Hits: 100

# 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: 100   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: 75     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: 84   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#6

Hits: 9   Question The equation x2 + 3px + p = 0, where p is a non-zero constant, has equal roots. Find the value of p. Solution We are given that; We are given that given equation has equal roots. For a quadratic equation , the expression for solution is; Where  is called discriminant. If , the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | June | Q#4

Hits: 15   Question Find the set of values of x for which a.    b.    c.   both  and Solution a.   We are given; b.   We are required to solve the inequality; We solve the following equation to find critical values of ; Now we have two options; Hence the critical points on the curve for the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | January | Q#7

Hits: 23   Question The equation kx2 + 4x + (5 – k) = 0, where k is a constant, has 2 different real solutions for x. a.   Show that k satisfies k2 – 5k + 4 > 0. b.   Hence find the set of possible values of k. Solution a.   We are given;   We are given […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | June | Q#4

Hits: 58   Question a.  The polynomial  is given by                     i.       Find the remainder when  is divided by .                   ii.       Use the Factor Theorem to show that  is a factor of .                  iii.       Express  in the form  , where b and c are integers.               iv.       The equation  has one root equal to -2. Show that equation has no other […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | January | Q#4

Hits: 52   Question a.                 i.               Express  in the form  , where p and q are integers.           ii.               Hence show that  is always positive. b.   A curve has equation  .                            i.               Write down the coordinates of the minimum point of the curve.                          ii.               Sketch the curve, showing the value of the intercept on […]

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

Hits: 35   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#6

Hits: 15   Question a.                       i.       Express  in the form  , where p and q are integers.                 ii.       Hence write down the minimum value of .               iii.       State the value of  for which the minimum value of  occurs.    b.   The point A has coordinates (5,4) and the point B has coordinates (x,7-x) . […]

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

Hits: 40   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#2

Hits: 16   Question a.   Factorise . b.   Hence, or otherwise, solve the inequality Solution a.   We are given the expression; b.     We are required to solve the inequality; We solve the following equation to find critical values of ; From (a) we know that this equation can be written as; Now we have two options. Hence the critical […]