Hits: 5

Quadratics (CIE)

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/11) | Q#2

Hits: 5 Question An increasing function, , is defined for x > n, where n is an integer. It is given that . Find the least possible value of n.  Solution We are given derivative of the function as; We are also given that it is an increasing function. To test whether a function is […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/13) | Q#7

Hits: 6 Question The coordinates of two points A and B are (1, 3) and (9, −1) respectively and D is the mid-point of  AB. A point C has coordinates (x, y), where x and y are variables. i.State the coordinates of D. ii.It is given that CD2 = 20. Write down an equation relating […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/13) | Q#1

Hits: 220 Question The function f is defined by for . i. Express in the form of . ii. Hence find the set of values of for which , giving your answer in exact form.   Solution i. We have the expression; We use method of “completing square” to obtain the desired form. We complete […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/11) | Q#5

Hits: 327 Question The function f is defined by  for .     i.      Express in the form of where and are constants.   ii.     State the greatest value of .    The function g is defined by  for .  iii.     Find the value of for which . Solution i.   We have the expression;   […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/11) | Q#2

Hits: 300 Question The line , where  is a constant, is a tangent to the curve  at the point  on the curve. i.Find the value of . ii.Find the coordinates of . Solution i. We are given equation of the line as; We are given equation of the curve as; It is given that line […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Feb-Mar | (P1-9709/12) | Q#8

Hits: 221 Question     i.      Express in the form of . The function f is defined by  for , where is constant.   ii.     State the largest value of for which is a decreasing function. The value of is now given to be 1.  iii.     Find an expression for and state the domain of . […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Feb-Mar | (P1-9709/12) | Q#5

Hits: 182 Question Two vectors,  and , are such that and Where is a constant.     i.      Find the values of for which is perpendicular to .   ii.     Find the angle between  and when q = 0. Solution i.   We are given that; If  and & , then  and  are perpendicular. Therefore, if […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#11

Hits: 311 Question     i.      Express in the form of where a, b and c are constants. The function f is defined by  for .    ii.       State the largest value of the constant k for which f is a one-one function.  iii.     For this value of k find an expression for and state the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#9

Hits: 149 Question A curve has equation  and a line has equation , where  is a constant. i.Show that, for all values of k, the curve and the line meet. ii.State the value of k for which the line is a tangent to the curve and find the coordinates of the  point where the line […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#2

Hits: 121 Question The function f is defined by  for . Determine, showing all necessary working, whether f is an increasing function, a decreasing  function or neither. Solution We are given function;   We are required to find whether is an increasing function, decreasing function or neither. To test whether a function is increasing or […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/12) | Q#9

Hits: 238 Question The function f is defined by  for .     i.      Express in the form of where a and b are constants.   ii.     State the range of .  The function g is defined by  for .  iii.       State the largest value of k for which g has an inverse.   iv.     Given that […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/11) | Q#11

Hits: 551 Question The one-one function f is defined by  for , where  is a constant. a.                    i.     State the greatest possible value of .              ii.     It is given that takes this greatest possible value. State the range of f and find an expression for .   b.    The function g is […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Feb-Mar | (P1-9709/12) | Q#10

Hits: 411 Question The functions f and g are defined by  for  for . i.   a.   State the range of the function f. b.   State the range of the function g. c.   State the range of the function fg.    ii.       Explain why the function gf cannot be formed.   iii.       Find the set […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Feb-Mar | (P1-9709/12) | Q#9

Hits: 319 Question A curve has equation  and a line has equation , where  is a constant. i.Find the set of values of  for which the curve and the line meet. ii.The line is a tangent to the curve for two particular values of . For each of these values find  the x-coordinate of the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/13) | Q#10

Hits: 686 Question The one-one function f is defined by  for , where c is a  constant.   i.       State the smallest possible value of c. In parts (ii) and (iii) the value of c is 4.    ii.       Find an expression for  and state the domain of .   iii.       Solve the equation , […]