Questions C1 (1442 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
OCR MEI C1 Q13
13 Rearrange \(y + 5 = x ( y + 2 )\) to make \(y\) the subject of the formula.
Edexcel C1 2005 January Q2
  1. Given that \(y = 5 x ^ { 3 } + 7 x + 3\), find
    (a) \(\frac { \mathrm { d } y } { \mathrm {~d} x }\), (b) \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\).
  2. Find \(\int \left( 1 + 3 \sqrt { } x - \frac { 1 } { x ^ { 2 } } \right) \mathrm { d } x\).
Edexcel C1 2008 January Q2
  1. Write down the value of \(16 ^ { \frac { 1 } { 4 } }\).
  2. Simplify \(\left( 16 x ^ { 12 } \right) ^ { \frac { 3 } { 4 } }\).
Edexcel C1 2008 January Q3
Simplify $$\frac { 5 - \sqrt { 3 } } { 2 + \sqrt { 3 } } ,$$ giving your answer in the form \(a + b \sqrt { } 3\), where \(a\) and \(b\) are integers.
Edexcel C1 2009 January Q2
Find \(\int \left( 12 x ^ { 5 } - 8 x ^ { 3 } + 3 \right) \mathrm { d } x\), giving each term in its simplest form.
Edexcel C1 2009 January Q3
Expand and simplify \(( \sqrt { } 7 + 2 ) ( \sqrt { } 7 - 2 )\).
Edexcel C1 2009 January Q4
A curve has equation \(y = \mathrm { f } ( x )\) and passes through the point (4, 22). Given that $$\mathrm { f } ^ { \prime } ( x ) = 3 x ^ { 2 } - 3 x ^ { \frac { 1 } { 2 } } - 7 ,$$ use integration to find \(\mathrm { f } ( x )\), giving each term in its simplest form.
Edexcel C1 2010 January Q2
  1. Expand and simplify \(( 7 + \sqrt { 5 } ) ( 3 - \sqrt { 5 } )\).
  2. Express \(\frac { 7 + \sqrt { 5 } } { 3 + \sqrt { 5 } }\) in the form \(a + b \sqrt { 5 }\), where \(a\) and \(b\) are integers.
Edexcel C1 2010 January Q3
The line \(l _ { 1 }\) has equation \(3 x + 5 y - 2 = 0\)
  1. Find the gradient of \(l _ { 1 }\). The line \(l _ { 2 }\) is perpendicular to \(l _ { 1 }\) and passes through the point \(( 3,1 )\).
  2. Find the equation of \(l _ { 2 }\) in the form \(y = m x + c\), where \(m\) and \(c\) are constants.
Edexcel C1 2011 January Q2
Find $$\int \left( 12 x ^ { 5 } - 3 x ^ { 2 } + 4 x ^ { \frac { 1 } { 3 } } \right) \mathrm { d } x$$ giving each term in its simplest form.
Edexcel C1 2012 January Q2
  1. Simplify $$\sqrt { } 32 + \sqrt { } 18$$ giving your answer in the form \(a \sqrt { } 2\), where \(a\) is an integer.
  2. Simplify $$\frac { \sqrt { } 32 + \sqrt { } 18 } { 3 + \sqrt { } 2 }$$ giving your answer in the form \(b \sqrt { } 2 + c\), where \(b\) and \(c\) are integers.
Edexcel C1 2013 January Q2
Express \(8 ^ { 2 x + 3 }\) in the form \(2 ^ { y }\), stating \(y\) in terms of \(x\).
Edexcel C1 2013 January Q3
  1. Express $$( 5 - \sqrt { } 8 ) ( 1 + \sqrt { } 2 )$$ in the form \(a + b \sqrt { } 2\), where \(a\) and \(b\) are integers.
  2. Express $$\sqrt { } 80 + \frac { 30 } { \sqrt { } 5 }$$ in the form \(c \sqrt { } 5\), where \(c\) is an integer.
Edexcel C1 2005 June Q2
Given that \(y = 6 x - \frac { 4 } { x ^ { 2 } } , x \neq 0\),
  1. find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\),
  2. find \(\int y \mathrm {~d} x\).
Edexcel C1 2005 June Q3
$$x ^ { 2 } - 8 x - 29 \equiv ( x + a ) ^ { 2 } + b ,$$ where \(a\) and \(b\) are constants.
  1. Find the value of \(a\) and the value of \(b\).
  2. Hence, or otherwise, show that the roots of $$x ^ { 2 } - 8 x - 29 = 0$$ are \(c \pm d \sqrt { } 5\), where \(c\) and \(d\) are integers to be found.
Edexcel C1 2006 June Q2
Find the set of values of \(x\) for which $$x ^ { 2 } - 7 x - 18 > 0 .$$
Edexcel C1 2007 June Q2
  1. Find the value of \(8 ^ { \frac { 4 } { 3 } }\).
  2. Simplify \(\frac { 15 x ^ { \frac { 4 } { 3 } } } { 3 x }\).
Edexcel C1 2007 June Q3
Given that \(y = 3 x ^ { 2 } + 4 \sqrt { } x , x > 0\), find
  1. \(\frac { \mathrm { d } y } { \mathrm {~d} x }\),
  2. \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\),
  3. \(\int y \mathrm {~d} x\).
Edexcel C1 2007 June Q4
A girl saves money over a period of 200 weeks. She saves 5 p in Week 1,7 p in Week 2, 9p in Week 3, and so on until Week 200. Her weekly savings form an arithmetic sequence.
  1. Find the amount she saves in Week 200.
  2. Calculate her total savings over the complete 200 week period.
Edexcel C1 2007 June Q5
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c0db3fe8-62ec-41e3-acaf-66b2c7b2754d-06_702_785_242_607} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of the curve with equation \(y = \frac { 3 } { x } , x \neq 0\).
  1. On a separate diagram, sketch the curve with equation \(y = \frac { 3 } { x + 2 } , x \neq - 2\), showing the coordinates of any point at which the curve crosses a coordinate axis.
  2. Write down the equations of the asymptotes of the curve in part (a).
Edexcel C1 2008 June Q2
Factorise completely $$x ^ { 3 } - 9 x .$$
Edexcel C1 2008 June Q9
The curve \(C\) has equation \(y = k x ^ { 3 } - x ^ { 2 } + x - 5\), where \(k\) is a constant.
  1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\). The point \(A\) with \(x\)-coordinate \(- \frac { 1 } { 2 }\) lies on \(C\). The tangent to \(C\) at \(A\) is parallel to the line with equation \(2 y - 7 x + 1 = 0\). Find
  2. the value of \(k\),
  3. the value of the \(y\)-coordinate of \(A\).
Edexcel C1 2011 June Q2
Given that \(y = 2 x ^ { 5 } + 7 + \frac { 1 } { x ^ { 3 } } , x \neq 0\), find, in their simplest form, (a) \(\frac { \mathrm { d } y } { \mathrm {~d} x }\),
(b) \(\int y \mathrm {~d} x\).
Edexcel C1 2011 June Q3
The points \(P\) and \(Q\) have coordinates \(( - 1,6 )\) and \(( 9,0 )\) respectively. The line \(l\) is perpendicular to \(P Q\) and passes through the mid-point of \(P Q\).
Find an equation for \(l\), giving your answer in the form \(a x + b y + c = 0\), where \(a\), \(b\) and \(c\) are integers.
Edexcel C1 2013 June Q2
Express \(\frac { 15 } { \sqrt { 3 } } - \sqrt { 27 }\) in the form \(k \sqrt { } 3\), where \(k\) is an integer.