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. Which of the following is a solution to the inequality: -2x + 4 > 0?
A.
x < 2
B.
x > 2
C.
x ≤ 2
D.
x ≥ 2
Show solution
Solution
Step 1: Subtract 4 from both sides: -2x > -4. Step 2: Divide by -2 (reverse the inequality): x < 2.
Correct Answer:
A
— x < 2
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Q. Which of the following is a solution to the inequality: -4x + 1 ≤ 9?
A.
x ≤ -2
B.
x ≥ -2
C.
x ≤ 2
D.
x ≥ 2
Show solution
Solution
Step 1: Subtract 1 from both sides: -4x ≤ 8. Step 2: Divide by -4 (reverse inequality): x ≥ -2.
Correct Answer:
A
— x ≤ -2
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Q. Which of the following is a solution to the inequality: 2(x - 3) > 4?
A.
x = 5
B.
x = 4
C.
x = 3
D.
x = 6
Show solution
Solution
Step 1: Divide by 2: x - 3 > 2. Step 2: Add 3 to both sides: x > 5. Thus, x = 5 is a solution.
Correct Answer:
A
— x = 5
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Q. Which of the following is a solution to the inequality: 2x + 3 > 11?
A.
x < 4
B.
x > 4
C.
x = 4
D.
x = 5
Show solution
Solution
Step 1: Subtract 3 from both sides: 2x > 8. Step 2: Divide by 2: x > 4.
Correct Answer:
B
— x > 4
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Q. Which of the following is a solution to the inequality: 2x + 3 ≥ 11?
A.
x = 2
B.
x = 3
C.
x = 4
D.
x = 5
Show solution
Solution
Step 1: Subtract 3 from both sides: 2x ≥ 8. Step 2: Divide by 2: x ≥ 4.
Correct Answer:
C
— x = 4
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Q. Which of the following is a solution to the inequality: 3x + 2 < 11?
A.
x = 1
B.
x = 2
C.
x = 3
D.
x = 4
Show solution
Solution
Step 1: Subtract 2 from both sides: 3x < 9. Step 2: Divide by 3: x < 3.
Correct Answer:
B
— x = 2
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Q. Which of the following is a solution to the inequality: 4x - 1 ≤ 3x + 2?
A.
x ≤ 3
B.
x ≥ 3
C.
x < 3
D.
x > 3
Show solution
Solution
Step 1: Subtract 3x from both sides: x - 1 ≤ 2. Step 2: Add 1: x ≤ 3.
Correct Answer:
A
— x ≤ 3
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Q. Which of the following is a solution to the inequality: 6 - 2x ≤ 4?
A.
x ≥ 1
B.
x ≤ 1
C.
x ≥ 2
D.
x ≤ 2
Show solution
Solution
Step 1: Subtract 6 from both sides: -2x ≤ -2. Step 2: Divide by -2 (reverse the inequality): x ≥ 1.
Correct Answer:
B
— x ≤ 1
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Q. Which of the following is a solution to the inequality: 7 - 2x > 1?
A.
x < 3
B.
x > 3
C.
x ≤ 3
D.
x ≥ 3
Show solution
Solution
Step 1: Subtract 7 from both sides: -2x > -6. Step 2: Divide by -2 (reverse the inequality): x < 3.
Correct Answer:
A
— x < 3
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Q. Which of the following is a solution to the inequality: 7 - 3x < 1?
A.
x > 2
B.
x < 2
C.
x > 1
D.
x < 1
Show solution
Solution
Step 1: Subtract 7 from both sides: -3x < -6. Step 2: Divide by -3 (reverse the inequality): x > 2.
Correct Answer:
A
— x > 2
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Q. Which of the following is a solution to the inequality: 7 - x > 2?
A.
x < 5
B.
x > 5
C.
x < 7
D.
x > 7
Show solution
Solution
Step 1: Subtract 7 from both sides: -x > -5. Step 2: Multiply by -1 (reverse the inequality): x < 5.
Correct Answer:
A
— x < 5
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Q. Which of the following is a solution to the inequality: x^2 + 2x - 8 < 0?
A.
x < -4
B.
-4 < x < 2
C.
x > 2
D.
x = -4
Show solution
Solution
Step 1: Factor: (x + 4)(x - 2) < 0. Step 2: Critical points are x = -4 and x = 2. Step 3: Test intervals: valid for -4 < x < 2.
Correct Answer:
B
— -4 < x < 2
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Q. Which of the following is a solution to the inequality: x^2 - 4x < 0?
A.
x < 0
B.
0 < x < 4
C.
x > 4
D.
x = 2
Show solution
Solution
Step 1: Factor the inequality: x(x - 4) < 0. Step 2: The critical points are x = 0 and x = 4. Step 3: Test intervals: (0, 4) is valid.
Correct Answer:
B
— 0 < x < 4
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Q. Which of the following is NOT a measure of dispersion?
A.
Range
B.
Variance
C.
Mean
D.
Standard Deviation
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Solution
Mean is a measure of central tendency, not dispersion.
Correct Answer:
C
— Mean
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Q. Which of the following is the amplitude of the function y = 3sin(x)?
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Solution
The amplitude of a sine function y = Asin(Bx) is |A|. Here, A = 3, so the amplitude is 3.
Correct Answer:
C
— 3
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Q. Which of the following is the correct expression for cot(x)?
A.
cos(x)/sin(x)
B.
1/tan(x)
C.
sin(x)/cos(x)
D.
tan(x)/1
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Solution
cot(x) = 1/tan(x) = cos(x)/sin(x).
Correct Answer:
B
— 1/tan(x)
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Q. Which of the following is the correct 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
To factor, find two numbers that multiply to 6 and add to -5.\nThe numbers are -2 and -3.\nThus, the factored form is (x - 2)(x - 3).
Correct Answer:
A
— (x - 2)(x - 3)
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Q. Which of the following is the correct factorization of 2x^2 + 8x?
A.
2x(x + 4)
B.
2(x^2 + 4x)
C.
x(2x + 8)
D.
2x^2(1 + 4)
Show solution
Solution
First, factor out the greatest common factor, which is 2x. This gives us 2x(x + 4).
Correct Answer:
A
— 2x(x + 4)
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Q. Which of the following is the correct factorization 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
Step 1: Find two numbers that multiply to 6 and add to 5: 2 and 3. Step 2: Factor as (x + 2)(x + 3).
Correct Answer:
A
— (x + 2)(x + 3)
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Q. Which of the following is the correct factorization 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
The polynomial factors to (x + 5)(x + 2) since 5 and 2 add to 7 and multiply to 10.
Correct Answer:
A
— (x + 5)(x + 2)
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Q. Which of the following is the correct factorization of 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 can be factored as (x - 3)(x - 3) or (x - 3)^2.
Correct Answer:
A
— (x - 3)(x - 3)
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Q. Which of the following is the correct factorization of x^2 - 9?
A.
(x - 3)(x + 3)
B.
(x - 3)(x - 3)
C.
(x + 3)(x + 3)
D.
(x - 9)(x + 1)
Show solution
Solution
Step 1: Recognize it as a difference of squares: a^2 - b^2 = (a - b)(a + b). Step 2: Here, a = x, b = 3. So, (x - 3)(x + 3).
Correct Answer:
A
— (x - 3)(x + 3)
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Q. Which of the following is the correct identity for cotangent?
A.
cot(x) = cos(x)/sin(x)
B.
cot(x) = sin(x)/cos(x)
C.
cot(x) = 1/tan(x)
D.
cot(x) = tan(x)/1
Show solution
Solution
cot(x) = cos(x)/sin(x) is the correct identity.
Correct Answer:
A
— cot(x) = cos(x)/sin(x)
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Q. Which of the following is the correct identity for sin²(θ) + cos²(θ)?
A.
1
B.
0
C.
sin(θ)
D.
cos(θ)
Show solution
Solution
sin²(θ) + cos²(θ) = 1
Correct Answer:
A
— 1
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Q. Which of the following is the correct phase shift of y = sin(x - π/4)?
Show solution
Solution
The phase shift is found by setting the inside of the sine function to zero, giving a shift of π/4 to the right.
Correct Answer:
B
— π/4
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Q. Which of the following is the factored form of 2x^2 + 8x?
A.
2x(x + 4)
B.
2(x + 4)(x + 2)
C.
x(2x + 8)
D.
2x(x + 2)
Show solution
Solution
First, factor out the greatest common factor, which is 2x. This gives us 2x(x + 4).
Correct Answer:
A
— 2x(x + 4)
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Q. Which of the following 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
To factor x^2 - 5x + 6, find two numbers that multiply to 6 and add to -5.\nThe numbers are -2 and -3.\nThus, the factored form is (x - 2)(x - 3).
Correct Answer:
A
— (x - 2)(x - 3)
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Q. Which of the following 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
To factor x^2 - 5x + 6, find two numbers that multiply to 6 and add to -5.\nThe numbers are -2 and -3.\nThus, the factored form is (x - 2)(x - 3).
Correct Answer:
A
— (x - 2)(x - 3)
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Q. Which of the following is the mode of the data set: 2, 3, 4, 4, 5, 5, 5?
Show solution
Solution
Mode is the number that appears most frequently. Here, 5 appears 3 times.
Correct Answer:
D
— 5
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Q. Which of the following is the Pythagorean identity?
A.
sin²θ + cos²θ = 1
B.
tanθ = sinθ/cosθ
C.
secθ = 1/cosθ
D.
cscθ = 1/sinθ
Show solution
Solution
The Pythagorean identity is sin²θ + cos²θ = 1.
Correct Answer:
A
— sin²θ + cos²θ = 1
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