Questions — OCR MEI C1 (472 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 Q5
5
  1. Solve, by factorising, the equation \(2 x ^ { 2 } - x - 3 = 0\).
  2. Sketch the graph of \(y = 2 x ^ { 2 } - x - 3\).
  3. Show that the equation \(x ^ { 2 } - 5 x + 10 = 0\) has no real roots.
  4. Find the \(x\)-coordinates of the points of intersection of the graphs of \(y = 2 x ^ { 2 } - x - 3\) and \(y = x ^ { 2 } - 5 x + 10\). Give your answer in the form \(a \pm \sqrt { b }\).
OCR MEI C1 Q1
1 Evaluate the following.
  1. \(200 ^ { \circ }\)
  2. \(\left( \frac { 25 } { 9 } \right) ^ { - \frac { 1 } { 2 } }\)
OCR MEI C1 Q2
2
  1. Evaluate \(\left( \frac { 1 } { 27 } \right) ^ { \frac { 2 } { 3 } }\).
  2. Simplify \(\frac { \left( 4 a ^ { 2 } c \right) ^ { 3 } } { 32 a ^ { 4 } c ^ { 7 } }\).
OCR MEI C1 Q3
3 You are given that \(n , n + 1\) and \(n + 2\) are three consecutive integers.
  1. Expand and simplify \(n ^ { 2 } + ( n + 1 ) ^ { 2 } + ( n + 2 ) ^ { 2 }\).
  2. For what values of \(n\) will the sum of the squares of these three consecutive integers be an even number? Give a reason for your answer.
OCR MEI C1 Q4
4
  1. Evaluate \(( 0.2 ) ^ { - 2 }\).
  2. Simplify \(\left( 16 a ^ { 12 } \right) ^ { \frac { 3 } { 4 } }\).
OCR MEI C1 Q5
5 Find the value of each of the following.
  1. \(\left( \frac { 5 } { 3 } \right) ^ { - 2 }\)
  2. \(81 ^ { \frac { 3 } { 4 } }\)
OCR MEI C1 Q6
6
  1. Evaluate \(\left( \frac { 1 } { 5 } \right) ^ { - 2 }\).
  2. Evaluate \(\left( \frac { 8 } { 27 } \right) ^ { \frac { 2 } { 3 } }\).
    \(7 \quad\) (i) Simplify \(\frac { 10 ( \sqrt { 6 } ) ^ { 3 } } { \sqrt { 24 } }\).
  3. Simplify \(\frac { 1 } { 4 - \sqrt { 5 } } + \frac { 1 } { 4 + \sqrt { 5 } }\).
OCR MEI C1 Q8
8
  1. Evaluate \(9 ^ { - \frac { 1 } { 2 } }\).
  2. Simplify \(\frac { \left( 4 x ^ { 4 } \right) ^ { 3 } y ^ { 2 } } { 2 x ^ { 2 } y ^ { 5 } }\).
OCR MEI C1 Q9
9 Expand and simplify \(( n + 2 ) ^ { 3 } - n ^ { 3 }\).
OCR MEI C1 Q10
10
  1. Evaluate \(\left( \frac { 9 } { 16 } \right) ^ { - \frac { 1 } { 2 } }\).
  2. Simplify \(\frac { \left( 2 a c ^ { 2 } \right) ^ { 3 } \times 9 a ^ { 2 } c } { 36 a ^ { 4 } c ^ { 12 } }\).
OCR MEI C1 Q11
11
  1. Write down the value of each of the following.
    (A) \(4 ^ { - 2 }\)
    (B) \(9 ^ { 0 }\)
  2. Find the value of \(\left( \frac { 64 } { 125 } \right) ^ { \frac { 4 } { 3 } }\).
OCR MEI C1 Q1
1
  1. Express \(\frac { 81 } { \sqrt { 3 } }\) in the form \(3 ^ { k }\).
  2. Express \(\frac { 5 + \sqrt { 3 } } { 5 - \sqrt { 3 } }\) in the form \(\frac { a + b \sqrt { 3 } } { c }\), where \(a , b\) and \(c\) are integers.
    \(2 \quad\) (i) Simplify \(\left( 5 a ^ { 2 } b \right) ^ { 3 } \times 2 b ^ { 4 }\).
  3. Evaluate \(\left( \frac { 1 } { 16 } \right) ^ { - 1 }\).
  4. Evaluate \(( 16 ) ^ { \frac { 3 } { 2 } }\).
OCR MEI C1 Q3
3 Make \(y\) the subject of the formula \(a = \frac { \sqrt { y } - 5 } { c }\).
OCR MEI C1 Q4
4
  1. Find the value of \(144 ^ { - \frac { 1 } { 2 } }\).
  2. Simplify \(\frac { 1 } { 5 + \sqrt { 7 } } + \frac { 4 } { 5 - \sqrt { 7 } }\). Give your answer in the form \(\frac { a + b \sqrt { 7 } } { c }\).
OCR MEI C1 Q5
5 Find the value of each of the following.
  1. \(5 ^ { 2 } \times 5 ^ { - 2 }\)
  2. \(100 ^ { \frac { 3 } { 2 } }\)
OCR MEI C1 Q6
6 State the value of each of the following.
  1. \(2 ^ { - 3 }\)
  2. \(9 ^ { 0 }\)
OCR MEI C1 Q8
8
  1. Find the value of \(\left( \frac { 1 } { 25 } \right) ^ { - \frac { 1 } { 2 } }\).
  2. Simplify \(\frac { \left( 2 x ^ { 2 } y ^ { 3 } z \right) ^ { 5 } } { 4 y ^ { 2 } z }\).
OCR MEI C1 Q9
9
  1. Write down the value of \(\left( \frac { 1 } { 4 } \right) ^ { 0 }\).
  2. Find the value of \(16 ^ { - \frac { 3 } { 2 } }\).
OCR MEI C1 Q10
10
  1. Find \(a\), given that \(a ^ { 3 } = 64 x ^ { 12 } y ^ { 3 }\).
  2. Find the value of \(\left( \frac { 1 } { 2 } \right) ^ { - 5 }\).
OCR MEI C1 Q11
11 Find the value of each of the following, giving each answer as an integer or fraction as appropriate.
  1. \(\quad \frac { 3 } { 2 }\)
  2. \(\left( \frac { 7 } { 3 } \right) ^ { - 2 }\)
OCR MEI C1 Q12
12
  1. Simplify \(6 \sqrt { 2 } \times 5 \sqrt { 3 } \quad \sqrt { 24 }\).
  2. Express \(( 23 \sqrt { 5 } ) ^ { 2 }\) in the form \(a + b \sqrt { 5 }\), where \(a\) and \(b\) are integers.
OCR MEI C1 Q13
13 Simplify the following.
  1. \(\frac { 16 ^ { \frac { 1 } { 2 } } } { 81 ^ { \frac { 3 } { 4 } } }\)
  2. \(\frac { 12 \left( a ^ { 3 } b ^ { 2 } c \right) ^ { 4 } } { 4 a ^ { 2 } c ^ { 6 } }\)
OCR MEI C1 Q1
1 Solve the inequality \(\frac { 4 x - 5 } { 7 } > 2 x + 1\).
OCR MEI C1 Q2
2 Solve the inequality \(3 x ^ { 2 } + 10 x + 3 > 0\).
OCR MEI C1 Q3
3 Solve the inequality \(5 x ^ { 2 } - 28 x - 12 \leqslant 0\).