Mathematics (School) MCQ & Objective Questions
Mathematics is a crucial subject in school education, forming the foundation for various competitive exams. Mastering Mathematics (School) not only enhances problem-solving skills but also boosts confidence during exams. Practicing MCQs and objective questions is essential for effective exam preparation, as it helps students identify important questions and understand concepts clearly.
What You Will Practise Here
Number Systems and their properties
Algebraic Expressions and Equations
Geometry: Angles, Triangles, and Circles
Statistics and Probability concepts
Mensuration: Area, Volume, and Surface Area
Trigonometry basics and applications
Functions and Graphs
Exam Relevance
Mathematics (School) is a significant part of the curriculum for CBSE and State Boards, as well as competitive exams like NEET and JEE. Students can expect a variety of question patterns, including direct application of formulas, conceptual understanding, and problem-solving scenarios. Familiarity with MCQs in this subject can greatly enhance performance in both board and competitive examinations.
Common Mistakes Students Make
Misinterpreting the question, leading to incorrect answers.
Overlooking the importance of units in measurement-related problems.
Confusing similar formulas, especially in Geometry and Algebra.
Neglecting to check calculations, resulting in simple arithmetic errors.
Failing to understand the underlying concepts, which affects problem-solving ability.
FAQs
Question: How can I improve my speed in solving Mathematics (School) MCQs?Answer: Regular practice with timed quizzes and mock tests can significantly enhance your speed and accuracy.
Question: Are there any specific topics I should focus on for competitive exams?Answer: Focus on Algebra, Geometry, and Statistics, as these areas frequently appear in competitive exams.
Start your journey towards mastering Mathematics (School) today! Solve practice MCQs to test your understanding and prepare effectively for your exams. Remember, consistent practice leads to success!
Q. What is the factored form of the quadratic expression x^2 - 9?
A.
(x - 3)(x + 3)
B.
(x - 9)(x + 1)
C.
(x - 1)(x + 1)
D.
(x + 3)(x + 3)
Show solution
Solution
The expression x^2 - 9 is a difference of squares, which factors to (x - 3)(x + 3).
Correct Answer:
A
— (x - 3)(x + 3)
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Q. What is the factored form of the quadratic x^2 - 5x + 6?
A.
(x - 2)(x - 3)
B.
(x + 2)(x + 3)
C.
(x - 1)(x - 6)
D.
(x + 1)(x + 6)
Show solution
Solution
Find two numbers that multiply to 6 and add to -5: -2 and -3. Thus, (x - 2)(x - 3).
Correct Answer:
A
— (x - 2)(x - 3)
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Q. What is the factored form of x^2 + 4x + 4?
A.
(x + 2)(x + 2)
B.
(x - 2)(x - 2)
C.
(x + 4)(x + 1)
D.
(x - 4)(x - 1)
Show solution
Solution
This is a perfect square trinomial. It factors to (x + 2)(x + 2) or (x + 2)^2.
Correct Answer:
A
— (x + 2)(x + 2)
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Q. What is the factored form of x^2 + 6x + 9?
A.
(x + 3)(x + 3)
B.
(x - 3)(x - 3)
C.
(x + 2)(x + 4)
D.
(x + 1)(x + 9)
Show solution
Solution
The expression x^2 + 6x + 9 is a perfect square trinomial. It factors to (x + 3)(x + 3) or (x + 3)^2.
Correct Answer:
A
— (x + 3)(x + 3)
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Q. What is the factored form of x^2 + 7x + 10?
A.
(x + 5)(x + 2)
B.
(x + 10)(x - 1)
C.
(x - 5)(x - 2)
D.
(x + 1)(x + 10)
Show solution
Solution
Step 1: Find two numbers that multiply to 10 and add to 7: 5 and 2. Step 2: Write in factored form: (x + 5)(x + 2).
Correct Answer:
A
— (x + 5)(x + 2)
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Q. What is the factored form of x^2 - 4?
A.
(x - 2)(x + 2)
B.
(x - 4)(x + 4)
C.
(x + 4)(x - 4)
D.
(x - 1)(x + 1)
Show solution
Solution
The expression x^2 - 4 is a difference of squares and can be factored as (x - 2)(x + 2).
Correct Answer:
A
— (x - 2)(x + 2)
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Q. What is the factored form of x^2 - 5x + 6?
A.
(x - 2)(x - 3)
B.
(x + 2)(x + 3)
C.
(x - 1)(x - 6)
D.
(x + 1)(x + 6)
Show solution
Solution
The polynomial factors to (x - 2)(x - 3) since the roots are 2 and 3.
Correct Answer:
A
— (x - 2)(x - 3)
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Q. What is the factored form of x^2 - 9?
A.
(x - 3)(x + 3)
B.
(x - 9)(x + 1)
C.
(x - 1)(x + 1)
D.
(x + 3)(x + 3)
Show solution
Solution
This is a difference of squares: x^2 - 9 = (x - 3)(x + 3).
Correct Answer:
A
— (x - 3)(x + 3)
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Q. What is the frequency of the function y = sin(2x)?
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Solution
The frequency of y = sin(Bx) is |B|/(2π). Here, B = 2, so the frequency is 2/(2π) = 1/π.
Correct Answer:
C
— 2
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Q. What is the height of a building if the angle of elevation from a point 50 meters away is 60°?
A.
25√3
B.
50
C.
50√3
D.
100
Show solution
Solution
Using tan(60°) = height/50, height = 50 * tan(60°) = 50√3.
Correct Answer:
A
— 25√3
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Q. What is the height of a triangle with a base of 8 cm and an area of 32 cm²?
A.
6 cm
B.
8 cm
C.
4 cm
D.
10 cm
Show solution
Solution
Area = 1/2 * base * height. Therefore, height = (2 * Area) / base = (2 * 32) / 8 = 8 cm.
Correct Answer:
A
— 6 cm
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Q. What is the height of a triangle with an area of 36 cm² and a base of 12 cm?
A.
6 cm
B.
8 cm
C.
4 cm
D.
10 cm
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Solution
Area = 1/2 * base * height; 36 = 1/2 * 12 * height; height = 36 / 6 = 6 cm.
Correct Answer:
A
— 6 cm
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Q. What is the height of a triangle with an area of 60 cm² and a base of 12 cm?
A.
10 cm
B.
5 cm
C.
8 cm
D.
6 cm
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Solution
Area = 1/2 * base * height. Therefore, 60 = 1/2 * 12 * height. Height = 60 / 6 = 10 cm.
Correct Answer:
D
— 6 cm
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Q. What is the inverse of sin(x)?
A.
sin⁻¹(x)
B.
cos(x)
C.
tan(x)
D.
sec(x)
Show solution
Solution
The inverse of sin(x) is sin⁻¹(x).
Correct Answer:
A
— sin⁻¹(x)
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Q. What is the leading coefficient of the polynomial 4x^3 - 2x^2 + 7?
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Solution
The leading coefficient is the coefficient of the term with the highest degree. Here, it is 4.
Correct Answer:
A
— 4
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Q. What is the leading coefficient of the polynomial 4x^3 - 2x^2 + x - 7?
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Solution
The leading coefficient is the coefficient of the term with the highest degree. Here, the leading term is 4x^3, so the leading coefficient is 4.
Correct Answer:
A
— 4
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Q. What is the length of a chord in a circle of radius 8 cm that subtends a central angle of 90 degrees?
A.
8 cm
B.
4√2 cm
C.
8√2 cm
D.
16 cm
Show solution
Solution
Chord length = 2r * sin(θ/2) = 2 * 8 * sin(45°) = 8√2 cm.
Correct Answer:
B
— 4√2 cm
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Q. What is the length of an arc of a circle with a radius of 10 cm and a central angle of 90 degrees?
A.
15.7 cm
B.
25 cm
C.
17.5 cm
D.
20 cm
Show solution
Solution
The length of an arc is given by L = (θ/360) * 2πr. Thus, L = (90/360) * 2 * π * 10 = 15.7 cm.
Correct Answer:
A
— 15.7 cm
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Q. What is the length of an arc of a circle with a radius of 10 cm and a central angle of 45°?
A.
5π cm
B.
10π/4 cm
C.
10π/8 cm
D.
10π/2 cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (45/360) * 2π(10) = (1/8) * 20π = 10π/4 cm.
Correct Answer:
B
— 10π/4 cm
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Q. What is the length of an arc of a circle with a radius of 10 cm that subtends an angle of 90 degrees at the center?
A.
5π cm
B.
10π cm
C.
15π cm
D.
20π cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (90/360) * 2π(10) = 5π cm.
Correct Answer:
A
— 5π cm
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Q. What is the length of an arc of a circle with a radius of 3 cm that subtends an angle of 90 degrees at the center?
A.
π cm
B.
1.5π cm
C.
3π cm
D.
6 cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (90/360) * 2π(3) = (1/4) * 6π = 1.5π cm.
Correct Answer:
B
— 1.5π cm
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Q. What is the length of an arc of a circle with a radius of 4 cm that subtends an angle of 90 degrees at the center?
A.
2π cm
B.
4π cm
C.
π cm
D.
6π cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (90/360) * 2π(4) = 2π cm.
Correct Answer:
A
— 2π cm
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Q. What is the length of an arc of a circle with a radius of 4 cm that subtends an angle of 90° at the center?
A.
2π cm
B.
4π cm
C.
π cm
D.
6.28 cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (90/360) * 2π(4) = 2π cm.
Correct Answer:
A
— 2π cm
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Q. What is the length of an arc of a circle with a radius of 5 cm that subtends an angle of 60 degrees at the center?
A.
5.24 cm
B.
3.14 cm
C.
5.00 cm
D.
10.47 cm
Show solution
Solution
The length of an arc is given by the formula L = (θ/360) * 2πr. For r = 5 cm and θ = 60°, L = (60/360) * 2π(5) = (1/6) * 10π ≈ 5.24 cm.
Correct Answer:
A
— 5.24 cm
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Q. What is the length of an arc of a circle with a radius of 6 cm and a central angle of 60 degrees?
A.
2π cm
B.
6π/3 cm
C.
π cm
D.
4π cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2π(6) = 2π cm.
Correct Answer:
A
— 2π cm
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Q. What is the length of an arc of a circle with a radius of 6 cm that subtends an angle of 60 degrees at the center?
A.
2π cm
B.
6π/3 cm
C.
π cm
D.
3π cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2π(6) = 2π cm.
Correct Answer:
A
— 2π cm
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Q. What is the length of an arc of a circle with a radius of 6 cm that subtends an angle of 60 degrees?
A.
2π cm
B.
6π/3 cm
C.
π cm
D.
3π cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2π(6) = 2π cm.
Correct Answer:
A
— 2π cm
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Q. What is the length of each side of a regular octagon inscribed in a circle of radius 10 cm?
A.
5√2 cm
B.
10 cm
C.
10√2 cm
D.
5 cm
Show solution
Solution
The length of each side of a regular octagon inscribed in a circle can be calculated using the formula s = r × √2(1 - cos(π/n)). For n=8 and r=10 cm, s = 10 cm × √2(1 - cos(π/8)) = 5√2 cm.
Correct Answer:
A
— 5√2 cm
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Q. What is the length of the altitude from point C(7, 2) to side AB of triangle ABC with A(1, 2) and B(4, 6)?
A.
3.0
B.
2.0
C.
4.0
D.
5.0
Show solution
Solution
Using the formula for the area of a triangle: Area = 1/2 * base * height. Area = 1/2 * 5 * height. Area = 5.0. Height = 3.0.
Correct Answer:
A
— 3.0
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Q. What is the length of the altitude from the vertex of a triangle to the base if the area is 40 cm² and the base is 10 cm?
A.
4 cm
B.
6 cm
C.
8 cm
D.
10 cm
Show solution
Solution
Using the area formula: Area = 1/2 * base * height, we can rearrange to find height: height = (2 * Area) / base = (2 * 40) / 10 = 8 cm.
Correct Answer:
B
— 6 cm
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