## Saturday, 17 July 2010

### A draft/list of next year's selection test

Just a reminder for me, too. This test is FOR F1,2 NEWBIES.
Time allowed : 1.5 hr
SECTION A (easier) 1@
1)Compare the size of -1.5, -5/6, 1/6, 3.
2)Solve the equation 0=6x-(3x+7)/2. Hence solve (9x-7)^2=0.
3)Evaluate 2007-2004+2001-1998...-4+1.
4)Evalaute 0.9+0.99+0.999+...
5)Factorize 7007.
Geometry
1)Given a rectangle with width 5 and length 7, find the length of its diagonals.
2)  <- too lazy to construct geom. quiestions...
Combinatorics
1)In how many ways we can reearange the digits 0,3,5,7 so that the 4-digits number is even?
2)In how many ways we can paint a cube in 4 colours so that
i)opposite faces have the same colour; and
Number Theory
1)Find the smallest multiple of 45 that it contains the digits 1~9.

Section B (medium diff)
Algebra
1)Compare the size of 2^7^2, (2^7)^2, 7^2^2, (7^2)^2, note that a^b^c = a^(b^c).
2)Evaluate (2010^4+2009^4+1)/(2010^2+2009^2+1).
3)Solve the equation 2x^2-x+3=0, hence solve 2x^4-x^3+1-x+2=0.
4)Express (a^3+b^3+c^3-3abc)/(a+b+c) in terms of x=(a-b) and y=(b-c).
5)Factorize 777777.
Geometry
1)Find the minimum difference between a square and a rhombus with side length a.
2)Which of the following parametic curve is odd?
i)x=t^2, y=t
ii)x=0.5(1-cos 2t), y=sin t
iii)x=log t^2, y=log t
iv)x=t^2-2t+1, y=t-1
Combinatorics
1)Given a 4*4 grid table, and you have to colour four of the 16 grids. If there's no three coloured grids in a row (ehtierh horizontal, vertical or diagonal), how many possible ways you can colour the grids?
2)Given three colours, say red, green and blue. How many ways you can colour the edges of a regular tetrahedron? Note that if the colour patterns are the same after spinning, then it only counts as one way.
Number Theory
1)Solve the equation 201{x}+209[x]=2010.

(Better? orz