# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | January | Q#10

Question Given that ,, a)   Express  in the form , where a and b are integers. The curve C with equation y = f(x), , meets the y-axis at P and has a minimum point at Q.  b)  In the space provided on page 19, sketch the graph of C, showing the coordinates of P and Q. The […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | January | Q#9

Question The gradient of the curve C is given by The point P(1,4) lies on C. a)   Find an equation of the normal to C at P. b)  Find an equation for the curve C in the form . c)   Using , show that there is no point on C which the tangent is […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | January | Q#8

Question The points A(1,7), B(20,7) and C(p,q) form the vertices of a triangle ABC, as shown in Figure 2. The  point D(8, 2) is the mid-point of AC. a)   Find the value of p and the value of q. The line l, which passes through D and is perpendicular to AC, intersects AB at E. b)  Find […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | January | Q#7

Question The curve C has equation , . The point P on C has x-coordinate 1.  a)   Show that the value of  at P is 3. b)  Find an equation of the tangent to C at P. This tangent meets the x-axis at the point (k,0). c)   Find the value of k. Solution a)     We need […]

# 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#5

Question The rth term of an arithmetic series is (2r – 5). a.   Write down the first three terms of this series. b.   State the value of the common difference. c.   Show that Solution a.     We are given that rth term of arithmetic series is represented by; Therefore, to find any term k we substitute […]

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

Question Solve the simultaneous equations Solution We are given simultaneous equations; Rearranging the first equation we get expression for ; Substituting this for  in the second equation; We have the algebraic formula; Therefore; Now we have two options. By substituting one-by-one these values of  in above derived expression of , we can find  corresponding values of . For For Hence, there […]

# 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 | January | Q#2

Question Given that , find a.   b.   c.   Find Solution a.   We are given; We are required to find . Rule for differentiation of  is: Rule for differentiation of  is: b.   We are required to find . Second derivative is the derivative of the derivative. If we have derivative of the curve   as  , then  […]

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

Question a.   Write down the value of . b.   Find the value of . Solution a.   b.