Reference no: EM131017147
1. Simplify (x - 5)(x2 + 3) - (x + 4)(x -1).
2. Express each of the following in the form 7k :
(i) 4√7,
(ii) 1/ 7√7,
(iii) 74 x 4910.
3 (i) Find the gradient of the line 1 which has equation 3x - 5y - 20 = 0.
(ii) The line l crosses the x-axis at P and the y-axis at Q. Find the coordinates of the mid-point of PQ.
4 (i) Express 2x2 - 20x + 49 in the form p(x - q)2 + r.
(ii) State the coordinates of the vertex of the curve y = 2x2 - 20x + 49.
5. (i) Sketch the curve y = √x.
(ii) Describe the transformation that transforms the curve y = √x to the curve y = √(x-4)
(iii) The curve y = √x is stretched by a scale factor of 5 parallel to the x-axis. State the equation of the transformed curve.
6. Find the equation of the normal to the curve y = (6/x2) - 5 at the point on the curve where x = 2. Give your answer in the form ax + by + c = 0, where a, b and c are integers.
7. Solve the equation x - 6x1/2 + 2 = 0, giving your answers in the form p ± q√r, where p, q and r are integers.
8. (i) Find the coordinates of the stationary point on the curve y = x4 + 32x.
9. (i) A rectangular tile has length 4x cm and width (x + 3)cm. The area of the rectangle is less than 112 cm2. By writing down and solving an inequality, determine the set of possible values of x.
(ii) A second rectangular tile of length 4ycm and width (y + 3)cm has a rectangle of length 2y cm and width y cm removed from one corner as shown in the diagram.
![1265_A rectangular tile.png](https://secure.expertsmind.com/CMSImages/1265_A%20rectangular%20tile.png)
Given that the perimeter of this tile is between 20 cm and 54cm, determine the set of possible values of y.
10. A circle has equation (x - 5)2 + (y + 2)2 = 25.
(i) Find the coordinates of the centre C and the length of the diameter.
(ii) Find the equation of the line which passes through C and the point P (7, 2).
(iii) Calculate the length of CP and hence determine whether P lies inside or outside the circle.
(iv) Determine algebraically whether the line with equation y = 2x meets the circle.
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