4.5.1.1 Natural, rational, irrational and real numbers Quiz: AQA Computer Science, Unit 5

The 20 questions

1. Which set is written as N = {0, 1, 2, 3, ...} in this specification?

   • The irrational numbers
   • The rational numbers
   • The real numbers
   • The natural numbers

2. Which of these numbers is irrational?

   • The integer -7
   • The square root of 2
   • The decimal 0.25
   • The fraction 3/4

3. Which set includes the natural numbers, the rational numbers and the irrational numbers?

   • The complex numbers only
   • The integers
   • The real numbers
   • The rational numbers

4. Why are all integers classed as rational numbers?

   • Integers are the only numbers that can be written as decimals
   • Every integer n can be written as n/1, a ratio of two integers
   • Integers are rational only when they are positive
   • Integers never contain a fractional part and so are irrational

5. What is an irrational number?

   • A number whose decimal form always repeats in a fixed pattern
   • A negative number that has a fractional part
   • A whole number that is greater than zero
   • A real number that cannot be written as a fraction of two integers

6. Which symbol denotes the set of rational numbers?

   • Z
   • Q
   • R
   • N

7. What do real numbers represent in the specification?

   • Only numbers that can be written as fractions of integers, including all the decimals
   • Only whole numbers used for counting objects, such as people and chairs in a room
   • All possible real world quantities, including natural, rational and irrational numbers
   • Only numbers that can be stored exactly in a computer, without any rounding or loss at all

8. Is 7 a rational number, and why?

   • No, because 7 has no fractional part
   • Yes, but only when it is written as 14/3
   • No, because rational numbers exclude all whole numbers
   • Yes, because 7 can be written as 7/1, a ratio of two integers

9. Which of these numbers is rational?

   • 0.75
   • The square root of 5
   • The number pi
   • The square root of 3

10. Which of these is NOT an integer?

    • 45
    • -12
    • 3/4
    • 0

11. Which number is an element of the natural numbers as defined in this specification?

    • 0
    • -1
    • 2.5
    • The square root of 7

12. A tape measure gives a length of 2.5 m. Which set best describes this value?

    • The real numbers, since measurement can give any real quantity
    • The natural numbers, since measurements are always counted
    • The natural numbers, since measurements start from zero
    • The integers, since lengths are always whole numbers

13. Which pair of numbers is both rational?

    • 2/3 and 0.5
    • The square root of 3 and 2/3
    • The number pi and 1/4
    • The square root of 2 and 0.5

14. Which number belongs to the integers Z but NOT to the natural numbers N as defined here?

    • 12
    • 7
    • -5
    • 0

15. What is the square root of 9, and which sets does it belong to?

    • 3, which is an irrational and real number only
    • 3, which is rational but not an integer
    • 3, which is not a real number because it is a root
    • 3, which is a natural, integer, rational and real number

16. A student claims every real number is either rational or irrational. Which evaluation is correct?

    • The claim is correct, since the reals are exactly the rationals together with the irrationals
    • The claim is wrong, because some real numbers are natural numbers only, and so are not rational
    • The claim is correct only for negative real numbers, because positive values behave differently
    • The claim is wrong, because irrational numbers are not considered real numbers at all in this course

17. Which set is closed under subtraction, so that subtracting any two members always gives a member?

    • The positive rational numbers, since they exclude zero and negatives
    • The irrational numbers, since differences of irrationals are irrational
    • The natural numbers, since differences are never negative
    • The integers, since the difference of any two integers is an integer

18. If x is rational and y is irrational, what is the type of x + y?

    • Rational, because adding a rational number always gives a rational
    • Undetermined, since an irrational plus a rational can be any type
    • Irrational, because if x + y were rational then y = (x + y) - x would be rational
    • Natural, because the sum of two real numbers is a whole number

19. Which statement best describes the standard proof that the square root of 2 is irrational?

    • Assume the root equals p/q in lowest terms, then show p and q are both even, which is a contradiction
    • Show that the root has a decimal expansion that repeats after a finite number of digits
    • Show that squaring 1.5 gives exactly 2, so the root equals 1.5
    • Compute the root to ten decimal places and check that the digits stop

20. What are the type and classification of the number 2 + sqrt(3)?

    • Irrational and real, since sqrt(3) is irrational and adding 2 keeps it irrational
    • Rational, since the sum of two numbers is always rational
    • Rational and natural, since 2 is a natural number and the total is whole
    • Irrational but not real, since square roots lie outside the real numbers

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