# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | January | Q#11

Question The curve C has equation , The point P on C has x-coordinate equal to 2. a.   Show that the equation of the tangent to C at the point P is y = 1 – 2x. b.   Find an equation of the normal to C at the point P. The tangent at P meets the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | January | Q#10

Question The line  passes through the point A (2, 5) and has gradient . a.  Find an equation of , giving your answer in the form y = mx + c. The point B has coordinates (–2, 7). b.   Show that B lies on . c.   Find the length of AB, giving your answer in the form […]

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

Question The first term of an arithmetic series is a and the common difference is d. The 18th term of the series is 25 and the 21st term of the series is . a.   Use this information to write down two equations for a and d. b.   Show that a = –17.5 and find the value […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | January | Q#8

Question The point P (1, a) lies on the curve with equation y = (x + 1)2(2– x). a.   Find the value of a. b.   On the axes below sketch the curves with the following equations: i.       y = (x + 1)2(2– x) ii.        On your diagram show clearly the coordinates of any points at […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | January | Q#7

Question The equation kx2 + 4x + (5 – k) = 0, where k is a constant, has 2 different real solutions for x. a.   Show that k satisfies k2 – 5k + 4 > 0. b.   Hence find the set of possible values of k. Solution a.   We are given;   We are given that given […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | January | Q#6

Question Given that  can be written in the form 2xp – xq, a.   Write down the value of p and the value of q. Given that , b.   find , simplifying the coefficient of each term. Solution a.   We are given that; Hence, p=3/2 while q=1. b.     We are given that; We […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | January | Q#5

Question Figure 1 shows a sketch of the curve C with equation y=f(x). There is a maximum at (0, 0), a  minimum at (2, –1) and C passes through (3, 0). On separate diagrams sketch the curve with equation a.   y = f(x + 3), b.   y = f(–x). On each diagram show clearly the coordinates of the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | January | Q#4

Question A curve has equation y=f(x) and passes through the point (4, 22). Given that use integration to find f(x), giving each term in its simplest form. Solution We are required to find f(x), when; We are also given that the curve passes through the point (4,1). Clearly it is the case of finding equation from its derivative. We […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | January | Q#3

Question Expand and simplify . Solution We are given; We have algebraic formula;

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | January | Q#2

Question Find , giving each term in its simplest form. Solution 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 2009 | January | Q#1

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