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Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/22) | Q#1

Hits: 24   Question Solve the equation . Solution SOLVING EQUATION: PIECEWISE Let, . We can write it as; We have to consider two separate cases; When When We have the equation; It  can be written as; We have to consider two separate cases; When ; When ; Hence, the only solutions for the given […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/21) | Q#1

Hits: 51 Question      i.       It is given that x satisfies the equation . Find the value of and, using  logarithms, find the value of x correct to 3 significant figures.    ii.       Hence state the values of x satisfying the equation . Solution i.   We are given; We can write it […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#8

Hits: 11   Question The gradient, , at the point (x,y) on a curve is given by a.                        i.               Find                   ii.               The curve passes through the point . Verify that the curve has a minimum point at P. b.                       i.               Show that at the points on the curve where y is decreasing                   ii.               Solve the inequality Solution a.   We are given;                     i. […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#6

Hits: 10   Question a.  A curve has equation .                     i.               Find the values of x where the curve crosses the x-axis, giving your answer in the form   , where m and n are integers.                   ii.               Sketch the curve, giving the value of the y-intercept. b. A line has equation  , where k is a constant.                     i.               Show that the x-coordinates of any points […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#3

Hits: 7   Question a.                         i.       Express  in the form  , where p and q are rational numbers.                   ii.       Hence write down the minimum value of . a.   Describe the geometrical transformation which maps the graph of  onto the graph  of  . Solution a.                               i.   We have the expression; We use method of “completing square” to obtain the desired form. First we […]

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: 345   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 | (P1-9709/13) | Q#4

Hits: 247   Question The function f is such that  for , where n is an integer. It is given that  f is an increasing function. Find the least possible value of n. Solution We are given function; We are also given that it is an increasing function. To test whether a function  is increasing or decreasing at a particular […]

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#1

Hits: 225   Question Find the set of values of k for which the curve  and the line  do not meet. Solution We can find the coordinates of intersection point of a curve and line. However, here we are required  to show that given curve and line do not meet that means there is no point of intersection   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#8

Hits: 503 Question a)   A cyclist completes a long-distance charity event across Africa. The total distance is 3050 km.  He starts the event on May 1st and cycles 200 km on that day. On each subsequent day he reduces  the distance cycled by 5 km. (i)          How far will he travel on May 15th? (ii)        On what date will he finish the […]

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#3

Hits: 273 Question A curve has equation .     i.       Find the set of values of  for which .    ii.       Find the value of the constant  for which the line  is a tangent to the curve. Solution i.   We are required to find the set of values of x for which . We are given that; Therefore; We solve the following equation […]

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#1

Hits: 215 Question i.    Express  in the form , where a and b are constants. ii.   Hence, or otherwise, find the set of values of  for which . Solution i.   We have the expression; We use method of “completing square” to obtain the desired form. Next we complete the square for the terms which involve . We have […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#7

Hits: 439 Question The point P(x,y) is moving along the curve  in such a way that the rate of change  of y is constant. Find the values of x at the points at which the rate of change of x is equal to half the rate of change of y. Solution We are required to find values of x […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/12) | Q#11

Hits: 485 Question The function  is defined by  for .      i.       Find the set of values of x for which f(x) ≤ 3.    ii.       Given that the line y=mx+c is a tangent to the curve y = f(x), show that The function g is defined by  for x ≥ k, where k is a constant.   iii.       Express   in the form […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/12) | Q#9

Hits: 660 Question A water tank holds 2000 litres when full. A small hole in the base is gradually getting bigger so that  each day a greater amount of water is lost.      i.       On the first day after filling, 10 litres of water are lost and this increases by 2 litres each day.          a.   […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/11) | Q#6

Hits: 414 Question a.   Find the values of the constant m for which the line  is a tangent to the curve . b.   The function f is defined for  by , where a and b are constants. The solutions of the equation  are x = 1 and x = 9. Find i.       the values of a and […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Feb-Mar | (P1-9709/12) | Q#8

Hits: 237 Question The function  is such that  for , where a and b are constants.      i.       For the case where  and , find the possible values of  a and b.    ii.       For the case where  and , find an expression for  and give the domain of  . Solution i.   We are given that function  is represented as; We are given that; […]