# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | May-Jun | (P2-9709/02) | Q#7

Question      i.       Differentiate ln(2x + 3).    ii.       Hence, or otherwise, show that   iii.       Find the quotient and remainder when 4×2 + 8x is divided by 2x + 3.   iv.       Hence show that Solution      i.   We are required to find; If we define , then derivative […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | May-Jun | (P2-9709/02) | Q#6

Question      i. By sketching a suitable pair of graphs, show that there is only one value of x that is a root of the  equation    ii. Verify, by calculation, that this root lies between 1 and 2.   iii. Show that, if a sequence of values given by the iterative formula […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | May-Jun | (P2-9709/02) | Q#5

Question The equation of a curve is 3×2 + 2xy + y2 = 6. It is given that there are two points on the curve where the tangent is parallel to the x-axis. i.       Show by differentiation that, at these points, y = −3x. ii.       Hence find the coordinates of the two […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | May-Jun | (P2-9709/02) | Q#2

Question i. Prove the identity    ii. Hence solve the equation For . Solution      i.   We are given that; We utilize following two addition formulae;    ii.   We are required to solve; As demonstrated in (i); Therefore; Using calculator we can find; Properties of Domain Range Periodicity Odd/Even Translation/ Symmetry All other […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | May-Jun | (P2-9709/02) | Q#1

Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let  and , then; We have to consider two separate cases; When When We have the inequality; It can be written as; We have to consider two separate cases; When When Therefore the inequality will hold for ; SOLVING INEQUALITY: ALGEBRAICALLY Let, . Since given […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | May-Jun | (P2-9709/02) | Q#4

Question The cubic polynomial , where  and  are constants, is denoted by . It is given that   and  are factors of .     i.       Find the values of  and .    ii.       When  and  have these values, find the other linear factor of . Solution      i.   We are given that; We […]