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Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | January | Q#10

Hits: 15   Question a.   On the same axes sketch the graphs of the curves with equations i.       y=x2(x –2), ii.     y=x(6 –x), and indicate on your sketches the coordinates of all the points where the curves  cross the x-axis. b.   Use algebra to find the coordinates of the points where the graphs intersect. Solution a.     […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | January | Q#10

Hits: 67   Question a.   Find the values of the constants a and b. b.   In the space provided below, sketch the graph of , indicating clearly the coordinates of any intersections with the coordinate axes. c.   Find the value of the discriminant of . Explain how the sign of the discriminant relates  to your sketch in […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | January | Q#3

Hits: 11   Question Given that the equation , where k is a positive constant, has equal roots, find the value of k. Solution We are given; We can given that given equation has equal roots. For a quadratic equation , the expression for solution is; Where  is called discriminant. If , the equation will have two distinct […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/13) | Q#6

Hits: 613 Question The functions f and g are defined by   for   for      i.       Find an expression for .    ii.       Solve the equation . Solution i.   We are given the function; We write it as; To find the inverse of a given function  we need to write it in terms of  rather than in terms of . As […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/12) | Q#6

Hits: 996   Question a.   The function f, defined by   for , is such that  and .                             i.       Find the values of the constants a and b.                           ii.       Evaluate . b.   The function g is defined by  for for . The range of g is given by  . Find the values of the constants c and d. Solution a.   i.   We […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/12) | Q#2

Hits: 654   Question A function f is defined by  for .      i.       Find an expression for  and find the point of intersection of the graphs of  and  .    ii.       Sketch, on the same diagram, the graphs of  and , making clear the  relationship between the graphs. Solution i.   We have; We write it as; To find the inverse of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/11) | Q#9

Hits: 552   Question Functions f and g are defined for x > 3 by;      i.       Find and simplify an expression for gg(x).    ii.       Find an expression for  and state the domain of .   iii.       Solve the equation .  Solution      i.   We are given that; It can be written as; Therefore for ;    ii. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/11) | Q#2

Hits: 520   Question A function f is defined by  for . It is given that f is an increasing  function. Find the largest possible value of the constant a. Solution We are given that function f is increasing function. To test whether a function  is increasing or decreasing at a particular point , we  take derivative of a function […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/12) | Q#10

Hits: 904   Question The function f is defined by , for .     i.       Solve the equation , giving your answer correct to 1 decimal place.    ii.       Find an expression for  and find the domain of .   iii.       Sketch, on the same diagram, the graphs of y=f(x) and . Solution      i.   We are given the function as; We […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Feb-Mar | (P1-9709/12) | Q#8

Hits: 585   Question The functions f and g are defined for  by i.       Show that  and obtain an unsimplified expression for . ii.       Find an expression for  and determine the domain of . iii.       Solve the equation . Solution      i.   We are given the functions; We can rewrite these as; First we find . Next we find .    […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/11) | Q#9

Hits: 575   Question The function f is defined by  for , .      i.        Find an expression for . The function g is defined by  for , where a is a constant.    ii.       Find the value of a for which .   iii.       Find the possible values of a given that the equation  has two equal roots. Solution      i. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/11) | Q#5

Hits: 837   Question The equation of a curve is .      i.       Sketch the graph of  for , stating the coordinates of the point of  intersection with the y-axis. Points P and Q lie on the curve and have x-coordinates of  and  respectively.    ii.       Find the length of PQ correct to 1 decimal place. The line through […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/13) | Q#8

Hits: 523   Question      i.      Express  in the form , where a, b and c are constants.    ii. Functions f and g are both defined for . It is given that  and     . Find .   iii.       Find  and give the domain of .   Solution      i.   We have the expression; We use method of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/12) | Q#10

Hits: 947 Question A function f is defined by  for .     i.       Find the range of f.    ii.       Sketch the graph of   iii.       Solve the equation , giving answers in terms of . The function  is defined by  for , where k is a constant.   iv.       State the largest value of k for which g has an inverse.    v.       For this value of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/11) | Q#8

Hits: 602 Question The functions f and g are defined by  for  for .      i.       Find and simplify an expression for  and state the range of .      ii.       Find an expression for  and find the domain of . Solution      i.   We are given;  for  for . We are required to find expression for ;   […]