Questions — AQA AS Paper 1 (133 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 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
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AQA AS Paper 1 Specimen Q10
7 marks Standard +0.3
A student conducts an experiment and records the following data for two variables, \(x\) and \(y\).
\(x\)123456
\(y\)1445130110013003400
\(\log_{10} y\)
The student is told that the relationship between \(x\) and \(y\) can be modelled by an equation of the form \(y = kb^x\)
  1. Plot values of \(\log_{10} y\) against \(x\) on the grid below. [2 marks] \includegraphics{figure_10}
  2. State, with a reason, which value of \(y\) is likely to have been recorded incorrectly. [1 mark]
  3. By drawing an appropriate straight line, find the values of \(k\) and \(b\). [4 marks]
AQA AS Paper 1 Specimen Q11
7 marks Standard +0.3
Chris claims that, "for any given value of \(x\), the gradient of the curve \(y = 2x^3 + 6x^2 - 12x + 3\) is always greater than the gradient of the curve \(y = 1 + 60x - 6x^2\)". Show that Chris is wrong by finding all the values of \(x\) for which his claim is not true. [7 marks]
AQA AS Paper 1 Specimen Q12
9 marks Moderate -0.3
A curve has equation \(y = 6x\sqrt{x} + \frac{32}{x}\) for \(x > 0\)
  1. Find \(\frac{dy}{dx}\) [4 marks]
  2. The point \(A\) lies on the curve and has \(x\)-coordinate 4 Find the coordinates of the point where the tangent to the curve at \(A\) crosses the \(x\)-axis. [5 marks]
AQA AS Paper 1 Specimen Q13
2 marks Easy -1.2
  1. The unit vectors \(\mathbf{i}\) and \(\mathbf{j}\) are perpendicular. Find the magnitude of the vector \(-20\mathbf{i} + 21\mathbf{j}\) Circle your answer. [1 mark] \(-1\) \(1\) \(\sqrt{41}\) \(29\)
  2. The angle between the vector \(\mathbf{i}\) and the vector \(-20\mathbf{i} + 21\mathbf{j}\) is \(\theta\) Which statement about \(\theta\) is true? Circle your answer. [1 mark] \(0° < \theta < 45°\) \(45° < \theta < 90°\) \(90° < \theta < 135°\) \(135° < \theta < 180°\)
AQA AS Paper 1 Specimen Q14
3 marks Moderate -0.8
In this question use \(g = 10\) m s⁻². A man of mass 80 kg is travelling in a lift. The lift is rising vertically. \includegraphics{figure_14} The lift decelerates at a rate of 1.5 m s⁻² Find the magnitude of the force exerted on the man by the lift. [3 marks]
AQA AS Paper 1 Specimen Q15
5 marks Moderate -0.8
The graph shows how the speed of a cyclist varies during a timed section of length 120 metres along a straight track. \includegraphics{figure_15}
  1. Find the acceleration of the cyclist during the first 10 seconds. [1 mark]
  2. After the first 15 seconds, the cyclist travels at a constant speed of 5 m s⁻¹ for a further \(T\) seconds to complete the 120-metre section. Calculate the value of \(T\). [4 marks]
AQA AS Paper 1 Specimen Q16
8 marks Moderate -0.3
A particle, of mass 400 grams, is initially at rest at the point \(O\). The particle starts to move in a straight line so that its velocity, \(v\) m s⁻¹, at time \(t\) seconds is given by \(v = 6t^2 - 12t^3\) for \(t > 0\)
  1. Find an expression, in terms of \(t\), for the force acting on the particle. [3 marks]
  2. Find the time when the particle next passes through \(O\). [5 marks]
AQA AS Paper 1 Specimen Q17
9 marks Moderate -0.3
In this question use \(g = 9.8\) m s⁻². A van of mass 1300 kg and a crate of mass 300 kg are connected by a light inextensible rope. The rope passes over a light smooth pulley, as shown in the diagram. The rope between the pulley and the van is horizontal. \includegraphics{figure_17} Initially, the van is at rest and the crate rests on the lower level. The rope is taut. The van moves away from the pulley to lift the crate from the lower level. The van's engine produces a constant driving force of 5000 N. A constant resistance force of magnitude 780 N acts on the van. Assume there is no resistance force acting on the crate.
    1. Draw a diagram to show the forces acting on the crate while it is being lifted. [1 mark]
    2. Draw a diagram to show the forces acting on the van while the crate is being lifted. [1 mark]
  2. Show that the acceleration of the van is 0.80 m s⁻² [4 marks]
  3. Find the tension in the rope. [2 marks]
  4. Suggest how the assumption of a constant resistance force could be refined to produce a better model. [1 mark]