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# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | June | Q#10

Hits: 0   Question The curve C has equation y = (x +1)(x + 3)2 a.   Sketch C, showing the coordinates of the points at which C meets the axes. b.   Show that . The point A, with x-coordinate -5, lies on C. c.   Find the equation of the tangent to C at A, giving your […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | June | Q#9

Hits: 0 Question a.   Calculate the sum of all the even numbers from 2 to 100 inclusive, 2 + 4 + 6 + …… + 100 b.   In the arithmetic series k + 2k + 3k + …… + 100 k is a positive integer and k is a factor of 100.                                         i.    Find, in terms of k, […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | June | Q#8

Hits: 0 Question Figure 1 shows a sketch of the curve C with equation y = f (x). The curve C passes through the origin and through (6, 0). The curve C has a minimum at the point (3, –1). On separate diagrams, sketch the curve with equation a.   y=f(2x), b.   y=-f(x) c.   y=f(x+p), where p is a constant […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | June | Q#7

Hits: 0   Question where k is a real constant. a.   Find the discriminant of f(x) in terms of k. b.   Show that the discriminant of f (x) can be expressed in the form (k + a)2 + b, where a and b are  integers to be found. c.   Show that, for all values of k, […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | June | Q#6

Hits: 0   Question Given that  can be written in the form , a.   Write down the value of p and the value of q. Given that  , and that y=90 when x=4; b.   find  in terms of x, simplifying the coefficient of each term. Solution a.   We are given; b.   We are required to […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | June | Q#5

Hits: 0   Question A sequence  is defined by   , Where  is a positive integer. a)   Write down an expression for  in terms of k. b)  Show that c)                         i.       Find  in terms of k, I its simplest form.                   ii.       Show that  is divisible by 6. Solution a)     We are given that sequence  is defined by We are […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | June | Q#4

Hits: 0   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 2011 | June | Q#3

Hits: 0                                             Question The points P and Q have coordinates (–1, 6) and (9, 0) respectively. The line  is perpendicular to PQ and passes through the mid-point of PQ. Find an equation for , […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | June | Q#2

Hits: 0   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 […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | June | Q#1

Hits: 0   Question Find the value of a.   b.   Solution a.   b.   Please follow and like us: 0

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#11

Hits: 1   Question The curve C has equation  , x>0 a.   Find b.   Show that the point P(4,−8) lies on C. c.   Find an equation of the normal to C at the point P, giving your answer in the form ax + by + c = 0  , where a, b and c are integers. […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#10

Hits: 1   Question a.   On the axes below, sketch the graphs of i.        ii.     showing clearly the coordinates of all the points where the curves cross the coordinate axes. b.   Using your sketch state, giving a reason, the number of real solutions to the equation Solution a.   i.   We are required to sketch; We need to […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#9

Hits: 0 Question The line L1 has equation 2y − 3x − k = 0, where k is a constant. Given that the point A (1, 4) lies on L1, find a.   the value of k, b.   the gradient of L1. The line L2 passes through A and is perpendicular to L1. c.   Find an equation of […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#8

Hits: 1   Question The equation x2 + (k − 3)x + (3− 2k) = 0, where k is a constant, has two distinct real roots. a.   Show that k satisfies k2 + 2k – 3>0 b.   Find the set of possible values of k. Solution a.   We are given that; We are given that given equation has […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#7

Hits: 5   Question The curve C with equation y=f(x) passes through the point (-1,0). Given that Find f(x). Solution We are required to find f(x), when; We are also given that the curve passes through the point P(-1,0). Clearly it is the case of finding equation from its derivative. We can find equation of the curve from […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#6

Hits: 3 Question An arithmetic sequence has first term a and common difference d. The sum of the first 10 terms of the sequence is 162. a.  Show that 10a + 45d =162 Given also that the sixth term of the sequence is 17, b.  write down a second equation in a and d, c.  find the value of a and […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#5

Hits: 2   Question Figure 1 shows a sketch of the curve with equation y = f (x) where  , The curve passes through the origin and has two asymptotes, with equations y=1 and x=2, as  shown in Figure. a.   In the space below, sketch the curve with equation y = f (x −1) and state the equations […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#4

Hits: 2   Question A sequence  is defined by Where  is a constant. a)   Find an expression for  in terms of c. Given that , b)  Find the value of c. Solution a)     We are given that sequence  is defined by We are required to find . We can utilize the given expression for general terms beyond first term […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#3

Hits: 3 Question Simplfy Giving your answer in the form , where p and q are rational numbers. Solution 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 of the form  then multiply both numerator and denominator […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#2

Hits: 2   Question Find giving each term in its simplest form. Solution We are given; Rule for integration of  is: Rule for integration of  is: Please follow and like us: 0