# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#11

Question The curve C has equation  , x>0 a.   Find b.   Show that the point P(4,−8) lies on C. c.   Find an equation of the normal to C at the point P, giving your answer in the form ax + by + c = 0  , where a, b and c are integers. Solution a. […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#10

Question a.   On the axes below, sketch the graphs of i.        ii.     showing clearly the coordinates of all the points where the curves cross the coordinate axes. b.   Using your sketch state, giving a reason, the number of real solutions to the equation Solution a.   i.   We are required to sketch; We need to expand it […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#9

Question The line L1 has equation 2y − 3x − k = 0, where k is a constant. Given that the point A (1, 4) lies on L1, find a.   the value of k, b.   the gradient of L1. The line L2 passes through A and is perpendicular to L1. c.   Find an equation of L2 giving […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#8

Question The equation x2 + (k − 3)x + (3− 2k) = 0, where k is a constant, has two distinct real roots. a.   Show that k satisfies k2 + 2k – 3>0 b.   Find the set of possible values of k. Solution a.   We are given that; We are given that given equation has two distinct […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#7

Question The curve C with equation y=f(x) passes through the point (-1,0). Given that Find f(x). Solution We are required to find f(x), when; We are also given that the curve passes through the point P(-1,0). Clearly it is the case of finding equation from its derivative. We can find equation of the curve from its derivative […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#6

Question An arithmetic sequence has first term a and common difference d. The sum of the first 10 terms of the sequence is 162. a.  Show that 10a + 45d =162 Given also that the sixth term of the sequence is 17, b.  write down a second equation in a and d, c.  find the value of a and the value […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#5

Question Figure 1 shows a sketch of the curve with equation y = f (x) where  , The curve passes through the origin and has two asymptotes, with equations y=1 and x=2, as  shown in Figure. a.   In the space below, sketch the curve with equation y = f (x −1) and state the equations of the  […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#4

Question A sequence  is defined by Where  is a constant. a)   Find an expression for  in terms of c. Given that , b)  Find the value of c. Solution a)     We are given that sequence  is defined by We are required to find . We can utilize the given expression for general terms beyond first term as; b)  […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#3

Question Simplfy Giving your answer in the form , where p and q are rational numbers. Solution We are given; If we need a rational number in the denominator of a fraction, we need to follow procedure of  “denominator rationalization” as given below. ü If the denominator is of the form  then multiply both numerator and denominator by .  […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#2

Question Find giving each term in its simplest form. Solution We are given; 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 2011 | January | Q#1

Question a.  Find the value of b.  Simplify Solution a.   b.