0$$ had centre \(C\) and radius \(r\).
  1. Find the coordinates of \(C\).
  2. Show that \(r = 5\) The line with equation \(x = 13\) crosses the circle at the points \(P\) and \(Q\) as shown in Figure 1 .
  3. Find the \(y\) coordinate of \(P\) and the \(y\) coordinate of \(Q\). A tangent to the circle from \(O\) touches the circle at point \(X\).
  4. Find, in surd form, the length \(O X\).
    \includegraphics[max width=\textwidth, alt={}, center]{0aafa21b-25f4-4f36-b914-bbaf6cae7a66-22_2673_1948_107_118}
Edexcel P2 2018 Specimen Q8
8. Figure 2 Figure 2 shows a sketch of part of the curves \(C _ { 1 }\) and \(C _ { 2 }\) with equations $$\begin{array} { l l } C _ { 1 } : y = 10 x - x ^ { 2 } - 8 & x > 0
C _ { 2 } : y = x ^ { 3 } & x > 0 \end{array}$$ The curves \(C _ { 1 }\) and \(C _ { 2 }\) intersect at the points \(A\) and \(B\).
  1. Verify that the point \(A\) has coordinates (1, 1)
  2. Use algebra to find the coordinates of the point \(B\) The finite region \(R\) is bounded by \(C _ { 1 }\) and \(C _ { 2 }\)
  3. Use calculus to find the exact area of \(R\)
    \includegraphics[max width=\textwidth, alt={}, center]{0aafa21b-25f4-4f36-b914-bbaf6cae7a66-23_936_759_118_582} \includegraphics[max width=\textwidth, alt={}, center]{0aafa21b-25f4-4f36-b914-bbaf6cae7a66-26_2674_1948_107_118}
Edexcel P2 2018 Specimen Q9
9. (i) Solve, for \(0 \leqslant \theta < \pi\), the equation $$\sin 3 \theta - \sqrt { 3 } \cos 3 \theta = 0$$ giving your answers in terms of \(\pi\)
(ii) Given that $$4 \sin ^ { 2 } x + \cos x = 4 - k , \quad 0 \leqslant k \leqslant 3$$
  1. find \(\cos x\) in terms of \(k\)
  2. When \(k = 3\), find the values of \(x\) in the range \(0 \leqslant x < 360 ^ { \circ }\)
    \includegraphics[max width=\textwidth, alt={}]{0aafa21b-25f4-4f36-b914-bbaf6cae7a66-30_2671_1942_107_121}
Edexcel P2 2018 Specimen Q5
An arithmetic series has first term \(a\) and common difference \(d\).
  1. Prove that the sum of the first \(n\) terms of the series is $$\frac { 1 } { 2 } n [ 2 a + ( n - 1 ) d ]$$ A company, which is making 200 mobile phones each week, plans to increase its production. The number of mobile phones produced is to be increased by 20 each week from 200 in week 1 to 220 in week 2, to 240 in week 3 and so on, until it is producing 600 in week \(N\).
  2. Find the value of \(N\) The company then plans to continue to make 600 mobile phones each week.
  3. Find the total number of mobile phones that will be made in the first 52 weeks starting from and including week 1.
    \includegraphics[max width=\textwidth, alt={}, center]{0aafa21b-25f4-4f36-b914-bbaf6cae7a66-16_2673_1948_107_118}