Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2013 | June | Q#11

Question The line  meets the the curve  at the points A and B as shown in the figure. a.   Find the coordinates of A and the coordinates of B. b.   Find the distance AB in the form  where r is a rational number. Solution a.   We are required to find the coordinates of the points […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2013 | June | Q#10

Question A curve has equation y=f(x). The point P with coordinates (9,0) lies on the curve. Given that  , a.   Find f(x). b.   Find the x-coordinates of two points on y=f(x) where the gradient of the curve is equal to 10. Solution a.   We are given; We are given coordinates of a point on the […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2013 | June | Q#9

Question Figure 1 shows a sketch of the curve C with equation y = f(x). The curve C passes through the point (-1,0) and touches the x-axis at the point (2,0). The curve C has a maximum at the point (0,4). a.   The equation of the curve C can be written in the form Where a, b […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2013 | June | Q#8

Question A rectangular room has a width of x m. The length of the room is 4 m longer than its width. Given that the perimeter of the room is greater than 19.2 m, a.   Show that Given also that the area of the room is less than 21 m2, b.                i. Write […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2013 | June | Q#7

Question Each year, Abbie pays into a saving scheme. In the first year she pays in £500. Her payments the  increase by £200 each year so that she pays £700 in the second year, £900 in the third year and so  on. a.   Find out how much Abbie pays into the saving scheme in the tenth year. Abbie […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2013 | June | Q#6

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

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2013 | June | Q#5

Question Solve a.   . b.   . Solution a.     We are given; b.     We are given; Since ;

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2013 | June | Q#4

Question The line  has equation 4x + 2y – 3 = 0. a.   Find the gradient of . The line  is perpendicular to  and passes through the point (2,5). b.   Find an equation of  in the form y = mx + +c, where m and c are constants. Solution a.     We are given equation of line ; We are […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2013 | June | Q#3

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 (C1-6663/01R) | Year 2013 | June | Q#2

Question Express in the form  , where k is an integer. 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 .  ü If the denominator is of the […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2013 | June | Q#1

Question Given , find the value of   when x=3. Solution 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: Rule for differentiation is […]