Hits: 242

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | May-Jun | (P2-9709/02) | Q#7

Hits: 242   Question The equation of the curve is .     i.       Show that    ii.       Find the coordinates of each of the points on the curve where the tangent is parallel to the x- axis. Solution      i.   We are given; We are required to find . To find from […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | May-Jun | (P2-9709/02) | Q#6

Hits: 206     Question It is given that the curve has one stationary point.      i.       Find the x-coordinates of this point.    ii.       Determine whether this point is a maximum or a minimum point. Solution      i.   We are required to find the coordinates of stationary point of the curve; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | Oct-Nov | (P2-9709/02) | Q#3

Hits: 1707   Question The variables x and y satisfy the equation y = A(b-x), where A and b are constants. The graph of ln y  against ln x is a straight line passing through the points (0, 1.3) and (1.6, 0.9), as shown in the  diagram. Find the values of A and b, correct […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | Oct-Nov | (P2-9709/02) | Q#1

Hits: 334     Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following with their corresponding inequality; When When When If then above four intervals translate […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | May-Jun | (P2-9709/02) | Q#1

Hits: 195     Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let  and , then; We have to consider two separate cases; When When We have the inequality; It can be written as; We have to consider two separate cases; When When Therefore the inequality will hold for ; SOLVING INEQUALITY: ALGEBRAICALLY Let, […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2008 | June | Q#10

Hits: 844   Question The points Q (1, 3) and R (7, 0) lie on the line , as shown in Figure. The length of QR is . a.   Find the value of a. The line l2 is perpendicular to , passes through Q and crosses the y-axis at the point P, as shown  in Figure. Find […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2008 | June | Q#9

Hits: 58   Question The curve C has equation , where k is a constant. a.   Find . Point A with x-coordinate  lies on C. The tangent to C at A is parallel to the line with equation  . Find b.   The value of k. c.   The value of y-coordinate of A. Solution a.   Gradient (slope) of […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2008 | January | Q#10

Hits: 55   Question The curve C has equation y=(x + 3)(x −1)2 . a.   Sketch C showing clearly the coordinates of the points where the curve meets the coordinate  axes. b.   Show that the equation of C can be written in the form y = x3 + x2 − 5x + k, where k is a […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2008 | January | Q#9

Hits: 25   Question The curve C has equation y = f(x), x > 0, and . Given that the point P(4,1) lies on C, a.   find f(x) and simplify your answer. b.   Find an equation of the normal to C at the point P(4, 1). Solution a.   We are required to find f(x), when; We are also […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2008 | January | Q#4

Hits: 22   Question The point A(–6, 4) and the point B (8, –3) lie on the line L. a.  Find an equation for L in the form ax + by + c = 0, where a, b and c are integers. b.  Find the distance AB, giving your answer in the form , where k is an integer.` […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | June | Q#1

Hits: 31   Question The straight line L has equation  and the curve C has equation a.   Sketch on the same axes the line L and the curve C, showing the values of the intercepts on the  x-axis and the y-axis. b.   Show that the x-coordinates of the points of intersection of L and C satisfy the equation  . c.   Hence find […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | June | Q#7

Hits: 137   Question The circle S has centre C(8,13) and touches the x-axis, as shown in the diagram. a.   Write down an equation for S, giving your answer in the form b.   The point P with coordinates (3,1) lies on the circle.                     i.       Find the gradient of the straight line passing through P and […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | June | Q#5

Hits: 31   Question The curve with equation  is sketched below. The points A(-2,0) , B(2,0) and C(1,15) lie on the curve.  a.   Find an equation of the straight line AC . b.                          i.       Find .                   ii.       Hence calculate the area of the shaded region bounded by the curve and the line AC . Solution a.   We are […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | January | Q#7

Hits: 23   Question The curve C has equation  . The line L has equation  , where k is a constant. a.   Show that the x-coordinates of any points of intersection of the line L with the curve C satisfy the  equation b.   The curve C and the line L intersect in two distinct points. Show that c.   Solve […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | January | Q#4

Hits: 43   Question A circle with centre C has equation .  a.   By completing the square, express this equation in the form b.    Write down:                            i.       the coordinates of C;                          ii.       the radius of the circle, leaving your answer in surd form. c.   A line has equation .                            i.       Show that the x-coordinate of any point of […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | January | Q#1

Hits: 29   Question The triangle ABC has vertices A(-2,3), B(4,1) and C(2,-5). a.   Find the coordinates of the mid-point of BC . b.                 i.  F ind the gradient of AB, in its simplest form.           ii.  Hence find an equation of the line AB , giving your answer in the form  , where q  and […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2008 | Oct-Nov | (P1-9709/01) | Q#8

Hits: 470 Question The equation of a curve is . i.       Show that the equation of the normal to the curve at the point  is This normal meets the curve again at the point Q.    ii.       Find the coordinates of Q.   iii.       Find the length of PQ. Solution i.   We are required to find the equation of the normal to the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2008 | May-Jun | (P1-9709/01) | Q#11

Hits: 1066 Question In the diagram, the points A and C lie on the x- and y-axes respectively and the equation of AC is . The point B has coordinates (2, 2). The perpendicular from B to AC meets AC at the point X. i.       Find the coordinates of  X. The point D is such that the quadrilateral ABCD has AC […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2008 | May-Jun | (P1-9709/01) | Q#4

Hits: 446 Question The equation of a curve C is  and the equation of a line L is . i. Find the x-coordinates of the points of intersection of L and C.    ii. Show that one of these points is also the stationary point of C. Solution i.   If two lines (or a line and […]