Questions — AQA FP1 (182 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
AQA FP1 2016 June Q3
7 marks Moderate -0.3
The variables \(y\) and \(x\) are related by an equation of the form $$y = a(b^x)$$ where \(a\) and \(b\) are positive constants. Let \(Y = \log_{10} y\).
  1. Show that there is a linear relationship between \(Y\) and \(x\). [2 marks]
  2. The graph of \(Y\) against \(x\), shown below, passes through the points \((0, 2.5)\) and \((5, 0.5)\). \includegraphics{figure_3}
    1. Find the gradient of the line. [1 mark]
    2. Find the value of \(a\) and the value of \(b\), giving each answer to three significant figures. [4 marks]
AQA FP1 2016 June Q4
7 marks Moderate -0.3
  1. Given that \(\sin \frac{\pi}{3} = \cos \frac{\pi}{k}\), state the value of the integer \(k\). [1 mark]
  2. Hence, or otherwise, find the general solution of the equation $$\cos \left( 2x - \frac{5\pi}{6} \right) = \sin \frac{\pi}{3}$$ giving your answer, in its simplest form, in terms of \(\pi\). [4 marks]
  3. Hence, given that \(\cos \left( 2x - \frac{5\pi}{6} \right) = \sin \frac{\pi}{3}\), show that there is only one finite value for \(\tan x\) and state its exact value. [2 marks]
AQA FP1 2016 June Q5
9 marks Standard +0.8
  1. Use the formulae for \(\sum_{r=1}^n r^2\) and \(\sum_{r=1}^n r\) to show that \(\sum_{r=1}^n (6r - 3)^2 = 3n(4n^2 - 1)\). [5 marks]
  2. Hence express \(\sum_{r=1}^{2n} r^3 - \sum_{r=1}^n (6r - 3)^2\) as a product of four linear factors in terms of \(n\). [4 marks]
AQA FP1 2016 June Q6
9 marks Standard +0.8
A parabola with equation \(y^2 = 4ax\), where \(a\) is a constant, is translated by the vector \(\begin{bmatrix} 2 \\ 3 \end{bmatrix}\) to give the curve \(C\). The curve \(C\) passes through the point \((4, 7)\).
  1. Show that \(a = 2\). [3 marks]
  2. Find the values of \(k\) for which the line \(ky = x\) does not meet the curve \(C\). [6 marks]
AQA FP1 2016 June Q7
10 marks Standard +0.3
  1. Solve the equation \(x^2 + 4x + 20 = 0\), giving your answers in the form \(c + di\), where \(c\) and \(d\) are integers. [3 marks]
  2. The roots of the quadratic equation $$z^2 + (4 + i + qi)z + 20 = 0$$ are \(w\) and \(w^*\).
    1. In the case where \(q\) is real, explain why \(q\) must be \(-1\). [2 marks]
    2. In the case where \(w = p + 2i\), where \(p\) is real, find the possible values of \(q\). [5 marks]
AQA FP1 2016 June Q8
10 marks Standard +0.3
The matrix \(\mathbf{A}\) is defined by \(\mathbf{A} = \begin{bmatrix} 2 & 0 \\ 0 & 1 \end{bmatrix}\).
    1. Find the matrix \(\mathbf{A}^2\). [1 mark]
    2. Describe fully the single geometrical transformation represented by the matrix \(\mathbf{A}^2\). [1 mark]
  2. Given that the matrix \(\mathbf{B}\) represents a reflection in the line \(x + \sqrt{3}y = 0\), find the matrix \(\mathbf{B}\), giving the exact values of any trigonometric expressions. [2 marks]
  3. Hence find the coordinates of the point \(P\) which is mapped onto \((0, -4)\) under the transformation represented by \(\mathbf{A}^2\) followed by a reflection in the line \(x + \sqrt{3}y = 0\). [6 marks]
AQA FP1 2016 June Q9
11 marks Standard +0.3
A curve \(C\) has equation \(y = \frac{x - 1}{(x - 2)(2x - 1)}\). The line \(L\) has equation \(y = \frac{1}{2}(x - 1)\).
  1. Write down the equations of the asymptotes of \(C\). [2 marks]
  2. By forming and solving a suitable cubic equation, find the \(x\)-coordinates of the points of intersection of \(L\) and \(C\). [3 marks]
  3. Given that \(C\) has no stationary points, sketch \(C\) and \(L\) on the same axes. [3 marks]
  4. Hence solve the inequality \(\frac{x - 1}{(x - 2)(2x - 1)} \geqslant \frac{1}{2}(x - 1)\). [3 marks]