Questions C1 (1442 questions)

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OCR MEI C1 Q2
4 marks Easy -1.2
2 \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{91e16597-234a-4730-8c4b-765ca574e6e2-1_522_528_867_803} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} Fig. 2 shows graphs \(A\) and \(B\).
  1. State the transformation which maps graph \(A\) onto graph \(B\).
  2. The equation of graph \(A\) is \(y = \mathrm { f } ( x )\). Which one of the following is the equation of graph \(B\) ? $$\begin{aligned} & y = \mathrm { f } ( x ) + 2 \\ & y = 2 \mathrm { f } ( x ) \end{aligned}$$ $$\begin{aligned} & y = \mathrm { f } ( x ) - 2 \\ & y = \mathrm { f } ( x + 3 ) \end{aligned}$$ $$\begin{aligned} & y = \mathrm { f } ( x + 2 ) \\ & y = \mathrm { f } ( x - 3 ) \end{aligned}$$
OCR MEI C1 Q3
12 marks Moderate -0.8
3 You are given that \(\mathrm { f } ( x ) = ( x + 3 ) ( x - 2 ) ( x - 5 )\).
  1. Sketch the curve \(y = \mathrm { f } ( x )\).
  2. Show that \(\mathrm { f } ( x )\) may be written as \(x ^ { 3 } - 4 x ^ { 2 } - 11 x + 30\).
  3. Describe fully the transformation that maps the graph of \(y = \mathrm { f } ( x )\) onto the graph of \(y = \mathrm { g } ( x )\), where \(\mathrm { g } ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 11 x - 6\).
  4. Show that \(\mathrm { g } ( - 1 ) = 0\). Hence factorise \(\mathrm { g } ( x )\) completely.
OCR MEI C1 Q4
13 marks Moderate -0.8
4
  1. You are given that \(\mathrm { f } ( x ) = ( 2 x - 5 ) ( x - 1 ) ( x - 4 )\).
    (A) Sketch the graph of \(y = \mathrm { f } ( x )\).
    (B) Show that \(\mathrm { f } ( x ) = 2 x ^ { 3 } - 15 x ^ { 2 } + 33 x - 20\).
  2. You are given that \(\mathrm { g } ( x ) = 2 x ^ { 3 } - 15 x ^ { 2 } + 33 x - 40\).
    (A) Show that \(\mathrm { g } ( 5 ) = 0\).
    (B) Express \(\mathrm { g } ( x )\) as the product of a linear and quadratic factor.
    (C) Hence show that the equation \(\mathrm { g } ( x ) = 0\) has only one real root.
  3. Describe fully the transformation that maps \(y = \mathrm { f } ( x )\) onto \(y = \mathrm { g } ( x )\).
OCR MEI C1 Q1
4 marks Moderate -0.8
1 Find and simplify the binomial expansion of \(( 3 x - 2 ) ^ { 4 }\).
OCR MEI C1 Q2
4 marks Moderate -0.8
2 Find the coefficient of \(x ^ { 4 }\) in the binomial expansion of \(( 5 + 2 x ) ^ { 7 }\).
OCR MEI C1 Q3
4 marks Moderate -0.8
3 Find the coefficient of \(x ^ { 3 }\) in the binomial expansion of \(( 2 - 4 x ) ^ { 5 }\).
OCR MEI C1 Q4
4 marks Standard +0.3
4 The binomial expansion of \(\left( 2 x + \frac { 5 } { x } \right) ^ { 6 }\) has a term which is a constant. Find this term.
OCR MEI C1 Q5
5 marks Easy -1.2
5
  1. Evaluate \({ } ^ { 5 } \mathrm { C } _ { 3 }\).
  2. Find the coefficient of \(x ^ { 3 }\) in the expansion of \(( 3 - 2 x ) ^ { 5 }\).
OCR MEI C1 Q6
4 marks Moderate -0.8
6 Find the coefficient of \(x ^ { 4 }\) in the binomial expansion of \(( 5 + 2 x ) ^ { 6 }\).
OCR MEI C1 Q7
4 marks Moderate -0.8
7 Find the first 3 terms, in ascending powers of \(x\), of the binomial expansion of \(( 2 - 3 x ) ^ { 5 }\), simplifying each term.
OCR MEI C1 Q8
5 marks Moderate -0.3
8 You are given that
  • the coefficient of \(x ^ { 3 }\) in the expansion of \(\left( 5 + 2 x ^ { 2 } \right) \left( x ^ { 3 } + k x + m \right)\) is 29 ,
  • when \(x ^ { 3 } + k x + m\) is divided by ( \(x - 3\) ), the remainder is 59 .
Find the values of \(k\) and \(m\).
OCR MEI C1 Q9
4 marks Easy -1.3
9 Expand \(\left( 1 + \frac { 1 } { 2 } x \right) ^ { 4 }\), simplifying the coefficients.
OCR MEI C1 Q10
4 marks Easy -1.2
10 Find the binomial expansion of \(\left( x + \frac { 5 } { x } \right) ^ { 3 }\), simplifying the terms.
OCR MEI C1 Q11
4 marks Easy -1.2
11
  1. Calculate \({ } ^ { 5 } \mathrm { C } _ { 3 }\).
  2. Find the coefficient of \(x ^ { 3 }\) in the expansion of \(( 1 + 2 x ) ^ { 5 }\).
OCR MEI C1 Q12
5 marks Easy -1.2
12
  1. Find the coefficient of \(x ^ { 3 }\) in the expansion of \(\left( x ^ { 2 } - 3 \right) \left( x ^ { 3 } + 7 x + 1 \right)\).
  2. Find the coefficient of \(x ^ { 2 }\) in the binomial expansion of \(( 1 + 2 x ) ^ { 7 }\).
OCR MEI C1 Q13
4 marks Moderate -0.8
13 Find the coefficient of \(x ^ { 3 }\) in the binomial expansion of \(( 5 - 2 x ) ^ { 5 }\).
OCR MEI C1 Q14
4 marks Easy -1.2
14
  1. Find the value of \({ } ^ { 8 } \mathrm { C } _ { 3 }\).
  2. Find the coefficient of \(x ^ { 3 }\) in the binomial expansion of \(\left( 1 - \frac { 1 } { 2 } x \right) ^ { 8 }\).
OCR MEI C1 Q15
4 marks Moderate -0.8
15 Find the coefficient of \(x ^ { 3 }\) in the expansion of \(( 3 - 2 x ) ^ { 5 }\).
OCR MEI C1 Q16
3 marks Easy -1.2
16 Calculate the coefficient of \(x ^ { 4 }\) in the expansion of \(( x + 5 ) ^ { 6 }\).
OCR MEI C1 Q17
4 marks Easy -1.2
17 Calculate \({ } ^ { 6 } \mathrm { C } _ { 3 }\).
Find the coefficient of \(x ^ { 3 }\) in the expansion of \(( 1 - 2 x ) ^ { 6 }\).
OCR MEI C1 Q18
4 marks Easy -1.2
18 Find the binomial expansion of \(( 2 + x ) ^ { 4 }\), writing each term as simply as possible.
Edexcel C1 2014 June Q1
3 marks Easy -1.8
  1. Find
$$\int \left( 8 x ^ { 3 } + 4 \right) d x$$ giving each term in its simplest form.
Edexcel C1 2014 June Q2
4 marks Easy -1.3
2.(a)Write down the value of \(32 ^ { \frac { 1 } { 5 } }\)
(b)Simplify fully \(\left( 32 x ^ { 5 } \right) ^ { - \frac { 2 } { 5 } }\)
I敖

Edexcel C1 2014 June Q3
7 marks Moderate -0.8
3. Find the set of values of \(x\) for which
  1. \(3 x - 7 > 3 - x\)
  2. \(x ^ { 2 } - 9 x \leqslant 36\)
  3. both \(3 x - 7 > 3 - x\) and \(x ^ { 2 } - 9 x \leqslant 36\)
Edexcel C1 2014 June Q4
5 marks Moderate -0.8
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{64f015bf-29fb-4374-af34-3745ea49aced-05_945_1026_269_466} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of the curve \(C\) with equation $$y = \frac { 1 } { x } + 1 , \quad x \neq 0$$ The curve \(C\) crosses the \(x\)-axis at the point \(A\).
  1. State the \(x\) coordinate of the point \(A\). The curve \(D\) has equation \(y = x ^ { 2 } ( x - 2 )\), for all real values of \(x\).
  2. A copy of Figure 1 is shown on page 7. On this copy, sketch a graph of curve \(D\).
    Show on the sketch the coordinates of each point where the curve \(D\) crosses the coordinate axes.
  3. Using your sketch, state, giving a reason, the number of real solutions to the equation $$x ^ { 2 } ( x - 2 ) = \frac { 1 } { x } + 1$$ \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{64f015bf-29fb-4374-af34-3745ea49aced-06_942_1026_516_466} \captionsetup{labelformat=empty} \caption{Figure 1}
    \end{figure}