1. Draw a number line to represent all the composite numbers less than 15. [2]


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
·
·
·
·
·
·
·






2 (a) Find the lowest common multiple of 24, 30 and 72. [2]

(b) Three bells chime at intervals of 24 minutes, 30 minutes and 72 minutes respectively. If they chime together at 22.45 pm, at what time will they next chime together? [1]

OR(a) Since , we consider LCM of 30 and 72.

2
24, 30, 72
3
12, 15, 36
4
4, 5, 12

1, 5, 3


LCM =
= 360

(b) 4.45 am


3. Evaluate . [3]

4. Express 504 and 3136 a product of their prime factors in index notation. [3]
Find (i) the largest integer which is a factor of 504 and 3136,
(ii) the smallest whole number, which when multiplied by 504, gives a perfect cube. [2]
2
3136
2
1568
2
784
2
392
2
196
2
98
7
49

7


2
504
2
252
2
126
3
63
3
21

7







(i)

(ii)


5. Given that and , find the value of
(i) ,
(ii) . [4]

(i)

(ii)


OR
(ii)


6. Evaluate the following
. [4]


7. Find the sum of the two recurring decimals and , leaving your answer as a fraction. [4]





OR











8. Determine the value(s) of a for which the 9-digit number, 20072008a, is divisible by 44. State clearly the divisibility tests that you have used. [3]

Since , we check for divisibility for 4 and 11.

Test for divisibility by 4: a = 0, 4, or 8

Test for divisibility by 11: (2 + 0 + 2 + 0 + a) – (0 + 7 + 0 + 8) is a multiple of 11
4 + a – 15 is a multiple of 11
a – 11 is a multiple of 11




OR
Test for divisibility by 11: (2 + 0 + 2 + 0 + a) – (0 + 7 + 0 + 8) is a multiple of 11
4 + a – 15 is a multiple of 11
a – 11 is a multiple of 11



Since


Note: If only divisibility test of 11 is done with correct value of a, only M1 awarded.






9. All rational number can be expressed as . State clearly the condition(s) on p and q.
Hence explain whether is a rational or irrational number.

Rational number can be expressed as where p and q are integers and .


can be expressed as fraction. Hence it is a rational number.