Class 8 math chapter 3 MCQ and One word question
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MCQ question
1. Which of the following is a three-dimensional object?
a) Cube
b) Rectangular Prism
c) Rectangular Cube
d) Sphere
2. Which of the following has a two-dimensional measurement?
a) Rhombus
b) Triangle
c) Parallelogram
d) Cube
3. In which dimensional object is height added as the third dimension?
a) One-dimensional
b) Three-dimensional
c) Two-dimensional
d) Both b and c
6. How many dimensions does a classroom window have?
a) One
b) Two
c) Three
d) Zero
Answer: b) Two
7. How many dimensions does a classroom have?
a) 4
b) 3
c) 2
d) 1
Answer: c) 2
8. The length of the classroom is 2 feet more than its width. If the width is x feet, what is the length?
a) 2x feet
b) (2 – x) feet
c) (x + 2) feet
d) (x – 2) feet
Answer: c) (x + 2) feet
9. Which of the following is a binomial expression?
a) \[ \frac{8}{3} \]
b) 4 × 3
c) 2x + 3
d) 3 + 2
Answer: c) 2x + 3
10. Which of the following is a binomial algebraic expression?
a) xy
b) 3x + 2
c) x
d) 2x × 3y
Answer: b) 3x + 2
11. The length of a rectangle is x and its width is y. If the length is three times the width, what is the length?
a) x = y + 3
b) x = 3y
c) x + y = 3
d) None of these
Answer: b) x = 3y
Solve the prblems 12 and 13 using the following figure
12. The length of land B is equal to the measurement of land A.
What is the length of land B?
a) \[ 2(x + y) \]
b) \[ 3(x + y) \]
c) \[ x + y \]
d) \[ x^2 + y^2 \]
Answer: c) \[ x + y \]
13. What is the sum of the length and width of land A called?
a) Monomial Expression
b) Binomial Expression
c) Trinomial Expression
d) Both a and b
Answer: b) Binomial Expression
Annual exam preparation questions: Part 1
14. Which dimension, when added to a rectangle, makes it a solid object?
a) Length
b) Width
c) Height
d) Perimeter
Answer: c) Height
15. A cube is an object of how many dimensions?
a) One
b) Three
c) Two
d) None of these
Answer: b) Three
16. Which of the following is the formula for the volume of a cube?
a) \[ V = l^3 \]
b) \[ V = 3l \]
c) \[ V = l^2 \]
d) \[ V = 3l^3 \]
Answer: a) \[ V = l^3 \]
17. Which of the following is the formula for the volume of a rectangular cuboid?
a) \[ V = \frac{l^3 w^3 h^3}{3} \]
b) \[ V = lwh \]
c) \[ V = (l + w + h)^3 \]
d) \[ V = 3(lwh)^3 \]
Answer: b) \[ V = lwh \]
18. If the length, width, and height of a rectangular cuboid are 2, 3, and 5 respectively, what is its volume?
a) 30 cubic units
b) 520 cubic units
c) 1000 cubic units
d) 3000 cubic units
Answer: a) 30 cubic units
19. How many dimensions does a square showcase have?
a) 2
b) 1
c) Zero
d) 3
Answer: a) 2
20. If there is a shelf placed in the middle along the length, width, and height of a showcase, how many compartments will be created?
a) 4
b) 8
c) 6
d) 2
Answer: b) 8
21. If one side of the shelf in the showcase is a and the other side is b, how many compartments of size \[ a \times a \times b \] will be created?
a) 6
b) 4
c) 3
d) 2
Answer: c) 3
22. What is the pattern for the expansion of a binomial raised to the cube (binomial expansion)?
a) \[ 1, 3, 3, 1 \]
b) \[ 1, 1, 3, 3 \]
c) \[ 3, 1, 3, 1 \]
d) \[ 3, 1, 1, 3 \]
Answer: a) \[ 1, 3, 3, 1 \]
23. What is the formula for \[ (a + b)^3 \]?
a) \[ (a + b)^3 = a^3 + b^3 + 3a^2b + 3ab^2 \]
b) \[ (a + b)^3 = a^3 – b^3 + 3ab(a + b) \]
c) \[ (a + b)^3 = (a + b)(a^2 + 2ab + b^2) \]
d) All of the above
Answer: a) \[ (a + b)^3 = a^3 + b^3 + 3a^2b + 3ab^2 \]
24. If \[ (a + b)^3 = (a + b) \times x \], what is the value of x?
a) \[ a^2 + 2ab + b^2 \]
b) \[ a^2 + ab + b^2 \]
c) \[ a^2 – ab + b^2 \]
d) None of these
Answer: a) \[ a^2 + 2ab + b^2 \]
25. Which of the following is the formula for \[ a^3 – 3a^2b + 3ab^2 – b^3 \]?
a) \[ (a + b)^3 \]
b) \[ (a – b)^3 \]
c) \[ a^3 – b^3 \]
d) \[ a^3 + b^3 \]
Answer: b) \[ (a – b)^3 \]
26. If \[ a^3 – b^3 = (a – b)^3 + 3ab \cdot x \], what is the value of x?
a) \[ a – b \]
b) \[ a + b \]
c) \[ a^2 + ab + b^2 \]
d) \[ a^2b^2 \]
Answer: c) \[ a^2 + ab + b^2 \]
27. If \[ a^3 + b^3 = (a + b)^3 – 3ab \cdot P \], what is the value of P?
a) \[ a – b \]
b) \[ a + b \]
c) \[ (a – b)^2 \]
d) \[ (a + b)^2 \]
Answer: d) \[ (a + b)^2 \]
28. Which of the following is correct?
a) \[ a^3 + b^3 = (a + b)^3 + 3ab(a + b) \]
b) \[ (a + b)^3 = (a + b)^3 – 3ab(a + b) \]
c) \[ a^3 + b^3 = (a + b)(a^2 – ab + b^2) \]
d) \[ a^3 – b^3 = (a – b)(a^2 – ab + b^2) \]
Answer: d) \[ a^3 – b^3 = (a – b)(a^2 – ab + b^2) \]
29. What is the value of \[ (2x + y)^3 \]?
a) \[ 2x^3 + 6x^2y + 6xy^2 + 2y^3 \]
b) \[ 8x^3 + 12x^2y + 6xy^2 + y^3 \]
c) \[ 2x^3 + 12x^2y + 3xy^2 + 2y^2 \]
d) \[ x^3 + 12x^2y + 3xy^2 + y^3 \]
Answer: b) \[ 8x^3 + 12x^2y + 6xy^2 + y^3 \]
30. What is the value of \[ (x – 1)^3 \]?
a) \[ x^3 – 3x^2 + 3x – 1 \]
b) \[ x^3 – 1 – 3(x + 1)x \]
c) \[ x^3 – 3x^2 + 3x + 1 \]
d) Both a and b
Answer: a) \[ x^3 – 3x^2 + 3x – 1 \]
Answer questions 31 and 32 based on the figure below.
The length of the cuboids M, N, and Q are x, y, and z respectively
31. What is the length of the P cuboid?
a) \[ x + y + z \]
b) \[ x – y + z \]
c) \[ x + y \]
d) \[ x – y \]
Answer: a) \[ x + y + z \]
32. What type of quantity is the length of a cuboid?
a) Binomial
b) Trinomial
c) Polynomial
d) Quadratic
Answer: b) Trinomial
33. In the equation \[ a^3 + b^3 + c^3 = (a + b + c)^3 – 3(a + b + c)(ab + bc + ca) + 3 \cdot x \], what is the value of x?
a) \[ 6abc \]
b) \[ -6abc \]
c) \[ 3abc \]
d) \[ -3abc \]
Answer: b) \[ -6abc \]
34. What is the factor of \[ x^2 – 1 \]?
a) \[ x + 1 \]
b) \[ x^2 + 1 \]
c) \[ x – 1 \]
d) Both a and c
Answer: d) Both a and c
35. What is a factor of \[ a^3 – b^3 \]?
a) \[ a^2 – ab + b^2 \]
b) \[ a^2 – ab – b^2 \]
c) \[ a^2 + ab + b^2 \]
d) \[ a^2 + ab – b^2 \]
Answer: a) \[ a^2 – ab + b^2 \]
36. How many factors does every quadratic quantity have at least?
a) 2
b) 4
c) 3
d) 5
Answer: a) 2
37. What is a factor of \[ 12 \times 10 \]?
a) \[ 2 \times 6 \]
b) \[ 4 \times 8 \]
c) \[ 3 \times 4 \]
d) Both a and b
Answer: d) Both a and b
38. If a cake with dimensions \[ 8 \times 10 \] is cut along its length and width at intervals of 2 units, how many pieces of cake will there be?
a) 10
b) 15
c) 20
d) 30
Answer: d) 30
39. How many \[ 4” \times 2” \] pieces are needed to cover a \[ 12” \times 10” \] mesh?
a) 3
b) 5
c) 8
d) 15
Answer: d) 15
40. Which of the following is a factor of \[ 1′ \times 1′ \times 6” \]?
a) \[ 6” \times 6” \times 5” \]
b) \[ 4” \times 4” \times 4” \]
c) \[ 3′ \times 3′ \times 3′ \]
d) \[ 3” \times 5” \times 4” \]
Answer: d) \[ 3” \times 5” \times 4” \]
41. How many \[ 1′ \times 1′ \times 6” \] egg boxes can fit in a \[ 3′ \times 3′ \times 3′ \] egg crate?
a) 7
b) 18
c) 27
d) 54
Answer: c) 27
42. What is the fundamental factor of \[ (x + y)^3 \]?
a) \[ x + y \]
b) \[ x – y \]
c) \[ x^3 + y^3 \]
d) \[ x^2 + y^2 \]
Answer: a) \[ x + y \]
43. What is the factorization of \[ x^3 + y^3 \]?
a) \[ (x – y)(x^2 + xy + y^2) \]
b) \[ (x + y)(x^2 + xy + y^2) \]
c) \[ (x + y)(x^2 – xy + y^2) \]
d) \[ (x – y)(x^2 – xy + y^2) \]
Answer: b) \[ (x + y)(x^2 + xy + y^2) \]
44. What is the LCM of \[ x^3 y, xy^3, x^3 y^3 \]?
a) \[ x^3 y^3 \]
b) \[ x^3 y \]
c) \[ xy^3 \]
d) \[ x^3 y^3 \]
Answer: a) \[ x^3 y^3 \]
45. What is the GCD of \[ x^3 y, x^2, xy^3 \]?
a) \[ x^3 y^3 \]
b) \[ xy^3 \]
c) \[ x \]
d) \[ y^3 \]
Answer: c) \[ x \]
46. What is the GCD of \[ 70^3 \] and \[ 80^3 \]?
a) 56
b) 1
c) \[ 10^3 \]
d) \[ 70^3 \]
Answer: b) 1
47. What is the GCD of \[ x \] and \[ y \] when the expression is \[ r \times x^4 \times y^4 \]?
a) \[ x y^4 \]
b) \[ x y \]
c) \[ r^4 \]
d) \[ r^2 \]
Answer: c) \[ r^4 \]
Question 1: What dimension is a rectangle?
Answer: Three-dimensional
Question 2: How many dimensions does a rectangle have?
Answer: Two
Question 3: Which geometric shape is a special case of a rectangle?
Answer: Square
Question 4: What additional dimension is added to a three-dimensional object?
Answer: Height
Question 5: What do you call a three-dimensional object that includes length, width, and height?
Answer: Solid (Cuboid)
Question 6: If the length is x and the width is y, and the length is 2 feet more than the width, what is the length?
Answer: \[ x = y + 2 \]
Question 7: If a binomial has two terms, what is it called?
Answer: Binomial
Question 8: What is it called when a quantity has two terms?
Answer: Binomial expression
Question 9: What is the dimension of a cube and a rectangular solid?
Answer: Three-dimensional
Question 10: If the length of a cube is l, what is its volume?
Answer: \[ l^3 \]
Question 11: What is the volume of a rectangular cuboid when the length, width, and height are l, w, and h respectively?
Answer: \[ lwh \]
Question 12: What is the volume of a unit length cube?
Answer: One cubic unit
Question 13: What is the dimension of a square showcase?
Answer: 31
Question 14: What is the volume of a square showcase with a side length of 2 units?
Answer: 8 cubic units
Question 15: What will be the volume of a square showcase if the length, width, and height are 3 units and 4 units respectively, and there is a cut along both sides?
Answer: 343 cubic units
Question 16: Why is a pattern needed?
Answer: A pattern is needed to create designs.
Question 17: What is the cube of the sum of a and b?
Answer: \[ (a + b)^3 \]
Question 18: What is \[ (a + b)^3 = ? \]
Answer: \[ (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 \]
Question 19: How many terms are generated when a binomial is cubed?
Answer: 4 terms
Question 20: According to the formula for the cube of a binomial difference, what is the value of (6−1)³?
Answer: 125
Question 21: What is the cube of the difference of x and y?
Answer: \[ (x – y)^3 \]
Question 22: What is \[ (a – b)^3 = ? \]
Answer: \[ (a – b)^3 = a^3 – 3a^2b + 3ab^2 – b^3 \]
Question 23: What is \[ a^3 + b^3 + 3ab(a + b) = ? \]
Answer: \[ (a + b)^3 \]
Question 24: What is \[ (a + b)(a^2 – ab + b^2) = ? \]
Answer: \[ a^3 + b^3 \]
Question 25: What is \[ a^3 – b^3 – 3ab(a – b) = ? \]
Answer: \[ (a – b)^3 \]
Question 26: What is \[ (a – b)(a^2 + ab + b^2) = ? \]
Answer: \[ a^3 – b^3 \]
Question 27: What is a quantity with three terms called?
Answer: Trinomial expression
Question 28: What type of trinomial expression is \[ x + y + z \]?
Answer: A trinomial with three variables
Question 29: If the dimensions of a cuboid are length x, width y, and height z, what is \[ x + y + z \] called?
Answer: Trinomial expression
Question 30: What is a number called when it divides another number exactly, with no remainder?
Answer: factor
Question 31: If one factor of \[ x^2 – 1 \] is \[ (x + 1) \], what is the other factor?
Answer: \[ x – 1 \]
Question 32: If one factor of \[ a^3 + b^3 \] is \[ (a^2 – ab + b^2) \], what is the other factor?
Answer: \[ (a + b) \]
Question 33: If the dimensions of a cuboid are \[ pqr, xyz \], how many equal parts can the cuboid be divided into?
Answer: \[ \frac{xyz}{pqr} \]
Question 35: What is the fundamental factor of \[ (x + y)^3 \]?
Answer: \[ x + y \]
Question 36: What is the product of the common prime factors of two or more algebraic expressions called?
Answer: The greatest common divisor (gcd) of the expressions
Question 37: What is the gcd of \[ x^3, x^2y, x^2y^2 \]?
Answer: \[ x^2 \]
Question 38: What is the lcm of \[ x^3y^2, x^2y^2, x^2y \]?
Answer: \[ x^3y^2 \]
Question 39: What is the gcd of \[ 30^3 \] and \[ 20^3 \]?
Answer: \[ 10^3 \]
Question 40: What is the gcd of \[ x^3y^3 \] and \[ xy^3 \]?
Answer: \[ xy \]
