REAL NUMBERS + LOGARITHMS

1

Which of the following is an irrational number?

A √7 B 3/4 C 0.333... D 0.6

2

Any non-zero real number raised to the power of 0 is equal to:

A 1 B 0 C The number itself D -1

3

What is the product of 2³ and 2⁵?

A 2⁸ B 2¹⁵ C 4⁸ D 2²

4

Simplify: log₁₀(10⁷).

A 7 B 10 C 10⁷ D 1

5

Which of the following numbers is an irrational number?

A √7 B 0.333... C 22/7 D √16

6

The standard notation of 5.67 × 10⁰ is:

A 5.67 B 567 C 0.567 D 5670

7

Which is the correct expansion of log₄(x/y)?

A log₄ x - log₄ y B log₄ x + log₄ y C log₄ x / log₄ y D log₄ x * log₄ y

8

Which property states that a × (b + c) = a × b + a × c?

A Distributive property B Commutative property C Associative property D Identity property

9

The set of real numbers R is the union of:

A The set of rational numbers Q and the set of irrational numbers Q' B The set of integers Z and the set of natural numbers N C The set of whole numbers W and the set of integers Z D The set of negative integers and the set of positive integers

10

Sana is comparing the numbers √2 and 1.5. She knows √2 is approximately 1.414. Which statement is true?

A √2 > 1.5 B √2 < 1.5 C √2 = 1.5 D √2 is an integer.

11

Simplify: (3x²y)².

A 6x⁴y² B 9x⁴y² C 9x²y² D 6x²y²

12

Which law is applied in logₐ(M/N) = logₐ M - logₐ N?

A Product law B Quotient law C Power law D Change of base law

13

Which of the following is NOT a property of real numbers?

A The product of two negative numbers is negative B Commutative property C Associative property D Distributive property

14

What is the value of logₑ(e²)?

A 1 B 2 C e D 0

15

Faisal is evaluating (8^2) ÷ (8^2). He uses the quotient property of exponents. What is the simplified result?

A 8^4 B 8^0 C 8^2 D 1^2

16

What is the value of (10²)⁰?

A 0 B 1 C 100 D 10

17

Which of the following is equivalent to log₂(32)?

A log₂(16) + log₂(2) B log₂(16) - log₂(2) C 2 log₂(16) D log₂(64) / 2

18

What is the simplified form of (x^3)^2 * x^4?

A x^9 B x^24 C x^10 D x^11

19

Which of the following is a rational number?

A √2 B √3 C π D √16

20

Tariq is identifying the property shown by a + 0 = a for any real number a. Which property is illustrated?

A Additive identity property B Multiplicative identity property C Additive inverse property D Distributive property

21

Waqas is identifying the property shown by a × (b + c) = a × b + a × c. Which property is illustrated?

A Commutative property B Associative property C Distributive property D Identity property

22

Bilal is evaluating the expression √(16 × 25). He uses the product property of radicals. What is the result?

A 20 B 40 C 41 D 9

23

Samina is identifying the multiplicative identity for real numbers. She knows that multiplying any real number by this identity leaves it unchanged. What is the multiplicative identity?

A 0 B -1 C 1 D 10

24

What is log₁₀(10⁵)?

A 5 B 10 C 50 D 0.5

25

Nadia is asked to find the value of √(81/144). She simplifies the numerator and denominator separately. What is the result?

A 9/12 B 3/4 C 9/16 D 4/3