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4x2 − 9 5 2. A curve has equation y = [5] x2 − 9 . x2 + 1 (i) Write down the coordinates of the points where the curve cuts the coordinate axes. [3] (ii) Explain why the curve has no vertical asymptotes, and give the equation of the horizontal asymptote. [2] (iii)Describe the behaviour of the curve for large positive and large negative values of x, justifying your description. [3] (iv) Sketch the curve. [4] x2 − 9 (v) The equation 2 = k has no real solutions. x +1 What can you say about the value of k?

2] (ii) Write down the equations of the three asymptotes. [3] (iii)Describe the behaviour of the curve for large positive and large negative values of x, justifying your description. [3] (iv) Sketch the curve. [4] (v) Solve the inequality x( x + 2) 1 < . 4x2 − 9 5 2. A curve has equation y = [5] x2 − 9 . x2 + 1 (i) Write down the coordinates of the points where the curve cuts the coordinate axes. [3] (ii) Explain why the curve has no vertical asymptotes, and give the equation of the horizontal asymptote.

4] 3. Solve the following inequalities. (i) ( x + 1)( x + 3) < 5 x + 9 5x + 9 x +1 [5] 1 1 ≤ 2x + 3 x − 2 [5] (ii) x + 3 < (iii) [3] © MEI, 03/01/07 1/2 Further Pure Mathematics 1 4 , giving the equations of the ( x − 2)( x + 2) asymptote(s) and the coordinates of the point(s) where the graph cuts the coordinate axes. [4] 4. (i) Sketch the graph of y = (ii) Write down the equation of the line of symmetry of the curve, and hence find the coordinates of the local maximum point. [2] 4 = k has no real solutions.

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MEI FP1 Study Resources Graphs And Inequalities 1-2 by Catherine Berry


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