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Real Numbers MCQs — Mathematics

230 multiple-choice questions on Real Numbers from Mathematics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.

1. Which property is shown by if x < y and y < 4 then x < 4?

  1. Transitive property of equality
  2. Commutative property of addition
  3. Transitive property of inequality
  4. Commutative property of multiplication

Answer: C) Transitive property of inequality

Explanation: if x < y and y < 4 then x < 4 is the transitive property of inequality. SLO M-09-A-03 · Knowledge

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2. Evaluate 27^ 43.

  1. 81
  2. 243
  3. 181
  4. 36

Answer: A) 81

Explanation: 27 = 3^3, so 27^ 43 = (3^3 )^ 43 = 3^4 = 81. SLO M-09-A-04 · Application

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3. In the Mayan base-20 system, a number with 3 in the twenties place and 7 in the ones place equals:

  1. 67
  2. 143
  3. 187
  4. 37

Answer: A) 67

Explanation: 3 20 + 7 = 67. SLO M-09-A-01 · Knowledge

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4. Simplify dfracx^7 x^-2x^2.

  1. x^3
  2. x^7
  3. x^4
  4. x^-16

Answer: A) x^3

Explanation: Add powers when multiplying and subtract when dividing: 7 + (-2) - 2 = 3. SLO M-09-A-04 · Application

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5. ln (e^5 ) =

  1. e^5
  2. 1
  3. 50
  4. 5

Answer: D) 5

Explanation: ln and e^x undo each other: ln(e^5) = 5. SLO M-09-A-07 · Knowledge

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6. Given log 2 = 0.3010 and log 3 = 0.4771, find log 1.5.

  1. 0.1761
  2. 0.1436
  3. 0.4771
  4. 0.8781

Answer: A) 0.1761

Explanation: log 1.5 = log 3 - log 2 = 0.1761. SLO M-09-A-08 · Application

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7. Which fraction has a terminating decimal expansion?

  1. 215
  2. 16
  3. 79
  4. 925

Answer: D) 925

Explanation: A fraction in lowest terms terminates only when its denominator has no prime factors other than 2 and 5. 925 = 0.36. SLO M-09-A-02 · Knowledge

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8. Which property is shown by if x = 9 then 9 = x?

  1. Associative property of addition
  2. Commutative property of addition
  3. Symmetric property of equality
  4. Commutative property of multiplication

Answer: C) Symmetric property of equality

Explanation: if x = 9 then 9 = x is the symmetric property of equality. SLO M-09-A-03 · Knowledge

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9. A shop has 23 of its stock left. It sells 14 of this. What fraction of the original stock is now left?

  1. 512
  2. 56
  3. 16
  4. 12

Answer: D) 12

Explanation: Left = 23 (1 - 14 ) = 12. SLO M-09-A-09 · Application

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10. Write 50 in simplest radical form.

  1. 6 2
  2. 2 5
  3. 5 4
  4. 5 2

Answer: D) 5 2

Explanation: 50 = 25 2, so 50 = 25 2 = 5 2. SLO M-09-A-04 · Application

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11. Write 1.6 10^6 as an ordinary number.

  1. 0.0000016
  2. 160,000
  3. 16,000,000
  4. 1,600,000

Answer: D) 1,600,000

Explanation: Move the decimal point 6 places to the right: 1,600,000. SLO M-09-A-05 · Understanding

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12. Sound level is L = 10 log ( II0 ) decibels. A sound 1,000,000,000 times as intense as I0 has a level of:

  1. 900 dB
  2. 100 dB
  3. 90 dB
  4. 9 dB

Answer: C) 90 dB

Explanation: L = 10 log 10^9 = 10 9 = 90 dB. SLO M-09-A-08 · Application

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13. Write 72 in simplest radical form.

  1. 6 2
  2. 7 2
  3. 2 6
  4. 6 4

Answer: A) 6 2

Explanation: 72 = 36 2, so 72 = 36 2 = 6 2. SLO M-09-A-04 · Application

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14. A bank pays a profit of 9.5% per year on savings. Profit on Rs. 120,000 for one year is:

  1. Rs. 12,400
  2. Rs. 12631.58
  3. Rs. 114,000
  4. Rs. 11,400

Answer: D) Rs. 11,400

Explanation: Profit = 9.5100 120000 = 11400. SLO M-09-A-09 · Application

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15. Which property is shown by either x < 5, x = 5 or x 5?

  1. Trichotomy property
  2. Commutative property of multiplication
  3. Associative property of addition
  4. Commutative property of addition

Answer: A) Trichotomy property

Explanation: either x < 5, x = 5 or x 5 is the trichotomy property. SLO M-09-A-03 · Knowledge

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16. Find log3 ( 181 ).

  1. 4
  2. -3
  3. -4
  4. -8

Answer: C) -4

Explanation: log3 x = y means 3^y = x. Since 3^-4 = 181, the answer is -4. SLO M-09-A-06 · Knowledge

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17. Which property is shown by if x < y then x + 6 < y + 6?

  1. Additive identity
  2. Additive property of inequality
  3. Additive property of equality
  4. Additive inverse

Answer: B) Additive property of inequality

Explanation: if x < y then x + 6 < y + 6 is the additive property of inequality. SLO M-09-A-03 · Knowledge

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18. In the Mayan base-20 system, a number with 2 in the twenties place and 12 in the ones place equals:

  1. 52
  2. 242
  3. 32
  4. 132

Answer: A) 52

Explanation: 2 20 + 12 = 52. SLO M-09-A-01 · Knowledge

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19. The set of real numbers mathbbR is the union of:

  1. the natural and the whole numbers
  2. the even and the odd numbers
  3. the rational and the irrational numbers
  4. the integers and the natural numbers

Answer: C) the rational and the irrational numbers

Explanation: mathbbR = mathbbQ cup mathbbQ': every real number is either rational or irrational. SLO M-09-A-02 · Knowledge

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20. In the Babylonian base-60 system, a number written as 2 sixties and 15 ones equals:

  1. 135
  2. 35
  3. 215
  4. 105

Answer: A) 135

Explanation: Each place is worth 60 times the one to its right: 2 60 + 15 = 135. SLO M-09-A-01 · Knowledge

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21. Which property is shown by 2 3 = 3 2?

  1. Commutative property of addition
  2. Commutative property of multiplication
  3. Associative property of addition
  4. Associative property of multiplication

Answer: B) Commutative property of multiplication

Explanation: 2 3 = 3 2 is the commutative property of multiplication. SLO M-09-A-03 · Knowledge

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22. Solve 3^x = 20, correct to 2 decimal places.

  1. x approx 6.67
  2. x approx 2.73
  3. x approx 1.30
  4. x approx 2.37

Answer: B) x approx 2.73

Explanation: x = log 20log 3 = 1.30100.4771 approx 2.73. SLO M-09-A-08 · Application

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23. Calculate dfrac8 10^64 10^-2.

  1. 2 10^-3
  2. 2 10^4
  3. 2 10^8
  4. 4 10^8

Answer: C) 2 10^8

Explanation: 8 div 4 = 2 and 10^6-(-2) = 10^8. SLO M-09-A-05 · Understanding

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24. Write 45 in simplest radical form.

  1. 3 5
  2. 5 3
  3. 4 5
  4. 3 10

Answer: A) 3 5

Explanation: 45 = 9 5, so 45 = 9 5 = 3 5. SLO M-09-A-04 · Application

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25. ln 1 =

  1. e
  2. undefined
  3. 1
  4. 0

Answer: D) 0

Explanation: e^0 = 1, so ln 1 = 0. SLO M-09-A-07 · Knowledge

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