# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | June | Q#9

Question  , x>0 a)   Show that , where A and B are constants to be found. b)  Find c)   Evaluate . Solution a)     We are given; Utilizing algebraic identity; b)   We are given; We are required to find . We can write the given equation/function as; Gradient (slope) of the curve is the derivative of […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | January | Q#10

Question a.   On the same axes sketch the graphs of the curves with equations i.       y=x2(x –2), ii.     y=x(6 –x), and indicate on your sketches the coordinates of all the points where the curves  cross the x-axis. b.   Use algebra to find the coordinates of the points where the graphs intersect. Solution a.         […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | June | Q#10

Question The curve C with equation y=f(x), x ≠ 0, passes through the point . Given that a.   find f(x). b.   Verify that f(–2) = 5. c.   Find an equation for the tangent to C at the point (–2, 5), giving your answer in the form ax + by +  c = 0, where a, b […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | June | Q#2

Question Find the set of values of x for which Solution 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 given condition are  & 9. Standard  orm of quadratic equation is; The graph of quadratic […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | January | Q#10

Question a.   Find the values of the constants a and b. b.   In the space provided below, sketch the graph of , indicating clearly the coordinates of any intersections with the coordinate axes. c.   Find the value of the discriminant of . Explain how the sign of the discriminant relates  to your sketch in part (b). […]

# 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 […]