2. Express each of the following in the form 7k: (i)47. [1] (ii)771. [2] (iii)74 x 4910. [2]
3. (i) Find the gradient of the line l which has equation 3x−5y−20=0. [1] (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]
4. (i) Express 2x2−20x+49 in the form p(x−q)2+r. [4] (ii) State the coordinates of the vertex of the curve y=2x2−20x+49. [2]
5. (i) Sketch the curve y=x. [2] (ii) Describe the transformation that transforms the curve y=x to the curve y=x−4. [2] (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. [2]
6. Find the equation of the normal to the curve y=x26−5 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]
7. Solve the equation x−6x21+2=0, giving your answers in the form p±qr, where p, q and r
are integers. [6]
8. (i) Find the coordinates of the stationary point on the curve y=x4+32x. [5] (ii) Determine whether this stationary point is a maximum or a minimum. [2] (iii) For what values of x does x4+32x increase as x increases? [1]
9. (i) A rectangular tile has length 4x cm and width (x+3) cm. The area of the rectangle is less than 112cm2. By writing down and solving an inequality, determine the set of possible values of x. [6] (ii) A second rectangular tile of length 4y cm 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.
Given that the perimeter of this tile is between 20cm and 54cm, determine the set of possible values of y. [5]
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. [3] (ii) Find the equation of the line which passes through C and the point P (7,2). [4] (iii) Calculate the length of CP and hence determine whether P lies inside or outside the circle. [3] (iv) Determine algebraically whether the line with equation y=2x meets the circle. [5]
How many marks do you think I would lose if I accidently put 2-6root7 for the other x value on qu7? 1 mark? Also if I got the perimeter wrong 9ii) and put 10y+3 instead of 10y+6 resulting in getting 1.7<x<5.1? 2 marks?