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 represents 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
To factor x^2 + 7x + 10, we look for two numbers that multiply to 10 and add to 7. The numbers 5 and 2 work, so the factored form is (x + 5)(x + 2).
Correct Answer:
A
— (x + 5)(x + 2)
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Q. Which of the following represents the inequality x + 3 > 5?
A.
x > 2
B.
x < 2
C.
x > 8
D.
x < 8
Show solution
Solution
To solve x + 3 > 5, subtract 3 from both sides.\n1. x > 2.
Correct Answer:
A
— x > 2
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Q. Which of the following represents the inequality x + 3 > 7?
A.
x > 4
B.
x < 4
C.
x > 10
D.
x < 10
Show solution
Solution
Subtract 3 from both sides: x > 7 - 3.\nThus, x > 4.
Correct Answer:
A
— x > 4
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Q. Which of the following represents the inequality x + 5 > 2?
A.
x > -3
B.
x < -3
C.
x > 7
D.
x < 7
Show solution
Solution
Subtract 5 from both sides: x > -3.
Correct Answer:
A
— x > -3
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Q. Which of the following represents the line with a slope of -1 and a y-intercept of 4?
A.
y = -x + 4
B.
y = x + 4
C.
y = -x - 4
D.
y = x - 4
Show solution
Solution
The slope-intercept form is y = mx + b.\nHere, m = -1 and b = 4, so the equation is y = -x + 4.
Correct Answer:
A
— y = -x + 4
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Q. Which of the following represents the phase shift of the function y = sin(x - π/4)?
Show solution
Solution
The phase shift of y = sin(x - C) is C. Here, C = π/4, so the phase shift is π/4 to the right.
Correct Answer:
B
— π/4
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Q. Which of the following represents the quadratic equation with roots 1 and -3?
A.
x^2 + 2x - 3 = 0
B.
x^2 - 2x - 3 = 0
C.
x^2 + 2x + 3 = 0
D.
x^2 - 4 = 0
Show solution
Solution
Using the roots, we can write the equation as (x - 1)(x + 3) = 0, which expands to x^2 + 2x - 3 = 0.
Correct Answer:
A
— x^2 + 2x - 3 = 0
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Q. Which of the following represents the roots of the equation 2x^2 - 8 = 0?
A.
-2 and 2
B.
0 and 4
C.
2 and -2
D.
4 and -4
Show solution
Solution
First, simplify the equation: 2x^2 = 8, so x^2 = 4. The roots are x = ±2.
Correct Answer:
A
— -2 and 2
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Q. Which of the following represents 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 represents the solution set for the inequality 2x + 5 > 3?
A.
x > -1
B.
x < -1
C.
x > 1
D.
x < 1
Show solution
Solution
Step 1: Subtract 5 from both sides: 2x > -2. Step 2: Divide by 2: x > -1.
Correct Answer:
A
— x > -1
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Q. Which of the following represents the solution set for the inequality x + 2 > 3?
A.
x < 1
B.
x > 1
C.
x < 5
D.
x > 5
Show solution
Solution
Subtracting 2 from both sides gives x > 1.
Correct Answer:
B
— x > 1
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Q. Which of the following represents the solution set for the inequality x + 5 > 2?
A.
x > -3
B.
x < -3
C.
x > 7
D.
x < 7
Show solution
Solution
Step 1: Subtract 5 from both sides: x > -3.
Correct Answer:
A
— x > -3
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Q. Which of the following represents the solution to the inequality: 4x + 1 ≥ 2x + 9?
A.
x ≥ 4
B.
x ≤ 4
C.
x > 4
D.
x < 4
Show solution
Solution
Step 1: Subtract 2x from both sides: 2x + 1 ≥ 9. Step 2: Subtract 1: 2x ≥ 8. Step 3: Divide by 2: x ≥ 4.
Correct Answer:
A
— x ≥ 4
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Q. Which of the following represents the solution to the inequality: 4x - 1 < 3x + 2?
A.
x < 3
B.
x > 3
C.
x < 1
D.
x > 1
Show solution
Solution
Step 1: Subtract 3x from both sides: x - 1 < 2. Step 2: Add 1 to both sides: x < 3.
Correct Answer:
A
— x < 3
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Q. Which of the following represents the solution to the inequality: 7 - 2x < 1?
A.
x > 3
B.
x < 3
C.
x > 4
D.
x < 4
Show solution
Solution
Step 1: Subtract 7 from both sides: -2x < -6. Step 2: Divide by -2 (reverse inequality): x > 3.
Correct Answer:
A
— x > 3
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Q. Which of the following represents the solution to the inequality: x^2 - 5x + 6 > 0?
A.
(2, 3)
B.
(3, ∞) ∪ (-∞, 2)
C.
(2, ∞)
D.
(3, 2)
Show solution
Solution
Step 1: Factor: (x - 2)(x - 3) > 0. Step 2: Test intervals: solution is (3, ∞) ∪ (-∞, 2).
Correct Answer:
B
— (3, ∞) ∪ (-∞, 2)
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Q. Which of the following represents the solution to the inequality: x^2 - 9 > 0?
A.
(-3, 3)
B.
(-∞, -3) ∪ (3, ∞)
C.
[-3, 3]
D.
(-3, 3]
Show solution
Solution
Step 1: Factor the inequality: (x - 3)(x + 3) > 0. Step 2: The solution is outside the roots: (-∞, -3) ∪ (3, ∞).
Correct Answer:
B
— (-∞, -3) ∪ (3, ∞)
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Q. Which of the following represents 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, where A, B, and C are constants.
Correct Answer:
B
— Ax + By = C
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Q. Which of the following shapes has all sides equal and all angles equal?
A.
Rectangle
B.
Square
C.
Rhombus
D.
Trapezoid
Show solution
Solution
A square has all sides equal and all angles equal (90 degrees).
Correct Answer:
B
— Square
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Q. Which of the following shapes is similar to a triangle with sides 2 cm, 3 cm, and 4 cm?
A.
4 cm, 6 cm, 8 cm
B.
2 cm, 3 cm, 5 cm
C.
1 cm, 1.5 cm, 2 cm
D.
3 cm, 4 cm, 5 cm
Show solution
Solution
Two triangles are similar if their corresponding sides are in proportion. The sides 4 cm, 6 cm, and 8 cm are double the sides of the original triangle.
Correct Answer:
A
— 4 cm, 6 cm, 8 cm
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Q. Which of the following statements is true about similar triangles?
A.
They have the same area
B.
Their corresponding angles are equal
C.
Their corresponding sides are equal
D.
They have the same perimeter
Show solution
Solution
Similar triangles have equal corresponding angles, which is the defining property of similarity.
Correct Answer:
B
— Their corresponding angles are equal
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Q. Which of the following statements is true for all quadrilaterals?
A.
They have four sides
B.
They have equal angles
C.
They have equal sides
D.
They have parallel sides
Show solution
Solution
All quadrilaterals have four sides, which is the defining property of a quadrilateral.
Correct Answer:
A
— They have four sides
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Q. Which of the following statements is true for congruent triangles?
A.
They have the same area
B.
They have the same perimeter
C.
They have the same shape and size
D.
All of the above
Show solution
Solution
Congruent triangles have the same shape and size, which implies they also have the same area and perimeter.
Correct Answer:
D
— All of the above
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Q. Which of the following statements is true for similar triangles?
A.
Their corresponding angles are equal
B.
Their corresponding sides are proportional
C.
Both A and B
D.
None of the above
Show solution
Solution
Similar triangles have equal corresponding angles and proportional corresponding sides.
Correct Answer:
C
— Both A and B
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Q. Which of the following triangles is congruent to a triangle with sides 3 cm, 4 cm, and 5 cm?
A.
3 cm, 4 cm, 6 cm
B.
5 cm, 12 cm, 13 cm
C.
6 cm, 8 cm, 10 cm
D.
3 cm, 4 cm, 5 cm
Show solution
Solution
Two triangles are congruent if they have the same side lengths. The triangle with sides 3 cm, 4 cm, and 5 cm is congruent to itself.
Correct Answer:
D
— 3 cm, 4 cm, 5 cm
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Q. Which of the following triangles is congruent to a triangle with sides 5 cm, 12 cm, and 13 cm?
A.
5 cm, 12 cm, 14 cm
B.
6 cm, 8 cm, 10 cm
C.
3 cm, 4 cm, 5 cm
D.
5 cm, 12 cm, 13 cm
Show solution
Solution
A triangle is congruent if it has the same side lengths. The triangle with sides 5 cm, 12 cm, and 13 cm is congruent to itself.
Correct Answer:
D
— 5 cm, 12 cm, 13 cm
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Q. Which of the following triangles is congruent to a triangle with sides 5, 12, and 13?
A.
5, 12, 14
B.
6, 8, 10
C.
5, 12, 13
D.
7, 24, 25
Show solution
Solution
A triangle with sides 5, 12, and 13 is congruent to itself.
Correct Answer:
C
— 5, 12, 13
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Q. Which of the following triangles is congruent to triangle ABC if AB = 5 cm, AC = 7 cm, and BC = 5 cm?
A.
Triangle DEF with DE = 5 cm, DF = 7 cm, EF = 5 cm
B.
Triangle GHI with GH = 5 cm, HI = 7 cm, IG = 6 cm
C.
Triangle JKL with JK = 6 cm, KL = 5 cm, JL = 5 cm
D.
Triangle MNO with MN = 5 cm, NO = 7 cm, OM = 5 cm
Show solution
Solution
Triangles are congruent if they have the same side lengths. Triangle DEF has the same side lengths as triangle ABC.
Correct Answer:
A
— Triangle DEF with DE = 5 cm, DF = 7 cm, EF = 5 cm
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Q. Which of the following triangles is congruent to triangle ABC if AB = 5, AC = 7, and BC = 5?
A.
Triangle DEF with DE = 5, DF = 7, EF = 5
B.
Triangle GHI with GH = 5, HI = 7, GI = 6
C.
Triangle JKL with JK = 5, KL = 5, JL = 7
D.
Triangle MNO with MN = 6, NO = 5, MO = 5
Show solution
Solution
Triangles are congruent if they have the same side lengths. Triangle DEF has the same side lengths as triangle ABC.
Correct Answer:
A
— Triangle DEF with DE = 5, DF = 7, EF = 5
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Q. Which of the following triangles is congruent to triangle ABC if angle A = angle D and side AB = side DE?
A.
Triangle DEF
B.
Triangle XYZ
C.
Triangle PQR
D.
Triangle LMN
Show solution
Solution
By the Angle-Side-Angle (ASA) postulate, if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
Correct Answer:
A
— Triangle DEF
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