CBSE Class 8 Maths Sample Question Paper

Class VIII Maths Sample Paper – Set 1 Max. Marks: 80 Time Allowed: 3 hours General Instructions: • • • • • • • • This Question Paper has 4 Sections (A-D). Section A: 20 MCQs carrying 1 mark each. Section B: 6 questions carrying 2 marks each. Section C: 8 questions carrying 3 marks each. Section D: 6 questions carrying 4 marks each. All Questions are compulsory. Draw neat figures wherever required. Take π = 22/7 wherever required if not stated. Q. No. 1. Questions Marks Which of the following properties of rational numbers is shown below? 1 4 3 7  4 3 7    −  =   −  5 4 3  5 4 3 a) Closure property b) Distributive property c) Associative property d) Commutative property 2. The property represented by 1 1 a  (b + c) = a  b + a  c is: a) Commutativity b) Distributive property c) Associativity d) Closure property 3. If −4 = 5x then the numerical value of 2 x − 7 is: 3 1 a) 0 b) 2 c) -1 d) 1 4. Solve: 1 5t − 3 = 3t − 5 a) 0 b) 2 c) 1 d) -1 5. For which of the following figures are the diagonals perpendicular to 1 each other? 2 a) Heptagon b) Octagon c) Nonagon d) Kite 6. State the name of a regular polygon with 9 sides. 1 a) Hexagon b) Octagon c) Nonagon d) Decagon 7. The length and breadth of a rectangle are in the ratio4:3. If the diagonal 1 measures 25 cm, then the perimeter of the rectangle is: a) 70 cm b) 60 cm c) 80 cm d) 56 cm 8. 7396students are sitting in an auditorium in such a manner that there 1 are as many students in a row as there are rows. How many rows are there? a) 4 3 b) 6 c) 5 d) 3 9. The smallest number by which 3087 must be multiplied to make it a 1 perfect cube is: a) 4 x3 ,9 x3 ,16 x3 b) x3 ,64 x3 ,125x3 c) 8x2 , 27 x2 ,64 x2 d) 4 x2 ,9 x2 ,16 x2 10. Find the cubes of x, 4x, 5x . 1 a) Rs 12, 000 b) Rs 13, 000 c) Rs 11, 000 d) Rs 10, 000 11. Find the compound interest on Rs 25,000 for 2 years at 20% per annum, compounded annually. 1 a) (r + 7)(r + 3) b) (r − 7)(r − 3) 4 c) (r − 7)(r + 3) d) (r − 1)(r − 4) 12. Factorized form of r 2 − 10r + 21 is: 1 a) Sphere b) Cone c) Hemisphere d) Cylinder 13. The three-dimensional figure formed by rotating a circle is: 1 a) Convex polyhedron b) Cylinder c) Concave polyhedron d) Polygon 14. A room is 15 meters long, 4 meters broad, and 3 meters high. Find the 1 cost of whitewashing its four walls at 50 P per m2 . a) 144cm2 b) 912cm2 c) 864cm2 d) 288cm2 5 15. If the volume of a cube is 1728cm3 , then its surface area is: 1 a) 144cm2 b) 912cm2 c) 864cm2 d) 288cm2 16. 17. 2 The value of   5 a) 4 25 b) 5 2 c) 4 5 d) 25 4 −2 is: If 3x +8 = 27 2 x +1 , then the value of x is: 1 1 a) 4 b) 27 c) 25 d) 8 6 18. 5   2 Simplify: (−3) 2    3 1 a) (3m + 2n)2 b) (3m − 2n)2 c) (3m − 2n) d) (3m + 2n) 19. 9m2 + 12mn + 4n 2 is the same as: 1 a) (3m + 2n)2 b) (3m − 2n)2 c) (3m − 2n) d) (3m + 2n) 20. Find the sum: −5 + a) 1 7 3 5  4 + + (−3) + +  −  10 7 14  5  −256 35 b) 12 c) 1 d) 0 7 21 Using −5 + 22 suitable rearrangement, find the sum: 2 7 3 5  4 + + (−3) + +  −  10 7 14  5  Solve the equation and verify your result: 2 5 x + 9 = 5 + 3x 23 A bag has 4 red balls and 2 yellow balls. A ball is drawn randomly 2 from the bag. (i) What is the probability of drawing a red ball? (ii) Is this probability greater or smaller than drawing a yellow ball? OR A survey was conducted to find the favorite beverage preferred by a group of young people. The following pie chart represents the data. (i) Which type of beverage is liked by the maximum number of people? (ii) If 45 people like tea, how many people were surveyed? 24 The dimensions of a rectangular field are 80 m and 18 m. Find the 2 length of its diagonal. 25 For the given solid, draw the side view and front view. 2 8 26 Find the value of x , so that 2 (−2)3  (−2)−6 = (−2)2 x−1 OR Simplify and write in exponential form: (−2)−3  (−2)−4 27 Solve: 5x + 28 3 7 = x − 14 2 In the following figure of a ship, ABDH and CEFG are two 3 parallelograms. Find the value of x .OR ABCD is a parallelogram. The bisector of angle A intersects CD at X and the bisector of angle C intersects AB at Y . Is AXCY a parallelogram? Justify your answer. 9 29 2025 plants are to be planted in a garden in such a way that each row 3 contains as many plants as the number of rows. Find the number of rows and the number of plants in each row. 30 Is 1188 a perfect cube? If not, by which smallest natural number 3 should 1188 be divided so that the quotient is a perfect cube? 31 The price of a TV is ₹13,000. The sales tax charged on it is at the rate 3 of 12%. Find the total amount that Vinod will have to pay if he buys it. OR The marked price of a DVD is ₹4500. A shopkeeper allows two successive discounts of 10% and 5%. Find the selling price of the DVD after applying both discounts. 32 Add: p3 − 1, p3 + p + 2, p 2 − 2 p + 1 3 33 Rukhsar painted the outside of a cabinet with dimensions 1 m × 2 m × 3 1.5 m. How much surface area did she cover if she painted all surfaces except the bottom of the cabinet? 34. Factorize: 5 (l + m)2 − (l − m)2 10 35 A sum of money becomes ₹17,640 in 2 years and ₹18,522 in 3 years at the same rate of interest compounded annually. Find the rate of interest. 5 36. A sum of money becomes ₹17,640 in 2 years and ₹18,522 in 3 years at the same rate of interest compounded annually. 5 Find the rate of interest. 37. Find the product of:  p 2 q   ( p3q 6 )  ( p −2/3 p 4 q 2 ) 4 Find the area of the following fields (diagram provided). 4   38. 1   OR The dimensions of a cuboid are in the ratio 2:3:4, and its total surface area is 208 m². Find its length, breadth, and height. 39. 4 Factorize: 6 x 2 − 13x + 6 OR Factorize the expression and divide: 40. (5 p 2 − 25 p + 20) ( p − 1) Consider the relation between the area (A) and side (x) of a square given by A = x 2 . (a) Draw a graph to show this relation. 11 (b) From the graph, find A when x = 4 . (c) Is this graph a linear graph? 12 Answer Key Section A 1. Solution: The given property follows the Associative Property of Multiplication. Answer: (c) Associative property 2. Solution: The equation represents the Distributive Property of Multiplication over Addition. Answer: (b) Distributive property 3. Solution: Given: −4 = 5x 3 Solving for x : x=− 43 12 =− 5 5 Now, 24 35 59  12  2x − 7 = 2   −  − 7 = − − = − 5 5 5  5 Answer: (c) -1 13 4. Solution: 5t − 3 = 3t − 5 Rearranging: 5t − 3t = −5 + 3 2t = −2  t = −1 Answer: (d) -1 5. Solution: The diagonals of a Kite are perpendicular. Answer: (b) Kite 6. Solution: A polygon with 9 sides is called a Nonagon. Answer: (c) Nonagon 7. Solution: Using the Pythagoras theorem for the rectangle: l 2 + b2 = d 2 Let length = 4x ,breadth = 3x , diagonal = 25. (4 x)2 + (3x)2 = 252 16 x 2 + 9 x 2 = 625 14 25 x 2 = 625  x 2 = 25  x = 5 l = 20, b = 15, Perimeter = 2(20 + 15) = 70 Answer: (a) 70 cm 8. Solution: Let the number of rows be x , then the number of students is: x 2 = 7396 Taking square root: x = 7396 = 86 Answer: (b) 86 9. Solution: Prime factorization of 3087: 3087 = 3  3  7  7  7 To make it a perfect cube, multiply by 3 . Answer: (d) 3 15 10. Solution: (4 x)3 = 64 x3 , (5 x)3 = 125 x3 Answer: (b) x3 ,64 x3 ,125x3 n r   11. Solution: C.I. = P 1 +  −P  100  2 20   = 25000 1 +  − 25000  100  2 6 = 25000    − 25000 5 = 25000  36 − 25000 25 = 36000 − 25000 = 11000 Answer: (c) ₹ 11,000 12. Solution: r 2 − 10r + 21 = (r − 7)(r − 3) Answer: (b) (r − 7)(r − 3) 16 13. Solution: Rotating a circle forms a sphere. Answer: (a) Sphere 14. Solution: Area of four walls: 2(l + b)h = 2(15 + 4)  3 = 114 m2 Cost of painting: 114  0.50 = 57 Answer: (c) ₹ 57 15. Solution: Volume of cube: a3 = 1728  a = 3 1728 = 12 Surface area: 6a 2 = 6(122 ) = 864 Answer: (c) 864 cm 2 17 16. Solution: −2 2 25 2 5   =  = 4 5 2 Answer: (d) 25 4 17. Solution: Given: 3x +8 = 27 2 x +1 Converting base: 27 = 33  3x +8 = 36 x +3 Equating exponents: x + 8 = 6x + 3 5x = 5  x = 1 Answer: (a) 1 18. Solution: 2 25 5 (−3)    = 9  = 25 9 3 2 Answer: (c) 25 18 19. Solution: Expanding: 9m2 + 12mn + 4n2 = (3m + 2n)2 Answer: (a) (3m + 2n)2 20. Solution: −5 + 7 3 5  4 + + (−3) + +  −  10 7 14  5  Taking LCM and simplifying: 6 10 8 −8 + + − 7 14 10 Final Answer: −256 . 35 Section B (Short Answer Questions) 21. Solution: −5 + 7 3 5  4 + + (−3) + +  −  10 7 14  5  Taking LCM and simplifying: 19 6 10 8 −8 + + − 7 14 10 Final Answer: −256 . 35 22. Solution: 5 x + 9 = 5 + 3x Rearranging: 5 x − 3x = 5 − 9 2 x = −4  x = −2 Answer: x = −2 23. Solution: Probability of drawing a red ball: P( R) = 4 2 = 6 3 Probability of drawing a yellow ball: P(Y ) = Since 2 1 = 6 3 2 1  , drawing a red ball is more likely. 3 3 20 24. Solution: Using Pythagoras theorem: d = 802 + 182 = 6400 + 324 = 6724 = 82 m Answer: 82 m 25. Solution: Draw the side and front view of the given solid figure. 26. Solution: Given: (−2)3  (−2)−6 = (−2)2 x−1 Using exponent rules: (−2)3−6 = (−2)2 x−1 (−2)−3 = (−2)2 x−1 Comparing powers: −3 = 2 x − 1 2 x = −2  x = −1 21 Answer: x = −1 OR (−2)−3  (−2)−4 Using exponent rules: (−2)−3−4 = (−2)−7 Answer: (−2)−7 27. Solution Solve the equation 5x + 7 = x − 14 2 Multiply by 2 to eliminate fractions: 10 x + 7 = 2 x − 28 Rearranging: 10 x − 2 x = −28 − 7 8 x = −35  x = − Answer x = − 35 8 35 8 22 28. Solution In parallelogram ABDH , opposite angles are equal: ABD = AHD = 130 Using the linear pair property: GHD = 180 − 130 = 50 Similarly, in parallelogram CEFG : EFG = 30 , FGC = 180 − 30 = 150 Using angle sum property in HGO : 50 + 30 + x = 180 x = 100 Answer x = 100 29. Solution Let the number of rows be x , then the number of plants per row is also x . x 2 = 2025 Taking square root: x = 2025 = 45 Answer 45 rows, 45 plants per row. 23 30. Solution: Prime factorization of 1188 : 1188 = 22  33 11 The factor 2 and 11 are not in groups of three, so divide by 4 11 = 44 . 1188 = 27 = 33 44 Answer Divide by 44 to make it a perfect cube. 31. Solution For TV with 12% Sales Tax: Sales tax = 13000  12 = 1560 100 Total cost = 13000 + 1560 = 14560 Answer ₹ 14,560 OR For DVD with two discounts: First discount = 4500  10 = 450 100 Price after first discount = 4500 − 450 = 4050 Second discount = 4050  5 = 202.50 100 24 Final price = 4050 − 202.50 = 3847.50 Answer ₹ 3,847.50 32. Solution Add the given expressions: ( p3 − 1) + ( p3 + p + 2) + ( p 2 − 2 p + 1) = p3 + p3 + p + 2 + p 2 − 2 p + 1 − 1 = 2 p3 + p 2 − p + 2 Answer 2 p3 + p 2 − p + 2 33. Solution Find the painted surface area for the cabinet (excluding the bottom): Total Surface Area = 2(lb + bh + hl ) − lb Given l = 2m , b = 1m , h = 1.5m : Area = 2(2 1 + 11.5 + 1.5  2) − (2 1) = 2(2 + 1.5 + 3) − 2 = 2(6.5) − 2 = 13 − 2 = 11m2 Answer 11 m2 25 34. Solution Factorize: (l + m)2 − (l − m)2 Using the identity a2 − b2 = (a − b)(a + b) : = [(l + m) − (l − m)]  [(l + m) + (l − m)] = [l + m − l + m]  [l + m + l − m] = (2m)  (2l ) = 4lm Answer 4lm 36. Solution: Given: Amount after 2 years A1 = 17,640, Amount after 3 years A2 = 18,522 Using compound interest formula: A = P(1 + r t ) 100 Dividing both equations: 18,522 r 3 r 2 = (1 + )  (1 + ) 17, 640 100 100 18,522 r = 1+ 17, 640 100 26 Solving for r , 1+ r 18522 21 = = 100 17640 20 r 1 =  r = 5% 100 20 Answer: 5% 37. Solution: Multiply the algebraic expressions: ( p1/2 q)  ( p3q6 )  ( p −2/3 p 4 q 2 ) Using exponent laws: p1/2+3−2/3+4  q1+6+2 p 1 9 2 + − +4 2 3 3 1 7 + +4 3 p2  q9  q9 Converting to a common denominator: p 1 7 12 + + 2 3 3 1 19 + 3 p2  q9  q9 25 6 Answer: p q 9 27 38. Solution: Given: The dimensions of a cuboid are in the ratio 2:3:4 and the total surface area is 208m 2 . Let the dimensions be 2x, 3x, 4x . The total surface area formula: 2(lb + bh + hl ) = 208 Substituting: 2(2 x  3x + 3x  4 x + 4 x  2 x) = 208 2(6 x2 + 12 x2 + 8x2 ) = 208 2(26 x 2 ) = 208 52 x 2 = 208 x2 = 4  x = 2 Dimensions: 2 x = 4m, 3x = 6m, 4 x = 8m Answer: 4m, 6m, 8m --- 39. Solution: Factorize: 6 x 2 − 13x + 6 Find two numbers whose sum is −13 and product is 6  6 = 36 : −9, −4 28 Split the middle term: 6 x2 − 9 x − 4 x + 6 Factorize: 3x(2 x − 3) − 2(2 x − 3) (2 x − 3)(3x − 2) Answer: (2 x − 3)(3x − 2) OR Divide: (5 p 2 − 25 p + 20) ( p − 1) Factorize numerator: 5( p 2 − 5 p + 4) 5( p − 1)( p − 4) Answer: 5( p − 4) 40. Solution: The relation between the area and side of a square is: 29 A = x2 Graph Values: Side (x) Area (A) 0 0 1 1 2 4 3 9 4 16 5 25 (a) Draw the graph by plotting the points ( x, A) . (b) From the graph, at x = 4 , A = 16 . (c) The graph is not linear since it follows a quadratic equation A = x 2 . 30