Class 8 Math Chapter 3 MCQ And One Word Question With Ans.

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: $x^2$