# F.2 Mathematics Final Revision Exercise _2009-06 - WordPress.com

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```					              F.2 Mathematics Final Revision Exercise (2009-06-04)
Part A : True or False

1.    2m  7n = 14m + n                       True / False

2.    2  2n = 4n                             True / False

3.    2m  2n = 4mn                           True / False

4.      m  m  m  3m                        True / False

5.    11103 is a scientific notation.       True / False

6.    2(x + 1)(2x + 3) = (2x + 2)(4x + 6)     True / False

7.    (a)10 = a10                         True / False

8.    (a)9 = a9                            True / False

9.    The place value of B is ABCD(16) is 11. True / False

1
10. 2x +      is a polynomial.                True / False
x

11. sin(10 + 10) = 2sin10                  True / False

12. If x2 = 10, then x =     10               True / False

13. a3  b3 = (a  b)3                        True / False

14. If x > 2, then x > 2.                   True / False

15. ( 3         2 )2 = 3  2 = 1             True / False

16.     64 is a surd.                         True / False

17.    1.21 is a surd.                        True / False

18. 4 is not a polynomial.                    True / False

19. The degree of 3x2y4 is 4.                 True / False

h       h          2h
20.                                         True / False
tan 10 tan 20 tan 10 tan 20
Part B: Short and Long Questions

21. Which of the following is/ are irrational numbers,       4 ,,    5 , 1. 2 ?

22. (a) Solve       8x2  22x = 5
(b) Solve       (x + 1)(x  2) = (x  2)(3x  9)

1  x 2  ax  a 2 x 2  ax  a 2 
23. Simplify                                  
2a  x 3  a 3         x3  a3 

1 2
24. (a) Make v as the subject in the formula        E     mv
2
2z  3
(b) Make z as the subject of the formula 1              y.
z2
25. Factorize 507(a + b)2  147c4 .
26. A circular region with diameter 60 cm is enclosed by a wire. A portion of the wire is now rusted
and useless, the remaining portion is bent again to form a smaller circular region, find the decrease in
the area of the new region compared with the original one. (The length of the useless portion is given to
be 30 cm.) (Give 3 significance figures if necessary)
2
27. Suppose tan =         , without finding the value of , find the value of cos.
5
28. The following figure shows the original position of a 3 metres long rod leaning against a vertical
wall. Suppose the end point A of the rod is 1.5 metres from the wall.
(a) Find the acute angle between the rod and the ground.
(b) The rod slides down to a position that the point A is now
1 metre further away from the wall. What is the decrease
in the acute angle between the rod and the ground?
(Give 3 significance figures if necessary)
A
29. In the figure, PQR is a straight line and RQ = QP = PS = SQ.
Find the size of PSR.

30. Refer to the figure, AB = 20 cm, BC = 15 cm, CA = x cm, the length of altitude from C to AB
is 10 cm (as shown).                                                                   C

(a) Find the value of x.                                          x cm D 15 cm
(b) Find the shortest distance from B to AC.                                            10 cm

A                              B         E
20 cm

31.
The cumulative frequency curve shows the money donated

by different people in a fund-raising campaign. Find
(a) the median,
(b) the number of people donating more than \$70,
(c) the percentage of people donating less than \$30.
32.
3     7
Form a quadratic equation with integral coefficients and roots      and   .
5      9

33.
In △ABC, B = 90, AB = x cm, BC = (3x  3) cm and CA = (2x + 3) cm. Find the area of △ABC.

34.
             9
10 x  8 y 
(a) Solve the simultaneous equation              5.
6 x  5 y  5

10 8 9
x y5

(b) Solve the simultaneous equation               .
6  5  5
x y


35
Suppose Ax 2  Bx  2 x  3B  A  5C  ( B  1) x 2  4 x where A, B and C are constants.
Find the values of A, B and C.

36.

Refer to the figure above. Given that △ABC is equilateral and the radius of the sector AFDE is 3 cm.
Find the area of △ABC. (Hint: AD  BC)

37.
3        8        27
Simplify                        .
6       24       54
38.

Refer to the figure above. △ABC and △ABE are right-angled triangles such that AC = CD = 2 cm,
AB = 3 cm and BE = 1 cm. Suppose C, A and B are collinear (i.e. lying on the same straight line), find
(a) the length of line segment DE and