PT3 Mathematics 2017, Question 3


Question 3 (a):
(i) Diagram 3.1 shows one of the methods of finding the highest common factor (HCF) and the lowest common multiples (LCM) for 12 and 32.

Match the correct answer.
Answer:


(ii) The difference between two prime numbers is 9.
Write the two prime numbers in the answer space.
Answer:
(  ) – (  ) = 9

Solution:
(i)




(ii)
( 11  ) – ( 2  ) = 9

 


Question 3 (b):
Diagram 3.2 in the answer space shows a straight line JK.
(i) Using only a ruler and a pair of compasses, construct triangle JKL with KL = 8 cm and ∠JKL = 135o. You may begin from the straight line JK provided in the answer space.

Answer:

(ii) Measure KJL by using a protractor.

Solution:
(i)


(ii)
KJL = 26o




Question 3 (c):
List all the integer values of x which satisfy the following linear inequalities:
–1 ≤ 1 + 2x < 5

Solution:
–1 ≤ 1 + 2x < 5
–1 ≤ 1 + 2x   and   1 + 2x < 5
–2x ≤ 1 + 1   and   2x < 5 – 1
–2x ≤ 2    and   2x < 4
x ≥ –1   and   x < 2
x = –1, 0, 1, 2, … and   x = 1, 0, –1,  –2 …

Thus x = –1, 0, 1.


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