Hits: 54

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | June | Q#11

Hits: 54   Question The line  passes through the points P(–1,2) and Q(11, 8). a.   Find an equation for  in the form y= mx + c, where m and c are constants. The line  passes through the point R(10, 0) and is perpendicular to . The lines  and  intersect at the point S. b.   Calculate the coordinates of S. […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | June | Q#10

Hits: 45   Question The curve C with equation y=f(x), x ≠ 0, passes through the point . Given that a.   find f(x). b.   Verify that f(–2) = 5. c.   Find an equation for the tangent to C at the point (–2, 5), giving your answer in the form ax + by +  c = 0, where […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | June | Q#9

Hits: 19   Question Given that f(x)=( x2 – 6x)(x – 2) + 3x, a.   express f(x) in the form x(ax2 + bx + c), where a, b and c are constants. b.   Hence factorise f(x) completely. c.   Sketch the graph of y = f(x), showing the coordinates of each point at which the graph meets the  […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | June | Q#8

Hits: 19   Question The equation , where p is a positive constant, has equal roots. a.   Find the value of p. b.   For this value of p, solve the equation . Solution a.   We are given the equation; It is evident that it is a quadratic equation.  We also given that it has equal […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | June | Q#7

Hits: 171 Question An athlete prepares for a race by completing a practice run on each of 11 consecutive days. On  each day after the first day, he runs further than he ran on the previous day. The lengths of his 11 practice runs form an arithmetic sequence with first term a km and common  difference d km. He […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | June | Q#6

Hits: 11   Question a.   Expand and simplify  . b.   Express  in the form , where a and b are integers. Solution a.   We are given; b.   We are required to differentiate; If we need a rational number in the denominator of a fraction, we need to follow procedure of  “denominator rationalization” as given below. ü […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | June | Q#5

Hits: 17   Question Differentiate with respect to x; a.   b.   Solution a.   We are required to differentiate; We are required to find . Rule for differentiation of  is: Rule for differentiation of  is: b.   We are required to differentiate; We are required to find . Rule for differentiation of  is: Rule for differentiation is of  is: […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | June | Q#4

Hits: 36   Question A sequence a1, a2, a3, . . . is defined by a1 = 3 an+1 = 3an– 5, n1. a.   Find the value of a2 and the value of a3. b.   Calculate the value of Solution a.   We are given that; an+1 = 3an – 5 a1 = 3 Therefore, we […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | June | Q#3

Hits: 60   Question On separate diagrams, sketch the graphs of a.   y = (x+3)2 b.   y = (x+3)2+k, where k is a positive constant. Show on each sketch the coordinates of each point at which the graph meets the axes. Solution a.   We are required to sketch the graph of; It is evident that it is a […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | June | Q#2

Hits: 29   Question Find the set of values of x for which Solution 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  & 9. Standard  orm of quadratic equation is; The graph […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | June | Q#1

Hits: 11   Question Find  , giving each term in its simplest form. Solution We are required to find; Rule for integration of  is: Rule for integration of  is: Rule for integration of  is: