Hits: 117

# 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: 117 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 | (P2-9709/23) | Q#4

Hits: 43 Question     i.       Find the quotient when   is divided by  ,  and show that the remainder  is 39.    ii.       Hence, show that the equation  has exactly one real root. Solution      i.   Hence quotient is and remainder is .    ii.   We are required to factorise; When a polynomial, , […]

# 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#6

Hits: 53 Question i.       Find the quotient and remainder when is divided by .    ii.       It is given that, when is divided by , the remainder is ZERO. Find the values of the constants  and .   iii.       When  and have these values, show that there is exactly one real value of satisfying the  […]

# 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#2

Hits: 94   Question      i.       Solve the equation .    ii.       Hence, using logarithms, solve the equation , giving the answer correct to  3 significant figures. Solution i.   SOLVING EQUATION: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases;  OR We have the equation; […]

# 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#1

Hits: 170   Question      i.       Solve the equation .    ii.       Hence, using logarithms, solve the equation , giving the answer correct to 3  significant figures. Solution     SOLVING EQUATION: ALGEBRAICALLY i.   Let, . We can write it as; We have to consider two separate cases; When When We have the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | May-Jun | (P2-9709/21) | Q#1

Hits: 370   Question      i.       Solve the equation .    ii.       Hence, using logarithms, solve the equation , giving the answer  correct to 3 significant figures. Solution i.   SOLVING EQUATION: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases;  OR We have the equation; […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2015 | June | Q#5

Hits: 38   Question The equation  , where p is a constant has no real roots. a.   Show that p satisfies p2 – 6p +1 > 0 b.   Hence, find the set of possible values of p. Solution a.   We are given that;   We are given that given equation has no real solutions of x (roots). For […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#8

Hits: 37   Question A curve has equation  and a line has equation  , where k is a  constant. a.   Show that the x-coordinate of any point of intersection of the curve and the line satisfies the equation b.   Given that the line and the curve do not intersect:.                    i.       Show […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#7

Hits: 33   Question a.   Sketch the curve with equation . b.   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.       Hence show that the equation  has exactly one real root and state its […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#5

Hits: 24   Question a.   Express  in the form  , where p and q are rational numbers. b.   A curve has equation .                     i.       Use the result from part (a) to write down the coordinates of the vertex of the curve.                   ii.       State the equation of the line of symmetry of the curve. c.   The curve with equation  is translated by vector . Find the […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#4

Hits: 48   Question A circle with center C has the equation .  a.   Express this equation in the form b.                                i.       State the coordinates of C.                          ii.       Find the radius of the circle, giving your answer in the form  . c.                         i.       The point P with coordinates (4,k) lies on the circle. Find the possible values of k. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/13) | Q#8

Hits: 803 Question The function  is defined by  for , where a is a constant. The function  is  defined  for .      i.       Find the largest value of a for which the composite function can be formed. For the case where ,    ii.       solve the equation ,   iii.       find the set of values of  which satisfy the inequality . Solution i. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/13) | Q#3

Hits: 549 Question i.       Express  in the form , where a, b and c are constants.  ii.   The function, where , is defined for . Find  and state, with       a reason, whether  is an increasing function, a decreasing function or neither. Solution i.   We have the expression; We use method of “completing square” to obtain […]