Hits: 130

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | Oct-Nov | (P2-9709/21) | Q#8

Hits: 130     Question The equation of a curve is y2 + 2xy − x2 = 2.      i.       Find the coordinates of the two points on the curve where x = 1.    ii.       Show by differentiation that at one of these points the tangent to the curve is parallel to […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | May-Jun | (P2-9709/02) | Q#8

Hits: 239     Question a)   Find the equation of the tangent to the curve at the point where . b)                  i.       Find the value of the constant A such that           ii.       Hence show that Solution a.     We are given that curve with […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | May-Jun | (P2-9709/02) | Q#7

Hits: 217     Question The diagram shows the curve and its minimum point M.      i.       Find the exact coordinates of M.    ii.       Show that the curve intersects the line y = 20 at the point whose x-coordinate is the root of  the equation   iii.       Use the iterative formula […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | Oct-Nov | (P2-9709/22) | Q#1

Hits: 104   Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following with their corresponding inequality; When When When If then above four intervals translate to […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | Oct-Nov | (P2-9709/21) | Q#1

Hits: 78     Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following with their corresponding inequality; When When When If then above four intervals translate […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | May-Jun | (P2-9709/02) | Q#2

Hits: 134     Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following with their corresponding inequality; When When When If then above four intervals translate […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | June | Q#11

Hits: 88   Question The curve C has equation The point P has coordinates (2, 7). a)   Show that P lies on C. b)  Find the equation of the tangent to C at P, giving your answer in the form y=mx+c, where m and c  are constants. The point Q also lies on C. Given that the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | June | Q#8

Hits: 137 Question The points A and B have coordinates (6, 7) and (8, 2) respectively. The line  passes through the point A and is perpendicular to the line AB, as shown in Figure 1. a)   Find an equation for  in the form ax + by + c = 0, where a, b and c are integers. […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | January | Q#11

Hits: 69 Question The curve C has equation , The point P on C has x-coordinate equal to 2. a.   Show that the equation of the tangent to C at the point P is y = 1 – 2x. b.   Find an equation of the normal to C at the point P. The tangent at P […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | January | Q#10

Hits: 178   Question The line  passes through the point A (2, 5) and has gradient . a.  Find an equation of , giving your answer in the form y = mx + c. The point B has coordinates (–2, 7). b.   Show that B lies on . c.   Find the length of AB, giving your answer in […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | January | Q#8

Hits: 35   Question The point P (1, a) lies on the curve with equation y = (x + 1)2(2– x). a.   Find the value of a. b.   On the axes below sketch the curves with the following equations: i.       y = (x + 1)2(2– x) ii.        On your diagram show clearly the coordinates of any […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | June | Q#5

Hits: 84   Question A circle with center C has equation .  a.   Write down:                            i.       the coordinates of C;                          ii.       the radius of the circle b.   The point D has coordinates (7,-2).                            i.       Verify that the circle passes through the origin O.                          ii.       Given that the circle also passes through the points (10,0) and (0,p), sketch the circle  and find the value […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | January | Q#6

Hits: 60   Question a.  The polynomial  is given by .                     i.       Use the Factor Theorem to show that  is a factor of .                   ii.       Express  in the form  , where a and b are constants. b. The curve C with equation  , sketched below, crosses the x-axis at the point .                     i.       Find the gradient of the curve C at the point Q.                   ii.       Hence […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | June | Q#7

Hits: 37   Question The curve C has equation  , where k is a constant. The line L has equation . a.   Show that the x-coordinates of any points of intersection of the curve C with the line L satisfy the  equation b.   The curve C and the line L intersect in two distinct points.       […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | June | Q#3

Hits: 31   Question The curve with equation  passes through the point P, where  . a.   Find                          i.                                  ii.        b.   Verify that the point P is a stationary point of the curve. c.                                i.       Find the value of  at the point P.                           ii.       Hence, or otherwise, determine whether […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | June | Q#1

Hits: 29   Question The line AB has equation . a.                        i.       Find the gradient of AB.                   ii.       The point A has coordinates (2,1) . Find an equation of the line which passes through the  point A and which is perpendicular to AB. b.  The line AB intersects the line with equation  at the point C. Find the            coordinates of C. Solution […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | January | Q#7

Hits: 41   Question A circle with center C has equation .  a.   Express this equation in the form b.   Write down:                            i.       the coordinates of C;                          ii.       the radius of the circle c.   The point D has coordinates (7,-2).                            i.       Verify that point D lies on the circle.                          ii.       Find an equation of the normal to the circle at the point […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | January | Q#1

Hits: 72   Question The points A and B have coordinates (1,6) and (5,-2) respectively. The mid-point of AB is M. a.   Find the coordinates of M. b.   Find the gradient of AB, giving your answer in its simplest form. c.   A straight line passes through M and is perpendicular to AB.                     i.       Show that this line has […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/12) | Q#10

Hits: 733 Question i.       The diagram shows the line  and the curve , which intersect at the points A and B. Find a.   the x-coordinates of A and B, b.   the equation of the tangent to the curve at B, c.   the acute angle, in degrees correct to 1 decimal place, between this tangent and the line . […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/12) | Q#9

Hits: 242 Question The diagram shows a rectangle . The point  is  and  is . The diagonal  is parallel to the x-axis.     i.       Explain why the y-coordinate of  is 6. The x-coordinate of  is .    ii.       Express the gradients of  and  in terms of .   iii.       Calculate the x-coordinates of  and .   iv.       Calculate the area of the rectangle . Solution i. […]