# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663A/01) | Year 2014 | January | Q#10

Question The curve C has equation . The point P, which lies on C, has coordinates (2, 1). a.   Show that an equation of the tangent to C at the point P is y = 3x – 5. The point Q also lies on C. Given that the tangent to C at Q is parallel to […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663A/01) | Year 2014 | January | Q#9

Question A curve with equation y=f(x) passes through the point (3,6). Given that a.   use integration to find f(x). Give your answer as a polynomial in its simplest form. b.   Show that , where p is a positive constant. State the value of p. c.   Sketch the graph of y = f(x), showing the coordinates of […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663A/01) | Year 2014 | January | Q#8

Question The equation 2×2 + 2kx + (k+2) = 0, where k is a constant, has two distinct real roots. a.   Show that k satisfies k2 – 2k – 4 > 0 b.   Find the set of possible values of k. Solution a.   We are given that; For a quadratic equation , the expression for solution […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663A/01) | Year 2014 | January | Q#7

Question Shelim starts his new job on a salary of £14 000. He will receive a rise of £1500 a year for each full  year that he works, so that he will have a salary of £15 500 in year 2, a salary of £17 000 in year 3  and so on. When Shelim’s salary reaches £26 000, […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663A/01) | Year 2014 | January | Q#6

Question The straight line  has equation 2y = 3x + 7. The line  crosses the y-axis at the point A as shown in Figure. a.                         i.       State the gradient of .                   ii.       Write down the coordinates of the point A. Another straight line  intersects  at the point B (1, 5) and crosses the x-axis at the point C, as  shown in […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663A/01) | Year 2014 | January | Q#5

Question Given that for all positive integers n, a)   find the value of b)  Find the value of Solution a.     We are given that; We are required to find . Therefore, we substitute n=5; b.     We are required to find . We can find  as follows; Therefore ;

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663A/01) | Year 2014 | January | Q#4

Question Figure 1 shows a sketch of a curve with equation y = f(x). The curve crosses the y-axis at (0, 3) and has a minimum at P (4, 2). On separate diagrams, sketch the curve with equation a.   y = f(x + 4), b.    y = 2f(x). On each diagram show the coordinates of minimum point and […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663A/01) | Year 2014 | January | Q#3

Question Solve the simultaneous equations Solution We are given simultaneous equations; We rearrange the first equation to find x in terms of y. Substituting this  from first equation in the second equation; We have the algebraic formula; Now we have two options. By substituting one-by-one these values of  in first equation, we can find corresponding values of . For […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663A/01) | Year 2014 | January | Q#2

Question , a.   Find , giving each term in its simplest form. b.   Find , giving each term in its simplest form. 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 […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663A/01) | Year 2014 | January | Q#1

Question Fully simplify a.   b.   Solution a.   We are given; b.     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 […]