Questions — Edexcel (9670 questions)

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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 C1 2014 June Q4
Easy -1.2
4. Given that \(y = 2 x ^ { 5 } + \frac { 6 } { \sqrt { } x } , x > 0\), find in their simplest form
  1. \(\frac { \mathrm { d } y } { \mathrm {~d} x }\)
  2. \(\int y \mathrm {~d} x\)
Edexcel C1 2014 June Q5
Moderate -0.8
5. Solve the equation $$10 + x \sqrt { 8 } = \frac { 6 x } { \sqrt { 2 } }$$ Give your answer in the form \(a \sqrt { } b\) where \(a\) and \(b\) are integers.
Edexcel C1 2014 June Q6
Moderate -0.3
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6db8acbd-7f61-46ff-8fdc-f0f4a8363aa6-08_917_1322_239_303} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows the plan of a garden. The marked angles are right angles.
The six edges are straight lines.
The lengths shown in the diagram are given in metres.
Given that the perimeter of the garden is greater than 40 m ,
  1. show that \(x > 1.7\) Given that the area of the garden is less than \(120 \mathrm {~m} ^ { 2 }\),
  2. form and solve a quadratic inequality in \(x\).
  3. Hence state the range of the possible values of \(x\).
Edexcel C1 2014 June Q7
Standard +0.3
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6db8acbd-7f61-46ff-8fdc-f0f4a8363aa6-10_869_1073_267_440} \captionsetup{labelformat=empty} \caption{Diagram NOT to scale}
\end{figure} Figure 2 Figure 2 shows a right angled triangle \(L M N\). The points \(L\) and \(M\) have coordinates ( \(- 1,2\) ) and ( \(7 , - 4\) ) respectively.
  1. Find an equation for the straight line passing through the points \(L\) and \(M\). Give your answer in the form \(a x + b y + c = 0\), where \(a\), \(b\) and \(c\) are integers. Given that the coordinates of point \(N\) are ( \(16 , p\) ), where \(p\) is a constant, and angle \(L M N = 90 ^ { \circ }\),
  2. find the value of \(p\). Given that there is a point \(K\) such that the points \(L , M , N\), and \(K\) form a rectangle,
  3. find the \(y\) coordinate of \(K\).
Edexcel C1 2014 June Q8
Moderate -0.8
8. $$\frac { \mathrm { d } y } { \mathrm {~d} x } = 6 x ^ { - \frac { 1 } { 2 } } + x \sqrt { } x , \quad x > 0$$ Given that \(y = 37\) at \(x = 4\), find \(y\) in terms of \(x\), giving each term in its simplest form.
Edexcel C1 2014 June Q9
Moderate -0.3
9. The curve \(C\) has equation \(y = \frac { 1 } { 3 } x ^ { 2 } + 8\) The line \(L\) has equation \(y = 3 x + k\), where \(k\) is a positive constant.
  1. Sketch \(C\) and \(L\) on separate diagrams, showing the coordinates of the points at which \(C\) and \(L\) cut the axes. Given that line \(L\) is a tangent to \(C\),
  2. find the value of \(k\).
Edexcel C1 2014 June Q10
Moderate -0.8
  1. Xin has been given a 14 day training schedule by her coach.
Xin will run for \(A\) minutes on day 1 , where \(A\) is a constant.
She will then increase her running time by ( \(d + 1\) ) minutes each day, where \(d\) is a constant.
  1. Show that on day 14 , Xin will run for $$( A + 13 d + 13 ) \text { minutes. }$$ Yi has also been given a 14 day training schedule by her coach.
    Yi will run for \(( A - 13 )\) minutes on day 1 .
    She will then increase her running time by ( \(2 d - 1\) ) minutes each day.
    Given that Yi and Xin will run for the same length of time on day 14,
  2. find the value of \(d\). Given that Xin runs for a total time of 784 minutes over the 14 days,
  3. find the value of \(A\).
Edexcel C1 2014 June Q11
Standard +0.3
11. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6db8acbd-7f61-46ff-8fdc-f0f4a8363aa6-17_700_1556_276_201} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} A sketch of part of the curve \(C\) with equation $$y = 20 - 4 x - \frac { 18 } { x } , \quad x > 0$$ is shown in Figure 3. Point \(A\) lies on \(C\) and has an \(x\) coordinate equal to 2
  1. Show that the equation of the normal to \(C\) at \(A\) is \(y = - 2 x + 7\) 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 2015 June Q1
Easy -1.3
Simplify
  1. \(( 2 \sqrt { } 5 ) ^ { 2 }\)
  2. \(\frac { \sqrt { } 2 } { 2 \sqrt { } 5 - 3 \sqrt { } 2 }\) giving your answer in the form \(a + \sqrt { } b\), where \(a\) and \(b\) are integers.
Edexcel C1 2015 June Q3
Easy -1.2
Given that \(y = 4 x ^ { 3 } - \frac { 5 } { x ^ { 2 } } , x \neq 0\), find in their simplest form
  1. \(\frac { \mathrm { d } y } { \mathrm {~d} x }\)
  2. \(\int y \mathrm {~d} x\)
Edexcel C1 2015 June Q5
Moderate -0.3
  1. The equation
$$( p - 1 ) x ^ { 2 } + 4 x + ( p - 5 ) = 0 , \text { where } p \text { is a constant }$$ has no real roots.
  1. Show that \(p\) satisfies \(p ^ { 2 } - 6 p + 1 > 0\)
  2. Hence find the set of possible values of \(p\).
Edexcel C1 2015 June Q6
Standard +0.3
  1. The curve \(C\) has equation
$$y = \frac { \left( x ^ { 2 } + 4 \right) ( x - 3 ) } { 2 x } , \quad x \neq 0$$
  1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in its simplest form.
  2. Find an equation of the tangent to \(C\) at the point where \(x = - 1\) Give your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers.
Edexcel C1 2015 June Q7
Moderate -0.8
  1. Given that \(y = 2 ^ { x }\),
    1. express \(4 ^ { x }\) in terms of \(y\).
    2. Hence, or otherwise, solve
    $$8 \left( 4 ^ { x } \right) - 9 \left( 2 ^ { x } \right) + 1 = 0$$
Edexcel C1 2015 June Q8
Moderate -0.8
  1. (a) Factorise completely \(9 x - 4 x ^ { 3 }\)
    (b) Sketch the curve \(C\) with equation
$$y = 9 x - 4 x ^ { 3 }$$ Show on your sketch the coordinates at which the curve meets the \(x\)-axis. The points \(A\) and \(B\) lie on \(C\) and have \(x\) coordinates of - 2 and 1 respectively.
(c) Show that the length of \(A B\) is \(k \sqrt { } 10\) where \(k\) is a constant to be found.
Edexcel C1 2015 June Q9
Moderate -0.8
Jess started work 20 years ago. In year 1 her annual salary was \(\pounds 17000\). Her annual salary increased by \(\pounds 1500\) each year, so that her annual salary in year 2 was \(\pounds 18500\), in year 3 it was \(\pounds 20000\) and so on, forming an arithmetic sequence. This continued until she reached her maximum annual salary of \(\pounds 32000\) in year \(k\). Her annual salary then remained at \(\pounds 32000\).
  1. Find the value of the constant \(k\).
  2. Calculate the total amount that Jess has earned in the 20 years.
Edexcel C1 2016 June Q1
Easy -1.2
  1. Find
$$\int \left( 2 x ^ { 4 } - \frac { 4 } { \sqrt { } x } + 3 \right) d x$$ giving each term in its simplest form.
Edexcel C1 2016 June Q2
Easy -1.3
Express \(9 ^ { 3 x + 1 }\) in the form \(3 ^ { y }\), giving \(y\) in the form \(a x + b\), where \(a\) and \(b\) are constants.
(2)
Edexcel C1 2016 June Q4
Easy -1.2
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b0413ecc-b780-4f77-b76a-da7c699c12cb-05_709_744_269_607} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of part of the curve with equation \(y = \mathrm { f } ( x )\). The curve has a maximum point \(A\) at \(( - 2,4 )\) and a minimum point \(B\) at \(( 3 , - 8 )\) and passes through the origin \(O\). On separate diagrams, sketch the curve with equation
  1. \(y = 3 \mathrm { f } ( x )\),
  2. \(y = \mathrm { f } ( x ) - 4\)
    (3) On each diagram, show clearly the coordinates of the maximum and the minimum points and the coordinates of the point where the curve crosses the \(y\)-axis.
Edexcel C1 2016 June Q5
Moderate -0.3
5. Solve the simultaneous equations $$\begin{gathered} y + 4 x + 1 = 0 \\ y ^ { 2 } + 5 x ^ { 2 } + 2 x = 0 \end{gathered}$$
Edexcel C1 2016 June Q6
Moderate -0.3
6. A sequence \(a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots\) is defined by $$\begin{aligned} a _ { 1 } & = 4 \\ a _ { n + 1 } & = 5 - k a _ { n } , \quad n \geqslant 1 \end{aligned}$$ where \(k\) is a constant.
  1. Write down expressions for \(a _ { 2 }\) and \(a _ { 3 }\) in terms of \(k\). Find
  2. \(\sum _ { r = 1 } ^ { 3 } \left( 1 + a _ { r } \right)\) in terms of \(k\), giving your answer in its simplest form,
  3. \(\sum _ { r = 1 } ^ { 100 } \left( a _ { r + 1 } + k a _ { r } \right)\)
Edexcel C1 2016 June Q7
Moderate -0.8
  1. Given that
$$y = 3 x ^ { 2 } + 6 x ^ { \frac { 1 } { 3 } } + \frac { 2 x ^ { 3 } - 7 } { 3 \sqrt { } x } , \quad x > 0$$ find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\). Give each term in your answer in its simplified form.
Edexcel C1 2016 June Q8
Standard +0.3
8. The straight line with equation \(y = 3 x - 7\) does not cross or touch the curve with equation \(y = 2 p x ^ { 2 } - 6 p x + 4 p\), where \(p\) is a constant.
  1. Show that \(4 p ^ { 2 } - 20 p + 9 < 0\)
  2. Hence find the set of possible values of \(p\).
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    VILV SIHI NI III HM ION OC
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Edexcel C1 2016 June Q9
Moderate -0.8
9. On John's 10th birthday he received the first of an annual birthday gift of money from his uncle. This first gift was \(\pounds 60\) and on each subsequent birthday the gift was \(\pounds 15\) more than the year before. The amounts of these gifts form an arithmetic sequence.
  1. Show that, immediately after his 12th birthday, the total of these gifts was \(\pounds 225\)
  2. Find the amount that John received from his uncle as a birthday gift on his 18th birthday.
  3. Find the total of these birthday gifts that John had received from his uncle up to and including his 21st birthday. When John had received \(n\) of these birthday gifts, the total money that he had received from these gifts was \(\pounds 3375\)
  4. Show that \(n ^ { 2 } + 7 n = 25 \times 18\)
  5. Find the value of \(n\), when he had received \(\pounds 3375\) in total, and so determine John's age at this time.
Edexcel C1 2016 June Q10
Moderate -0.3
10. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b0413ecc-b780-4f77-b76a-da7c699c12cb-12_593_1166_260_397} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} The points \(P ( 0,2 )\) and \(Q ( 3,7 )\) lie on the line \(l _ { 1 }\), as shown in Figure 2.
The line \(l _ { 2 }\) is perpendicular to \(l _ { 1 }\), passes through \(Q\) and crosses the \(x\)-axis at the point \(R\), as shown in Figure 2. Find
  1. an equation for \(l _ { 2 }\), giving your answer in the form \(a x + b y + c = 0\), where \(a\), b and \(c\) are integers,
  2. the exact coordinates of \(R\),
  3. the exact area of the quadrilateral \(O R Q P\), where \(O\) is the origin.
Edexcel C1 2016 June Q11
Moderate -0.8
11. The curve \(C\) has equation \(y = 2 x ^ { 3 } + k x ^ { 2 } + 5 x + 6\), where \(k\) is a constant.
  1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) The point \(P\), where \(x = - 2\), lies on \(C\). The tangent to \(C\) at the point \(P\) is parallel to the line with equation \(2 y - 17 x - 1 = 0\)
    Find
  2. the value of \(k\),
  3. the value of the \(y\) coordinate of \(P\),
  4. the equation of the tangent to \(C\) at \(P\), giving your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers.