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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
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Edexcel C2 2017 June Q2
4 marks Standard +0.3
2. In the triangle \(A B C , A B = 16 \mathrm {~cm} , A C = 13 \mathrm {~cm}\), angle \(A B C = 50 ^ { \circ }\) and angle \(B C A = x ^ { \circ }\) Find the two possible values for \(x\), giving your answers to one decimal place.
\includegraphics[max width=\textwidth, alt={}, center]{752efc6c-8d0e-46a6-b75d-5125956969d8-05_104_107_2631_1774}
Edexcel C2 2017 June Q3
6 marks Moderate -0.8
3. (a) \(\quad y = 5 ^ { x } + \log _ { 2 } ( x + 1 ) , \quad 0 \leqslant x \leqslant 2\) Complete the table below, by giving the value of \(y\) when \(x = 1\)
\(x\)00.511.52
\(y\)12.82112.50226.585
(b) Use the trapezium rule, with all the values of \(y\) from the completed table, to find an approximate value for $$\int _ { 0 } ^ { 2 } \left( 5 ^ { x } + \log _ { 2 } ( x + 1 ) \right) \mathrm { d } x$$ giving your answer to 2 decimal places.
(c) Use your answer to part (b) to find an approximate value for $$\int _ { 0 } ^ { 2 } \left( 5 + 5 ^ { x } + \log _ { 2 } ( x + 1 ) \right) d x$$ giving your answer to 2 decimal places.
Edexcel C2 2017 June Q4
8 marks Standard +0.3
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{752efc6c-8d0e-46a6-b75d-5125956969d8-10_508_960_212_477} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Diagram not drawn to scale Figure 1 is a sketch representing the cross-section of a large tent \(A B C D E F\). \(A B\) and \(D E\) are line segments of equal length.
Angle \(F A B\) and angle \(D E F\) are equal.
\(F\) is the midpoint of the straight line \(A E\) and \(F C\) is perpendicular to \(A E\).
\(B C D\) is an arc of a circle of radius 3.5 m with centre at \(F\).
It is given that $$\begin{aligned} A F & = F E = 3.7 \mathrm {~m} \\ B F & = F D = 3.5 \mathrm {~m} \\ \text { angle } B F D & = 1.77 \text { radians } \end{aligned}$$ Find
  1. the length of the arc \(B C D\) in metres to 2 decimal places,
  2. the area of the sector \(F B C D\) in \(\mathrm { m } ^ { 2 }\) to 2 decimal places,
  3. the total area of the cross-section of the tent in \(\mathrm { m } ^ { 2 }\) to 2 decimal places.
Edexcel C2 2017 June Q5
7 marks Moderate -0.8
5. The circle \(C\) has equation $$x ^ { 2 } + y ^ { 2 } - 10 x + 6 y + 30 = 0$$ Find
  1. the coordinates of the centre of \(C\),
  2. the radius of \(C\),
  3. the \(y\) coordinates of the points where the circle \(C\) crosses the line with equation \(x = 4\), giving your answers as simplified surds.
Edexcel C2 2017 June Q6
9 marks Standard +0.3
6. $$f ( x ) = - 6 x ^ { 3 } - 7 x ^ { 2 } + 40 x + 21$$
  1. Use the factor theorem to show that \(( x + 3 )\) is a factor of \(\mathrm { f } ( x )\)
  2. Factorise f(x) completely.
  3. Hence solve the equation $$6 \left( 2 ^ { 3 y } \right) + 7 \left( 2 ^ { 2 y } \right) = 40 \left( 2 ^ { y } \right) + 21$$ giving your answer to 2 decimal places.
Edexcel C2 2017 June Q7
7 marks Moderate -0.3
7. (i) \(2 \log ( x + a ) = \log \left( 16 a ^ { 6 } \right)\), where \(a\) is a positive constant Find \(x\) in terms of \(a\), giving your answer in its simplest form.
(ii) \(\quad \log _ { 3 } ( 9 y + b ) - \log _ { 3 } ( 2 y - b ) = 2\), where \(b\) is a positive constant Find \(y\) in terms of \(b\), giving your answer in its simplest form.
Edexcel C2 2017 June Q8
8 marks Moderate -0.3
8. (a) Show that the equation $$\cos ^ { 2 } x = 8 \sin ^ { 2 } x - 6 \sin x$$ can be written in the form $$( 3 \sin x - 1 ) ^ { 2 } = 2$$ (b) Hence solve, for \(0 \leqslant x < 360 ^ { \circ }\), $$\cos ^ { 2 } x = 8 \sin ^ { 2 } x - 6 \sin x$$ giving your answers to 2 decimal places.
Edexcel C2 2017 June Q9
12 marks Standard +0.3
9. The first three terms of a geometric sequence are $$7 k - 5,5 k - 7,2 k + 10$$ where \(k\) is a constant.
  1. Show that \(11 k ^ { 2 } - 130 k + 99 = 0\) Given that \(k\) is not an integer,
  2. show that \(k = \frac { 9 } { 11 }\) For this value of \(k\),
    1. evaluate the fourth term of the sequence, giving your answer as an exact fraction,
    2. evaluate the sum of the first ten terms of the sequence.
Edexcel C2 2017 June Q10
10 marks Standard +0.3
10. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{752efc6c-8d0e-46a6-b75d-5125956969d8-28_761_1120_258_411} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows a sketch of part of the curve with equation $$y = 4 x ^ { 3 } + 9 x ^ { 2 } - 30 x - 8 , \quad - 0.5 \leqslant x \leqslant 2.2$$ The curve has a turning point at the point \(A\).
  1. Using calculus, show that the \(x\) coordinate of \(A\) is 1 The curve crosses the \(x\)-axis at the points \(B ( 2,0 )\) and \(C \left( - \frac { 1 } { 4 } , 0 \right)\) The finite region \(R\), shown shaded in Figure 2, is bounded by the curve, the line \(A B\), and the \(x\)-axis.
  2. Use integration to find the area of the finite region \(R\), giving your answer to 2 decimal places.
Edexcel C2 2018 June Q1
5 marks Moderate -0.8
1. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8daf56fa-bfce-454e-bbb8-fecd8170d77e-02_575_812_214_566} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of part of the curve with equation $$y = \frac { ( x + 2 ) ^ { \frac { 3 } { 2 } } } { 4 } , \quad x \geqslant - 2$$ The finite region \(R\), shown shaded in Figure 1, is bounded by the curve, the \(x\)-axis and the line with equation \(x = 10\) The table below shows corresponding values of \(x\) and \(y\) for \(y = \frac { ( x + 2 ) ^ { \frac { 3 } { 2 } } } { 4 }\)
  1. Complete the table, giving values of \(y\) corresponding to \(x = 2\) and \(x = 6\)
    \(x\)- 22610
    \(y\)0\(6 \sqrt { } 3\)
  2. Use the trapezium rule, with all the values of \(y\) from the completed table, to find an approximate value for the area of \(R\), giving your answer to 3 decimal places.
Edexcel C2 2018 June Q2
7 marks Moderate -0.8
  1. (a) Find the first 4 terms, in ascending powers of \(x\), of the binomial expansion of
$$( 2 + k x ) ^ { 7 }$$ where \(k\) is a non-zero constant. Give each term in its simplest form. Given that the coefficient of \(x ^ { 3 }\) in this expansion is 1890
(b) find the value of \(k\).
Edexcel C2 2018 June Q3
8 marks Moderate -0.3
3. $$f ( x ) = 24 x ^ { 3 } + A x ^ { 2 } - 3 x + B$$ where \(A\) and \(B\) are constants.
When \(\mathrm { f } ( x )\) is divided by \(( 2 x - 1 )\) the remainder is 30
  1. Show that \(A + 4 B = 114\) Given also that ( \(x + 1\) ) is a factor of \(\mathrm { f } ( x )\),
  2. find another equation in \(A\) and \(B\).
  3. Find the value of \(A\) and the value of \(B\).
  4. Hence find a quadratic factor of \(\mathrm { f } ( x )\).
Edexcel C2 2018 June Q4
9 marks Moderate -0.3
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8daf56fa-bfce-454e-bbb8-fecd8170d77e-10_310_716_214_621} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Not to scale Figure 2 shows a flag \(X Y W Z X\). The flag consists of a triangle \(X Y Z\) joined to a sector \(Z Y W\) of a circle with radius 5 cm and centre \(Y\). The angle of the sector, angle \(Z Y W\), is 0.7 radians. The points \(X , Y\) and \(W\) lie on a straight line with \(X Y = 7 \mathrm {~cm}\) and \(Y W = 5 \mathrm {~cm}\). Find
  1. the area of the sector \(Z Y W\) in \(\mathrm { cm } ^ { 2 }\),
  2. the area of the flag, in \(\mathrm { cm } ^ { 2 }\), to 2 decimal places,
  3. the length of the perimeter, \(X Y W Z X\), of the flag, in cm to 2 decimal places.
Edexcel C2 2018 June Q5
10 marks Moderate -0.8
  1. The circle \(C\) has equation
$$x ^ { 2 } + y ^ { 2 } - 2 x + 14 y = 0$$ Find
  1. the coordinates of the centre of \(C\),
  2. the exact value of the radius of \(C\),
  3. the \(y\) coordinates of the points where the circle \(C\) crosses the \(y\)-axis.
  4. Find an equation of the tangent to \(C\) at the point ( 2,0 ), giving your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers.
Edexcel C2 2018 June Q6
7 marks Moderate -0.8
  1. A geometric series with common ratio \(r = - 0.9\) has sum to infinity 10000 For this series,
    1. find the first term,
    2. find the fifth term,
    3. find the sum of the first twelve terms, giving this answer to the nearest integer.
Edexcel C2 2018 June Q7
8 marks Moderate -0.3
7. (i) Find the value of \(y\) for which $$1.01 ^ { y - 1 } = 500$$ Give your answer to 2 decimal places.
(ii) Given that $$2 \log _ { 4 } ( 3 x + 5 ) = \log _ { 4 } ( 3 x + 8 ) + 1 , \quad x > - \frac { 5 } { 3 }$$
  1. show that $$9 x ^ { 2 } + 18 x - 7 = 0$$
  2. Hence solve the equation $$2 \log _ { 4 } ( 3 x + 5 ) = \log _ { 4 } ( 3 x + 8 ) + 1 , \quad x > - \frac { 5 } { 3 }$$ DO NOTI WRITE IN THIS AREA
Edexcel C2 2018 June Q8
9 marks Moderate -0.3
8 In this question solutions based entirely on graphical or numerical methods are not acceptable.
  1. Solve for \(0 \leqslant x < 360 ^ { \circ }\), $$4 \cos \left( x + 70 ^ { \circ } \right) = 3$$ giving your answers in degrees to one decimal place.
  2. Find, for \(0 \leqslant \theta < 2 \pi\), all the solutions of $$6 \cos ^ { 2 } \theta - 5 = 6 \sin ^ { 2 } \theta + \sin \theta$$ giving your answers in radians to 3 significant figures.
Edexcel C2 2018 June Q9
12 marks Standard +0.3
9. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8daf56fa-bfce-454e-bbb8-fecd8170d77e-28_751_876_214_539} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Figure 3 shows a sketch of part of the curve with equation $$y = 7 x ^ { 2 } ( 5 - 2 \sqrt { x } ) , \quad x \geqslant 0$$ The curve has a turning point at the point \(A\), where \(x > 0\), as shown in Figure 3.
  1. Using calculus, find the coordinates of the point \(A\). The curve crosses the \(x\)-axis at the point \(B\), as shown in Figure 3.
  2. Use algebra to find the \(x\) coordinate of the point \(B\). The finite region \(R\), shown shaded in Figure 3, is bounded by the curve, the line through \(A\) parallel to the \(x\)-axis and the line through \(B\) parallel to the \(y\)-axis.
  3. Use integration to find the area of the region \(R\), giving your answer to 2 decimal places.
    END
Edexcel C2 Q1
4 marks Moderate -0.8
1. $$f ( x ) = 2 x ^ { 3 } - x ^ { 2 } + p x + 6$$ where \(p\) is a constant.
Given that \(( x - 1 )\) is a factor of \(\mathrm { f } ( x )\), find
  1. the value of \(p\),
  2. the remainder when \(\mathrm { f } ( x )\) is divided by \(( 2 x + 1 )\).
Edexcel C2 Q2
5 marks Easy -1.3
2. (a) Find \(\quad \int \left( 3 + 4 x ^ { 3 } - \frac { 2 } { x ^ { 2 } } \right) \mathrm { d } x\).
(b) Hence evaluate \(\quad \int _ { 1 } ^ { 2 } \left( 3 + 4 x ^ { 3 } - \frac { 2 } { x ^ { 2 } } \right) \mathrm { d } x\).
\includegraphics[max width=\textwidth, alt={}]{9e4e1626-238b-4afd-b81c-68c5ab1624c2-04_2573_1927_146_52}
Edexcel C2 Q4
6 marks Standard +0.3
  1. Solve
$$2 \log _ { 3 } x - \log _ { 3 } ( x - 2 ) = 2 , \quad x > 2 .$$
Edexcel C2 Q5
7 marks Moderate -0.3
5. The second and fifth terms of a geometric series are 9 and 1.125 respectively. For this series find
  1. the value of the common ratio,
  2. the first term,
  3. the sum to infinity.
    5.
    continued
Edexcel C2 Q6
7 marks Standard +0.3
  1. The circle \(C\), with centre \(A\), has equation
$$x ^ { 2 } + y ^ { 2 } - 6 x + 4 y - 12 = 0$$
  1. Find the coordinates of \(A\).
  2. Show that the radius of \(C\) is 5 . The points \(P , Q\) and \(R\) lie on \(C\). The length of \(P Q\) is 10 and the length of \(P R\) is 3 .
  3. Find the length of \(Q R\), giving your answer to 1 decimal place.
    \includegraphics[max width=\textwidth, alt={}]{9e4e1626-238b-4afd-b81c-68c5ab1624c2-09_2540_1718_150_93}
Edexcel C2 Q7
8 marks Standard +0.8
  1. The first four terms, in ascending powers of \(x\), of the binomial expansion of \(( 1 + k x ) ^ { n }\) are
$$1 + A x + B x ^ { 2 } + B x ^ { 3 } + \ldots$$ where \(k\) is a positive constant and \(A\), \(B\) and \(n\) are positive integers.
  1. By considering the coefficients of \(x ^ { 2 }\) and \(x ^ { 3 }\), show that \(3 = ( n - 2 ) k\). Given that \(A = 4\),
  2. find the value of \(n\) and the value of \(k\).
    7. continuedLeave blank
Edexcel C2 Q8
10 marks Moderate -0.3
  1. (a) Solve, for \(0 \leq x < 360 ^ { \circ }\), the equation \(\cos \left( x - 20 ^ { \circ } \right) = - 0.437\), giving your answers to the nearest degree.
    (b) Find the exact values of \(\theta\) in the interval \(0 \leq \theta < 360 ^ { \circ }\) for which
$$3 \tan \theta = 2 \cos \theta$$
\includegraphics[max width=\textwidth, alt={}]{9e4e1626-238b-4afd-b81c-68c5ab1624c2-13_2536_1737_150_98}