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Mathematics: All Topics
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Cambridge IGCSE Mathematics
Mathematics: All TopicsComplete deck
01·1.1 Types of number
What is a natural number?
Answer
A counting number: 1, 2, 3, 4, ... .
02·1.1 Types of number
Is 0 a natural number in the counting-number convention used here?
Answer
No. Natural numbers begin at 1; 0 is an integer.
03·1.1 Types of number
Write six billion in figures.
Answer
6 000 000 000.
04·1.1 Types of number
Write 10 007 in words.
Answer
Ten thousand and seven.
05·1.1 Types of number
Write seven million, forty thousand and six in figures.
Answer
7 040 006.
06·1.1 Types of number
Write 2 305 019 in words.
Answer
Two million, three hundred and five thousand and nineteen.
07·1.1 Types of number
Which of −3, 0, 4.5 and 9 are natural numbers?
Answer
Only 9: it is a positive whole counting number.
08·1.1 Types of number
How many natural numbers lie strictly between 48 and 63?
Answer
14: the numbers from 49 to 62 inclusive.
09·1.1 Types of number
What is an integer?
Answer
A whole number that can be positive, negative or zero.
10·1.1 Types of number
Give three negative integers.
Answer
For example −1, −4 and −12.
11·1.1 Types of number
Is zero an integer?
Answer
Yes. Zero is an integer but is neither positive nor negative.
12·1.1 Types of number
Is −8.0 an integer?
Answer
Yes. −8.0 equals the whole number −8.
13·1.1 Types of number
Which of −7, 0, 3/2, 11 and √9 are integers?
Answer
−7, 0, 11 and √9 (= 3); 3/2 is not an integer.
14·1.1 Types of number
Is every natural number an integer?
Answer
Yes. All positive counting numbers are integers.
15·1.1 Types of number
Why is −2.5 not an integer?
Answer
It has a fractional part; integers have no nonzero fractional part.
16·1.1 Types of number
A number is both a negative integer and a perfect square. Is this possible?
Answer
No. A square number cannot be negative.
17·1.1 Types of number
What is a prime number?
Answer
A whole number greater than 1 with exactly two positive factors: 1 and itself.
18·1.1 Types of number
List the prime numbers below 20.
Answer
2, 3, 5, 7, 11, 13, 17 and 19.
19·1.1 Types of number
Why is 1 not a prime number?
Answer
It has only one positive factor, not exactly two.
20·1.1 Types of number
What is the only even prime number?
Answer
21·1.1 Types of number
What is a composite number?
Answer
An integer greater than 1 with more than two positive factors.
22·1.1 Types of number
Is 51 prime? Explain.
Answer
No. 51 = 3 × 17, so it has factors other than 1 and 51.
23·1.1 Types of number
Express 72 as a product of prime factors.
Answer
72 = 2³ × 3².
24·1.1 Types of number
Express 180 as a product of prime factors.
Answer
180 = 2² × 3² × 5.
25·1.1 Types of number
Why is 91 not a prime number?
Answer
91 = 7 × 13.
26·1.1 Types of number
Explain how to check whether 97 is prime.
Answer
Test divisibility by primes up to √97: 2, 3, 5 and 7. None divides 97; it is prime.
27·1.1 Types of number
Find the smallest prime factor of 221.
Answer
13, since 221 = 13 × 17.
28·1.1 Types of number
A number has prime factorisation 2³ × 3 × 5². Find the number.
Answer
8 × 3 × 25 = 600.
29·1.1 Types of number
Why is the product of two different primes always composite?
Answer
Each prime is a positive factor of the product, so the product has factors other than 1 and itself.
30·1.1 Types of number
What is a square number?
Answer
A number of the form n × n, where n is an integer.