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 the result of (x + 2)(x - 2)?
A.
x^2 - 4
B.
x^2 + 4
C.
x^2 - 2
D.
x^2 + 2
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Solution
Use the difference of squares: (x + 2)(x - 2) = x^2 - 4.
Correct Answer:
A
— x^2 - 4
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Q. Which of the following is the result of factoring 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 2 and 3 multiply to 6 and add to 5.
Correct Answer:
A
— (x + 2)(x + 3)
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Q. Which of the following is the solution set for the inequality 2x + 1 ≥ 5?
A.
x ≤ 2
B.
x ≥ 2
C.
x < 2
D.
x > 2
Show solution
Solution
Step 1: Subtract 1 from both sides: 2x ≥ 4. Step 2: Divide by 2: x ≥ 2.
Correct Answer:
B
— x ≥ 2
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Q. Which of the following is the solution set for the inequality 2x + 3 > 7?
A.
x < 2
B.
x > 2
C.
x < 3
D.
x > 3
Show solution
Solution
Step 1: Subtract 3 from both sides: 2x > 4. Step 2: Divide by 2: x > 2.
Correct Answer:
B
— x > 2
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Q. Which of the following is the solution set for the inequality x + 2 > 3?
A.
x < 1
B.
x > 1
C.
x < 5
D.
x > 5
Show solution
Solution
To solve the inequality, subtract 2 from both sides: x > 1.
Correct Answer:
B
— x > 1
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Q. Which of the following is the solution set for the inequality x + 3 > 2?
A.
x > -1
B.
x < -1
C.
x > 1
D.
x < 1
Show solution
Solution
To solve the inequality, subtract 3 from both sides: x > -1.
Correct Answer:
A
— x > -1
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Q. Which of the following is the solution set for the inequality x + 4 > 2?
A.
x > -2
B.
x < -2
C.
x > 6
D.
x < 6
Show solution
Solution
Step 1: Subtract 4 from both sides: x > -2.
Correct Answer:
A
— x > -2
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Q. Which of the following is the solution set for the inequality x^2 - 4 > 0?
A.
(-∞, -2) ∪ (2, ∞)
B.
(-2, 2)
C.
[-2, 2]
D.
[2, ∞)
Show solution
Solution
Factor: (x - 2)(x + 2) > 0. The solution is x < -2 or x > 2.
Correct Answer:
A
— (-∞, -2) ∪ (2, ∞)
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Q. Which of the following is the solution to the equation 3x + 4 = 10?
A.
x = 2
B.
x = 3
C.
x = 4
D.
x = 1
Show solution
Solution
Subtract 4 from both sides: 3x = 6. Then divide by 3: x = 2.
Correct Answer:
A
— x = 2
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Q. Which of the following is the solution to the equation 4x^2 - 12x + 9 = 0?
A.
x = 1
B.
x = 2
C.
x = 3
D.
x = 4
Show solution
Solution
Step 1: Factor the equation: (2x - 3)(2x - 3) = 0. Step 2: Set the factor to zero: 2x - 3 = 0. Step 3: Solve for x: x = 3/2.
Correct Answer:
B
— x = 2
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Q. Which of the following is the solution to the inequality 2x + 1 > 3?
A.
x < 1
B.
x > 1
C.
x < 2
D.
x > 2
Show solution
Solution
Step 1: Subtract 1 from both sides: 2x > 2. Step 2: Divide by 2: x > 1.
Correct Answer:
B
— x > 1
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Q. Which of the following is the solution to the inequality 2x + 3 ≥ 7?
A.
x ≤ 2
B.
x ≥ 2
C.
x < 2
D.
x > 2
Show solution
Solution
Step 1: Subtract 3 from both sides: 2x ≥ 4. Step 2: Divide both sides by 2: x ≥ 2.
Correct Answer:
B
— x ≥ 2
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Q. Which of the following is the solution to the inequality: -4x + 1 < 3?
A.
x > -1/2
B.
x < -1/2
C.
x > 1/2
D.
x < 1/2
Show solution
Solution
Step 1: Subtract 1 from both sides: -4x < 2. Step 2: Divide by -4 (reverse inequality): x > -1/2.
Correct Answer:
B
— x < -1/2
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Q. Which of the following is the solution to the inequality: 2x + 3 ≥ 11?
A.
x ≥ 4
B.
x ≤ 4
C.
x > 4
D.
x < 4
Show solution
Solution
Step 1: Subtract 3 from both sides: 2x ≥ 8. Step 2: Divide by 2: x ≥ 4.
Correct Answer:
A
— x ≥ 4
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Q. Which of the following is the standard form of a linear equation?
A.
y = mx + b
B.
Ax + By = C
C.
y = ax^2 + bx + c
D.
x^2 + y^2 = r^2
Show solution
Solution
The standard form of a linear equation is Ax + By = C.
Correct Answer:
B
— Ax + By = C
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Q. Which of the following is the standard form of a quadratic equation?
A.
ax^2 + bx + c = 0
B.
y = mx + b
C.
ax + b = c
D.
x^2 + y^2 = r^2
Show solution
Solution
The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.
Correct Answer:
A
— ax^2 + bx + c = 0
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Q. Which of the following is the standard form of the equation of a line with slope 5 and y-intercept -3?
A.
y = 5x - 3
B.
5x + y = -3
C.
y = -5x + 3
D.
5x - y = 3
Show solution
Solution
The slope-intercept form is y = mx + b.\n1. y = 5x - 3 can be rearranged to 5x - y = 3.\nThus, the standard form is 5x - y = 3.
Correct Answer:
B
— 5x + y = -3
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Q. Which of the following lines is parallel to the line y = -1/2x + 3?
A.
y = 1/2x - 1
B.
y = -1/2x + 1
C.
y = 2x + 3
D.
y = -2x + 3
Show solution
Solution
Parallel lines have the same slope.\nThe slope of the given line is -1/2, so a parallel line must also have a slope of -1/2.
Correct Answer:
B
— y = -1/2x + 1
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Q. Which of the following pairs of triangles are congruent by the ASA criterion?
A.
Angle A = 30°, Angle B = 60°, Side AB = 5 cm
B.
Angle A = 30°, Angle B = 60°, Side AC = 5 cm
C.
Angle A = 60°, Angle B = 30°, Side AB = 5 cm
D.
Angle A = 60°, Angle B = 30°, Side AC = 5 cm
Show solution
Solution
For ASA, two angles and the included side must be equal. The second option meets this criterion.
Correct Answer:
B
— Angle A = 30°, Angle B = 60°, Side AC = 5 cm
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Q. Which of the following points lies inside the circle with center (0, 0) and radius 5?
A.
(3, 4)
B.
(5, 0)
C.
(6, 0)
D.
(0, 5)
Show solution
Solution
Distance from (0,0) to (3,4) is √(3² + 4²) = 5, which is on the circle. (5,0) and (0,5) are on the circle, (6,0) is outside.
Correct Answer:
A
— (3, 4)
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Q. Which of the following points lies on the line defined by the equation y = 2x + 1?
A.
(0, 1)
B.
(1, 2)
C.
(2, 5)
D.
(3, 6)
Show solution
Solution
For (2, 5): y = 2(2) + 1 = 5, so (2, 5) lies on the line.
Correct Answer:
C
— (2, 5)
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Q. Which of the following points lies on the line y = 2x + 1?
A.
(0, 1)
B.
(1, 2)
C.
(2, 5)
D.
(3, 6)
Show solution
Solution
Substituting x=2: y = 2(2) + 1 = 5, so (2, 5) lies on the line.
Correct Answer:
C
— (2, 5)
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Q. Which of the following quadrilaterals has all sides equal and all angles equal?
A.
Rectangle
B.
Rhombus
C.
Square
D.
Trapezoid
Show solution
Solution
A square is defined as a quadrilateral with all sides equal and all angles equal (90 degrees).
Correct Answer:
C
— Square
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Q. Which of the following represents a linear equation?
A.
y = 2x + 3
B.
y = x^2 + 1
C.
y = sqrt(x)
D.
y = ln(x)
Show solution
Solution
A linear equation is in the form y = mx + b. y = 2x + 3 fits this form.
Correct Answer:
A
— y = 2x + 3
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Q. Which of the following represents a quadratic equation?
A.
x + 1 = 0
B.
x^2 - 4x + 4 = 0
C.
3x^3 + 2 = 0
D.
5x - 2 = 0
Show solution
Solution
A quadratic equation is in the form ax^2 + bx + c = 0. The second option fits this form.
Correct Answer:
B
— x^2 - 4x + 4 = 0
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Q. Which of the following represents the binomial expansion of (x + 2)^2?
A.
x^2 + 4
B.
x^2 + 4x + 4
C.
x^2 + 2x + 2
D.
x^2 + 2
Show solution
Solution
Step 1: Use the formula (a + b)^2 = a^2 + 2ab + b^2. Step 2: Here, a = x and b = 2. Step 3: The expansion is x^2 + 2(2)x + 2^2 = x^2 + 4x + 4.
Correct Answer:
B
— x^2 + 4x + 4
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Q. Which of the following represents the equation of a line with a slope of -3 and y-intercept of 2?
A.
y = -3x + 2
B.
y = 3x + 2
C.
y = -3x - 2
D.
y = 3x - 2
Show solution
Solution
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
Correct Answer:
A
— y = -3x + 2
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Q. Which of the following represents the equation of a line with a slope of 2 and y-intercept of -3?
A.
y = 2x + 3
B.
y = 2x - 3
C.
y = -2x + 3
D.
y = -2x - 3
Show solution
Solution
The slope-intercept form is y = mx + b. Here, m = 2 and b = -3, so y = 2x - 3.
Correct Answer:
B
— y = 2x - 3
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Q. Which of the following represents the expression 2x^2 + 8x factored?
A.
2x(x + 4)
B.
2(x^2 + 4)
C.
x(2x + 8)
D.
2(x + 4)
Show solution
Solution
Step 1: Factor out the common term 2x: 2x(x + 4).
Correct Answer:
A
— 2x(x + 4)
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Q. Which of the following represents 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
Factor the polynomial: x^2 + 5x + 6 = (x + 2)(x + 3).
Correct Answer:
A
— (x + 2)(x + 3)
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