Questions — Edexcel (10514 questions)

Browse by module
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 P1 P2 P3 P4 PMT Mocks PURE Paper 1 Paper 2 Paper 3 Pre-U 9794/1 Pre-U 9794/2 Pre-U 9794/3 Pre-U 9795 Pre-U 9795/1 Pre-U 9795/2 S1 S2 S3 S4 Unit 1 Unit 2 Unit 3 Unit 4
Browse by board
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 PURE 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 PURE S1 S2 S3 S4 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 Pre-U Pre-U 9794/1 Pre-U 9794/2 Pre-U 9794/3 Pre-U 9795 Pre-U 9795/1 Pre-U 9795/2 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
Sort by: Default | Easiest first | Hardest first
Edexcel C1 2014 June Q3
5 marks Moderate -0.5
A sequence \(a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots\) is defined by $$\begin{array} { l l } a _ { n + 1 } = 4 a _ { n } - 3 , & n \geqslant 1 \\ a _ { 1 } = k , & \text { where } k \text { is a positive integer. } \end{array}$$
  1. Write down an expression for \(a _ { 2 }\) in terms of \(k\). Given that \(\sum _ { r = 1 } ^ { 3 } a _ { r } = 66\)
  2. find the value of \(k\).
Edexcel C1 2015 June Q2
7 marks Moderate -0.3
Solve the simultaneous equations $$\begin{gathered} y - 2 x - 4 = 0 \\ 4 x ^ { 2 } + y ^ { 2 } + 20 x = 0 \end{gathered}$$
Edexcel C1 2015 June Q4
8 marks Moderate -0.8
  1. A sequence \(U _ { 1 } , U _ { 2 } , U _ { 3 } , \ldots\) is defined by $$\begin{gathered} U _ { n + 2 } = 2 U _ { n + 1 } - U _ { n } , \quad n \geqslant 1 \\ U _ { 1 } = 4 \text { and } U _ { 2 } = 4 \end{gathered}$$ Find the value of
    1. \(U _ { 3 }\)
    2. \(\sum _ { n = 1 } ^ { 20 } U _ { n }\)
    3. Another sequence \(V _ { 1 } , V _ { 2 } , V _ { 3 } , \ldots\) is defined by
      (a) Find \(V _ { 3 }\) and \(V _ { 4 }\) in terms of \(k\). $$\begin{gathered} V _ { n + 2 } = 2 V _ { n + 1 } - V _ { n } , \quad n \geqslant 1 \\ V _ { 1 } = k \text { and } V _ { 2 } = 2 k , \text { where } k \text { is a constant } \end{gathered}$$ a) Find \(V _ { 3 }\)
Edexcel C1 2015 June Q10
10 marks Standard +0.3
A curve with equation \(y = \mathrm { f } ( x )\) passes through the point \(( 4,9 )\). Given that $$f ^ { \prime } ( x ) = \frac { 3 \sqrt { } x } { 2 } - \frac { 9 } { 4 \sqrt { } x } + 2 , \quad x > 0$$
  1. find \(\mathrm { f } ( x )\), giving each term in its simplest form. Point \(P\) lies on the curve. The normal to the curve at \(P\) is parallel to the line \(2 y + x = 0\)
  2. Find the \(x\) coordinate of \(P\).
Edexcel C1 2016 June Q3
5 marks Easy -1.3
  1. Simplify $$\sqrt { 50 } - \sqrt { 18 }$$ giving your answer in the form \(a \sqrt { 2 }\), where \(a\) is an integer.
  2. Hence, or otherwise, simplify $$\frac { 12 \sqrt { 3 } } { \sqrt { 50 } - \sqrt { 18 } }$$ giving your answer in the form \(b \sqrt { c }\), where \(b\) and \(c\) are integers and \(b \neq 1\)
Edexcel C1 Q4
5 marks Easy -1.2
A sequence \(a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots\) is defined by $$a _ { 1 } = k , \quad a _ { n + 1 } = 4 a _ { n } - 7 ,$$ where \(k\) is a constant.
  1. Write down an expression for \(a _ { 2 }\) in terms of \(k\).
  2. Find \(a _ { 3 }\) in terms of \(k\), simplifying your answer. Given that \(a _ { 3 } = 13\),
  3. find the value of \(k\).
Edexcel P2 2018 Specimen Q5
11 marks Easy -1.2
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}
Edexcel C2 2005 January Q2
6 marks Easy -1.2
The points \(A\) and \(B\) have coordinates \(( 5 , - 1 )\) and \(( 13,11 )\) respectively.
  1. Find the coordinates of the mid-point of \(A B\). Given that \(A B\) is a diameter of the circle \(C\),
  2. find an equation for \(C\).
Edexcel C2 2009 January Q2
5 marks Moderate -0.5
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{12e54724-64a3-4dc0-b7d5-6ef6cc04124c-03_870_1027_205_406} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows part of the curve \(C\) with equation \(y = ( 1 + x ) ( 4 - x )\).
The curve intersects the \(x\)-axis at \(x = - 1\) and \(x = 4\). The region \(R\), shown shaded in Figure 1, is bounded by \(C\) and the \(x\)-axis. Use calculus to find the exact area of \(R\).
Edexcel C2 2005 June Q2
6 marks Moderate -0.8
Solve
  1. \(5 ^ { x } = 8\), giving your answer to 3 significant figures,
  2. \(\log _ { 2 } ( x + 1 ) - \log _ { 2 } x = \log _ { 2 } 7\).
Edexcel C2 2005 June Q3
6 marks Moderate -0.8
  1. Use the factor theorem to show that \(( x + 4 )\) is a factor of \(2 x ^ { 3 } + x ^ { 2 } - 25 x + 12\).
  2. Factorise \(2 x ^ { 3 } + x ^ { 2 } - 25 x + 12\) completely.
Edexcel C2 2005 June Q4
6 marks Standard +0.3
  1. Write down the first three terms, in ascending powers of \(x\), of the binomial expansion of \(( 1 + p x ) ^ { 12 }\), where \(p\) is a non-zero constant. Given that, in the expansion of \(( 1 + p x ) ^ { 12 }\), the coefficient of \(x\) is \(( - q )\) and the coefficient of \(x ^ { 2 }\) is \(11 q\),
  2. find the value of \(p\) and the value of \(q\).
Edexcel C2 2006 June Q2
5 marks Easy -1.2
Use calculus to find the exact value of \(\int _ { 1 } ^ { 2 } \left( 3 x ^ { 2 } + 5 + \frac { 4 } { x ^ { 2 } } \right) \mathrm { d } x\).
Edexcel C2 2006 June Q3
4 marks Easy -1.2
  1. Write down the value of \(\log _ { 6 } 36\).
  2. Express \(2 \log _ { a } 3 + \log _ { a } 11\) as a single logarithm to base \(a\).
Edexcel C2 2006 June Q4
8 marks Moderate -0.8
$$f ( x ) = 2 x ^ { 3 } + 3 x ^ { 2 } - 29 x - 60$$
  1. Find the remainder when \(\mathrm { f } ( x )\) is divided by \(( x + 2 )\).
  2. Use the factor theorem to show that \(( x + 3 )\) is a factor of \(\mathrm { f } ( x )\).
  3. Factorise \(\mathrm { f } ( x )\) completely.
Edexcel C2 2007 June Q2
6 marks Moderate -0.8
$$f ( x ) = 3 x ^ { 3 } - 5 x ^ { 2 } - 16 x + 12$$
  1. Find the remainder when \(\mathrm { f } ( x )\) is divided by ( \(x - 2\) ). Given that \(( x + 2 )\) is a factor of \(\mathrm { f } ( x )\),
  2. factorise \(\mathrm { f } ( x )\) completely.
Edexcel C2 Specimen Q2
4 marks Easy -1.2
The circle \(C\) has centre \(( 3,4 )\) and passes through the point \(( 8 , - 8 )\). Find an equation for C
Edexcel C2 Specimen Q3
6 marks Moderate -0.8
The trapezium rule, with the table below, was used to estimate the area between the curve \(y = \sqrt { x ^ { 3 } + 1 }\), the lines \(x = 1 , x = 3\) and the \(x\)-axis.
\(x\)11.522.53
\(y\)1.4142.0923.000
  1. Calculate, to 3 decimal places, the values of \(y\) for \(x = 2.5\) and \(x = 3\).
  2. Use the values from the table and your answers to part (a) to find an estimate, to 2 decimal places, for this area.
Edexcel C3 2012 January Q2
6 marks Standard +0.3
[diagram]
Figure 1 shows the graph of equation \(y = \mathrm { f } ( x )\).
The points \(P ( - 3,0 )\) and \(Q ( 2 , - 4 )\) are stationary points on the graph.
Sketch, on separate diagrams, the graphs of
  1. \(y = 3 \mathrm { f } ( x + 2 )\)
  2. \(y = | \mathrm { f } ( x ) |\) On each diagram, show the coordinates of any stationary points.
Edexcel C3 2006 June Q2
6 marks Moderate -0.8
Differentiate, with respect to \(x\),
  1. \(\mathrm { e } ^ { 3 x } + \ln 2 x\),
  2. \(\left( 5 + x ^ { 2 } \right) ^ { \frac { 3 } { 2 } }\).
Edexcel C3 2006 June Q3
9 marks Moderate -0.3
\begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{f0f328ed-3550-4b8d-8b80-016df8773b21-04_568_881_312_504}
\end{figure} Figure 1 shows part of the curve with equation \(y = \mathrm { f } ( x ) , x \in \mathbb { R }\), where f is an increasing function of \(x\). The curve passes through the points \(P ( 0 , - 2 )\) and \(Q ( 3,0 )\) as shown. In separate diagrams, sketch the curve with equation
  1. \(y = | f ( x ) |\),
  2. \(y = \mathrm { f } ^ { - 1 } ( x )\),
  3. \(y = \frac { 1 } { 2 } \mathrm { f } ( 3 x )\). Indicate clearly on each sketch the coordinates of the points at which the curve crosses or meets the axes.
Edexcel C3 2007 June Q2
10 marks Standard +0.3
$$f ( x ) = \frac { 2 x + 3 } { x + 2 } - \frac { 9 + 2 x } { 2 x ^ { 2 } + 3 x - 2 } , \quad x > \frac { 1 } { 2 }$$
  1. Show that \(\mathrm { f } ( x ) = \frac { 4 x - 6 } { 2 x - 1 }\).
  2. Hence, or otherwise, find \(\mathrm { f } ^ { \prime } ( x )\) in its simplest form.
Edexcel C3 2011 June Q2
8 marks Standard +0.3
$$\mathrm { f } ( x ) = 2 \sin \left( x ^ { 2 } \right) + x - 2 , \quad 0 \leqslant x < 2 \pi$$
  1. Show that \(\mathrm { f } ( x ) = 0\) has a root \(\alpha\) between \(x = 0.75\) and \(x = 0.85\) The equation \(\mathrm { f } ( x ) = 0\) can be written as \(x = [ \arcsin ( 1 - 0.5 x ) ] ^ { \frac { 1 } { 2 } }\).
  2. Use the iterative formula $$x _ { n + 1 } = \left[ \arcsin \left( 1 - 0.5 x _ { n } \right) \right] ^ { \frac { 1 } { 2 } } , \quad x _ { 0 } = 0.8$$ to find the values of \(x _ { 1 } , x _ { 2 }\) and \(x _ { 3 }\), giving your answers to 5 decimal places.
  3. Show that \(\alpha = 0.80157\) is correct to 5 decimal places.
Edexcel C3 2012 June Q8
12 marks Standard +0.3
$$f ( x ) = 7 \cos 2 x - 24 \sin 2 x$$ Given that \(\mathrm { f } ( x ) = R \cos ( 2 x + \alpha )\), where \(R > 0\) and \(0 < \alpha < 90 ^ { \circ }\),
  1. find the value of \(R\) and the value of \(\alpha\).
  2. Hence solve the equation $$7 \cos 2 x - 24 \sin 2 x = 12.5$$ for \(0 \leqslant x < 180 ^ { \circ }\), giving your answers to 1 decimal place.
  3. Express \(14 \cos ^ { 2 } x - 48 \sin x \cos x\) in the form \(a \cos 2 x + b \sin 2 x + c\), where \(a , b\), and \(c\) are constants to be found.
  4. Hence, using your answers to parts (a) and (c), deduce the maximum value of $$14 \cos ^ { 2 } x - 48 \sin x \cos x$$
Edexcel C4 2009 January Q2
9 marks Moderate -0.3
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a5579938-e202-4543-8513-6483ede49850-03_410_552_205_694} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows part of the curve \(y = \frac { 3 } { \sqrt { } ( 1 + 4 x ) }\). The region \(R\) is bounded by the curve, the \(x\)-axis, and the lines \(x = 0\) and \(x = 2\), as shown shaded in Figure 1.
  1. Use integration to find the area of \(R\). The region \(R\) is rotated \(360 ^ { \circ }\) about the \(x\)-axis.
  2. Use integration to find the exact value of the volume of the solid formed.