4E5N AMP2 Prelim 2021 with Answer Key_MSS

3 1 Express in partial fractions. [6]

4 2 (a) The variables x and y are related in such a way that, when is plotted against , a straight line is obtained which passes through (4, 6) and (6, 10). Find the exact values of y for which . [4] (b) The table shows experimental values of x and y. 1.5 2.0 2.5 3.0 3.5 35 79 176 394 890 It is known that x and y are related by an equation of the form , where U and p are constants. (i) On the grid on page 5, draw a straight line graph to illustrate this data. [2] (ii) Use your graph to estimate the value of U and of p. [4] (iii) Estimate the value of x for which y = 500. [2]

5

6 x 3 The diagram shows part of the curve . The normal to the curve at R where x = 1 meets the line x = 3 at S. (i) Find the equation of normal RS. [4] y R S

7 (ii) Find the area bounded by the curve, the normal RS and the line x = 3. [5]

8 4 (a) A curve has equation and a line has equation . (i) Find the range of values of m for which the line intersects the curve at 2 distinct points. [4] (ii) Give an example of a possible value for m for which the line does not intersect the curve. [1]

9 (b) The curve with equation , where a and c are constants, lies completely above the x-axis. (i) Write down the conditions which must apply to a and c. [3] (ii) Give an example of possible values for a and c which satisfy the conditions in part (i). [2]

10 5 (i) Express in the form , where a and b are constants and hence find . [4] (ii) Given that , find an expression for . [2]

11 (iii) Using the results from (i) and (ii), find . [3]

12 6 The diagram shows two isosceles triangles AOB and COD. It is given that OA = OB = 6 cm, OC = OD = 4 cm, and . The sum of the areas of and is A cm2. (i) Show that . [2] (ii) Find the value of R and for which , where R > 0 and . [3] C B 6 cm x O 4 cm D A