Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2003 | Oct-Nov | (P2-9709/02) | Q#7

Question      i.       By differentiating  , show that if y = cot x then    ii.       Hence, show that   By using appropriate trigonometrical identities, find the exact value of     iii.     iv.   Solution      i.   We are given; Gradient (slope) of the curve is the derivative of equation of the curve. Hence gradient of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2003 | Oct-Nov | (P2-9709/02) | Q#6

Question The diagram shows the curve y=(4−x)ex and its maximum point M. The curve cuts the x-axis at A  and the y-axis at B.     i.       Write down the coordinates of A and B.    ii.       Find the x-coordinate of M.   iii.       The point P on the curve has x-coordinate p. The tangent to the curve at P passes through the  […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2003 | Oct-Nov | (P2-9709/02) | Q#5

Question      i.       By sketching a suitable pair of graphs, for x < 0, show that exactly one root of the equation    is negative.    ii.       Verify by calculation that this root lies between -1.0 and -0.5.   iii.       Use the iterative formula to determine the root correct to 2 decimal places, showing the result of each iteration. Solution      […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2003 | Oct-Nov | (P2-9709/02) | Q#4

Question i.       Express  in the form , where  and , giving exact  value of . ii.       Hence show that one solution of the equation , and find the other solution in the interval 0 < θ < 2π. Solution      i.   We are given that; We are required to write it in the form; If  and  are positive, then; […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2003 | Oct-Nov | (P2-9709/02) | Q#3

Question The polynomial  is denoted by .     i.       It is given that  is a factor of . Find the value of .  ii.   When  has this value, verify that  is also a factor of  and hence factorise  completely. Solution i.  We are given that; We are also given that  is a factor of . When a polynomial, , is […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2003 | Oct-Nov | (P2-9709/02) | Q#2

Question Two variable quantities x and y are related by the equation where a and k are constants. Four pairs of values of x and y are measured experimentally. The result of plotting ln y against x is  shown in the diagram. Use the diagram to estimate the values of a and k. Solution We […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2003 | Oct-Nov | (P2-9709/02) | Q#1

Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . It can be written as; We have to deal with two separate cases; When ; When Therefore; Therefore; Hence, Hence, We have the inequality; It can be written in standard form as; We have to consider two separate cases; When When Therefore […]