Grade 9 : Mathematics - 3. Number Systems (Set 2)

Question 1

Which of the following numbers is a rational number?

Accepted Answer

C) $\sqrt{4}$

Answer

A) $\sqrt{2}$

Answer

B) $\sqrt{3}$

Answer

D) $\pi$

Question 2

What is the decimal expansion of the fraction $\frac{7}{8}$?

Accepted Answer

A) 0.875 (terminating)

Answer

B) 0.88 (terminating)

Answer

C) $0.\bar{875}$ (non-terminating recurring)

Answer

D) 0.785 (terminating)

Question 3

What is the rationalising factor of the denominator in $\frac{1}{3 + \sqrt{5}}$?

Accepted Answer

B) $3 - \sqrt{5}$

Answer

A) $3 + \sqrt{5}$

Answer

C) \sqrt{5} - 3

Answer

D) $5 - \sqrt{3}$

Question 4

Evaluate the expression $(125)^{1/3}$.

Accepted Answer

C) 5

Answer

A) 25

Answer

B) 15

Answer

D) $5\sqrt{5}$

Question 5

Convert the repeating decimal $0.\bar{4}$ into a fraction in lowest terms.

Accepted Answer

B) $\frac{4}{9}$

Answer

A) $\frac{4}{10}$

Answer

C) $\frac{2}{5}$

Answer

D) $\frac{44}{100}$

Question 6

A carpenter needs to simplify a wooden board of length $\sqrt{50}$ metres into radical form.

Which of the following represents $\sqrt{50}$ in simplest radical form?

Accepted Answer

B) $5\sqrt{2}$

Answer

A) $2\sqrt{5}$

Answer

C) $25\sqrt{2}$

Answer

D) $10\sqrt{5}$

Question 7

Simplify the expression: $3\sqrt{7} + 5\sqrt{7}$.

Accepted Answer

C) $8\sqrt{7}$

Answer

A) $8\sqrt{14}$

Answer

B) $15\sqrt{7}$

Answer

D) $2\sqrt{7}$

Question 8

Using the laws of exponents, simplify $2^{2/3} \cdot 2^{1/3}$.

Accepted Answer

C) 2

Answer

A) $2^{2/9}$

Answer

B) $4^{1/3}$

Answer

D) 1

Question 9

Which of the following real numbers is an irrational number lying between 2 and 3?

Accepted Answer

B) $\sqrt{5}$

Answer

A) $\sqrt{3}$

Answer

C) $\sqrt{10}$

Answer

D) $\sqrt{16}$

Question 10

Simplify the product: $(3 + \sqrt{3})(3 - \sqrt{3})$.

Accepted Answer

A) 6

Answer

B) 9

Answer

C) 3

Answer

D) 12

Question 11

An art board has a square shape with an area of $49cm^2$. The side length is calculated as $s = \sqrt{49}cm$.

How is the side length $s$ correctly classified?

Accepted Answer

B) A rational number equal to 7 cm

Answer

A) An irrational number equal to $\sqrt{7}cm$

Answer

C) An imaginary number

Answer

D) A non-terminating non-repeating decimal

Question 12

Evaluate $\frac{11^{1/2}}{11^{1/4}}$ using laws of exponents.

Accepted Answer

C) $11^{1/4}$

Answer

A) $11^{1/8}$

Answer

B) $11^{3/4}$

Answer

D) $11^{2}$

Question 13

Statement I: Every point on a real number line represents a unique real number.
Statement II: Every real number corresponds to a unique point on the real number line.

Which of the statements above is correct?

Accepted Answer

C) Both Statement I and Statement II are correct

Answer

A) Only Statement I is correct

Answer

B) Only Statement II is correct

Answer

D) Neither statement is correct

Question 14

Rationalise the denominator of $\frac{1}{\sqrt{7} - \sqrt{6}}$.

Accepted Answer

B) $\sqrt{7} + \sqrt{6}$

Answer

A) $\sqrt{7} - \sqrt{6}$

Answer

C) $\frac{\sqrt{7} + \sqrt{6}}{13}$

Answer

D) 1

Question 15

Calculate the value of $(81)^{3/4}$.

Accepted Answer

B) 27

Answer

A) 9

Answer

C) 81

Answer

D) 3

Question 16

Which of the following numbers can be written in the form $\frac{p}{q}$ where $p, q \in \mathbb{Z}$ and $q eq 0$?

Accepted Answer

C) 0.35

Answer

A) $\sqrt{7}$

Answer

B) $\pi$

Answer

D) $\sqrt{11}$

Question 17

Find a rational number lying exactly halfway between $\frac{1}{4}$ and $\frac{1}{2}$.

Accepted Answer

A) $\frac{3}{8}$

Answer

B) $\frac{3}{4}$

Answer

C) $\frac{1}{3}$

Answer

D) $\frac{2}{5}$

Question 18

Simplify $7^{1/2} \cdot 8^{1/2}$ using exponent power laws.

Accepted Answer

B) $56^{1/2}$

Answer

A) $56^{1/4}$

Answer

C) $15^{1/2}$

Answer

D) $56^{1}$

Question 19

Number	Type
$\sqrt{9}$	Rational
$\sqrt{2}$	Irrational
$0.1212...$	Rational
$0.101001000...$	?

What is the correct classification for $0.101001000...$ in the table?

Accepted Answer

C) Non-terminating Non-recurring Irrational Number

Answer

A) Terminating Rational Number

Answer

B) Non-terminating Recurring Rational Number

Answer

D) Integer

Question 20

Expand and simplify the product $(5 + \sqrt{7})(2 + \sqrt{5})$.

Accepted Answer

A) $10 + 5\sqrt{5} + 2\sqrt{7} + \sqrt{35}$

Answer

B) $10 + \sqrt{35}$

Answer

C) $10 + 7\sqrt{35}$

Answer

D) $7 + 5\sqrt{5} + 2\sqrt{7} + \sqrt{12}$

Grade 9 : Mathematics - 3. Number Systems (Set 2)