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 AEA 2011 June Q6
19 marks Hard +2.3
The line \(L\) has equation $$\mathbf{r} = \begin{pmatrix} 13 \\ -3 \\ -8 \end{pmatrix} + t \begin{pmatrix} -5 \\ 3 \\ 4 \end{pmatrix}$$ The point \(P\) has position vector \(\begin{pmatrix} -7 \\ 2 \\ 7 \end{pmatrix}\). The point \(P'\) is the reflection of \(P\) in \(L\).
  1. Find the position vector of \(P'\). [6]
  2. Show that the point \(A\) with position vector \(\begin{pmatrix} -7 \\ 9 \\ 8 \end{pmatrix}\) lies on \(L\). [1]
  3. Show that angle \(PAP' = 120°\). [3]
% Figure 3 shows kite APBP' with angle at A = 120° \includegraphics{figure_3} Figure 3 The point \(B\) lies on \(L\) and \(APBP'\) forms a kite as shown in Figure 3. The area of the kite is \(50\sqrt{3}\)
  1. Find the position vector of the point \(B\). [5]
  2. Show that angle \(BPA = 90°\). [2]
The circle \(C\) passes through the points \(A\), \(P\), \(P'\) and \(B\).
  1. Find the position vector of the centre of \(C\). [2]
[Total 19 marks]
Edexcel AEA 2011 June Q7
20 marks Challenging +1.8
% Figure 4 shows curves with asymptotic behavior at x = 3 \includegraphics{figure_4} Figure 4
  1. Figure 4 shows a sketch of the curve with equation \(y = f(x)\), where $$f(x) = \frac{x^2 - 5}{3-x}, \quad x \in \mathbb{R}, x \neq 3$$ The curve has a minimum at the point \(A\), with \(x\)-coordinate \(\alpha\), and a maximum at the point \(B\), with \(x\)-coordinate \(\beta\). Find the value of \(\alpha\), the value of \(\beta\) and the \(y\)-coordinates of the points \(A\) and \(B\). [5]
  2. The functions \(g\) and \(h\) are defined as follows $$g: x \to x + p \quad x \in \mathbb{R}$$ $$h: x \to |x| \quad x \in \mathbb{R}$$ where \(p\) is a constant. % Figure 5 shows curve with minimum points at C and D symmetric about y-axis \includegraphics{figure_5} Figure 5 Figure 5 shows a sketch of the curve with equation \(y = h(fg(x) + q)\), \(x \in \mathbb{R}\), \(x \neq 0\), where \(q\) is a constant. The curve is symmetric about the \(y\)-axis and has minimum points at \(C\) and \(D\).
    1. Find the value of \(p\) and the value of \(q\).
    2. Write down the coordinates of \(D\).
    [5]
  3. The function \(\mathrm{m}\) is given by $$\mathrm{m}(x) = \frac{x^2 - 5}{3-x} \quad x \in \mathbb{R}, x < \alpha$$ where \(\alpha\) is the \(x\)-coordinate of \(A\) as found in part (a).
    1. Find \(\mathrm{m}^{-1}\)
    2. Write down the domain of \(\mathrm{m}^{-1}\)
    3. Find the value of \(t\) such that \(\mathrm{m}(t) = \mathrm{m}^{-1}(t)\)
    [10]
[Total 20 marks]
Edexcel AEA 2015 June Q1
6 marks Moderate -0.5
  1. Sketch the graph of the curve with equation $$y = \ln(2x + 5), \quad x > -\frac{5}{2}$$ On your sketch you should clearly state the equations of any asymptotes and mark the coordinates of points where the curve meets the coordinate axes. [3]
  2. Solve the equation \(\ln(2x + 5) = \ln 9\) [3]
Edexcel AEA 2015 June Q2
9 marks Challenging +1.8
  1. Show that \((x + 1)\) is a factor of \(2x^3 + 3x^2 - 1\) [1]
  2. Solve the equation $$\sqrt{x^2 + 2x + 5} = x + \sqrt{2x + 3}$$ [8]
Edexcel AEA 2015 June Q3
9 marks Challenging +1.8
Solve for \(0 < x < 360°\) $$\cot 2x - \tan 78° = \frac{(\sec x)(\sec 78°)}{2}$$ where \(x\) is not an integer multiple of \(90°\) [9]
Edexcel AEA 2015 June Q4
15 marks Challenging +1.8
  1. Find the binomial series expansion for \((4 + y)^{\frac{1}{2}}\) in ascending powers of \(y\) up to and including the term in \(y^3\). Simplify the coefficient of each term. [3]
  2. Hence show that the binomial series expansion for \((4 + 5x + x^2)^{\frac{1}{2}}\) in ascending powers of \(x\) up to and including the term in \(x^3\) is $$2 + \frac{5x}{4} - \frac{9x^2}{64} + \frac{45x^3}{512}$$ [3]
  3. Show that the binomial series expansion of \((4 + 5x + x^2)^{\frac{1}{2}}\) will converge for \(-\frac{1}{2} < x \leq \frac{1}{2}\) [6]
  4. Use the result in part (b) to estimate $$\int_{-\frac{1}{2}}^{\frac{1}{2}} \sqrt{4 + 5x + x^2} \, dx$$ Give your answer as a single fraction. [3]
Edexcel AEA 2015 June Q5
16 marks Challenging +1.2
% Figure shows a curve with maximum at point A, passing through origin O, with horizontal asymptote \includegraphics{figure_1} Figure 1 shows a sketch of the curve with equation \(y = f(x)\) where $$f(x) = \frac{x^2 + 16}{3x} \quad x \neq 0$$ The curve has a maximum at the point \(A\) with coordinates \((a, b)\).
  1. Find the value of \(a\) and the value of \(b\). [4] The function g is defined as $$g : x \mapsto \frac{x^2 + 16}{3x} \quad a \leq x < 0$$ where \(a\) is the value found in part (a).
  2. Write down the range of g. [1]
  3. On the same axes sketch \(y = g(x)\) and \(y = g^{-1}(x)\). [3]
  4. Find an expression for \(g^{-1}(x)\) and state the domain of \(g^{-1}\) [5]
  5. Solve the equation \(g(x) = g^{-1}(x)\). [3]
Edexcel AEA 2015 June Q6
19 marks Challenging +1.8
The lines \(L_1\) and \(L_2\) have vector equations $$L_1 : \mathbf{r} = \begin{pmatrix} 1 \\ 10 \\ -3 \end{pmatrix} + \lambda \begin{pmatrix} 2 \\ -5 \\ 4 \end{pmatrix}$$ $$L_2 : \mathbf{r} = \begin{pmatrix} -1 \\ 2 \\ 3 \end{pmatrix} + \mu \begin{pmatrix} 1 \\ 2 \\ 2 \end{pmatrix}$$
  1. Show that \(L_1\) and \(L_2\) are perpendicular. [2]
  2. Show that \(L_1\) and \(L_2\) are skew lines. [3] The point \(A\) with position vector \(-\mathbf{i} + 2\mathbf{j} + 3\mathbf{k}\) lies on \(L_2\) and the point \(X\) lies on \(L_1\) such that \(\overrightarrow{AX}\) is perpendicular to \(L_1\)
  3. Find the position vector of \(X\). [5]
  4. Find \(|\overrightarrow{AX}|\) [2] The point \(B\) (distinct from \(A\)) also lies on \(L_2\) and \(|\overrightarrow{BX}| = |\overrightarrow{AX}|\)
  5. Find the position vector of \(B\). [5]
  6. Find the cosine of angle \(AXB\). [2]
Edexcel AEA 2015 June Q7
19 marks Hard +2.3
  1. Use the substitution \(x = \sec\theta\) to show that $$\int_{\sqrt{2}}^{2} \frac{1}{(x^2 - 1)^{\frac{3}{2}}} \, dx = \frac{\sqrt{6} - 2}{\sqrt{3}}$$ [5]
  2. Use integration by parts to show that $$\int \cos\theta \cot^2\theta \, d\theta = \frac{1}{2}[\ln|\cos\theta + \cot\theta| - \cos\theta \cot\theta] + c$$ [6] % Figure shows a curve y = 1/(x^2-1)^(1/2) for x > 1, with shaded region R between x = sqrt(2) and x = 2 \includegraphics{figure_2} Figure 2 shows a sketch of part of the curve with equation \(y = \frac{1}{(x^2 - 1)^{\frac{1}{2}}}\) for \(x > 1\) The region \(R\), shown shaded in Figure 2, is bounded by the curve, the \(x\)-axis and the lines \(x = \sqrt{2}\) and \(x = 2\) The region \(R\) is rotated through \(2\pi\) radians about the \(x\)-axis.
  3. Show that the volume of the solid formed is $$\pi \left[\frac{3}{8}\ln\left(\frac{1 + \sqrt{2}}{\sqrt{3}}\right) + \frac{7}{36} - \frac{\sqrt{2}}{8}\right]$$ [8]
Edexcel D1 2022 January Q17
Moderate -0.8
17 & 9 & 15 & 8 & 20 & 13 & 28 & 4 & 12 & 5 \end{array}$$ The numbers in the list shown above are the weights, in kilograms, of ten boxes. The boxes are to be transported in containers that will each hold a maximum weight of 40 kilograms.
  1. Calculate a lower bound for the number of containers that will be needed to transport the boxes. You must show your working.
  2. Use the first-fit bin packing algorithm to allocate the boxes to the containers.
  3. Using the list provided, carry out a quick sort to produce a list of the weights in ascending order. You must make your pivots clear.
  4. Use the binary search algorithm to try to locate the weight of 9 in the sorted list. Clearly indicate how you choose your pivots and which part of the list is being rejected at each stage.
Edexcel D1 2022 January Q0
Easy -1.8
0 \leqslant x & \leqslant 27
Edexcel D1 2023 January Q10
Moderate -0.8
10 x + 7 y & \leqslant 140
& x + y \leqslant 15
& 2 x + 3 y \geqslant 36
& x \geqslant 0 , \quad y \geqslant 0 \end{aligned} \end{array}$$ (c) Represent these constraints on Diagram 1 in the answer book. Hence determine, and label, the feasible region, \(R\).
(d) Use the objective line method to find the optimal number of each type of cake that Martin should make, and the amount of sugar used.
(e) Determine how much flour and how many eggs Martin will have left over after making the optimal number of cakes. BLANK PAGE \end{document}
Edexcel D1 2022 January Q7
Moderate -0.8
7. \section*{Question 7 continued} \section*{Question 7 continued} \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{765ea64e-d4b8-4f0f-9a43-2619f9db0c18-19_2109_1335_299_372} \captionsetup{labelformat=empty} \caption{Diagram 1}
\end{figure} \section*{Question 7 continued} \section*{Pearson Edexcel International Advanced Level} Time 1 hour 30 minutes \section*{Paper reference WDM11/01} \section*{Mathematics} \section*{You must have:} Decision Mathematics Answer Book (enclosed), calculator Candidates may use any calculator permitted by Pearson regulations. Calculators must not have the facility for symbolic algebra manipulation, differentiation and integration, or have retrievable mathematical formulae stored in them. \section*{Instructions}
  • Use black ink or ball-point pen.
  • If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
  • Write your answers for this paper in the Decision Mathematics answer book provided.
  • Fill in the boxes at the top of the answer book with your name, centre number and candidate number.
  • Do not return the question paper with the answer book.
  • Answer all questions and ensure that your answers to parts of questions are clearly labelled.
  • Answer the questions in the spaces provided
  • there may be more space than you need.
  • You should show sufficient working to make your methods clear. Answers without working may not gain full credit.
  • Inexact answers should be given to three significant figures unless otherwise stated.
\section*{Information}
  • There are 7 questions in this question paper. The total mark for this paper is 75.
  • The marks for each question are shown in brackets
  • use this as a guide as to how much time to spend on each question.
\section*{Advice}
  • Read each question carefully before you start to answer it.
  • Try to answer every question.
  • Check your answers if you have time at the end.
  • If you change your mind about an answer, cross it out and put your new answer and any working underneath.
\section*{Write your answers in the D1 answer book for this paper.}
Edexcel D1 2023 January Q6
Easy -1.3
6. \section*{Question 6 continued}
\includegraphics[max width=\textwidth, alt={}]{ed8418c4-cdc9-480f-aa09-a16e16933acb-17_1845_1463_296_303}
\section*{Diagram 1} \section*{Question 6 continued} \section*{Question 6 continued} \section*{Question 6 continued} \section*{Pearson Edexcel International Advanced Level} Time 1 hour 30 minutes \section*{Paper reference} \section*{Mathematics} \section*{You must have:} Decision Mathematics Answer Book (enclosed), calculator Candidates may use any calculator allowed by Pearson regulations. Calculators must not have the facility for symbolic algebra manipulation, differentiation and integration, or have retrievable mathematical formulae stored in them. \section*{Instructions}
  • Use black ink or ball-point pen.
  • If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). Coloured pencils and highlighter pens must not be used.
  • Fill in the boxes on the top of the answer book with your name, centre number and candidate number.
  • Answer all questions and ensure that your answers to parts of questions are clearly labelled.
  • Answer the questions in the D1 answer book provided - there may be more space than you need.
  • You should show sufficient working to make your methods clear. Answers without working may not gain full credit.
  • When a calculator is used, the answer should be given to an appropriate degree of accuracy.
  • Do not return the question paper with the answer book.
\section*{Information}
  • The total mark for this paper is 75.
  • The marks for each question are shown in brackets
  • use this as a guide as to how much time to spend on each question.
\section*{Advice}
  • Read each question carefully before you start to answer it.
  • Try to answer every question.
  • Check your answers if you have time at the end.
\section*{Write your answers in the D1 answer book for this paper.}