# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#10

Question Figure 2 shows a sketch of the curve C with equation  , x ≠ 0 The curve crosses the x-axis at the point A. a.   Find the coordinates of A. b.   Show that the equation of the normal to C at A can be written as 2x+8y−1=0 The normal to C at A meets C again at the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#9

Question A company offers two salary schemes for a 10-year period, Year 1 to Year 10 inclusive. Scheme 1: Salary in Year 1 is £P. Salary increases by £(2T) each year, forming an arithmetic sequence. Scheme 2: Salary in Year 1 is £(P+1800). Salary increases by £T each year, forming an arithmetic sequence. a.   Show that the total earned under […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#8

Question The curve  has equation a.   Find . b.   Sketch , showing the coordinates of the points where C1 meets the x-axis. c.   Find the gradient of  at each point where C1 meets the x-axis. The curve  has equation where k is a constant and . d.   Sketch , showing the coordinates of the points where  meets the x […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#7

Question A curve with equation y = f (x) passes through the point (2,10). Given that f ′(x) = 3×2 − 3x + 5 find the value of f (1). Solution We are required to find f(1) but we are not given f(x) but f ′(x). f ′(x) = 3×2 − 3x + 5 Therefore, we need to […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#6

Question The line  has equation 2x − 3y +12 = 0. a.   Find the gradient of . The line  crosses the x-axis at the point A and the y-axis at the point B, as shown in Figure. The line  is perpendicular to  and passes through B. b.   Find an equation of . The line  crosses the x-axis at the point […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#5

Question The curve C has equation y=x(5−x) and the line L has equation 2y=5x+4. a.   Use algebra to show that C and L do not intersect. b.   In the space on page 11, sketch C and L on the same diagram, showing the coordinates of the  points at which C and L meet the axes. Solution […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#4

Question A sequence  is defined by   , Where  is a positive integer. a)   Write down an expression for  in terms of a. b)  Show that Given that c)   Find the possible values of a. 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 2012 | January | Q#3

Question Find the set of values of x for which a.  b. 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 are 6 & -2. Standard form […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#2

Question a.   Simplify giving your answer in the form  , where  is an integer.   b.   Simplify  giving your answer in the form  , where b and c are integers. Solution a.   We are given; Since ; Since ; b.   As demonstrated in (a) we can write the numerator as; If we need a rational number in the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#1

Question Given that , , find, in their simplest form, a.   b.   . 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: […]