Hits: 346

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

Hits: 346   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: 983 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: 186 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: 41   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: 42   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: 39   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: 24   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: 622                                             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: 26   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: 36   Question Find the value of a.   b.   Solution a.   b.