S5_Mock02_E

Figure 2 shows a rectangle ABCD. The diagonals AC and BD meet at P. DC = (x + 2) cm and the perimeter of PCD is (5x – 4) cm.
https://www.flickr.com/photos/130230543@N06/16120530596/in/photostream
(b)Suppose BC = 3x cm. Find the value of x. (4 marks)
(Just wanna ask why part b cannot be a fraction answer, have to reject it)

Figure 3(a) shows a solid wooden right cylinder of base radius 26 cm and height 52 cm.
https://www.flickr.com/photos/130230543@N06/16146810345/in/photostream
https://www.flickr.com/photos/130230543@N06/15961054257/in
(b)A hemispherical vessel of radius 40 cm is held vertically on a horizontal surface. The vessel is fully filled with water.
(i)Find the volume of the water in the vessel in terms of pi.
(ii)The cylinder is now held vertically in the vessel as shown in Figure 3(b). A student claims that the volume of the water remaining in the vessel is less than 0.06 m3. Do you agree? Explain your answer.

Consider a quadratic equation ax2 - 2bx + c = 0, where a, b and c are constants.
(a)If a, b, c form a geometric sequence,
(i)show that the equation has one double root,
(ii)express the root of the equation in terms of a and b.
(I cannot understand aii)

Which of the following may represent the nth term of the sequence 0, -2/3, 4/5, -6/7, 8/9 ... ?
A. (-1)n+1 x 2n/2n-1
B. (-1)n x 2n-2/2n+1
C. (-1)n+1 x 2n-2/2n-1
D. (-1)n x 2n-2/2n-1
(Answer is C)

The figure shows a square tile with side length 6 cm. A coin with centre P and radius 1 cm is thrown onto the tile at random. If P must lie on the tile, find the probability that the whole coin lies on the tile.
https://www.flickr.com/photos/130230543@N06/16161215332/in/photostream
A.1/6
B. 4/9
C. 2/3
D.1
(Answer is B)

If the roots of the quadratic equation x2 + hx + 2 = 0 are alpha and beta, where alpha > beta, then alpha2 – beta2 =
A.h sqt(h2-8).
B.–h sqt(h2-8).
C.h sqt(8 - h2).
D.–h sqt(8 - h2).
(Answer is B)