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 equation of a line with a slope of 2 that passes through the point (1, 1)?
A.
y = 2x + 1
B.
y = 2x - 1
C.
y = 2x + 2
D.
y = 2x - 2
Show solution
Solution
Using the point-slope form of the equation of a line: y - y1 = m(x - x1), we have y - 1 = 2(x - 1). Simplifying gives y = 2x - 2 + 1, or y = 2x - 1.
Correct Answer:
A
— y = 2x + 1
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Q. What is the equation of the line passing through the points (2, 3) and (4, 7)?
A.
y = 2x - 1
B.
y = 2x + 1
C.
y = 2x + 3
D.
y = 2x - 3
Show solution
Solution
Slope m = (y2 - y1) / (x2 - x1) = (7 - 3) / (4 - 2) = 2. Using point-slope form: y - 3 = 2(x - 2) => y = 2x + 1.
Correct Answer:
B
— y = 2x + 1
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Q. What is the equation of the line perpendicular to y = 3x + 1 that passes through the point (2, 5)?
A.
y = -1/3x + 7
B.
y = 3x - 1
C.
y = -3x + 11
D.
y = 1/3x + 3
Show solution
Solution
The slope of the given line is 3.\nThe slope of the perpendicular line is -1/3.\nUsing point-slope form: y - 5 = -1/3(x - 2) gives y = -1/3x + 7.
Correct Answer:
A
— y = -1/3x + 7
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Q. What is the equation of the line that is perpendicular to y = 2x + 1 and passes through the point (1, 2)?
A.
y = -1/2x + 5/2
B.
y = 1/2x + 3/2
C.
y = -2x + 4
D.
y = 2x - 1
Show solution
Solution
The slope of the perpendicular line is -1/2. Using point-slope form: y - 2 = -1/2(x - 1) => y = -1/2x + 5/2.
Correct Answer:
A
— y = -1/2x + 5/2
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Q. What is the equation of the line that passes through the point (2, 3) with a slope of 2?
A.
y = 2x + 1
B.
y = 2x - 1
C.
y = 2x + 3
D.
y = 2x - 3
Show solution
Solution
Using point-slope form: y - y1 = m(x - x1) => y - 3 = 2(x - 2) => y = 2x - 4 + 3 => y = 2x - 1.
Correct Answer:
A
— y = 2x + 1
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Q. What is the equation of the line that passes through the point (2, 3) with a slope of -1?
A.
y = -x + 5
B.
y = -x + 3
C.
y = x + 1
D.
y = -x + 2
Show solution
Solution
Using point-slope form: y - 3 = -1(x - 2) => y = -x + 5.
Correct Answer:
A
— y = -x + 5
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Q. What is the equation of the line that passes through the point (2, 3) with a slope of 4?
A.
y = 4x - 5
B.
y = 4x + 5
C.
y = 4x - 3
D.
y = 4x + 3
Show solution
Solution
Using point-slope form: y - y1 = m(x - x1) => y - 3 = 4(x - 2) => y = 4x - 8 + 3 => y = 4x - 5.
Correct Answer:
C
— y = 4x - 3
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Q. What is the equation of the line that passes through the points (1, 2) and (2, 3)?
A.
y = x + 1
B.
y = 2x
C.
y = x + 2
D.
y = 3x - 1
Show solution
Solution
First, find the slope: m = (3 - 2) / (2 - 1) = 1. Using point-slope form: y - 2 = 1(x - 1) => y = x + 1.
Correct Answer:
A
— y = x + 1
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Q. What is the equation of the line that passes through the points (1, 2) and (3, 4)?
A.
y = x + 1
B.
y = 2x
C.
y = 2x - 1
D.
y = x + 2
Show solution
Solution
Slope = (4 - 2) / (3 - 1) = 1. Using point-slope form: y - 2 = 1(x - 1) => y = x + 1.
Correct Answer:
A
— y = x + 1
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Q. What is the equation of the line that passes through the points (1, 2) and (3, 6)?
A.
y = 2x
B.
y = 3x - 1
C.
y = 4x - 2
D.
y = x + 1
Show solution
Solution
Calculate the slope: m = (y2 - y1)/(x2 - x1) = (6 - 2)/(3 - 1) = 2.\nUsing point-slope form: y - 2 = 2(x - 1) gives y = 2x.
Correct Answer:
A
— y = 2x
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Q. What is the factored form of 2x^2 + 8x?
A.
2x(x + 4)
B.
2(x + 4)(x + 2)
C.
2x(x + 2)
D.
x(2x + 8)
Show solution
Solution
First, factor out the common term 2x from 2x^2 + 8x. This gives us 2x(x + 4).
Correct Answer:
A
— 2x(x + 4)
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Q. What is the factored form of 2x^2 - 8?
A.
2(x - 4)(x + 4)
B.
2(x - 2)(x + 2)
C.
2(x - 4)
D.
2(x + 4)
Show solution
Solution
Factor out the common term 2: 2(x^2 - 4). Then factor x^2 - 4 as (x - 2)(x + 2). Thus, the final factorization is 2(x - 4)(x + 4).
Correct Answer:
A
— 2(x - 4)(x + 4)
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Q. What is the factored form of the expression 4x^2 - 12x?
A.
4x(x - 3)
B.
2x(2x - 3)
C.
4(x^2 - 3)
D.
2(2x^2 - 6x)
Show solution
Solution
The greatest common factor is 4x. Factoring it out gives us 4x(x - 3).
Correct Answer:
A
— 4x(x - 3)
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Q. What is the factored form of the expression x^2 + 7x + 10?
A.
(x + 5)(x + 2)
B.
(x - 5)(x - 2)
C.
(x + 10)(x - 1)
D.
(x - 10)(x + 1)
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 the expression 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
To factor x^2 - 5x + 6, we need two numbers that multiply to 6 and add to -5. The numbers -2 and -3 work. Thus, the factored form is (x - 2)(x - 3).
Correct Answer:
A
— (x - 2)(x - 3)
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Q. What is the factored form of the expression x^2 - 6x + 9?
A.
(x - 3)(x - 3)
B.
(x + 3)(x + 3)
C.
(x - 9)(x + 1)
D.
(x + 6)(x - 3)
Show solution
Solution
This is a perfect square trinomial. The factored form is (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 the expression x^2 - 9?
A.
(x - 3)(x + 3)
B.
(x - 9)(x + 1)
C.
(x + 9)(x - 1)
D.
(x - 1)(x + 1)
Show solution
Solution
This is a difference of squares. The factored form is (x - 3)(x + 3).
Correct Answer:
A
— (x - 3)(x + 3)
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Q. What is the factored form of the polynomial 2x^2 + 8x?
A.
2x(x + 4)
B.
2(x + 4)(x + 2)
C.
2x(x + 2)
D.
2(x + 2)(x + 4)
Show solution
Solution
Step 1: Factor out the common term: 2x(x + 4).
Correct Answer:
A
— 2x(x + 4)
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Q. What is the factored form of the polynomial 2x^2 - 8?
A.
2(x - 4)(x + 4)
B.
2(x - 2)(x + 2)
C.
2(x - 4)(x - 2)
D.
2(x + 4)(x + 2)
Show solution
Solution
Step 1: Factor out the common term: 2(x^2 - 4). Step 2: Recognize the difference of squares: 2(x - 4)(x + 4).
Correct Answer:
A
— 2(x - 4)(x + 4)
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Q. What is the factored form of the polynomial 3x^2 - 12?
A.
3(x - 4)(x + 4)
B.
3(x - 2)(x + 2)
C.
3(x - 4)
D.
3(x + 4)
Show solution
Solution
First, factor out 3: 3(x^2 - 4). Then, factor the difference of squares: 3(x - 2)(x + 2).
Correct Answer:
A
— 3(x - 4)(x + 4)
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Q. What is the factored form of the polynomial x^2 + 5x + 6?
A.
(x + 2)(x + 3)
B.
(x - 2)(x - 3)
C.
(x + 1)(x + 6)
D.
(x + 3)(x + 2)
Show solution
Solution
Step 1: Find two numbers that multiply to 6 and add to 5: 2 and 3. Step 2: Factor: (x + 2)(x + 3).
Correct Answer:
A
— (x + 2)(x + 3)
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Q. What is the factored form of the polynomial x^2 + 7x + 10?
A.
(x + 5)(x + 2)
B.
(x - 5)(x - 2)
C.
(x + 10)(x - 1)
D.
(x - 10)(x + 1)
Show solution
Solution
Step 1: Find two numbers that multiply to 10 and add to 7: 5 and 2. Step 2: Factor as (x + 5)(x + 2).
Correct Answer:
A
— (x + 5)(x + 2)
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Q. What is the factored form of the polynomial x^2 - 10x + 24?
A.
(x - 4)(x - 6)
B.
(x - 2)(x - 12)
C.
(x + 4)(x + 6)
D.
(x + 2)(x + 12)
Show solution
Solution
To factor, we look for two numbers that multiply to 24 and add to -10. The numbers -4 and -6 work, so the factored form is (x - 4)(x - 6).
Correct Answer:
A
— (x - 4)(x - 6)
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Q. What is the factored form of the polynomial x^2 - 16?
A.
(x - 4)(x + 4)
B.
(x - 8)(x + 2)
C.
(x - 2)(x + 2)
D.
(x - 4)(x - 4)
Show solution
Solution
This is a difference of squares: x^2 - 4^2 = (x - 4)(x + 4).
Correct Answer:
A
— (x - 4)(x + 4)
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Q. What is the factored form of the polynomial x^2 - 4?
A.
(x - 2)(x + 2)
B.
(x - 4)(x + 4)
C.
(x + 4)(x + 2)
D.
(x - 1)(x + 1)
Show solution
Solution
This is a difference of squares: x^2 - 4 = (x - 2)(x + 2).
Correct Answer:
A
— (x - 2)(x + 2)
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Q. What is the factored form of the polynomial x^2 - 6x + 9?
A.
(x - 3)(x - 3)
B.
(x + 3)(x + 3)
C.
(x - 9)(x + 1)
D.
(x + 6)(x - 3)
Show solution
Solution
The polynomial x^2 - 6x + 9 can be factored as (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 the polynomial 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
Step 1: Recognize it as a difference of squares: x^2 - 3^2. Step 2: Factor: (x - 3)(x + 3).
Correct Answer:
A
— (x - 3)(x + 3)
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Q. What is the factored form of the quadratic equation x^2 + 6x + 9?
A.
(x + 3)(x + 3)
B.
(x - 3)(x - 3)
C.
(x + 9)(x + 1)
D.
(x - 9)(x - 1)
Show solution
Solution
This quadratic can be factored as (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 the quadratic equation 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
Step 1: Find two numbers that multiply to 6 and add to -5: -2 and -3. Step 2: Write the factors: (x - 2)(x - 3).
Correct Answer:
A
— (x - 2)(x - 3)
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Q. What is the factored form of the quadratic expression x^2 - 7x + 10?
A.
(x - 5)(x - 2)
B.
(x - 10)(x + 1)
C.
(x - 1)(x - 10)
D.
(x - 2)(x - 5)
Show solution
Solution
To factor, we look for two numbers that multiply to 10 and add to -7. The numbers -2 and -5 work, so the factored form is (x - 2)(x - 5).
Correct Answer:
D
— (x - 2)(x - 5)
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