Pole Star Seven Days Guess Paper Class VIII Mathematics PDF

## POLE STAR SEVEN DAYS GUESS PAPER ### CLASS - VIII SUBJECT - MATHEMATICS ### MOST EXPECTED QUESTIONS FOR BOARD EXAMINATION **DAY-ONE** #### Part A 1. All questions are compulsory. 2. Part A will have Question number 1 to 3: - Question No. 1 will consist of 16 Multiple Choice Questions carryi...

## POLE STAR SEVEN DAYS GUESS PAPER ### CLASS - VIII SUBJECT - MATHEMATICS ### MOST EXPECTED QUESTIONS FOR BOARD EXAMINATION **DAY-ONE** #### Part A 1. All questions are compulsory. 2. Part A will have Question number 1 to 3: - Question No. 1 will consist of 16 Multiple Choice Questions carrying 1 mark each. - Question No. 2 will consist of 7 True/False carrying 1 mark each. - Question No. 3 will consist of 7 Fill in the Blanks carrying 1 mark each. #### Chapter 1 (Rational Numbers) **Multiple Choice Questions:** 1. Which of the following is the commutative property of addition? - *xxy = yxx* - *(x + y) = (y + x)* - *(x + y) + z = x + (y + z)* - *(x - y) = (y - x)* 2. Which of the following is the associative property of addition? - *xxy = yxx* - *(x + y) = (y + x)* - *(x + y) + z = x + (y + z)* - *(x - y) = (y - x)* 3. The additive inverse of *(-5/9)* is: - *5/9* - *-5/9* - *0* - *-3/2* 4. The additive identity of 3 is: - *0* - *-2/3* - *3/2* - *2* 5. Which of the following is not true for rational numbers x, y, and z? - *xxy = yxx* - *x x (y−z) = xxy-xxz* - *x-y = y-x* - *x x (y xz) = (x x y) x z* 6. The multiplicative identity of a rational number 'a' is: - *1* - *0* - *1/a* - *-a* 7. Which of the following numbers does not have a multiplicative inverse? - *0* - *-1* - *1* - *-2/3* 8. Which of the following numbers is its own multiplicative inverse? - *0* - *-1* - *1* - *(b) and (c) both* **True/False:** 1. All integers are rational numbers. **(True)** 2. If *a* and *b* (b ≠ 0) are rational numbers, then *a/b = (a x c)/ (b x d)*. **(True)** 3. The multiplicative inverse of 0 is *0*. **(False)** 4. Division by zero is not possible. **(True)** 5. The commutative property holds true in subtraction of rational numbers. **(False)** **Fill in the Blanks:** 1. Name the property of multiplication of rational numbers that states that the product remains the same irrespective of the order in which numbers are multiplied. **(Commutative property of multiplication)** 2. State the multiplicative property that states that the product remains the same irrespective of the order in which the numbers are multiplied. **(Associative property of multiplication)** 3. In the equation, (x + y) + z = x + (y + z), the symbol *+* is the *distributive* property. **(Distributive property of addition)** 4. The multiplicative inverse of a number is also called its *reciprocal*. **(Reciprocal)** 5. The property in multiplication for rational numbers states that if the product of any number and *1* is the number itself. **(Multiplicative Identity)** #### Chapter 2 (Linear Equations in One Variable) **Multiple Choice Questions:** 1. The power of the variable in a linear equation in one variable is always: - *1* - *2* - *3* - *4* 2. The value of *x* for which the expressions 3*x* – 4 and 2*x* + 1 are equal is: - *3* - *2* - *5* - *4* 3. Five years ago, I was *x* years old. Ten years later my age will be: - *(x + 15) years* - *(x – 15) years* - *(x + 10) years* - *(x – 10) years* 4. The ones digit of a number with tens digit *y* and ones digit *x* is : - *10*y* + *x* - *10*x* + *y* - *10*y* - *x* - *10*x* - *y* 5. The value of *x* in the equation *3/4* *x* = 7 – *x* is: - *3* - *7/3* - *7/4* - *4* **True/False:** 1. A constant term is a quantity that cannot be changed. **(True)** 2. An equation containing only one algebraic expression is called a linear equation in one variable. **(True)** 3. *3z²– 1 = 7* is a linear equation in one variable. **(False)** 4. If *x* is the solution of the equation, then the left-hand side will not be equal to the right-hand side for the value of *x*. **(False)** 5. The LCM of (4, 3, 3) is 36. **(False)** **Fill in the Blanks:** 1. The term *variable* refers to a quantity that can change. **(Variable)** 2. In an equation, the symbol *equals* (=) divides the equation into two parts. **(Equals)** 3. An equation is called a *linear equation*, whenever the symbol for equality in the equation shows a balanced relationship between the expressions on both its left and right sides. **(Linear equation)** 4. The left-hand side of the equation shows an imbalance in terms of variable/s and constant. **(Variable/s and constant)** 5. The property in subtraction of rational numbers states that if the product of any number and *1* is the number itself. **(Multiplicative Identity)** #### Chapter 3 (Understanding Quadrilaterals) **Multiple Choice Questions:** 1. If the length of one diagonal of a rectangle is 6 cm, then the length of the other diagonal is: - *3 cm* - *6 cm* - *12 cm* - *4 cm* 2. If the opposite sides of a parallelogram are equal, then the sum of the two adjacent angles is: - *90°* - *180°* - *360°* - *None of the above* 3. If two adjacent angles of a parallelogram are equal, then the parallelogram formed is a: - *Rectangle* - *Rhombus* - *Square* - *Trapezium* 4. If the opposite angles of a quadrilateral are equal, then it is a: - *Rectangle* - *Square* - *Rhombus* - *Trapezium* 5. The sum of the adjacent angles of a parallelogram is: - *90°* - *180°* - *360°* - *None of the above:* 6. If the adjacent angles of a parallelogram are equal, then which quadrilateral is formed? - *Rectangle* - *Rhombus* - *Square* - *Trapezium* 7. Which of the following quadrilaterals does not exist? - *Square* - *Rectangle* - *Triangle* - *Trapezium* 8. If *3y°* and *120°* are two adjacent angles of a rhombus, then what is the value of *y*? - *15°* - *90°* - *20°* - *60°* 9. Which of the following quadrilaterals is not a quadrilateral? - *Square* - *Rectangle* - *Triangle* - *Trapezium* 10. If ∠A and ∠C are opposite angles of a parallelogram, then: - *∠A > ∠C* - *∠A = ∠C* - *∠A < ∠C* - *None of these* 11. The sum of the exterior angles of a quadrilateral is: - *180°* - *360°* - *540°* - *None of the above* **True/False:** 1. Opposite sides of a parallelogram are equal. **(True)** 2. The sum of the two adjacent angles of a parallelogram is 360°. **(False)** 3. The diagonals of a rhombus bisect each other at 90°. **(True)** 4. Diagonals of a rectangle are equal. **(True)** 5. A rectangle with all sides equal is called rhombus. **(False)** 6. The sum of the interior angles of a triangle is 180°. **(True)** 7. All sides of a rhombus are equal in length. **(True)** 8. A rhombus is always a square **(False)** **Fill in the Blanks:** 1. In a parallelogram, opposite sides are always **parallel**. **(Parallel)** 2. The diagonals of a **parallelogram** bisect each other. **(Parallelogram)** 3. The sum of the interior angles of a quadrilateral is **360** degrees. **(360)** 4. In a **parallelogram** the opposite angles are equal. **(Parallelogram)** 5. The diagonals of a **rectangle** are equal. **(Rectangle)** 6. Opposite sides of a parallelogram are **equal** in length. **(Equal)** 7. A **square** is a type of rectangle and a rhombus. **(Square)** #### Chapter 4 (Data Handling) **Multiple Choice Questions:** 1. The upper class limit of the class interval 20-30 is: - *25* - *20* - *30* - *50* 2. The class interval 40-60 is: - *10* - *20* - *40* - *60* 3. The class mark of the class interval 100-150 is: - *100* - *120* - *150* - *125* 4. The class intervals 0–10, 10–20, 20–30 are: - *Continuous* - *Discontinuous* - *Incomplete data* - *Ungrouped data* 5. Tally mark is used to find: - *Frequency* - *Lower class limit* - *Upper class limit* - *None of these* **True/False:** 1. All whole numbers are rational numbers. **(True)** 2. In a parallelogram, sum of any two consecutive angles is 360 degrees. **(False)** 3. The diagonals of a rectangle bisect each other at right angles. **(True)** 4. In a rhombus, opposite angles are unequal. **(False)** 5. The diagonals of a square bisect each other at right angles. **(True)** 6. The sum of the interior angles of a quadrilateral is 180°. **(False)** **Fill in the Blanks:** 1. The term *constant* refers to a quantity that does not change. **(Constant)** 2. There exists a **constant** term in the equation, *3x²– 1 = 7*. **(Constant)** 3. The diagonals of a **rhombus** bisect each other at right angles. **(Rhombus)** 4. The left-hand side of the equation shows an imbalance in terms of variable/s and *constant*. **(Constant)** 5. The frequency of a data is represented by **tally mark**. **(Tally mark)** #### Chapter 5 (Squares and Square Roots) **Multiple Choice Questions:** 1. The number of zeros in the square of 600 is: - *1* - *2* - *3* - *4* 2. The square of a proper fraction is : - *Smaller than the fraction* - *Greater than the fraction* - *Equal to the fraction* - *None of these* 3. Which of the following is not a perfect square? - *625* - *728* - *729* - *144* 4. Which number should be multiplied with 32 to make it a perfect square? - *2* - *3* - *4* - *6* 5. The number of digits in the square root of 676 is: - *1* - *2* - *3* - *4* 6. The smallest number to be added to *140* to make it a perfect square is: - *4* - *2* - *8* - *12* 7. The square root of *676* is: - *12* - *26* - *76* - *38* 8. Which of the following is incorrect? - *√15625* - *√156 25* - *√156 25* - *√15 625* 9. The square root of 24.01 has digits after decimal: - *One* - *Two* - *Three* - *Four* **True/False:** 1. The ones digit of a square number can only be 0, 1, 4, 5, 6 or 9. **(True)** 2. The square of an odd number can be an odd number. **(True)** 3. The square of a negative integer is always positive. **(True)** 4. The number of zeros at the end of a perfect square is always odd. **(False)** 5. The square of a number *n* can be represented as the sum of the first *n* consecutive odd numbers. **(True)** 6. The ones digit of the square of *52698* is *4*. **(True)** **Fill in the Blanks:** 1. The square of an even number is always **even**. **(Even)** 2. The square of an odd number is always **odd**. **(Odd)** 3. *√* represents the **square root**. **(Square root)** 4. The square of a number is known as **its square**. **(Square)** #### Chapter 6 (Cubes and Cube Roots) **Multiple Choice Questions:** 1. If the unit digit of a number is 2, then its cube will have the unit digit: - *4* - *2* - *6* - *8* 2. How many cubes of a side 1 cm are required to make a cube with side 2 cm? - *2* - *4* - *6* - *8* 3. The unit digit of the cube of 626 is: - *2* - *3* - *4* - *6* 4. By which number should 108 be multiplied to make it a perfect cube? - *2* - *3* - *4* - *6* 5. Which of the following is not a perfect cube? - *16* - *27* - *64* - *125* 6. The cube of 7 – 6 is: - *127* - *397* - *1141* - *200* 7. Find the cube root of 1331: - *11* - *21* - *31* - *23* 8. If the unit digit of a perfect cube is 2, then the unit digit of its cube root will be: - *8* - *2* - *6* - *4* **True/False:** 1. When the power of a number is 3, then it is the cube of that number. **(True)** 2. *9* is a perfect cube. **(True)** 3. The symbol *√* represents the cube root. **(True)** 4. The cube of *–4* is 64. **(True)** 5. A cube is a type of prism. **(True)** **Fill in the Blanks:** 1. The unit digit of the cube of *7* is **3**. **(3)** 2. The cube root of *512* is **8**. **(8)** 3. The cube root of *125* is **5**. **(5)** 4. If the cube root of a number is 5, then the unit digit of that number will be **5**. **(5)** #### Chapter 7 (Ratio and Proportion) **Multiple Choice Questions:** 1. The ratio of 6 km to 600 m is? - *1:100* - *10:1* - *1:10* - *100:1* 2. The ratio of 200 paise to ₹ 3 is: - *2 : 3* - *3:2* - *200:3* - *3:200* 3. The percentage representation of the ratio 3:5 is: - *30%* - *50%* - *60%* - *80%* 4. The deduction is calculated on: - *Selling price* - *Marked price* - *Cost price* - *None of the above* 5. What will be the sales tax for a commodity that is marked at ₹200 and the sales tax rate is 5%? - *₹ 5* - *₹ 10* - *₹15* - *₹ 20* 6. For a period of more than 1 year, in simple interest (S.I.) and compound interest (C.I.): - *S.I. < C.I.* - *C.I. > S.I.* - *S.I. = C.I.* - *The relationship cannot be determined* 7. There are how many different tax slabs in GST? - *1* - *5* - *3* - *8* 8. GST is levied on which of the following? - *Food* - *Petroleum Products* - *Alcoholic drinks* - *Electricity* **True/False:** 1. GST stands for Goods and Service Tax. **(True)** 2. GST was implemented in India on July 1, 2019. **(True)** 3. A withdrawal slip needs to be filled to withdraw money from an account. **(True)** 4. PIN stands for *Personal Identification Number*. **(True)** 5. Marked price is also known as the list price. **(True)** **Fill in the Blanks:** 1. Simple Interest = (P × R × T)/ 100 **( P × R × T / 100 )** 2. Compound Interest (C.I.) = Amount (A) – Principal (P) ** (Amount(A) – Principal (P))** 3. A bank account opened in the names of two people is called a **joint** account. **(Joint)** 4. To deposit money into an account, we have to fill in the **deposit** slip. **(Deposit)** 5. The *transaction* details related to accounts are shown in the passbook. **(Transaction)** #### Chapter 8 (Algebraic Expressions and identities) **Multiple Choice Questions:** 1. What is the coefficient of *y* in *7*y* - 5 ? - *7* - *-5* - *5* - *12* 2. Identify the binomial expression. - *5*x* + 2* - *x + x + 1* - *6*z* - *√*t* 3. Which pair of terms are like terms? - *7*x* and 7*y* - *3*x* and 3*x²* - *x* and *3*x* - *x³* + 3 4. The given figure represents: - *x+3* - *2*x* + 3* - *2*x* -3* - *x²* + 3 5. Find the area of the rectangle if its sides are *2ab* and *3bc*. - *6abc* - *6ab²c* - *2ab* + *3bc* - *6* + *ab* + *bc* 6. Find the product of *y x y² x y³ x y*. - *y¹⁰* - *y²⁵* - *y* - *y¹⁰* 7. Find the product of *xy+4z+3x* and *0*. - *xy* + *yz* + *3x* - *xyz* - *0* - *x²y²z²* 8. For solving *(2*x* - 3) (*2*x* + 5), which identity is used? - *(a + b) (a - b) = a²-b²* - *(a + b)² = a² + 2ab + b²* - *(x + a) (x + b) = x² + (a + b) x + ab* - *(a - b)² = a² - 2ab + b²* **True/False:** 1. A polynomial having only two terms is called a monomial. **(False)** 2. Terms that are not alike are called unlike terms. **(True)** 3. The product of a monomial and a binomial results in a trinomial. **(False)** 4. An equation that is always true for all values of the variable is called an identity. **(True)** 5. *5*x* and *7xy* are terms of the polynomial *-5x* + *7xy*. **(True)** **Fill in the Blanks:** 1. The product of two monomials is always a **monomial**. **(Monomial)** 2. The product of three monomials is always a **trinomial**. **(Trinomial)** 3. Complete the identity (a+b)² - = **- (a-b)²**. **(- (a-b)²)** 4. **(a + b) (a – b) =** a² - b² **(a² - b²)** 5. (x + a) (x + b) = x² + **(a + b) x + ab**. **(a + b) x + ab** 6. **ab + ac =** a (b + c) **( a (b + c))** 7. **x²y² and x²y³** are common factors of the given terms. **(x²y² and x²y³)** #### Chapter 9 (Mensuration) **Multiple Choice Questions:** 1. Find the area of the rhombus if its diagonals are 4 cm and 6 cm: - *24 cm²* - *12 cm²* - *10 cm²* - *18 cm²* 2. The area of a square with diagonal *d* is: - *d²* - *d²/2* - *2d²* - *d²/4* 3. Find the area of the given figure: - *70 cm²* - *180 cm²* - *90 cm²* - *120 cm²* 4. The lateral surface area of the cube is: - *6/²* - *51²/2* - *4/²* - *21²* 5. The curved surface area of the cylinder is: - *2πrh* - *πrh* - *2πr* - *πr²h* 6. If the side of the cube becomes double, then its surface area will be: - *2 times* - *4 times* - *3 times* - *8 times* 7. Find the volume of the cuboid of size *4m × 2.5m × 2m*. - *20 m³* - *40 m³* - *30 m³* - *200 m³* 8. The volume of the cube with side *1.1* is: - *13.31* - *1.331* - *133.1* - *1331* 9. The area of the triangle with base *b* and height *h* is: - *bh* - *bh/2* - *bh/4* - *None* 10. The area of a rhombus with diagonals *2bh* and *8.2 cm* is: - *41 cm²* - *82 cm²* - *410 cm²* - *820 cm²* 11. A cuboid has **6** pairs of congruent faces. **(6)** **True/False:** 1. The base of a cuboid is a rectangle. **(True)** 2. The curved surface area of a cylinder is *2*π*r*. **(False)** 3. Volume refers to the space occupied by an object.. **(True)** 4. The area of rhombus = *1/2* × product of diagonals. **(True)** 5. A rectangle with all sides equal is called a rhombus. **(False)** 6. Two faces of a cube have the same area. **(True)** 7. The volume of a cylinder with radius *p* and height *q* is πp²q. **(True)** 8. The base of a right circular cylinder is a circle. **(True)** **Fill in the Blanks:** 1. *l* cm, *b* cm, *h* cm are the **dimensions** of cuboid. **(Dimensions)** 2. The number of faces of a **cuboid** are **6**. **(Cuboid)** 3. Two opposite faces of a **cuboid** are always **congruent** to each other. **(Congruent)** 4. The volume of a cuboid of dimensions **l**, **b**, **h** is **lbh**. **(lbh)** #### Chapter 10 (Exponents and Powers) **Multiple Choice Questions:** 1. Express 3⁷³⁸ in the expanded form: - *3¹⁵* - *3⁵⁶* - *3* - *3³* 2. Find the value of (5³)⁴. - *5⁷* - *5¹²* - *5⁻¹* - *5⁸* 3. If 5²¹ = 5ˣ, then find the value of *x*. - *2* - *3* - *4* - *5* 4. Find the standard form of 1040352. - *1.040352 × 10⁶* - *1.040352 × 10⁷* - *10.40352 × 10⁶* - *10.40352 × 10⁷* 5. Express 1.6 × 10⁹ in the standard form. - *16000* - *1600* - *160000* - *1.60000* 6. Find the standard form of 0.00001225. - *1.225 × 10⁻⁵* - *1.225 × 10⁵* - *122.5 × 10⁻⁷* - *1.22 × 10⁻⁵* 7. Find the standard form of *3.2805 × 10¹*. - *302805* - *32805* - *0.32805* - *0.00032805* 8. Express 3.03 × 10⁶ as a standard number. - *303000* - *30300000* - *3030000* - *300000* 9. What will be the value of *100*° + *20*° + *5*°? - *125* - *25* - *1/125* - *3* 10. What will be the value of *(-1)²⁰*? - *-1* - *1* - *0* - *20* 11. What is the standard form of *0.09 × 10⁸*? - *900000000* - *9000000* - *9000* - *9* **True/False:** 1. The ones digit of a square number is always 0, 1, 4, 5, 6 or 9. **(True)** 2. The square of an odd number always results in an odd number. **(True)** 3. The square of a negative integer always results in a positive integer. **(True)** 4. The number of zeros at the end of a perfect square is always odd. **(False)** 5. The square of a number *n* is equal to the sum of the first *n* consecutive odd numbers. **(True)** 6. The ones digit of the square of *52698* is *4*. **(True)** **Fill in the Blanks:** 1. The square of any even number is always **even**. **(Even)** 2. The square of any odd number is always **odd**. **(Odd)** 3. *√* represents the **square root**. **(Square Root)** 4. The square of a number is known as it **square**. **(Square)** 5. The square root of 144 is **12**. **(12)** 6. The square root of 121 is **11**. **(11)** 7. The multiplicative inverse of any number is also called **reciprocal**. **(Reciprocal)** #### Chapter 11 (Direct and Inverse Proportion) **Multiple Choice Questions:** 1. A machine can fill 680 bottles in 5 hours. How many bottles can it fill in 3 hours? 2. A hostel has enough food for 200 students for 10 days. If 50 more students join the hostel, how many days will the food last? 3. What will be the sales tax for a commodity that is marked at ₹200 and the sales tax rate is 5%? **True/False:** 1. Every rational number has a multiplicative inverse. **(True)** 2. If the product of two quantities is a constant, then the quantities are in inverse proportion. **(True)** 3. *x* and *y* are in inverse proportion if *x* is equal to *y*. **(False)** 4. If the power of a number is zero, then its value will be always *0*. **(False)** 5. The multiplicative inverse of a negative number is always a positive number. **(False)** 6. The cube of a number has the same number of zeros as the original number. **(False)** <b>Fill in the Blanks:</b> 1. Two quantities are said to be in **direct proportion** if they increase or decrease together at a constant rate. **(Direct Proportion)** 2. The **multiplicative inverse** of a number is also called its reciprocal. **(Multiplicative Inverse)** 3. A **constant** term is a quantity that cannot be changed. **(Constant)** #### Chapter 12 (Algebraic Expressions and identities) **Multiple Choice Questions:** 1. *x + 2* is the factor of the equation *x² - 2x - 8*. **(True)** 2. *x + 2* is a factor of *x³ + 8*. **(True)** 3. *4x³+ 16*x* is the factor of *4x² - 4x*. **(False)** 4. *x - 1* is the factor of *4x² + 16x*. **(True)** **True/False:** 1. If the unit digit of a number is 5, then its square will end with a *25*. **(True)** 2. The sum of