Hits: 22

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | January | Q#10

Hits: 22   Question a.   On the same axes sketch the graphs of the curves with equations i.       y=x2(x –2), ii.     y=x(6 –x), and indicate on your sketches the coordinates of all the points where the curves  cross the x-axis. b.   Use algebra to find the coordinates of the points where the graphs intersect. Solution a.     […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | January | Q#9

Hits: 141   Question Ann has some sticks that are all of the same length. She arranges them in squares  and has made the following 3 rows of patterns: She notices that 4 sticks are required to make the single square in the first row, 7  sticks to make 2 squares in the second row and in the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | January | Q#8

Hits: 75   Question The curve C has equation , x > 0. a.   Find an expression for . b.   Show that the point P (4, 8) lies on C. c.   Show that an equation of the normal to C at the point P is 3y=x + 20. The normal to C at P cuts the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | January | Q#7

Hits: 31 Question The curve C has equation y= f(x), x ≠ 0, and the point P(2,1) lies on C. Given that; a.   find f(x). b.   Find an equation for the tangent to C at the point P, giving your answer in the form  y =mx + c, where m and c are integers. Solution a.   […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | January | Q#6

Hits: 7   Question a.   Show that  can be written as , where k is a constant to be found. b.   Find Solution a.   We are given; We have algebraic formula; b.   We are required to find; From (a), we know that; Therefore; Rule for integration of  is: Rule for integration of  is: Rule for integration […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | January | Q#5

Hits: 4   Question The equation , where k is a constant, has no real roots. Find the set of possible values of k. Solution We are given; We are given that given equation has equal roots. For a quadratic equation , the expression for solution is; Where  is called discriminant. If , the equation will have […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | January | Q#4

Hits: 4   Question Solve the simultaneous equations Solution We are given simultaneous equations; Substituting this for  from first equation in the second equation; We have the algebraic formula; Therefore; Now we have two options. By substituting one-by-one these values of  in first equation, we can find corresponding values of . For For Hence, there are following two solutions of the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | January | Q#3

Hits: 14   Question Given that  , x ≠0, a.   Sketch the graph of y=f(x)+3 and state the equations of the asymptotes. b.   Find the coordinates of the point where y=f(x)+3 crosses a coordinate axis. Solution a.   We are given that; We are required to sketch y=f(x)+3. Translation through vector  represents the move,  units in the x-direction and […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | January | Q#2

Hits: 6   Question a.   Express  in the form , where a is an integer. b.   Express  in the form , where b and c are integers to be found. Solution a.   We are given; Since ; b.   We are given; We have algebraic formula;

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | January | Q#1

Hits: 10   Question Given that    , Find . Solution We are required to differentiate; We are required to find . Rule for differentiation of  is: Rule for differentiation of  is: Rule for differentiation is of  is: