Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2015 | June | Q#10

Question A curve with equation y=f(x) passes through the point (4,9). Given that  , x > 0 a.   find f(x), giving each term in its simplest form. Point P lies on the curve. The normal to the curve at P is parallel to the line 2y + x = 0 b.   Find x coordinate of […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2015 | June | Q#9

Question Jess started work 20 years ago. In year 1 her annual salary was £17000. Her annual salary  increased by £1500 each year, so that her annual salary in year 2 was £18500, in year 3 it was  £20000 and so on, forming an arithmetic sequence. This continued until she reached her maximum  annual salary of £32000 […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2015 | June | Q#8

Question a.   Factorise completely 9x – 4×3 b.   Sketch the curve C with equation y = 9x – 4×3 Show on your sketch the coordinates at which the curve meets the x-axis. The points A and B lie on C and have x coordinates of –2 and 1 respectively. c.   Show that the length of AB is […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2015 | June | Q#7

Question Given that , a.   Express  in terms of y. b.   Hence, or otherwise, solve  Solution a)     We have; We are given; Therefore; b)    We are given; As demonstrated in (a)  and given , therefore; Now we have two options. Substituting these values in following given equation yields corresponding values of x. For ; For ;

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2015 | June | Q#6

Question The curve C has equation  , a. Find  in its simplest form. b. Find an equation of the tangent to C at the point where x=-1. Give your answer in the form ax+by+c=0, where a, b and c are integers. Solution a.   We are given; We are required to find . Gradient (slope) of the curve […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2015 | June | Q#5

Question The equation  , where p is a constant has no real roots. a.   Show that p satisfies p2 – 6p +1 > 0 b.   Hence, find the set of possible values of p. Solution a.   We are given that;   We are given that given equation has no real solutions of x (roots). For a quadratic […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2015 | June | Q#4

Question      i.       A sequence  is defined by  ,  and Find the value of a)     b)     ii.       A sequence  is defined by  ,  and , where k is a constant a)   Find  and  in terms of k. Given that , b)  Find the value of k. Solution i.   a)     We are given that sequence  is defined by […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2015 | June | Q#3

Question Given that , ,  , find in their simplest form, a.   b.   . 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 differentiation is of  is: Rule for differentiation is […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2015 | June | Q#2

Question Solve the simultaneous equations Solution We are given simultaneous equations; We rearrange the first equation to find y in terms of x. 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 (C1-6663/01) | Year 2015 | June | Q#1

Question Simplify a.   b.    giving your answer in the form a + √b , where a and b are integers. 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 […]