# 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 2006 | January | Q#9

Question Figure 2 shows part of the curve C with equation The curve cuts the x-axis at the points P, (1, 0) and Q, as shown in Figure 2. a.   Write down the x-coordinate of P, and the x-coordinate of Q. b.   Show that . c.   Show that y=x+7 is an equation of the tangent to […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | January | Q#8

Question The curve with equation y=f (x) passes through the point (1,6). Given that , , find f(x) and simplify your answer. Solution We are required to find f(x), when; We are also given that , and the curve passes through the point (1,6). Clearly it is the case of finding equation from its derivative. We can find equation of […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | January | Q#7

Question On Alice’s 11th birthday she started to receive an annual allowance. The first annual allowance was  £500 and on each following birthday the allowance was increased by £200. a.   Show that, immediately after her 12th birthday, the total of the allowances that Alice had received  was £1200. b.   Find the amount of Alice’s annual allowance on her […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | January | Q#6

Question Figure 1 shows a sketch of the curve with equation y=f(x). The curve passes through the points  (0,3) and (4,0) and touches the x-axis at point (1,0). On separate diagrams sketch the curve with equation a.   y=f(x+1), b.   y=2f(x), c.   On each diagram show clearly the coordinates of all the points where the curve meets the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | January | Q#5

Question a.   Write  in the form , where a is an integer. b.   Express  in the form , where b and c are integers. Solution a.   We are given; Since ; b.   We are given; If we need a rational number in the denominator of a fraction, we need to follow procedure of  “denominator rationalization” as […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | January | Q#4

Question Given that , , a.   Find b.   Find Solution a.   We are given; We are required to find . Rule for differentiation of  is: Rule for differentiation of  is: b.   We are given; We are required to find . Rule for integration of  is: Rule for integration of  is: Rule for integration of  is:

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | January | Q#3

Question The line L has equation y=5 – 2x. a.   Show that the point P (3, –1) lies on L. b.   Find an equation of the line perpendicular to L, which passes through P. Give your answer in the form ax + by + c = 0, where a, b and c are integers. […]

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

Question The sequence of positive numbers , , , … is given by: , a.   Find ,  and . b.   Write down the value of . Solution a.   We are given that (n+1)th term of arithmetic series is represented by; Therefore, to find nth term we substitute (n-1) for n in the given expression. Hence; […]

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

Question Factorise completely Solution