CLASS 8 – GRID OF ARITHMETIC

Total Marks: 14 | Questions per Set: 3 | Model Sets: 14

Grid Distribution

\([1+1]K \quad [1+1+2]U \quad [2+1+2]A \quad [1+2]HA\)

Decimal, Binary and Quinary Number System
Conversion from one number system to another
Scientific Notation
Addition, Subtraction, Multiplication and Division of Numbers
Rational and Irrational Numbers
Conversion of recurring decimal into fraction
Difference between rational and irrational numbers
Representation of \(\sqrt{2},\sqrt{3},\sqrt{5},\sqrt{7}\) on number line

SET 1 MODEL QUESTION – 1

1. Ram has a mobile number 9841526732.

(a) Write the number in scientific notation. [1K]

(b) Convert \(243\) into binary number system. [1A]

(d) Convert \(0.\overline{36}\) into fraction. [2U]

2. Teacher wrote these numbers:

\[ \sqrt5,\ \frac79,\ (1010)_2,\ \sqrt{16} \]

(a) Which is an irrational number? [1K]

(b) Why is the chosen number irrational? [1HA]

(d) Represent \( \sqrt5 \) on number line. [2A]

3. Three players scored:

\[ \text{Hari}=(11101)_2 \] \[ \text{Sita}=(234)_5 \] \[ \text{Gita}=48 \]

(a) Find total score of Hari and Sita. [2A]

(b) Compare the scores and identify the winner with reason. [2HA]

SET 2 MODEL QUESTION – 2

1. A bus number is 56789.

(a) Express the number in scientific notation. [1K]

(b) Convert \(156\) into quinary number system. [1A]

(c) A milk bottle contains \(1.25\) L milk. Find milk in \(8\) bottles and express the answer in scientific notation. [1A]

(d) Convert \(0.\overline{81}\) into fraction. [2U]

2. Observe the numbers:

\[ \sqrt7,\ 0.75,\ (1101)_2,\ \sqrt{49} \]

(a) Identify irrational number. [1K]

(b) Explain why it is irrational. [1HA]

(d) Show \( \sqrt7 \) on number line. [2A]

3. Scores obtained are:

\[ \text{Anil}=(10111)_2 \] \[ \text{Bimal}=(321)_5 \] \[ \text{Roshan}=39 \]

(a) Add scores of Anil and Bimal. [2A]

(b) Arrange all scores in ascending order and justify. [2HA]

SET 3 MODEL QUESTION – 3

1. A car number is 72814.

(a) Write the number in scientific notation. [1K]

(b) Convert \(97\) into binary number system. [1A]

(c) One notebook costs Rs. \(12.5\). Find the cost of \(12\) notebooks and express the answer in scientific notation. [1A]

(d) Convert \(0.\overline{45}\) into fraction. [2U]

2. Given numbers are:

\[ \sqrt2,\ \frac38,\ (111)_2,\ \sqrt{64} \]

(a) Which is irrational? [1K]

(b) Why cannot irrational numbers be expressed as fraction? [1HA]

(d) Represent \( \sqrt2 \) on number line. [2A]

SET 4 MODEL QUESTION – 4

1. A post office has a pin code number 123456.

(a) Write the pin code in scientific notation.[1K]

(b) Convert \(175\) into binary number system.[1A]

(c) A bag of rice weighs \(0.75\) kg. Find the total weight of \(15\) bags and express the answer in scientific notation.[1A]

(d) Convert \(0.\overline{27}\) into fraction.[2U]

2. Observe the following numbers:

\[\sqrt{3},\quad \dfrac{5}{6},\quad (1001)_2,\quad \sqrt{25}\]

(a) Which is an irrational number?[1K]

(b) Explain why the chosen number is irrational.[1HA]

(d) Represent \(\sqrt{3}\) on the number line.[2A]

3. Three students scored the following marks in a game:

\[\text{Ram} = (11011)_2 \qquad \text{Shyam} = (412)_5 \qquad \text{Prem} = 55\]

(a) Find the total score of Ram and Shyam.[2A]

(b) Compare all scores and identify the winner with reason.[2HA]

SET 5 MODEL QUESTION – 5

1. A school has a registration number 45231.

(a) Express the number in scientific notation.[1K]

(b) Convert \(84\) into quinary number system.[1A]

(d) Convert \(0.\overline{63}\) into fraction.[2U]

2. Teacher listed the following numbers:

\[\sqrt{6},\quad 0.75,\quad (1100)_2,\quad \sqrt{36}\]

(a) Identify the irrational number.[1K]

(b) Why cannot \(\sqrt{6}\) be expressed as a fraction?[1HA]

(d) Represent \(\sqrt{6}\) on the number line (using \(\sqrt{5}\) and Pythagoras theorem).[2A]

3. Three players scored:

\[\text{Anil} = (10110)_2 \qquad \text{Bimal} = (243)_5 \qquad \text{Roshan} = 42\]

(a) Find the total score of Anil and Bimal.[2A]

(b) Arrange all scores in ascending order and justify.[2HA]

SET 6 MODEL QUESTION – 6

1. A library has a book catalogue number 987654.

(a) Write the catalogue number in scientific notation.[1K]

(b) Convert \(213\) into binary number system.[1A]

(d) Convert \(0.\overline{54}\) into fraction.[2U]

2. Study the numbers below:

\[\sqrt{11},\quad \dfrac{4}{7},\quad (10011)_2,\quad \sqrt{121}\]

(a) Which number is irrational?[1K]

(b) Explain why the chosen number is irrational.[1HA]

(d) Represent \(\sqrt{5}\) on the number line.[2A]

3. Players obtained these scores:

\[\text{Mohan} = (111001)_2 \qquad \text{Sohan} = (124)_5 \qquad \text{Rohan} = 62\]

(a) Find the sum of scores of Mohan and Sohan.[2A]

(b) Arrange all three scores in descending order and justify.[2HA]

SET 7 MODEL QUESTION – 7

1. A hospital has a patient ID number 320056.

(a) Write the patient ID in scientific notation.[1K]

(b) Convert \(136\) into quinary number system.[1A]

(d) Convert \(0.\overline{72}\) into fraction.[2U]

2. The following numbers are given:

\[\sqrt{13},\quad 1.25,\quad (10101)_2,\quad \sqrt{169}\]

(a) Identify the irrational number from above.[1K]

(b) Explain with reason why it is called irrational.[1HA]

(d) Represent \(\sqrt{7}\) on the number line.[2A]

3. Competition scores of three athletes:

\[\text{Kiran} = (101110)_2 \qquad \text{Milan} = (231)_5 \qquad \text{Siran} = 47\]

(a) Add the scores of Kiran and Milan.[2A]

(b) Compare all three scores and find the winner with justification.[2HA]

SET 8 MODEL QUESTION – 8

1. A vehicle has a chassis number 654321.

(a) Express the chassis number in scientific notation.[1K]

(b) Convert \(119\) into binary number system.[1A]

(d) Convert \(0.\overline{18}\) into fraction.[2U]

2. A student wrote:

\[\sqrt{8},\quad \dfrac{11}{4},\quad (11000)_2,\quad \sqrt{4}\]

(a) Pick the irrational number.[1K]

(b) Justify why the selected number is irrational.[1HA]

(d) Represent \(\sqrt{2}\) on the number line.[2A]

3. Marks of three players in a quiz:

\[\text{Laxmi} = (110101)_2 \qquad \text{Puja} = (344)_5 \qquad \text{Mina} = 68\]

(a) Find the sum of marks of Laxmi and Puja.[2A]

(b) Rank all three from highest to lowest score with full justification.[2HA]

SET 9 MODEL QUESTION – 9

1. A satellite has a code number 804512.

(a) Write the code in scientific notation.[1K]

(b) Convert \(200\) into quinary number system.[1A]

(d) Convert \(0.\overline{09}\) into fraction.[2U]

2. Observe the following set of numbers:

\[\sqrt{10},\quad 0.8\overline{3},\quad (10000)_2,\quad \sqrt{100}\]

(a) Which is an irrational number?[1K]

(b) Why is \(\sqrt{10}\) called an irrational number?[1HA]

(d) Represent \(\sqrt{3}\) on the number line.[2A]

3. Three friends scored in a maths olympiad:

\[\text{Dina} = (100111)_2 \qquad \text{Bina} = (432)_5 \qquad \text{Rina} = 76\]

(a) Find the total score of Dina and Bina.[2A]

(b) Compare all three scores and determine the winner with reason.[2HA]

SET 10 MODEL QUESTION – 10

1. A factory produces items with serial number 500000.

(a) Express the serial number in scientific notation.[1K]

(b) Convert \(163\) into binary number system.[1A]

(d) Convert \(0.\overline{15}\) into fraction.[2U]

2. Following numbers are given:

\[\sqrt{15},\quad \dfrac{7}{12},\quad (10100)_2,\quad \sqrt{144}\]

(a) Identify the irrational number.[1K]

(b) Why cannot \(\sqrt{15}\) be written as \(\dfrac{p}{q}\)?[1HA]

(d) Represent \(\sqrt{5}\) on the number line.[2A]

3. Scores of players in a chess tournament:

\[\text{Pratap} = (111010)_2 \qquad \text{Pratima} = (312)_5 \qquad \text{Pratik} = 58\]

(a) Add the scores of Pratap and Pratima.[2A]

(b) Arrange all scores in ascending order with full justification.[2HA]

SET 11 MODEL QUESTION – 11

1. The population of a village is 78450.

(a) Write the population in scientific notation.[1K]

(b) Convert \(241\) into binary number system.[1A]

(c) A jar contains \(0.55\) kg of honey. Find the total weight of honey in \(60\) jars and express in scientific notation.[1A]

(d) Convert \(0.\overline{48}\) into fraction.[2U]

2. A teacher wrote the following numbers:

\[\sqrt{17},\quad 2.5,\quad (11111)_2,\quad \sqrt{81}\]

(a) Which number is irrational?[1K]

(b) Give reason why the chosen number is irrational.[1HA]

(d) Represent \(\sqrt{2}\) on the number line.[2A]

3. Marks obtained in a science quiz:

\[\text{Suraj} = (101011)_2 \qquad \text{Bikash} = (421)_5 \qquad \text{Naresh} = 73\]

(a) Find the total marks of Suraj and Bikash.[2A]

(b) Compare the three scores and find the highest scorer with justification.[2HA]

SET 12 MODEL QUESTION – 12

1. A mountain has an elevation of 8849 m.

(a) Write 8849 in scientific notation.[1K]

(b) Convert \(189\) into quinary number system.[1A]

(d) Convert \(0.\overline{90}\) into fraction.[2U]

2. Consider the numbers:

\[\sqrt{19},\quad \dfrac{3}{11},\quad (10001)_2,\quad \sqrt{361}\]

(a) Identify the irrational number.[1K]

(b) How do you know that \(\sqrt{19}\) is irrational? Justify your answer.[1HA]

(d) Represent \(\sqrt{7}\) on the number line.[2A]

3. Three students participated in a drawing competition and scored:

\[\text{Tulsi} = (110010)_2 \qquad \text{Ganga} = (134)_5 \qquad \text{Yamuna} = 53\]

(a) Find the sum of scores of Tulsi and Ganga.[2A]

(b) Arrange all three scores in ascending order and justify.[2HA]

SET 13 MODEL QUESTION – 13

1. An aeroplane ticket number is 250340.

(a) Write the ticket number in scientific notation.[1K]

(b) Convert \(102\) into binary number system.[1A]

(d) Convert \(0.\overline{57}\) into fraction.[2U]

2. A student listed these numbers:

\[\sqrt{23},\quad 0.625,\quad (111100)_2,\quad \sqrt{529}\]

(a) Which is an irrational number?[1K]

(b) Justify why the number you chose cannot be expressed as \(\dfrac{p}{q}\).[1HA]

(d) Represent \(\sqrt{5}\) on the number line.[2A]

3. Points scored in a table tennis match:

\[\text{Dipak} = (100101)_2 \qquad \text{Bipak} = (302)_5 \qquad \text{Nipak} = 44\]

(a) Calculate the total points of Dipak and Bipak.[2A]

(b) Compare all three scores and declare the winner with justification.[2HA]

SET 14 MODEL QUESTION – 14 (BONUS)

1. A city has a telephone area code 014500.

(a) Write the area code in scientific notation.[1K]

(b) Convert \(228\) into quinary number system.[1A]

(c) A pipe releases \(5.5\) litres of water per minute. Find the total water released in \(24\) minutes and express in scientific notation.[1A]

(d) Convert \(0.\overline{42}\) into fraction.[2U]

2. A teacher gave the following numbers:

\[\sqrt{21},\quad \dfrac{9}{13},\quad (101010)_2,\quad \sqrt{441}\]

(a) Which number is irrational?[1K]

(b) Prove with reason why the chosen number is irrational.[1HA]

(d) Represent \(\sqrt{3}\) on the number line.[2A]

3. Final scores in an inter-school competition:

\[\text{Suman} = (111011)_2 \qquad \text{Raman} = (423)_5 \qquad \text{Naman} = 83\]

(a) Find the total score of Suman and Raman.[2A]

(b) Arrange all three scores in descending order and justify each step.[2HA]

New Millennium Academy | Birauta, Pokhara-17, Nepal

Class 8 – Grid of Arithmetic · Model Question Sets 1 – 14 (14 Sets) · Total Marks per Set: 14

Worksheet - Arithmetic (First Term)

CLASS 8 – GRID OF ARITHMETIC

Grid Distribution

1. Ram has a mobile number 9841526732.

2. Teacher wrote these numbers:

3. Three players scored:

1. A bus number is 56789.

2. Observe the numbers:

3. Scores obtained are:

1. A car number is 72814.

2. Given numbers are:

1. A post office has a pin code number 123456.

2. Observe the following numbers:

3. Three students scored the following marks in a game:

1. A school has a registration number 45231.

2. Teacher listed the following numbers:

3. Three players scored:

1. A library has a book catalogue number 987654.

2. Study the numbers below:

3. Players obtained these scores:

1. A hospital has a patient ID number 320056.

2. The following numbers are given:

3. Competition scores of three athletes:

1. A vehicle has a chassis number 654321.

2. A student wrote:

3. Marks of three players in a quiz:

1. A satellite has a code number 804512.

2. Observe the following set of numbers:

3. Three friends scored in a maths olympiad:

1. A factory produces items with serial number 500000.

2. Following numbers are given:

3. Scores of players in a chess tournament:

1. The population of a village is 78450.

2. A teacher wrote the following numbers:

3. Marks obtained in a science quiz:

1. A mountain has an elevation of 8849 m.

2. Consider the numbers:

3. Three students participated in a drawing competition and scored:

1. An aeroplane ticket number is 250340.

2. A student listed these numbers:

3. Points scored in a table tennis match:

1. A city has a telephone area code 014500.

2. A teacher gave the following numbers:

3. Final scores in an inter-school competition: