Hits: 92

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/22) | Q#7

Hits: 92     Question The equation of a curve is        i.       Show that    ii.       Find the coordinates of each of the points on the curve where the tangent is parallel to the x- axis. Solution      i.   We are given; We are required to find . To find from an […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/23) | Q#4

Hits: 79   Question The parametric equations of a curve are for t < 0.      i.       Show that in terms of t.    ii.       Find the exact coordinates of the only point on the curve at which the gradient is 3. Solution      i.   We are required to find  for the parametric equations […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/21) | Q#4

Hits: 62   Question The parametric equations of a curve are for t < 0.      i.       Show that in terms of t.    ii.       Find the exact coordinates of the only point on the curve at which the gradient is 3. Solution      i.   We are required to find  for the parametric equations […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/22) | Q#5

Hits: 92   Question The parametric equations of a curve are      i.       Find an expression for in terms of t.      i.       Find the equation of the normal to the curve at the point for which t = 0. Give your answer in  the form ax + by + c = 0, where a, […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/23) | Q#1

Hits: 49   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 2012 | Oct-Nov | (P2-9709/22) | Q#1

Hits: 47     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 2012 | Oct-Nov | (P2-9709/21) | Q#1

Hits: 51   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 2012 | May-Jun | (P2-9709/23) | Q#1

Hits: 42     Question Solve the equation . Solution SOLVING EQUATION: PIECEWISE Let, . We can write it as; We have to consider two separate cases; When When We have the equation; We have to consider two separate cases; When ; When ; Hence, the only solutions for the given equation are; SOLVING EQUATION: […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/22) | Q#1

Hits: 86     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 2012 | May-Jun | (P2-9709/21) | Q#1

Hits: 126     Question Solve the equation . Solution SOLVING EQUATION: PIECEWISE Let, . We can write it as; We have to consider two separate cases; When When We have the equation; We have to consider two separate cases; When ; When ; Hence, the only solutions for the given equation are; SOLVING EQUATION: […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | June | Q#10

Hits: 43   Question Figure 1 shows a sketch of the curve C with equation y = f(x) where f (x) = x2(9 –2x) There is a minimum at the origin, a maximum at the point (3, 27) and C cuts the x-axis at the point  A. a.   Write down the coordinates of the point A. b.   […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | June | Q#9

Hits: 24   Question The line L1 has equation 4y + 3 = 2x. The point A (p, 4) lies on L1. a.   Find the value of the constant p. The line L2 passes through the point C (2, 4) and is perpendicular to L1. b.   Find an equation for L2 giving your answer in the form ax […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | June | Q#8

Hits: 19   Question Where p and q are integers. a.   Find the value of p and the value of q. b.   Calculate the discriminant of  . c.  On the axes on page 17, sketch the curve with equation  showing clearly the  coordinates of any points where the curve crosses the coordinate axes. Solution a.   We have the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | June | Q#7

Hits: 17 Question The point P(4,–1) lies on the curve C with equation y = f(x), x > 0, and a.   Find the equation of the tangent to C at the point P, giving your answer in the form y = mx + c,  where m and c are integers. b.   Find f(x). Solution a.   We are […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#10

Hits: 36 Question Figure 2 shows a sketch of the curve C with equation  , x ≠ 0 The curve crosses the x-axis at the point A. a.   Find the coordinates of A. b.   Show that the equation of the normal to C at A can be written as 2x+8y−1=0 The normal to C at A meets C again […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#6

Hits: 23 Question The line  has equation 2x − 3y +12 = 0. a.   Find the gradient of . The line  crosses the x-axis at the point A and the y-axis at the point B, as shown in Figure. The line  is perpendicular to  and passes through B. b.   Find an equation of . The line  crosses the x-axis at […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#5

Hits: 19   Question The curve C has equation y=x(5−x) and the line L has equation 2y=5x+4. a.   Use algebra to show that C and L do not intersect. b.   In the space on page 11, sketch C and L on the same diagram, showing the coordinates of the  points at which C and L meet the […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | June | Q#7

Hits: 23   Question The gradient,  , of a curve C at the point (x,y) is given by a.                         i.       Show that y is increasing when .                   ii.       Solve the inequality . b.   The curve C passes through the point P(2,3).                     i.       Verify that the tangent to the curve at P is parallel to the x-axis.                   ii.       The point Q(3,-1) also […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | June | Q#6

Hits: 72   Question The circle with centre C(5,8) touches the y-axis, as shown in the diagram. a.   Express the equation of the circle in the form b.                         i.       Verify that the point A(2,12) lies on the circle.                   ii.       Find an equation of the tangent to the circle at the point A, giving your answer in the form    , […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | June | Q#5

Hits: 58   Question a.                         i.       Express  in the form .                   ii.       Hence write down the equation of the line of symmetry of the curve with equation . b.   The curve C with equation  and the straight line  intersect at the point  A(0,5) and at the point B, as shown in the diagram below. i.       Find the coordinates of the point B. […]