Hits: 211

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2017 | June | Q#10

Hits: 211   Question Figure shows a sketch of part of the curve y = f(x), , where f(x) = (2x – 5)2(x + 3) a.   Given that                     i.       the curve with equation y = f(x) – k, , passes through the origin, find the value of the  constant k,                   ii.       the curve with equation y = f(x + c), […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2017 | June | Q#7

Hits: 930 Question The curve C has equation y=f(x), x>0, where Given tht the point P(4,-8) lies on the curve C; a.   find the equation of the tangent to C at P, giving your answer in the form y = mx + c, where m and  c are constants. a.   find f(x), giving each term in […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2017 | June | Q#2

Hits: 88 Question Given , find the value of   when x=8, writing your answer in the form  where a is a rational number. Solution 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 […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2016 | June | Q#11

Hits: 114 Question The curve C has equation  , where k is a constant. a.   Find . The point P, where x=-2, lies on C. The tangent to C at the point P is parallel to the line with equation 2y – 17x – 1=0. Find b.  the value of k. c.  the value of y-coordinate of P. d.  the equation of […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2016 | June | Q#7

Hits: 32   Question Given that , Find , giving each term in your answer in its simplest form. Solution 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 […]

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

Hits: 151   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 […]

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

Hits: 88   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 […]

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

Hits: 24   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 […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2014 | June | Q#11

Hits: 227   Question A sketch of part of the curve C with equation , x>0 is shown in Figure. Point A lies on C and has an x coordinate equal to 2 a.   Show that the equation of the normal to C at A is y = –2x + 7. The normal to C at A […]

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

Hits: 20   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 […]

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

Hits: 52   Question A curve with equation y=f(x) passes through the point (4,25). Given that a.   find f(x) simplifying each term. b.   Find an equation of the normal to the curve at the point (4, 25). Give your answer in the form ax + by + c = 0, where a, b and c are […]

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

Hits: 22 Question Differentiate with respect to x, giving each answer in its 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; We have algebraic formula; Rule for differentiation […]

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

Hits: 110   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 […]

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

Hits: 24 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; […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2013 | June | Q#10

Hits: 41   Question A curve has equation y=f(x). The point P with coordinates (9,0) lies on the curve. Given that  , a.   Find f(x). b.   Find the x-coordinates of two points on y=f(x) where the gradient of the curve is equal to 10. Solution a.   We are given; We are given coordinates of a point […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2013 | June | Q#1

Hits: 13   Question Given , find the value of   when x=3. Solution 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 of  is: Rule for […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2013 | June | Q#9

Hits: 22 Question  , a.   Show that Where A and B are constants to be found. b.   Find Given that the point (-3,10) lies on the curve with equation y=f(x), c.   Find f(x). Solution a.   We are given; Therefore; b.   We are given; We are required to find . Second derivative is the derivative of […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2013 | January | Q#11

Hits: 52 Question The curve C has equation , a.   Find , giving each term in its simplest form. The point P on C has x-coordinate equal to . b.   Find the equation of the tangent to C at P, giving your answer in the form y = ax + b, where a and  b are […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | June | Q#4

Hits: 12 Question a.   Find , giving each term in its simplest form. b.   Find . 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 […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#10

Hits: 75 Question Figure 2 shows a sketch of the curve C with equation  , x ≠ 0 The curve crosses the x-axis at the point A. a.   Find the coordinates of A. b.   Show that the equation of the normal to C at A can be written as 2x+8y−1=0 The normal to C at A meets C again […]