Questions AS Paper 1 (378 questions)

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Edexcel AS Paper 1 Q13
10 marks Moderate -0.3
\includegraphics{figure_4} The value of a sculpture, \(£V\), is modelled by the equation \(V = Ap^t\), where \(A\) and \(p\) are constants and \(t\) is the number of years since the value of the painting was first recorded on 1st January 1960. The line \(l\) shown in Figure 4 illustrates the linear relationship between \(t\) and \(\log_{10}V\) for \(t \geq 0\). The line \(l\) passes through the point \((0, \log_{10}20)\) and \((50, \log_{10}2000)\).
  1. Write down the equation of the line \(l\). [3]
  2. Using your answer to part a or otherwise, find the values of \(A\) and \(p\). [4]
  3. With reference to the model, interpret the values of the constant \(A\) and \(p\). [2]
  4. Use your model, to predict the value of the sculpture, on 1st January 2020, giving your answer to the nearest pounds. [1]
Edexcel AS Paper 1 Q14
11 marks Standard +0.3
A curve with centre \(C\) has equation $$x^2 + y^2 + 2x - 6y - 40 = 0$$
    1. State the coordinates of \(C\).
    2. Find the radius of the circle, giving your answer as \(r = n\sqrt{2}\). [3]
  2. The line \(l\) is a tangent to the circle and has gradient \(-7\). Find two possible equations for \(l\), giving your answers in the form \(y = mx + c\). [8]
Edexcel AS Paper 1 Q15
Challenging +1.2
\includegraphics{figure_5} Figure 5 shows a sketch of part of the curve \(y = 2x + \frac{8}{x^2} - 5\), \(x > 0\). The point \(A(4, \frac{7}{2})\) lies on C. The line \(l\) is the tangent to C at the point A. The region \(R\), shown shaded in figure 5 is bounded by the line \(l\), the curve C, the line with equation \(x = 1\) and the \(x\)-axis. Find the exact area of \(R\). (Solutions based entirely on graphical or numerical methods are not acceptable.)