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 2018 June Q1
5 marks Easy -1.3
  1. (i) Simplify
$$\sqrt { 48 } - \frac { 6 } { \sqrt { 3 } }$$ Write your answer in the form \(a \sqrt { 3 }\), where \(a\) is an integer to be found.
(ii) Solve the equation $$3 ^ { 6 x - 3 } = 81$$ Write your answer as a rational number.
Edexcel C1 2018 June Q2
7 marks Easy -1.3
  1. Given
$$y = 3 \sqrt { x } - 6 x + 4 , \quad x > 0$$
  1. find \(\int y \mathrm {~d} x\), simplifying each term.
    1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\)
    2. Hence find the value of \(x\) such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 0\)
Edexcel C1 2018 June Q3
6 marks Moderate -0.8
3. $$f ( x ) = x ^ { 2 } - 10 x + 23$$
  1. Express \(\mathrm { f } ( x )\) in the form \(( x + a ) ^ { 2 } + b\), where \(a\) and \(b\) are constants to be found.
  2. Hence, or otherwise, find the exact solutions to the equation $$x ^ { 2 } - 10 x + 23 = 0$$
  3. Use your answer to part (b) to find the larger solution to the equation $$y - 10 y ^ { 0.5 } + 23 = 0$$ Write your solution in the form \(p + q \sqrt { r }\), where \(p , q\) and \(r\) are integers.
Edexcel C1 2018 June Q4
7 marks Easy -1.3
  1. Each year, Andy pays into a savings scheme. In year one he pays in \(\pounds 600\). His payments increase by \(\pounds 120\) each year so that he pays \(\pounds 720\) in year two, \(\pounds 840\) in year three and so on, so that his payments form an arithmetic sequence.
    1. Find out how much Andy pays into the savings scheme in year ten.
      (2)
    Kim starts paying money into a different savings scheme at the same time as Andy. In year one she pays in \(\pounds 130\). Her payments increase each year so that she pays \(\pounds 210\) in year two, \(\pounds 290\) in year three and so on, so that her payments form a different arithmetic sequence. At the end of year \(N\), Andy has paid, in total, twice as much money into his savings scheme as Kim has paid, in total, into her savings scheme.
  2. Find the value of \(N\).
Edexcel C1 2018 June Q5
5 marks Moderate -0.8
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{937246f9-2b6a-48df-b919-c6db3d6f863b-12_963_1239_255_354} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows the sketch of a curve with equation \(y = \mathrm { f } ( x ) , x \in \mathbb { R }\). The curve crosses the \(y\)-axis at \(( 0,4 )\) and crosses the \(x\)-axis at \(( 5,0 )\). The curve has a single turning point, a maximum, at (2, 7). The line with equation \(y = 1\) is the only asymptote to the curve.
  1. State the coordinates of the turning point on the curve with equation \(y = \mathrm { f } ( x - 2 )\).
  2. State the solution of the equation f( \(2 x\) ) \(= 0\)
  3. State the equation of the asymptote to the curve with equation \(y = \mathrm { f } ( - x )\). Given that the line with equation \(y = k\), where \(k\) is a constant, meets the curve \(y = \mathrm { f } ( x )\) at only one point,
  4. state the set of possible values for \(k\).
Edexcel C1 2018 June Q6
7 marks Moderate -0.8
  1. A sequence \(a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots\) is defined by
$$\begin{aligned} a _ { 1 } & = 4 \\ a _ { n + 1 } & = \frac { a _ { n } } { a _ { n } + 1 } , \quad n \geqslant 1 , n \in \mathbb { N } \end{aligned}$$
  1. Find the values of \(a _ { 2 } , a _ { 3 }\) and \(a _ { 4 }\) Write your answers as simplified fractions. Given that $$a _ { n } = \frac { 4 } { p n + q } , \text { where } p \text { and } q \text { are constants }$$
  2. state the value of \(p\) and the value of \(q\).
  3. Hence calculate the value of \(N\) such that \(a _ { N } = \frac { 4 } { 321 }\)
Edexcel C1 2018 June Q7
8 marks Moderate -0.3
  1. The equation \(20 x ^ { 2 } = 4 k x - 13 k x ^ { 2 } + 2\), where \(k\) is a constant, has no real roots.
    1. Show that \(k\) satisfies the inequality
    $$2 k ^ { 2 } + 13 k + 20 < 0$$
  2. Find the set of possible values for \(k\).
Edexcel C1 2018 June Q8
8 marks Moderate -0.3
8. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{937246f9-2b6a-48df-b919-c6db3d6f863b-20_1063_1319_251_365} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows the straight line \(l _ { 1 }\) with equation \(4 y = 5 x + 12\)
  1. State the gradient of \(l _ { 1 }\) The line \(l _ { 2 }\) is parallel to \(l _ { 1 }\) and passes through the point \(E ( 12,5 )\), as shown in Figure 2.
  2. Find the equation of \(l _ { 2 }\). Write your answer in the form \(y = m x + c\), where \(m\) and \(c\) are constants to be determined. The line \(l _ { 2 }\) cuts the \(x\)-axis at the point \(C\) and the \(y\)-axis at the point \(B\).
  3. Find the coordinates of
    1. the point \(B\),
    2. the point \(C\). The line \(l _ { 1 }\) cuts the \(y\)-axis at the point \(A\).
      The point \(D\) lies on \(l _ { 1 }\) such that \(A B C D\) is a parallelogram, as shown in Figure 2.
  4. Find the area of \(A B C D\).
Edexcel C1 2018 June Q9
12 marks Moderate -0.3
  1. The curve \(C\) has equation \(y = \mathrm { f } ( x )\), where
$$f ^ { \prime } ( x ) = ( x - 3 ) ( 3 x + 5 )$$ Given that the point \(P ( 1,20 )\) lies on \(C\),
  1. find \(\mathrm { f } ( x )\), simplifying each term.
  2. Show that $$f ( x ) = ( x - 3 ) ^ { 2 } ( x + A )$$ where \(A\) is a constant to be found.
  3. Sketch the graph of \(C\). Show clearly the coordinates of the points where \(C\) cuts or meets the \(x\)-axis and where \(C\) cuts the \(y\)-axis.
Edexcel C1 2018 June Q10
10 marks Standard +0.3
10. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{937246f9-2b6a-48df-b919-c6db3d6f863b-28_643_1171_260_518} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Figure 3 shows a sketch of part of the curve \(C\) with equation $$y = \frac { 1 } { 2 } x + \frac { 27 } { x } - 12 , \quad x > 0$$ The point \(A\) lies on \(C\) and has coordinates \(\left( 3 , - \frac { 3 } { 2 } \right)\).
  1. Show that the equation of the normal to \(C\) at \(A\) can be written as \(10 y = 4 x - 27\) The normal to \(C\) at \(A\) meets \(C\) again at the point \(B\), as shown in Figure 3.
  2. Use algebra to find the coordinates of \(B\).
Edexcel C1 Q1
3 marks Easy -1.2
  1. Solve the inequality \(10 + x ^ { 2 } > x ( x - 2 )\).
    (3)
Edexcel C1 Q2
4 marks Easy -1.2
2. Find \(\int \left( x ^ { 2 } - \frac { 1 } { x ^ { 2 } } + \sqrt [ 3 ] { x } \right) \mathrm { d } x\)
Edexcel C1 Q3
4 marks Easy -1.8
Find the value of
  1. \(81 ^ { \frac { 1 } { 2 } }\),
  2. \(81 ^ { \frac { 3 } { 4 } }\),
  3. \(81 ^ { - \frac { 3 } { 4 } }\).
Edexcel C1 Q5
7 marks Moderate -0.8
5. (a) Show that eliminating \(y\) from the equations $$\begin{gathered} 2 x + y = 8 \\ 3 x ^ { 2 } + x y = 1 \end{gathered}$$ produces the equation $$x ^ { 2 } + 8 x - 1 = 0$$ (b) Hence solve the simultaneous equations $$\begin{gathered} 2 x + y = 8 \\ 3 x ^ { 2 } + x y = 1 \end{gathered}$$ giving your answers in the form \(a + b \sqrt { } 17\), where \(a\) and \(b\) are integers.
5. continuedLeave blank
Edexcel C1 Q6
9 marks Easy -1.2
6. $$f ( x ) = \frac { ( 2 x + 1 ) ( x + 4 ) } { \sqrt { x } } , \quad x > 0$$
  1. Show that \(\mathrm { f } ( x )\) can be written in the form \(P x ^ { \frac { 3 } { 2 } } + Q x ^ { \frac { 1 } { 2 } } + R x ^ { - \frac { 1 } { 2 } }\), stating the values of the constants \(P , Q\) and \(R\).
  2. Find f \({ } ^ { \prime } ( x )\).
  3. Show that the tangent to the curve with equation \(y = \mathrm { f } ( x )\) at the point where \(x = 1\) is parallel to the line with equation \(2 y = 11 x + 3\).
    (3)
    6. continuedLeave blank
Edexcel C1 Q7
9 marks Moderate -0.8
7. (a) Factorise completely \(x ^ { 3 } - 4 x\).
(3)
(b) Sketch the curve with equation \(y = x ^ { 3 } - 4 x\), showing the coordinates of the points where the curve crosses the \(x\)-axis.
(3)
(c) On a separate diagram, sketch the curve with equation \(y = ( x - 1 ) ^ { 3 } - 4 ( x - 1 ) ,\) showing the coordinates of the points where the curve crosses the \(x\)-axis.
(3)
\end{tabular} & Leave blank
\hline \end{tabular} \end{center}
\includegraphics[max width=\textwidth, alt={}]{6400bb0c-f199-45f2-a4b1-55534e2c63b0-11_2608_1924_141_75}
\begin{center} \begin{tabular}{|l|l|} \hline \begin{tabular}{l}
Edexcel C1 Q8
10 marks Moderate -0.8
8. The straight line \(l _ { 1 }\) has equation \(y = 3 x - 6\).
The straight line \(l _ { 2 }\) is perpendicular to \(l _ { 1 }\) and passes through the point (6, 2).
  1. Find an equation for \(l _ { 2 }\) in the form \(y = m x + c\), where \(m\) and \(c\) are constants.
    (3)
    The lines \(l _ { 1 }\) and \(l _ { 2 }\) intersect at the point \(C\).
  2. Use algebra to find the coordinates of \(C\).
    (3)
    The lines \(l _ { 1 }\) and \(l _ { 2 }\) cross the \(x\)-axis at the points \(A\) and \(B\) respectively.
  3. Calculate the exact area of triangle \(A B C\).
    (4) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \end{tabular} & Leave blank
    \hline \end{tabular} \end{center}
    8. continuedLeave blank
    \begin{center} \begin{tabular}{|l|l|} \hline \begin{tabular}{l}
Edexcel C1 Q9
11 marks Moderate -0.8
9. 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 \(\frac { 1 } { 2 } n [ 2 a + ( n - 1 ) d ] .\) (4)
    A polygon has 16 sides. The lengths of the sides of the polygon, starting with the shortest side, form an arithmetic sequence with common difference \(d \mathrm {~cm}\).
    The longest side of the polygon has length 6 cm and the perimeter of the polygon is 72 cm .
    Find
  2. the length of the shortest side of the polygon,
    (5)
  3. the value of \(d\).
    (2) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \end{tabular} & Leave blank
    \hline \end{tabular} \end{center}
    Leave blank
    \begin{center} \begin{tabular}{|l|l|} \hline \begin{tabular}{l}
Edexcel C1 Q10
13 marks Moderate -0.8
10. For the curve \(C\) with equation \(y = \mathrm { f } ( x )\), \(\frac { d y } { d x } = x ^ { 3 } + 2 x - 7 .\)
  1. Find \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\).
    (2)
  2. Show that \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } \geq 2\) for all values of \(x\).
    (1)
    Given that the point \(P ( 2,4 )\) lies on \(C\),
  3. find \(y\) in terms of \(x\),
    (5)
  4. find an equation for the normal to \(C\) at \(P\) in the form \(a x + b y + c = 0\), where \(a\), \(b\) and \(c\) are integers.
    (5)
    1. continued
Edexcel P2 2020 January Q1
7 marks Standard +0.3
  1. The table below shows corresponding values of \(x\) and \(y\) for \(y = \log _ { 2 } ( 2 x )\)
The values of \(y\) are given to 2 decimal places as appropriate. Using the trapezium rule with all the values of \(y\) in the given table,
  1. obtain an estimate for \(\int _ { 2 } ^ { 14 } \log _ { 2 } ( 2 x ) \mathrm { d } x\), giving your answer to one decimal place. Using your answer to part (a) and making your method clear, estimate
    1. \(\quad \int _ { 2 } ^ { 14 } \frac { \log _ { 2 } \left( 4 x ^ { 2 } \right) } { 5 } \mathrm {~d} x\)
    2. \(\int _ { 2 } ^ { 14 } \log _ { 2 } \left( \frac { 2 } { x } \right) \mathrm { d } x\)
      \(x\)2581114
      \(y\)23.3244.464.81
Edexcel P2 2020 January Q2
7 marks Standard +0.3
2. One of the terms in the binomial expansion of \(( 3 + a x ) ^ { 6 }\), where \(a\) is a constant, is \(540 x ^ { 4 }\)
  1. Find the possible values of \(a\).
  2. Hence find the term independent of \(x\) in the expansion of $$\left( \frac { 1 } { 81 } + \frac { 1 } { x ^ { 6 } } \right) ( 3 + a x ) ^ { 6 }$$
Edexcel P2 2020 January Q3
8 marks Standard +0.3
3. $$f ( x ) = 6 x ^ { 3 } + 17 x ^ { 2 } + 4 x - 12$$
  1. Use the factor theorem to show that ( \(2 x + 3\) ) is a factor of \(\mathrm { f } ( x )\).
  2. Hence, using algebra, write \(\mathrm { f } ( x )\) as a product of three linear factors.
  3. Solve, for \(\frac { \pi } { 2 } < \theta < \pi\), the equation $$6 \tan ^ { 3 } \theta + 17 \tan ^ { 2 } \theta + 4 \tan \theta - 12 = 0$$ giving your answers to 3 significant figures.
Edexcel P2 2020 January Q4
6 marks Moderate -0.8
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{08aac50c-7317-4510-927a-7f5f2e00f485-08_858_654_118_671} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of the curve with equation $$y = 2 x ^ { 2 } + 7 \quad x \geqslant 0$$ The finite region \(R\), shown shaded in Figure 1, is bounded by the curve, the \(y\)-axis and the line with equation \(y = 17\) Find the exact area of \(R\).
Edexcel P2 2020 January Q5
8 marks Moderate -0.3
5. In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. A colony of bees is being studied. The number of bees in the colony at the start of the study was 30000 Three years after the start of the study, the number of bees in the colony is 34000 A model predicts that the number of bees in the colony will increase by \(p \%\) each year, so that the number of bees in the colony at the end of each year of study forms a geometric sequence. Assuming the model,
  1. find the value of \(p\), giving your answer to 2 decimal places. According to the model, at the end of \(N\) years of study the number of bees in the colony exceeds 75000
  2. Find, showing all steps in your working, the smallest integer value of \(N\).
Edexcel P2 2020 January Q6
8 marks Standard +0.3
6. The circle \(C\) has equation $$x ^ { 2 } + y ^ { 2 } + 6 x - 4 y - 14 = 0$$
  1. Find
    1. the coordinates of the centre of \(C\),
    2. the exact radius of \(C\). The line with equation \(y = k\), where \(k\) is a constant, is a tangent to \(C\).
  2. Find the possible values of \(k\). The line with equation \(y = p\), where \(p\) is a negative constant, is a chord of \(C\).
    Given that the length of this chord is 4 units,
  3. find the value of \(p\).
    VIXV SIHIANI III IM IONOOVIAV SIHI NI JYHAM ION OOVI4V SIHI NI JLIYM ION OO