# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | January | Q#6

Question Figure 1 shows a sketch of the curve with equation y = f(x). The curve crosses the x-axis at the  points (2, 0) and (4, 0). The minimum point on the curve is P(3, –2). In separate diagrams sketch the curve with equation a.   y=–f(x), b.   y=f(2x). On each diagram, give the coordinates of the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | January | Q#3

Question Given that the equation , where k is a positive constant, has equal roots, find the value of k. Solution We are given; We can given that given equation has equal roots. For a quadratic equation , the expression for solution is; Where  is called discriminant. If , the equation will have two distinct roots. If […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | June | Q#4

Question Figure 1 shows a sketch of the curve with equation y = f(x). The curve passes through the origin O  and through the point (6, 0). The maximum point on the curve is (3, 5).  On separate diagrams, sketch the curve with equation a.   y = 3f(x), b.   y = f(x + 2). On each […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2005 | May-Jun | (P1-9709/01) | Q#7

Question The function  is defined for the domain .      i.       Find the range of .    ii.       Sketch the graph of . A function g is defined by , for , where A is a constant.   iii.     State the largest value of  for which  has an inverse.   iv.       When  has this value, obtain an expression, in terms of , […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2005 | Oct-Nov | (P1-9709/01) | Q#8

Question A function f is defined by  for .      i.       Find an expression, in terms of , for  and show that f is an increasing function.    ii.       Find an expression, in terms of , for  and find the domain of . Solution i.   We have the function; The expression for  represents derivative of . Rule for differentiation is of  is: Rule for differentiation […]