Questions C1 (1562 questions)

Browse by module
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 P1 P2 P3 P4 PMT Mocks PURE Paper 1 Paper 2 Paper 3 Pre-U 9794/1 Pre-U 9794/2 Pre-U 9794/3 Pre-U 9795 Pre-U 9795/1 Pre-U 9795/2 S1 S2 S3 S4 Unit 1 Unit 2 Unit 3 Unit 4
Browse by board
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 PURE 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 PURE S1 S2 S3 S4 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 Pre-U Pre-U 9794/1 Pre-U 9794/2 Pre-U 9794/3 Pre-U 9795 Pre-U 9795/1 Pre-U 9795/2 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
Sort by: Default | Easiest first | Hardest first
OCR MEI C1 Q9
4 marks Moderate -0.8
Rearrange the equation \(5c + 9t = a(2c + t)\) to make \(c\) the subject. [4]
OCR MEI C1 Q10
3 marks Easy -1.2
Factorise and hence simplify the following expression. $$\frac{x^2 - 9}{x^2 + 5x + 6}$$ [3]
OCR MEI C1 Q11
3 marks Easy -1.8
Rearrange the following equation to make \(h\) the subject. $$4h + 5 = 9a - ha^2$$ [3]
OCR MEI C1 Q1
3 marks Moderate -0.8
Expand \((2x + 5)(x - 1)(x + 3)\), simplifying your answer. [3]
OCR MEI C1 Q2
3 marks Easy -1.2
Find the discriminant of \(3x^2 + 5x + 2\). Hence state the number of distinct real roots of the equation \(3x^2 + 5x + 2 = 0\). [3]
OCR MEI C1 Q3
4 marks Moderate -0.5
Make \(x\) the subject of the formula \(y = \frac{1 - 2x}{x + 3}\). [4]
OCR MEI C1 Q4
3 marks Standard +0.3
Factorise \(n^3 + 3n^2 + 2n\). Hence prove that, when \(n\) is a positive integer, \(n^3 + 3n^2 + 2n\) is always divisible by 6. [3]
OCR MEI C1 Q5
4 marks Moderate -0.5
Express \(5x^2 + 20x + 6\) in the form \(a(x + b)^2 + c\). [4]
OCR MEI C1 Q6
3 marks Moderate -0.8
Rearrange the formula \(c = \sqrt{\frac{a + b}{2}}\) to make \(a\) the subject. [3]
OCR MEI C1 Q7
3 marks Easy -1.2
Make \(a\) the subject of the formula \(s = ut + \frac{1}{2}at^2\). [3]
OCR MEI C1 Q8
3 marks Moderate -0.5
Prove that, when \(n\) is an integer, \(n^3 - n\) is always even. [3]
OCR MEI C1 Q11
3 marks Easy -1.2
Solve the equation \(\frac{3x + 1}{2x} = 4\). [3]
OCR MEI C1 Q12
4 marks Standard +0.3
Find the range of values of \(k\) for which the equation \(2x^2 + kx + 18 = 0\) does not have real roots. [4]
OCR MEI C1 Q13
4 marks Moderate -0.5
Rearrange \(y + 5 = x(y + 2)\) to make \(y\) the subject of the formula. [4]
OCR MEI C1 Q1
5 marks Moderate -0.8
  1. Solve the equation \(2x^2 + 3x = 0\). [2]
  2. Find the set of values of \(k\) for which the equation \(2x^2 + 3x - k = 0\) has no real roots. [3]
OCR MEI C1 Q2
4 marks Moderate -0.5
Make \(x\) the subject of the equation \(y = \frac{x + 3}{x - 2}\). [4]
OCR MEI C1 Q3
4 marks Moderate -0.8
Solve the equation \(y^2 - 7y + 12 = 0\). Hence solve the equation \(x^4 - 7x^2 + 12 = 0\). [4]
OCR MEI C1 Q4
5 marks Easy -1.2
  1. Write \(\sqrt{48} + \sqrt{3}\) in the form \(a\sqrt{b}\), where \(a\) and \(b\) are integers and \(b\) is as small as possible. [2]
  2. Simplify \(\frac{1}{5 + \sqrt{2}} + \frac{1}{5 - \sqrt{2}}\). [3]
OCR MEI C1 Q5
3 marks Moderate -0.8
Solve the equation \(\frac{4x + 5}{2x} = -3\). [3]
OCR MEI C1 Q6
3 marks Moderate -0.8
Make \(a\) the subject of the equation $$2a + 5c = af + 7c.$$ [3]
OCR MEI C1 Q7
4 marks Standard +0.3
Find the set of values of \(k\) for which the equation \(2x^2 + kx + 2 = 0\) has no real roots. [4]
OCR MEI C1 Q8
2 marks Moderate -0.8
One root of the equation \(x^3 + ax^2 + 7 = 0\) is \(x = -2\). Find the value of \(a\). [2]
OCR MEI C1 Q9
2 marks Moderate -0.8
\(n\) is a positive integer. Show that \(n^2 + n\) is always even. [2]
OCR MEI C1 Q10
4 marks Moderate -0.5
Make \(C\) the subject of the formula \(P = \frac{C}{C + 4}\). [4]
OCR MEI C1 Q11
5 marks Moderate -0.8
  1. Find the range of values of \(k\) for which the equation \(x^2 + 5x + k = 0\) has one or more real roots. [3]
  2. Solve the equation \(4x^2 + 20x + 25 = 0\). [2]