Hits: 125

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/23) | Q#7

Hits: 125 Question The equation of a curve is      i.       Show that;    ii.       Find the x-coordinate of each stationary point of the curve in the interval . Give each answer correct to 3 significant figures. Solution      i.   We are required to show that; We are given; We utilize Quotient Rule to […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/22) | Q#5

Hits: 48 Question Find the x-coordinates of the stationary points of the following curves:      i.      ii.   Solution      i.   First we are required to find the x-coordinate of the stationary points of the following curve. A stationary point on the curve is the point where gradient of the curve is […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/21) | Q#7

Hits: 126   Question The parametric equations of a curve are for .  The curve crosses the x-axis at points B and D and the stationary points are A and C, as shown in the diagram. i.       Show that .    ii.       Find the values of t at A and C, giving each answer correct […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/21) | Q#2

Hits: 37     Question The equation of a curve is Find the coordinates of the points on the curve at which the gradient is −4. Solution We are given equation of the curve as; We need expression for gradient of the curve. Gradient (slope) of the curve is the derivative of equation of the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | May-Jun | (P2-9709/23) | Q#7

Hits: 91 Question A.  Find the gradient of the curve At the point (1,1). B.  The parametric equations of a curve are Find the gradient of the curve at the point (−3, 3). Solution A.    We are given equation of the curve as; We are required to find expression for gradient of the curve. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | May-Jun | (P2-9709/23) | Q#4

Hits: 155 Question The diagram shows the curve  and its minimum point M.      i.       Show that the x-coordinate of M is .    ii.       The region shaded in the diagram is enclosed by the curve and the lines ,   and  . Use integration to show that the area of the shaded region is . […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | May-Jun | (P2-9709/22) | Q#7

Hits: 129 Question A.  Find the gradient of the curve At the point (1,1). B.  The parametric equations of a curve are Find the gradient of the curve at the point (−3, 3). Solution A.    We are given equation of the curve as; We are required to find expression for gradient of the curve. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | May-Jun | (P2-9709/22) | Q#4

Hits: 126     Question The diagram shows the curve  and its minimum point M.      i.       Show that the x-coordinate of M is .    ii.       The region shaded in the diagram is enclosed by the curve and the lines ,   and  . Use integration to show that the area of the shaded region […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | May-Jun | (P2-9709/21) | Q#7

Hits: 456 Question The equation of a curve is y3+4xy=16      i.       Show that .    ii.       Show that the curve has no stationary points.   iii.       Find the coordinates of the point on the curve where the tangent is parallel to the y-axis. Solution      i.   We are required to find . Hence; […]