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

Hits: 10   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 + […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2017 | June | Q#9

Hits: 5   Question a.   On separate axes sketch the graphs of                     i.       y = –3x + c, where c is a positive constant,                   ii.        On each sketch show the coordinates of any point at which the graph crosses the y-axis and the equation of any horizontal asymptote. Given that y = –3x + c, where c is a positive […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2017 | June | Q#8

Hits: 13   Question The straight line  , shown in Figure, has equation 5y = 4x + 10. The point P with x coordinate 5 lies on . The straight line  is perpendicular to  and passes through P. a.   Find an equation for  , writing your answer in the form ax + by + c = […]

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

Hits: 7 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#6

Hits: 7 Question a.   Given y = 2x, show that can be written in the form b.   Hence solve Solution a)     We have the equation; We are given that y = 2x; b)    We are required to solve; As demonstrated in (a) this can be written as; Now we have two options. For these values of y, we can find […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2017 | June | Q#5

Hits: 1 Question f(x) = x2 – 8x + 19 a.   (a) Express f(x) in the form (x + a)2 + b, where a and b are constants. The curve C with equation y = f(x) crosses the y-axis at the point P and has a minimum point at the  point Q. b.   Sketch the graph of C […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2017 | June | Q#4

Hits: 7 Question A company, which is making 140 bicycles each week, plans to increase its production. The number of bicycles produced is to be increased by d each week, starting from 140 in week 1, to 140 + d in week 2, to 140 + 2d in week 3 and so on, until the company is producing  206 […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2017 | June | Q#3

Hits: 4 Question A sequence  is defined by  ,  , Where k is a positive constant. a)   Write down expressions for  and  in terms of k, giving your answers in their simplest form. Given that , b)  Find an exact value for k. Solution a.     We are given that sequence  is defined by We are required to find […]

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

Hits: 3 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 2017 | June | Q#1

Hits: 9 Question Find giving each term in its simplest form. Solution We are given; Rule for integration of  is: Rule for integration of  is: Rule for integration of  is: Please follow and like us: 0

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

Hits: 0 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#10

Hits: 1   Question The points P(0, 2) and Q(3, 7) lie on the line , as shown in Figure. The line  is perpendicular to , passes through Q and crosses the x-axis at the point R, as shown in Figure. Find a.   an equation for , giving your answer in the form ax + by + […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2016 | June | Q#9

Hits: 3 Question On John’s 10th birthday he received the first of an annual birthday gift of money from his uncle. This  first gift was £60 and on each subsequent birthday the gift was £15 more than the year before.  The amounts of these gifts form an arithmetic sequence. a.   Show that, immediately after his 12th birthday, the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2016 | June | Q#8

Hits: 2 Question The straight line with equation y = 3x – 7 does not cross or touch the curve with equation y = 2px2 – 6px + 4p, where p is a constant. a.   Show that 4p2 – 20p + 9 < 0 b.   Hence find the set of possible values of p. Solution a.   […]

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

Hits: 1   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 2016 | June | Q#6

Hits: 3 Question A sequence  is defined by  , Where  is a constant. a)   Write down expressions for  and  in terms of k. Find, b)   in terms of k, giving your answer in its simplest form. c)   . Solution a)     We are given that sequence  is defined by We are required to find  and . We can utilize the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2016 | June | Q#5

Hits: 1   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 […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2016 | June | Q#4

Hits: 3 Question Figure  shows a sketch of part of the curve with equation y = f(x). The curve has a maximum point A  at (–2, 4) and a minimum point B at (3, –8) and passes through the origin O.  On separate diagrams, sketch the curve with equation a.   y = 3f(x), b.   y = f(x) – 4 […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2016 | June | Q#3

Hits: 4 Question a.   Simplify Giving your answer in the form  , where a is an integer. b.    Hence, or otherwise, simplify Giving your answer in the form , where b and c is are integers and . Solution a.   We are given; Since ; Since ; b.     We are given; We have found in (a) that; Therefore; If we […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2016 | June | Q#2

Hits: 2 Question Express  in the form , giving y in the form ax + b, where a and b are constants. Solution We are given; Hence; Therefore; Please follow and like us: 0