Hits: 844

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | June | Q#10

Hits: 844   Question The curve C has equation . The point P has coordinates (3, 0). a)   Show that P lies on C. b)  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. Another point Q also lies on C. The tangent […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | June | Q#9

Hits: 523   Question An arithmetic series has first term  and common difference . a)   Prove that the sum of the first n terms of the series is Sean repays a loan over a period of  months. His monthly repayments form an arithmetic sequence. He repays £149 in the first month, £147 in the second month, £145 in the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | June | Q#8

Hits: 28   Question The line  passes through the point (9, – 4) and has gradient . a)   Find an equation for  in the form ax+by+c=0, where a, b and c are integers. The line  passes through the origin O and has gradient –2. The lines  and  intersect at the point  P. b)  Calculate the coordinates of P. […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | June | Q#7

Hits: 23   Question a)   Show that  can be written as . Given that , , and that  at , b)  Find y in terms of x. Solution a)     We are given; We have the algebraic formula; b)   We are required to find y in terms of x, when; We are also given that , and that […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | June | Q#6

Hits: 23   Question Find the set of values of x for which a)   b)  c)   Both  and . Solution a)     We are required to solve the inequality; We can rearrange the inequality as; b)   We are required to solve the inequality; We solve the following equation to find critical values of ; Now we have two options; […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | June | Q#5

Hits: 17   Question Solve the simultaneous equations Solution We are given simultaneous equations; Rearranging the first equation we get expression for ; Substituting this for  in the second equation; We have the algebraic formula; Therefore; For a quadratic equation , the expression for solution is; For the above equation; Now we have two options. By substituting one-by-one these values of […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | June | Q#4

Hits: 110   Question Figure 1 shows a sketch of the curve with equation y = f(x). The curve passes through the origin O  and through the point (6, 0). The maximum point on the curve is (3, 5).  On separate diagrams, sketch the curve with equation a.   y = 3f(x), b.   y = f(x + 2). […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | June | Q#3

Hits: 38   Question where a and b are constants. a.   Find the value of a and the value of b. b.   Hence, or otherwise, show that the roots of are  , where c and d are integers to be found. Solution a.   We are given; We can write L.H.S of the equation by completing square. […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | June | Q#2

Hits: 24   Question Given that , , a.   Find b.   Find Solution a.   We are given; We are required to find . Rule for differentiation of  is: Rule for differentiation of  is: b.   We are given; We are required to find . Rule for integration of  is: Rule for integration of  is: Rule for integration of […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | June | Q#1

Hits: 32   Question a.   Write down the value of . b.   Find the value of . Solution a.   b.