Questions C1 (1442 questions)

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All questions AEA AS Paper 1 AS Paper 2 AS Pure 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 Further AS Paper 1 Further AS Paper 2 Discrete Further AS Paper 2 Mechanics Further AS Paper 2 Statistics Further Additional Pure Further Additional Pure AS Further Discrete Further Discrete AS Further Extra Pure Further Mechanics Further Mechanics A AS Further Mechanics AS Further Mechanics B AS Further Mechanics Major Further Mechanics Minor Further Numerical Methods Further Paper 1 Further Paper 2 Further Paper 3 Further Paper 3 Discrete Further Paper 3 Mechanics Further Paper 3 Statistics Further Paper 4 Further Pure Core Further Pure Core 1 Further Pure Core 2 Further Pure Core AS Further Pure with Technology Further Statistics Further Statistics A AS Further Statistics AS Further Statistics B AS Further Statistics Major Further Statistics Minor Further Unit 1 Further Unit 2 Further Unit 3 Further Unit 4 Further Unit 5 Further Unit 6 H240/01 H240/02 H240/03 M1 M2 M3 M4 M5 Mechanics 1 P1 P2 P3 P4 PMT Mocks PURE Paper 1 Paper 2 Paper 3 Pure 1 S1 S2 S3 S4 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 Stats 1 Unit 1 Unit 2 Unit 3 Unit 4
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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 Q1
Easy -1.3
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
Easy -1.2
3 Make \(y\) the subject of the formula \(a = \frac { \sqrt { y } - 5 } { c }\).
OCR MEI C1 Q4
Easy -1.2
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
Easy -1.8
5 Find the value of each of the following.
  1. \(5 ^ { 2 } \times 5 ^ { - 2 }\)
  2. \(100 ^ { \frac { 3 } { 2 } }\)
OCR MEI C1 Q6
Easy -1.8
6 State the value of each of the following.
  1. \(2 ^ { - 3 }\)
  2. \(9 ^ { 0 }\)
OCR MEI C1 Q8
Easy -1.3
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
Easy -1.8
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
Easy -1.3
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
Easy -1.8
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
Easy -1.2
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
Easy -1.3
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
Easy -1.8
1 Solve the inequality \(\frac { 4 x - 5 } { 7 } > 2 x + 1\).
OCR MEI C1 Q2
Moderate -0.8
2 Solve the inequality \(3 x ^ { 2 } + 10 x + 3 > 0\).
OCR MEI C1 Q3
Moderate -0.8
3 Solve the inequality \(5 x ^ { 2 } - 28 x - 12 \leqslant 0\).
OCR MEI C1 Q4
Easy -1.8
4 Solve the following inequality. $$\frac { 2 x + 1 } { 5 } < \frac { 3 x + 4 } { 6 }$$
OCR MEI C1 Q5
Easy -1.8
5 Solve the inequality \(6 ( x + 3 ) > 2 x + 5\).
OCR MEI C1 Q6
Easy -1.8
6 Solve the inequality \(5 - 2 x < 0\).
OCR MEI C1 Q7
Easy -1.2
7 Solve the following inequalities.
  1. \(2 ( 1 - x ) > 6 x + 5\)
  2. \(( 2 x - 1 ) ( x + 4 ) < 0\)
OCR MEI C1 Q8
Easy -1.8
8 Solve the inequality \(\frac { 5 x - 3 } { 2 } < x + 5\).
OCR MEI C1 Q9
Easy -1.2
9 Solve the inequality \(x ( x - 6 ) > 0\).
OCR MEI C1 Q10
Easy -1.8
10 Solve the inequality \(7 - x < 5 x - 2\).
OCR MEI C1 Q11
Easy -1.8
11 Solve the inequality \(3 x - 1 > 5 - x\).
OCR MEI C1 Q12
Easy -1.8
12 Solve the inequality \(1 - 2 x < 4 + 3 x\).
OCR MEI C1 Q13
Easy -1.2
13 Solve the inequality \(x ^ { 2 } + 2 x < 3\).
OCR MEI C1 Q14
Easy -1.8
14 Solve the inequality \(\frac { 3 ( 2 x + 1 ) } { 4 } > - 6\).