(a) Use the list of numbers shown below to answer the following questions. 2
__ 2
1 0 1 3
__ 7
2 –5 6
–7
9
(i) Identify as many natural numbers as possible from the list. Justify your answers using your knowledge of the defi nition of natural numbers.
(ii) Identify as many integers as possible from the list. Justify your answers using your knowledge of the defi nition of integers.
(iii) Identify as many rational numbers as possible from the list. Justify your answers, using your knowledge of the defi nition of rational numbers.
(b) Taking the list of numbers given in part (a) as the universal set, draw a Venn diagram to represent the following sets:
A = {prime numbers} B = {factors of 12}
Use the Venn diagram to answer the following questions. (i) List the elements of A∪ B (ii) List the elements of a subset of B containing two elements. (iii) Find #(A∩B)
Negative numbers can’t be prime.
(c) Pick a number from the list given in part (a) above to answer each of the following questions. (i) What is the probability of getting a 7 when you throw a standard six-sided die? (ii) What is the probability of getting heads when you fl ip a fair coin? (iii) What is the probability of picking a day of the week beginning with S?
(d) Use any combination of the numbers in the list given in part (a) above to demonstrate the following:
(i) The associative property of addition (ii) The commutative property of multiplication (iii) The distributive property of multiplication
2. Pat is an avid hillwalker and he decides to walk from Bray seafront to Greystones Harbour, and back again. He wants to work out how long the round trip is going to take him.
The route is a 6 km walk beginning at the seafront in Bray and ending at the harbour in Greystones.
Pat would like to include a few breaks during his trip: a short break of 10 minutes for a snack on the way; 30 minutes in Greystones to take photos and have lunch; and another 10 minute break at some point on the way back.
Pat knows that he can travel 5 km in one hour. (a) (i) How long does it take to cover 1 kilometre along the route?
(ii) Taking breaks into account, how long would it take Pat to complete his round trip from Bray to Greystones and back to his starting point in Bray?
Section A Introducing concepts and building skills