Hits: 56

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

Hits: 56   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#5

Hits: 27 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 2016 | June | Q#8

Hits: 27 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 2015 | June | Q#5

Hits: 17   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 […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2014 | June | Q#6

Hits: 52 Question Figure 1 shows the plan of a garden. The marked angles are right angles. The six edges are straight lines. The lengths shown in the diagram are given in metres. Given that the perimeter of the garden is greater than 40 m, a.   show that x > 1.7 Given that the area of the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#3

Hits: 9 Question Find the set of values of x for which a.   b.   c.  both  and . Solution a.   We are given; b.   We are required to solve the inequality; We solve the following equation to find critical values of ; Now we have two options; Hence the critical points on the curve for the given condition are […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663A/01) | Year 2014 | January | Q#8

Hits: 20   Question The equation 2×2 + 2kx + (k+2) = 0, where k is a constant, has two distinct real roots. a.   Show that k satisfies k2 – 2k – 4 > 0 b.   Find the set of possible values of k. Solution a.   We are given that; For a quadratic equation , the expression […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2013 | June | Q#8

Hits: 21   Question A rectangular room has a width of x m. The length of the room is 4 m longer than its width. Given that the perimeter of the room is greater than 19.2 m, a.   Show that Given also that the area of the room is less than 21 m2, b.             […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2013 | June | Q#5

Hits: 7   Question Find the set of values of x for which a. b. Solution a.   We are given; b.   We are required to solve the inequality; We solve the following equation to find critical values of ; Now we have two options; Hence the critical points on the curve for the given condition are  & -3. […]

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

Hits: 9 Question a.   Find the values of the constants a, b and c. b.   On the axes on page 27, sketch the curve with equation y = 4×2 + 8x + 3, showing clearly the coordinates of any points where the curve crosses the coordinate axes. Solution a.   We are given that; In  order to find […]

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

Hits: 7 Question The equation (k + 3)x2 + 6x + k = 5, where k is a constant, has two distinct real solutions for x. a.   Show that k satisfies k2 – 2k – 24 < 0 b.   Hence, find the set of possible values of k. Solution a.   We are given that; We are given that given […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#5

Hits: 17   Question The curve C has equation y=x(5−x) and the line L has equation 2y=5x+4. a.   Use algebra to show that C and L do not intersect. b.   In the space on page 11, sketch C and L on the same diagram, showing the coordinates of the  points at which C and L meet the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#3

Hits: 12 Question Find the set of values of x for which a.  b. Solution a.   We are given; b.   We are required to solve the inequality; We solve the following equation to find critical values of ; Now we have two options; Hence the critical points on the curve for the given condition are 6 & -2. […]

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

Hits: 20   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 | January | Q#8

Hits: 15   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 2010 | June | Q#3

Hits: 17   Question Find the set of values of x for which a.   b.   c.   both  and Solution a.   We are given; b.   We are required to solve the inequality; We solve the following equation to find critical values of ; Now we have two options; Hence the critical points on the curve for the given condition […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2010 | January | Q#10

Hits: 45   Question f(x) = x2 + 4kx + (3+11k), where k is a constant. a)   Express f(x) in the form (x + p)2 + q, where p and q are constants to be found in terms of k.  Given that the equation f(x) = 0 has no real roots, b)  find the set of possible […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | June | Q#4

Hits: 10   Question Find the set of values of x for which a.    b.    c.   both  and Solution a.   We are given; b.   We are required to solve the inequality; We solve the following equation to find critical values of ; Now we have two options; Hence the critical points on the curve for the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | January | Q#7

Hits: 12   Question The equation kx2 + 4x + (5 – k) = 0, where k is a constant, has 2 different real solutions for x. a.   Show that k satisfies k2 – 5k + 4 > 0. b.   Hence find the set of possible values of k. Solution a.   We are given;   We are given […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2008 | June | Q#8

Hits: 155   Question Given that the equation 2qx2 + qx – 1 = 0, where q is a constant, has no real roots, a.   show that q2 + 8q < 0. b.   Hence find the set of possible values of q. Solution a.   We are given; We are given that given equation has no real roots. […]