Questions — OCR MEI C1 (499 questions)

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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.
OCR MEI C1 2007 January Q1
3 marks Easy -1.8
1 Find, in the form \(y = a x + b\), the equation of the line through \(( 3,10 )\) which is parallel to \(y = 2 x + 7\).
OCR MEI C1 2007 January Q2
3 marks Easy -1.8
2 Sketch the graph of \(y = 9 - x ^ { 2 }\).
OCR MEI C1 2007 January Q3
3 marks Easy -1.8
3 Make \(a\) the subject of the equation $$2 a + 5 c = a f + 7 c$$
OCR MEI C1 2007 January Q4
3 marks Moderate -0.8
4 When \(x ^ { 3 } + k x + 5\) is divided by \(x - 2\), the remainder is 3 . Use the remainder theorem to find the value of \(k\).
OCR MEI C1 2007 January Q5
3 marks Easy -1.2
5 Calculate the coefficient of \(x ^ { 4 }\) in the expansion of \(( x + 5 ) ^ { 6 }\).
OCR MEI C1 2007 January Q6
4 marks Easy -1.5
6 Find the value of each of the following, giving each answer as an integer or fraction as appropriate.
  1. \(25 ^ { \frac { 3 } { 2 } }\)
  2. \(\left( \frac { 7 } { 3 } \right) ^ { - 2 }\)
OCR MEI C1 2007 January Q7
4 marks Standard +0.8
7 You are given that \(a = \frac { 3 } { 2 } , b = \frac { 9 - \sqrt { 17 } } { 4 }\) and \(c = \frac { 9 + \sqrt { 17 } } { 4 }\). Show that \(a + b + c = a b c\).