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 y-intercept of the line represented by the equation y = -3x + 6?
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Solution
The y-intercept is the constant term when x = 0, which is 6.
Correct Answer:
A
— 6
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Q. What is the y-intercept of the line represented by the equation y = -3x + 7?
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Solution
The y-intercept is the constant term when x = 0, which is 7.
Correct Answer:
A
— 7
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Q. What type of angles are formed when a transversal intersects two parallel lines?
A.
Complementary angles
B.
Supplementary angles
C.
Equal angles
D.
All of the above
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Solution
When a transversal intersects two parallel lines, it forms complementary, supplementary, and equal angles.
Correct Answer:
D
— All of the above
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Q. What type of polygon has all sides and angles equal?
A.
Scalene triangle
B.
Isosceles triangle
C.
Regular polygon
D.
Irregular polygon
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Solution
A regular polygon is defined as a polygon with all sides and angles equal.
Correct Answer:
C
— Regular polygon
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Q. What type of polygon is a shape with 5 sides?
A.
Triangle
B.
Quadrilateral
C.
Pentagon
D.
Hexagon
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Solution
A polygon with 5 sides is called a pentagon.
Correct Answer:
C
— Pentagon
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Q. What type of quadrilateral has all sides equal and all angles equal?
A.
Square
B.
Rectangle
C.
Rhombus
D.
Trapezoid
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Solution
A square is a type of quadrilateral that has all sides equal and all angles equal (90 degrees).
Correct Answer:
A
— Square
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Q. What type of quadrilateral has one pair of parallel sides?
A.
Rectangle
B.
Square
C.
Trapezoid
D.
Rhombus
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Solution
A trapezoid is defined as a quadrilateral that has at least one pair of parallel sides.
Correct Answer:
C
— Trapezoid
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Q. What type of quadrilateral has opposite sides that are equal and all angles are right angles?
A.
Rectangle
B.
Rhombus
C.
Trapezoid
D.
Parallelogram
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Solution
A rectangle is defined as a quadrilateral with opposite sides equal and all angles measuring 90 degrees.
Correct Answer:
A
— Rectangle
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Q. What type of triangle has all sides of different lengths?
A.
Equilateral
B.
Isosceles
C.
Scalene
D.
Right
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Solution
A triangle with all sides of different lengths is called a scalene triangle.
Correct Answer:
C
— Scalene
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Q. What type of triangle is formed by the vertices (0,0), (4,0), and (2,3)?
A.
Equilateral
B.
Isosceles
C.
Scalene
D.
Right
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Solution
The triangle has two sides of equal length (the distances from (0,0) to (2,3) and from (4,0) to (2,3)), making it an isosceles triangle.
Correct Answer:
B
— Isosceles
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Q. When two parallel lines are intersected by a transversal, which angles are always equal?
A.
Same-side interior angles
B.
Alternate interior angles
C.
Vertical angles
D.
Same-side exterior angles
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Solution
Alternate interior angles are equal when two parallel lines are cut by a transversal.
Correct Answer:
B
— Alternate interior angles
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Q. Which equation represents the double angle identity for sine?
A.
sin(2x) = 2sin(x)cos(x)
B.
sin(2x) = sin²(x) + cos²(x)
C.
sin(2x) = sin(x) + cos(x)
D.
sin(2x) = 2sin²(x)
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Solution
The double angle identity for sine is sin(2x) = 2sin(x)cos(x).
Correct Answer:
A
— sin(2x) = 2sin(x)cos(x)
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Q. Which expression represents the difference of squares for a^2 - b^2?
A.
(a + b)(a - b)
B.
(a - b)(a + b)
C.
(a + b)^2
D.
(a - b)^2
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Solution
The difference of squares is factored as (a + b)(a - b).
Correct Answer:
A
— (a + b)(a - b)
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Q. Which expression represents the difference of squares for x^2 - 16?
A.
(x - 4)(x + 4)
B.
(x - 8)(x + 8)
C.
(x - 2)(x + 2)
D.
(x - 16)(x + 16)
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Solution
The expression can be factored as (x - 4)(x + 4) since 16 is 4^2.
Correct Answer:
A
— (x - 4)(x + 4)
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Q. Which expression represents the expansion of (x + 2)(x - 3)?
A.
x^2 - x - 6
B.
x^2 - x + 6
C.
x^2 + x - 6
D.
x^2 + x + 6
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Solution
Use the distributive property: x^2 - 3x + 2x - 6 = x^2 - x - 6.
Correct Answer:
A
— x^2 - x - 6
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Q. Which expression represents the expansion of (x + 2)^2?
A.
x^2 + 4
B.
x^2 + 4x + 4
C.
x^2 + 2x + 2
D.
x^2 + 2x + 4
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Solution
Use the formula (a + b)^2 = a^2 + 2ab + b^2: (x + 2)^2 = x^2 + 4x + 4.
Correct Answer:
B
— x^2 + 4x + 4
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Q. Which expression 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)
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Solution
The expression factors to (x + 2)(x + 3) since 2 and 3 add to 5 and multiply to 6.
Correct Answer:
A
— (x + 2)(x + 3)
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Q. Which expression represents the factored form of x^2 + 7x + 10?
A.
(x + 5)(x + 2)
B.
(x - 5)(x - 2)
C.
(x + 10)(x - 1)
D.
(x - 10)(x + 1)
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Solution
The expression 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 expression represents the factored form of x^2 - 16?
A.
(x - 4)(x + 4)
B.
(x - 8)(x + 2)
C.
(x - 2)(x + 2)
D.
(x + 4)(x + 4)
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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. Which expression represents the factored form of x^2 - 9?
A.
(x - 3)(x + 3)
B.
(x - 1)(x + 1)
C.
(x - 2)(x + 2)
D.
(x - 4)(x + 4)
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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. Which expression represents the polynomial 3x^2 + 5x - 2 factored?
A.
(3x - 1)(x + 2)
B.
(3x + 2)(x - 1)
C.
(x + 2)(3x - 1)
D.
(x - 2)(3x + 1)
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Solution
To factor, find two numbers that multiply to -6 and add to 5: (3x - 1)(x + 2).
Correct Answer:
A
— (3x - 1)(x + 2)
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Q. Which expression represents the sum of the first n terms of an arithmetic series with first term a and common difference d?
A.
n/2 * (2a + (n-1)d)
B.
n * (a + d)
C.
n * a + d
D.
n/2 * (a + d)
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Solution
The formula for the sum of the first n terms is S_n = n/2 * (2a + (n-1)d).
Correct Answer:
A
— n/2 * (2a + (n-1)d)
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Q. Which expression represents the sum of the polynomials (2x^2 + 3x) and (4x^2 - x)?
A.
6x^2 + 2x
B.
2x^2 + 4x
C.
6x^2 + 4x
D.
2x^2 + 2x
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Solution
Step 1: Combine like terms: (2x^2 + 4x^2) + (3x - x) = 6x^2 + 2x.
Correct Answer:
A
— 6x^2 + 2x
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Q. Which expression represents the sum of the polynomials (3x^2 + 2x) and (4x^2 - 5x)?
A.
7x^2 - 3x
B.
7x^2 + 3x
C.
x^2 - 3x
D.
x^2 + 3x
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Solution
Step 1: Combine like terms: (3x^2 + 4x^2) + (2x - 5x) = 7x^2 - 3x.
Correct Answer:
A
— 7x^2 - 3x
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Q. Which expression represents the sum of the roots of the equation x^2 - 6x + 8 = 0?
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Solution
Step 1: The sum of the roots is given by -b/a: 6/1 = 6.
Correct Answer:
A
— 6
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Q. Which expression represents the sum of the roots of the quadratic equation x^2 + 6x + 8 = 0?
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Solution
The sum of the roots is given by -b/a. Here, b = 6, so the sum is -6.
Correct Answer:
A
— -6
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Q. Which inequality represents the solution set for x + 4 < 10?
A.
x < 6
B.
x > 6
C.
x ≤ 6
D.
x ≥ 6
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Solution
To solve the inequality, subtract 4 from both sides: x < 6.
Correct Answer:
A
— x < 6
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Q. Which inequality represents the solution set for x^2 - 4 < 0?
A.
x < -2 or x > 2
B.
-2 < x < 2
C.
x > -2 and x < 2
D.
x < 2
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Solution
The inequality x^2 - 4 < 0 can be factored as (x - 2)(x + 2) < 0. The solution set is -2 < x < 2.
Correct Answer:
B
— -2 < x < 2
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Q. Which inequality represents the solution to the equation 4x - 8 = 0?
A.
x < 2
B.
x > 2
C.
x = 2
D.
x ≤ 2
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Solution
To solve the equation, add 8 to both sides: 4x = 8. Then divide by 4: x = 2. The solution is x = 2.
Correct Answer:
C
— x = 2
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Q. Which measure of central tendency is most affected by extreme values?
A.
Mean
B.
Median
C.
Mode
D.
Range
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Solution
The mean is most affected by extreme values, as it takes all values into account.
Correct Answer:
A
— Mean
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