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

Question The curve C has equation The point P has coordinates (2, 7). a)   Show that P lies on C. b)  Find the equation of the tangent to C at P, giving your answer in the form y=mx+c, where m and c  are constants. The point Q also lies on C. Given that the tangent to […]

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

Question a)   Factorise completely x3 – 6×2 + 9x b)  Sketch the curve with equation y = x3 – 6×2 + 9x showing the coordinates of the points at which the curve meets the x-axis. Using your answer to part (b), or otherwise, c)   (c) sketch, on a separate diagram, the curve with equation y = (x […]

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 2009 | June | Q#8

Question The points A and B have coordinates (6, 7) and (8, 2) respectively. The line  passes through the point A and is perpendicular to the line AB, as shown in Figure 1. a)   Find an equation for  in the form ax + by + c = 0, where a, b and c are integers. Given that […]

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

Question A sequence  is defined by , , Where  is a constant. a)   Write down an expression for  in terms of k. b)  Show that . Given that , c)   Find the value of k. Solution a)     We are given that sequence  is defined by  We are required to find . We can utilize the given expression […]

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

Question The equation x2 + 3px + p = 0, where p is a non-zero constant, has equal roots. Find the value of p. Solution We are given that; We are given that given equation has equal roots. For a quadratic equation , the expression for solution is; Where  is called discriminant. If , the equation will […]

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

Question A 40-year building programme for new houses began in Oldtown in the year 1951 (Year 1) and finished in 1990 (Year 40). The numbers of houses built each year form an arithmetic sequence with first term a and common  difference d. Given that 2400 new houses were built in 1960 and 600 new houses were built […]

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

Question Find the set of values of x for which a.    b.    c.   both  and Solution a.   We are given; b.   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 […]

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

Question Given that  , , find a.   b.  , simplifying each term. Solution a.   We are given; We are required to find . Gradient (slope) of the curve is the derivative of equation of the curve. Hence gradient of curve  with respect to  is: Therefore; Rule for differentiation is of  is: Rule for differentiation is of  is: […]

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

Question Given that , find the value of a. Solution We are given;

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

Question Simply a. b. Solution a.     We are given; 63 b.     We are given; Since ;