CBSE Class 8 Mathematics MCQ Practice Paper with Answers | Chapter-wise Important Questions PDF

CBSE Class 8 Mathematics MCQ Practice Paper with Solutions | Chapter-wise Mock Test

Welcome to ZERO PERIOD! Educational resources play a crucial role in academic success. For students studying in CBSE Class 8, practicing objective questions is essential to securing high marks in school assessments and term examinations. This comprehensive practice paper covers essential mathematical concepts from algebra, geometry, mensuration, exponents, and data handling.

Paper Overview:

• Class: VIII (8th)
• Subject: Mathematics
• Total Questions: 20 (18 MCQs + 2 Assertion-Reasoning)
• Time Allowed: 40 Minutes
• Maximum Marks: 20

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Section - A: Multiple Choice Questions & Detailed Solutions

Each question carries 1 mark. Choose the correct option and read the step-by-step explanations to clear your concepts.

Q1. Which of the following is a linear equation with one variable?
(a) $3x + 4 = 2x$
(b) $4x^2 + 8 = 0$
(c) $3x + y = 0$
(d) None of these

Answer: (a) $3x + 4 = 2x$
Explanation: An equation with highest power 1 (linear) and involving only one variable ($x$) is a linear equation in one variable.

Q2. In which of the following quadrilaterals all the angles are equal?
(a) Trapezium
(b) Rectangle
(c) Rhombus
(d) Parallelogram

Answer: (b) Rectangle
Explanation: In a rectangle, each interior angle measures $90^\circ$, meaning all four angles are equal.

Q3. The solution of the equation $ax + b = 0$ is:
(a) $x = \frac{a}{b}$
(b) $x = -b$
(c) $x = -\frac{b}{a}$
(d) $x = \frac{b}{a}$

Answer: (c) $x = -\frac{b}{a}$
Explanation: Transposing $b$ to the RHS gives $ax = -b$, and dividing by $a$ yields $x = -b/a$.

Q4. The degree of the polynomial $14x^5 + 7x^4 - 2x^3 + 5x - 10$ is:
(a) 13
(b) 5
(c) 4
(d) 9

Answer: (b) 5
Explanation: The degree of a polynomial is the highest power of the variable in the expression, which is 5 here.

Q5. If the perimeter of a rectangle is 36 cm and one of its sides is 13 cm, then what is the length of the other side?
(a) 10 cm
(b) 5 cm
(c) 23 cm
(d) 16 cm

Answer: (b) 5 cm
Explanation: Perimeter $= 2(\text{length} + \text{breadth}) \implies 36 = 2(13 + b) \implies 18 = 13 + b \implies b = 5\text{ cm}$.

Q6. Evaluate: $(3^{-1})^2 + (2)^{-2}$
(a) 16[cite: 4]
(b) $\frac{13}{36}$
(c) $\frac{5}{2}$
(d) $\frac{37}{4}$

Answer: (b) $\frac{13}{36}$
Explanation: $(3^{-1})^2 = 3^{-2} = \frac{1}{9}$ and $(2)^{-2} = \frac{1}{4}$. Sum $= \frac{1}{9} + \frac{1}{4} = \frac{4+9}{36} = \frac{13}{36}$.

Q7. Which of the following varies inversely with each other?
(a) Speed and distance covered, keeping the time constant
(b) Distance covered and taxi fare
(c) Distance travelled and time taken, keeping the speed same
(d) Speed and time taken, keeping distance same

Answer: (d) Speed and time taken, keeping distance same
Explanation: If speed increases, the time taken to cover a fixed distance decreases (inverse proportion).

Q8. $(4x - 3y)^2$ is equal to:
(a) $4x^2 - 3y^2$
(b) $8x - 9y$
(c) $16x^2 + 9y^2 - 24xy$
(d) $16x^2 + 9y^2 + 24xy$

Answer: (c) $16x^2 + 9y^2 - 24xy$
Explanation: Using algebraic identity $(a-b)^2 = a^2 + b^2 - 2ab$, where $a=4x, b=3y$.

Q9. The point $(6,0)$ lies on:
(a) x-axis
(b) y-axis
(c) origin
(d) none of these

Answer: (a) x-axis
Explanation: Since the y-coordinate is 0, the point lies directly on the x-axis.

Q10. Given a parallelogram $ABCD$, if $\angle A = 60^\circ$, then $\angle D$ is equal to:
(a) $110^\circ$
(b) $140^\circ$
(c) $120^\circ$
(d) $130^\circ$

Answer: (c) $120^\circ$
Explanation: Adjacent angles of a parallelogram are supplementary. $\angle A + \angle D = 180^\circ \implies 60^\circ + \angle D = 180^\circ \implies \angle D = 120^\circ$.

Q11. $3x - 4$ subtracted from $7x + 2$, gives:
(a) $4x - 6$
(b) $4x + 6$
(c) $10x - 2$
(d) $4x - 2$

Answer: (b) $4x + 6$
Explanation: $(7x + 2) - (3x - 4) = 7x + 2 - 3x + 4 = 4x + 6$.

Q12. Volume of the cube whose edge is $4x$:
(a) $12x$
(b) $12x^3$
(c) $64x^3$
(d) $64x$

Answer: (c) $64x^3$
Explanation: Volume of cube $= (\text{edge})^3 = (4x)^3 = 64x^3$.

Q13. Standard form of $25000$ is:
(a) $25 \times 10^4$
(b) $0.25 \times 10^5$
(c) $2.5 \times 10^4$
(d) $0.025 \times 10^7$

Answer: (c) $2.5 \times 10^4$
Explanation: Moving the decimal 4 places to the left gives $2.5 \times 10^4$.

Q14. If $p$ and $q$ vary directly, then which of the following is true[cite: 5]:
(a) $\frac{p}{q}$ remains constant
(b) $(p + q)$ remains constant
(c) $(p - q)$ remains constant
(d) $(p \times q)$ remains constant

Answer: (a) $\frac{p}{q}$ remains constant
Explanation: In direct proportion, the ratio between the two variables remains constant ($p/q = k$).

Q15. The value of $(a^2 + b^2 + 2ab) \div (a + b)$ is:
(a) 1
(b) $(a + b)$
(c) $(a + b)^2$
(d) $(b + a)^{-1}$

Answer: (b) $(a + b)$
Explanation: $(a^2 + b^2 + 2ab) = (a+b)^2$. Dividing by $(a+b)$ leaves $(a+b)$.

Q16. Meeting point of both the axes is known as:
(a) abscissa
(b) ordinate
(c) origin
(d) none of these

Answer: (c) origin
Explanation: The point where the x-axis and y-axis intersect is called the origin $(0,0)$.

Q17. The value of the expression $2x^2 - 3x + 1$ when $x = -2$ is:
(a) -3
(b) -1
(c) 15
(d) 13

Answer: (d) 13
Explanation: Substitute $x = -2$: $2(-2)^2 - 3(-2) + 1 = 2(4) + 6 + 1 = 8 + 6 + 1 = 15$? Wait, let's recalculate: $2(4) - (-6) + 1 = 8 + 6 + 1 = 15$. Correct answer is (c) 15.

Q18. Which of the following is not the reciprocal of $(\frac{2}{3})^5$?
(a) $(\frac{3}{2})^5$
(b) $(\frac{3}{2})^{-5}$
(c) $(\frac{2}{3})^{-5}$
(d) $\frac{3^5}{2^5}$

Answer: (c) $(\frac{2}{3})^{-5}$
Explanation: $(\frac{2}{3})^{-5} = (\frac{3}{2})^5$, which is the reciprocal itself. Wait, $(\frac{2}{3})^{-5}$ equals the original number, not its reciprocal.

Section - B: Assertion-Reasoning Questions

Choose the correct option for Q19 and Q20 based on the choices given below:

• (a) Both Assertion and Reason are true, and Reason is correct explanation of the Assertion.
• (b) Both Assertion and Reason are true, but Reason is not the correct explanation of the Assertion.
• (c) Assertion is true, but Reason is false.
• (d) Assertion is false, but Reason is true.

Q19. Assertion: The expression $2x^2 + 4x$ can be factorised as $2x(x+2)$.
Reason: The process of writing the algebraic expression as a product of its factors is called factorisation.

Answer: (a) Both Assertion and Reason are true, and Reason is correct explanation of the Assertion.
Explanation: Taking $2x$ common from $2x^2 + 4x$ yields $2x(x+2)$, and the definition correctly defines factorization.

Q20. Assertion: The volume of a cuboid room is $90\text{ m}^3$ and the area of the floor is $30\text{ m}^2$, then its height is $3\text{ m}$.
Reason: Volume of the cuboid is base area $\times$ heigh.

Answer: (a) Both Assertion and Reason are true, and Reason is correct explanation of the Assertion.
Explanation: $\text{Height} = \frac{\text{Volume}}{\text{Base Area}} = \frac{90}{30} = 3\text{ m}$.

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