# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/21) | Q#8

Question i.       By first expanding cos(2x + x), show that    ii.       Hence show that Solution      i.   We are given that   and we are required to express as; Therefore; We have the trigonometric identity; From this we can write; Hence;    ii.   We are required to show that; We have […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/21) | Q#7

Question The parametric equations of a curve are  ,  , i.       Show that . ii.       Show that the tangent to the curve at the point (1, 3) is parallel to the x-axis. iii.       Find the exact coordinates of the other point on the curve at which the tangent is parallel to the  x-axis. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/21) | Q#6

Question      i.       Verify by calculation that the cubic equation has a root that lies between x=0.7 and x=0.8.    ii.       Show that this root also satisfies an equation of the form where the values of a and b are to be found.   iii.       With these values of a and b, use the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/21) | Q#5

Question The polynomial 4×3 + ax2 + 9x + 9, where a is a constant, is denoted by p(x). It is given that when  p(x) is divided by (2x − 1) the remainder is 10. i.       Find the value of a and hence verify that (x − 3) is a factor of p(x).  ii. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/21) | Q#3

Question The diagram shows the part of the curve  for . Find the x-coordinates of the  points on this part of the curve at which the gradient is 4. Solution We are required to find the x-coordinate of the points on the curve where gradient is 4. Therefore first we need to find […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/21) | Q#2

Question Show that Solution We are required to show that; Rule for integration of  is: This integral is valid only when . Division Rule; Power Rule;

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/21) | Q#4

Question Solve the equation 32x − 7(3x) + 10 = 0, giving your answers correct to 3 significant figures. Solution We are given; Let; Hence; Now we have two options. Since ; 2 Taking natural logarithm of both sides; Power Rule;

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/21) | 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 as; We have to consider two separate cases; When When Therefore the inequality will […]