# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/22) | Q#6

Question The polynomial is defined by The diagram shows the curve which crosses the x-axis at  and .      i.       Divide by a suitable linear factor and hence show that is a root of the equation    ii.       Use the iterative formula to find correct to 2 decimal places. Give the   result of each iteration […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/23) | Q#5

Question i.       Given that  and  are factors of    ii.       When a and b have these values, factorise completely, and hence solve the equation giving any answers correct to 3 significant figures. Solution      i.   We are given that;   We are also given that and are factors of . We can write the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/21) | Q#5

Question i.       Given that  and  are factors of    ii.       When a and b have these values, factorise completely, and hence solve the equation giving any answers correct to 3 significant figures. Solution      i.   We are given that;    We are also given that and are factors of . We can write […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/23) | Q#6

Question The polynomial p(x) is defined by where a is a constant.     i.       Given that (x + 2) is a factor of p(x), find the value of a. ii.       When a has this value, find the quotient when p(x) is divided by (x + 2) and hence show that the  equation […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/22) | Q#6

Question The polynomial p(x) is defined by where a is a constant.     i.       Given that (x + 2) is a factor of p(x), find the value of a. ii.       When a has this value, find the quotient when p(x) is divided by (x + 2) and hence show that the  equation […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/21) | Q#3

Question     i.       Find the quotient when  is divided by ,  and confirm that the  remainder is 7. ii.       Hence solve the equation . Solution      i.   Hence quotient is and remainder is .    ii.  We are required to solve; When a polynomial, , is divided by a non-constant divisor, […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2014 | June | Q#1

Question Factorise fully Solution We are given; We have algebraic formula; Therefore;

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#4

Question Figure 1 shows a sketch of the curve C with equation  , x ≠ 0. The curve C crosses the x-axis at the point A. a.   State the x coordinate of the point A. The curve D has equation y = x2(x – 2), for all real values of x. b.   A copy of Figure 1 […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663A/01) | Year 2014 | January | Q#9

Question A curve with equation y=f(x) passes through the point (3,6). Given that a.   use integration to find f(x). Give your answer as a polynomial in its simplest form. b.   Show that , where p is a positive constant. State the value of p. c.   Sketch the graph of y = f(x), showing the coordinates of […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2014 | June | Q#5

Question The polynomial  is given by . where c and d are integers. a.    Given that  is a factor of  show that b.   The remainder when  is divided by  is 65. Obtain a function in c and d. c.   Use equations from parts (a) and (b) to find the value of c and the value of d. Solution a.   Factor […]