2.2.2 Number Patterns and Sequences, PT3 Practice


Question 6:
How many prime numbers are there between 10 and 40?

Solution:
Prime numbers between 10 and 40
= 11, 13, 17, 19, 23, 29, 31, 37
There are 8 prime numbers between 10 and 40.


Question 7:
Diagram below shows a sequence of prime numbers.
13, 17, x, y, 29 Find the value of x + y.

Solution:
Value of x + y
= 19 + 23
= 42


Question 8:
The following data shows a sequence of prime numbers in ascending order.
 5, 7, x, 13, 17, 19, 23, 29, y, z  Find the value of x, y and of z.

Solution:
x = 11, y = 31, z = 37


Question 9:
The following data shows a sequence of prime numbers in ascending order.
  p, 61, 67, q, 73, r, 83  Find the value of p, q and of r.

Solution:
p = 59, q = 71, r = 79



Question 10:
Diagram below shows several number cards.
    49     39     29         87     97     77          5      15     25     List three prime numbers from the diagram.

Solution:
Prime number card from the diagram = 5, 29 and 97.


2.2.1 Number Patterns and Sequences, PT3 Practice


Question 1:
Diagram below is part of a number line.
What is the value of P and of Q?

Solution:
Each gradation on the number line represents 4 units. Thus P = –12 and Q = 12.



Question 2:
Diagram below shows a sequence of numbers. K and M represent two numbers.
    19     13     K      1      M     What are the values of K and M?

Solution:



K
= 13 – 6 = 7
M = 1 – 6 = –5



Question 3:
Diagram below shows five integers.


Find the sum of the largest integer and the smallest integer.

Solution:
The largest integer = 1
The smallest integer = –10
Sum of the largest integer and the smallest integer
= 1 + (–10) 
= –9


2.2.4 Number Patterns and Sequences, PT3 Practice


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Question 16:
State the first two common multiples of 3, 5 and 6.

Solution:
Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, …
Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, …
Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …

The first two common multiples of 3, 5 and 6 are 30 and 60.


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Question 17:
Find the lowest common multiple (LCM) of 4, 8 and 24.

Solution:




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Question 18:
Find the lowest common multiple (LCM) of 8, 12 and 15.

Solution:




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Question 19:
Find the highest common factor (HCF) of 26, 52 and 156.

Solution:




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Question 20:
Given that (m + 5) is the highest common factor of 81 and 108, find the value of m.

Solution:



2.2.3 Number Patterns and Sequences, PT3 Practice


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Question 11:
State all the prime factors of 156.

Solution:
Factors of 156: 1 × 156 2  × 78 3  × 52 × 39 × 26 12 ×  13 2, 3 and 13 are the prime factors of 156.


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Question 12:
State all the prime factors of 182.

Solution:
Factors of 182: 1 × 182 2  × 91 7  × 26 13  × 14 2, 7, 13 and 91 are the prime factors of 182.