# 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.