76. If a b and c < 0, then:
- a + c < b + c
- ac bc
- ac < bc
- ac = bc
Answer: C) ac < bc
Explanation: Multiplying both sides of an inequality by a negative number reverses the inequality sign. SLO M-09-A-03 · Knowledge
MCQs / Mathematics / Real Numbers
Real Numbers MCQs — Mathematics (page 4)
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.
77. Evaluate 8^ 23.
- 14
- 4
- 163
- 8
Answer: B) 4
Explanation: 8 = 2^3, so 8^ 23 = (2^3 )^ 23 = 2^2 = 4. SLO M-09-A-04 · Application
78. The characteristic of log 0.0045 is:
- bar3
- 3
- 0
- 5
Answer: A) bar3
Explanation: For a number ge 1 the characteristic is one less than the number of digits before the decimal point; for a number < 1 it is negative — one more than the number of zeros right after the decimal point (written with a bar). SLO M-09-A-07 · Knowledge
79. Write 45,600,000 in scientific notation.
- 4.56 10^6
- 4.56 10^8
- 4.56 10^7
- 4.56 10^-7
Answer: C) 4.56 10^7
Explanation: Move the decimal point so that one non-zero digit is before it: 45,600,000 = 4.56 10^7 (left by 7 places). SLO M-09-A-05 · Understanding
80. Write 0.000367 in scientific notation.
- 3.67 10^-5
- 3.67 10^4
- 3.67 10^-4
- 3.67 10^-3
Answer: C) 3.67 10^-4
Explanation: Move the decimal point so that one non-zero digit is before it: 0.000367 = 3.67 10^-4 (right by 4 places). SLO M-09-A-05 · Understanding
81. Write 2^5 = 32 in logarithmic form.
- log2 5 = 32
- log5 32 = 2
- log32 2 = 5
- log2 32 = 5
Answer: D) log2 32 = 5
Explanation: a^y = x iff loga x = y. So 2^5 = 32 becomes log2 32 = 5. SLO M-09-A-06 · Knowledge
82. ln e =
- 1
- 10
- 0
- e
Answer: A) 1
Explanation: ln e = loge e = 1. SLO M-09-A-07 · Knowledge
83. The Roman numeral MCMXCIV stands for:
- 2004
- 1996
- 1994
- 2094
Answer: C) 1994
Explanation: Read left to right: a smaller symbol before a larger one is subtracted (e.g. CM = 900, XC = 90, IV = 4). So MCMXCIV = 1994. SLO M-09-A-01 · Knowledge
84. A shirt marked at Rs. 950 is sold at a 20% discount. The sale price is:
- Rs. 760
- Rs. 190
- Rs. 1,140
- Rs. 930
Answer: A) Rs. 760
Explanation: Discount = 20% of 950 = 190. Sale price = 950 - 190 = 760. SLO M-09-A-09 · Application
85. Money grows by 8% per year (compound): A = A0(1.08)^t. About how many years until it becomes 2 times as much? (use logarithms)
- 12.5 years
- 7.0 years
- 11.0 years
- 9.0 years
Answer: D) 9.0 years
Explanation: (1.08)^t = 2 Rightarrow t = log 2log 1.08 approx 9.0 years. SLO M-09-A-08 · Application
86. A natural logarithm has base:
- pi
- 10
- e
- 2
Answer: C) e
Explanation: Natural logarithms (ln x) use base e. SLO M-09-A-07 · Knowledge
87. Simplify dfracx^5 x^3x^4.
- x^4
- x^-2
- x^12
- x^11
Answer: A) x^4
Explanation: Add powers when multiplying and subtract when dividing: 5 + (3) - 4 = 4. SLO M-09-A-04 · Application
88. Which property is shown by 10 = 10?
- Associative property of addition
- Reflexive property of equality
- Commutative property of addition
- Commutative property of multiplication
Answer: B) Reflexive property of equality
Explanation: 10 = 10 is the reflexive property of equality. SLO M-09-A-03 · Knowledge
89. For any valid base a, loga 1 =
- a
- 1
- undefined
- 0
Answer: D) 0
Explanation: a^0 = 1, so loga 1 = 0. SLO M-09-A-06 · Knowledge
90. The characteristic of log 734,000 is:
- 3
- bar3
- 0
- 5
Answer: D) 5
Explanation: For a number ge 1 the characteristic is one less than the number of digits before the decimal point; for a number < 1 it is negative — one more than the number of zeros right after the decimal point (written with a bar). SLO M-09-A-07 · Knowledge
91. Simplify dfrac(2a^2b^3)^24a^3b^2.
- ab^4
- a^2b^4
- ab^42
- 4ab^4
Answer: A) ab^4
Explanation: (2a^2b^3)^2 = 4a^4b^6; dividing by 4a^3b^2 gives a^4-3b^6-2 = ab^4. SLO M-09-A-04 · Application
92. The relation between natural and common logarithms is:
- log x approx 2.303 ln x
- ln x = 10 log x
- ln x = log x
- ln x approx 2.303 log x
Answer: D) ln x approx 2.303 log x
Explanation: ln x = log xlog e = log x0.4343 approx 2.303 log x. SLO M-09-A-07 · Knowledge
93. Write 0.00008 in scientific notation.
- 8 10^-5
- 8 10^5
- 8 10^-4
- 8 10^-6
Answer: A) 8 10^-5
Explanation: Move the decimal point so that one non-zero digit is before it: 0.00008 = 8 10^-5 (right by 5 places). SLO M-09-A-05 · Understanding
94. Money grows by 10% per year (compound): A = A0(1.10)^t. About how many years until it becomes 2 times as much? (use logarithms)
- 10.0 years
- 7.3 years
- 5.3 years
- 9.3 years
Answer: B) 7.3 years
Explanation: (1.10)^t = 2 Rightarrow t = log 2log 1.10 approx 7.3 years. SLO M-09-A-08 · Application
95. We divide an hour into 60 minutes and a circle into 360 degrees. This comes from the number system of the:
- Romans
- Egyptians
- Greeks
- Babylonians
Answer: D) Babylonians
Explanation: Both come from the Babylonian base-60 system: 60 minutes, 60 seconds and 360 = 6 60 degrees. SLO M-09-A-01 · Knowledge
96. Evaluate 125^- 13.
- 5
- 15
- - 1253
- 1
Answer: B) 15
Explanation: 125 = 5^3, so 125^- 13 = (5^3 )^- 13 = 5^-1 = 15. SLO M-09-A-04 · Application
97. Zakat is 2.5% of savings. The zakat on Rs. 1,250,000 is:
- Rs. 312,500
- Rs. 31,250
- Rs. 33,750
- Rs. 3,125
Answer: B) Rs. 31,250
Explanation: 2.5% 1250000 = 2.5100 1250000 = 31250. SLO M-09-A-09 · Application
98. Which rational number lies between 25 and 35?
- 12
- 710
- 65
- 310
Answer: A) 12
Explanation: The average 12 ( 25 + 35 ) = 12 always lies between them. SLO M-09-A-02 · Knowledge
99. A shop has 34 of its stock left. It sells 25 of this. What fraction of the original stock is now left?
- 920
- 310
- 710
- 720
Answer: A) 920
Explanation: Left = 34 (1 - 25 ) = 920. SLO M-09-A-09 · Application
100. ln 1 =
- e
- undefined
- 1
- 0
Answer: D) 0
Explanation: e^0 = 1, so ln 1 = 0. SLO M-09-A-07 · Knowledge