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. Determine the x-intercepts of the equation y = x^2 - 4.
A.
x = 2, -2
B.
x = 4, -4
C.
x = 0, 4
D.
x = -4, 0
Show solution
Solution
Set y = 0: x^2 - 4 = 0. Factoring gives (x - 2)(x + 2) = 0. Thus, x = 2 and x = -2.
Correct Answer:
A
— x = 2, -2
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Q. Factor the expression 2x^2 + 8x + 6.
A.
2(x + 3)(x + 1)
B.
2(x + 2)(x + 3)
C.
2(x + 1)(x + 3)
D.
2(x + 4)(x + 1)
Show solution
Solution
First, factor out the common term 2: 2(x^2 + 4x + 3). Then, factor the quadratic: 2(x + 3)(x + 1).
Correct Answer:
A
— 2(x + 3)(x + 1)
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Q. Factor the expression 2x^2 - 8.
A.
2(x - 4)(x + 4)
B.
2(x - 2)(x + 2)
C.
2(x - 4)
D.
x(2x - 8)
Show solution
Solution
To factor 2x^2 - 8, first factor out 2: 2(x^2 - 4). Then, recognize x^2 - 4 as a difference of squares: 2(x - 2)(x + 2).
Correct Answer:
A
— 2(x - 4)(x + 4)
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Q. Factor the expression 3x^2 - 12.
A.
3(x^2 - 4)
B.
(3x - 6)(x + 2)
C.
3(x - 4)(x + 1)
D.
3(x - 2)(x + 2)
Show solution
Solution
First, factor out the greatest common factor, which is 3. This gives us 3(x^2 - 4). Then, x^2 - 4 can be factored as (x - 2)(x + 2). So, the complete factorization is 3(x - 2)(x + 2).
Correct Answer:
A
— 3(x^2 - 4)
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Q. Factor the expression 4x^2 - 12x + 9.
A.
(2x - 3)(2x - 3)
B.
(2x + 3)(2x + 3)
C.
(4x - 3)(x - 3)
D.
(2x - 1)(2x - 9)
Show solution
Solution
The expression 4x^2 - 12x + 9 is also a perfect square trinomial. It factors to (2x - 3)(2x - 3) or (2x - 3)^2.
Correct Answer:
A
— (2x - 3)(2x - 3)
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Q. Factor the expression 4x^2 - 16.
A.
4(x - 4)(x + 4)
B.
4(x^2 - 4)
C.
(2x - 4)(2x + 4)
D.
4(x - 2)(x + 2)
Show solution
Solution
First, factor out the greatest common factor, which is 4. This gives us 4(x^2 - 4). Then, x^2 - 4 can be factored as (x - 2)(x + 2). So, the complete factorization is 4(x - 2)(x + 2).
Correct Answer:
A
— 4(x - 4)(x + 4)
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Q. Factor the expression x^2 + 4x - 12.
A.
(x + 6)(x - 2)
B.
(x - 6)(x + 2)
C.
(x + 12)(x - 1)
D.
(x - 4)(x + 3)
Show solution
Solution
We need two numbers that multiply to -12 and add to 4. The numbers 6 and -2 work. Thus, the factored form is (x + 6)(x - 2).
Correct Answer:
A
— (x + 6)(x - 2)
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Q. Factor the expression 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
The expression x^2 - 4 is a difference of squares. It factors to (x - 2)(x + 2).
Correct Answer:
A
— (x - 2)(x + 2)
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Q. Factor the expression: 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, we can 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. Factor the expression: 4x^2 - 25.
A.
(2x - 5)(2x + 5)
B.
(4x - 5)(4x + 5)
C.
(2x - 25)(2x + 25)
D.
(4x - 5)(4x + 5)
Show solution
Solution
The expression 4x^2 - 25 is a difference of squares. It can be factored as (2x - 5)(2x + 5).
Correct Answer:
A
— (2x - 5)(2x + 5)
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Q. Factor the expression: x^2 + 3x - 10
A.
(x + 5)(x - 2)
B.
(x - 5)(x + 2)
C.
(x + 10)(x - 1)
D.
(x - 10)(x + 1)
Show solution
Solution
We need two numbers that multiply to -10 and add to 3. The numbers 5 and -2 work. Thus, the factorization is (x + 5)(x - 2).
Correct Answer:
A
— (x + 5)(x - 2)
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Q. Factor the expression: x^2 + 6x + 9.
A.
(x + 3)(x + 3)
B.
(x + 2)(x + 4)
C.
(x - 3)(x - 3)
D.
(x + 1)(x + 9)
Show solution
Solution
The expression x^2 + 6x + 9 is a perfect square trinomial. It factors to (x + 3)(x + 3) or (x + 3)^2.
Correct Answer:
A
— (x + 3)(x + 3)
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Q. Factor the expression: x^2 + 7x + 10.
A.
(x + 2)(x + 5)
B.
(x - 2)(x - 5)
C.
(x + 1)(x + 10)
D.
(x - 1)(x - 10)
Show solution
Solution
To factor x^2 + 7x + 10, we need two numbers that multiply to 10 and add to 7. The numbers 2 and 5 work. Thus, the factorization is (x + 2)(x + 5).
Correct Answer:
A
— (x + 2)(x + 5)
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Q. Factor 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 look for two numbers that multiply to 6 and add to -5. The numbers -2 and -3 work. Thus, the factorization is (x - 2)(x - 3).
Correct Answer:
A
— (x - 2)(x - 3)
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Q. Factor the expression: x^2 - 9.
A.
(x - 3)(x + 3)
B.
(x - 4)(x + 4)
C.
(x - 1)(x + 1)
D.
(x + 3)(x + 3)
Show solution
Solution
The expression x^2 - 9 is a difference of squares. It can be factored as (x - 3)(x + 3).
Correct Answer:
A
— (x - 3)(x + 3)
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Q. Factor the polynomial 2x^2 - 8.
A.
2(x - 4)(x + 4)
B.
2(x - 2)(x + 2)
C.
2(x - 4)
D.
x(2x - 8)
Show solution
Solution
Factor out the common term 2: 2(x^2 - 4) = 2(x - 2)(x + 2).
Correct Answer:
A
— 2(x - 4)(x + 4)
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Q. Factor the polynomial 3x^2 - 12.
A.
3(x - 4)(x + 4)
B.
3(x - 2)(x + 2)
C.
3(x + 4)(x + 4)
D.
3(x - 6)(x + 2)
Show solution
Solution
First, factor out the greatest common factor, which is 3. This gives us 3(x^2 - 4). Then, factor x^2 - 4 as a difference of squares: 3(x - 2)(x + 2).
Correct Answer:
A
— 3(x - 4)(x + 4)
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Q. Factor the polynomial 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, we look for two numbers that multiply to 10 and add to 7. The numbers are 5 and 2. Thus, the factorization is (x + 5)(x + 2).
Correct Answer:
A
— (x + 5)(x + 2)
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Q. Factor the polynomial 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 look for two numbers that multiply to 6 and add to -5. The numbers -2 and -3 work. Thus, the factorization is (x - 2)(x - 3).
Correct Answer:
A
— (x - 2)(x - 3)
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Q. Factor the polynomial x^2 - 9.
A.
(x - 3)(x + 3)
B.
(x - 9)(x + 1)
C.
(x + 3)(x + 3)
D.
(x - 1)(x + 9)
Show solution
Solution
The expression x^2 - 9 is a difference of squares, which factors to (x - 3)(x + 3).
Correct Answer:
A
— (x - 3)(x + 3)
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Q. Factor the polynomial x^3 - 3x^2 - 4x.
A.
x(x^2 - 3x - 4)
B.
x(x + 4)(x - 1)
C.
x^2(x - 3) - 4
D.
x(x^2 + 4)
Show solution
Solution
First, factor out the common term x: x(x^2 - 3x - 4). Now, factor the quadratic x^2 - 3x - 4 to get x(x - 4)(x + 1).
Correct Answer:
A
— x(x^2 - 3x - 4)
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Q. Factor the polynomial: 3x^2 + 12x
A.
3x(x + 4)
B.
3(x^2 + 4)
C.
x(3x + 12)
D.
3x^2 + 4x
Show solution
Solution
Factor out the common term 3x: 3x(x + 4).
Correct Answer:
A
— 3x(x + 4)
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Q. Factor the quadratic expression x^2 + 7x + 10.
A.
(x + 5)(x + 2)
B.
(x - 5)(x - 2)
C.
(x + 10)(x - 1)
D.
(x - 7)(x - 10)
Show solution
Solution
We need two numbers that multiply to 10 and add to 7. The numbers 5 and 2 work. Thus, the factored form is (x + 5)(x + 2).
Correct Answer:
A
— (x + 5)(x + 2)
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Q. Factor the quadratic 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 factorization is (x - 2)(x - 3).
Correct Answer:
A
— (x - 2)(x - 3)
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Q. Find the coordinates of the point that divides the line segment joining (1, 2) and (4, 6) in the ratio 1:2.
A.
(2, 3)
B.
(3, 4)
C.
(1.5, 3.5)
D.
(2.5, 4)
Show solution
Solution
Using the section formula: P = ((1*4 + 2*1)/(1+2), (1*6 + 2*2)/(1+2)) = (3, 4).
Correct Answer:
B
— (3, 4)
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Q. Find the coordinates of the point that divides the line segment joining (3, 4) and (9, 10) in the ratio 1:1.
A.
(6, 7)
B.
(5, 6)
C.
(4, 5)
D.
(7, 8)
Show solution
Solution
Using the section formula: P = ((1*9 + 1*3)/(1+1), (1*10 + 1*4)/(1+1)) = (6, 7).
Correct Answer:
A
— (6, 7)
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Q. Find the coordinates of the point that divides the segment joining (1, 2) and (3, 4) in the ratio 1:3.
A.
(2, 3)
B.
(1.5, 2.5)
C.
(2.5, 3.5)
D.
(3, 4)
Show solution
Solution
Using the section formula: (mx2 + nx1)/(m+n), (my2 + ny1)/(m+n) = (1*3 + 3*1)/(1+3), (1*4 + 3*2)/(1+3) = (3 + 3)/4, (4 + 6)/4 = (6/4, 10/4) = (1.5, 2.5).
Correct Answer:
C
— (2.5, 3.5)
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Q. Find the coordinates of the point that divides the segment joining (1, 2) and (3, 4) in the ratio 2:1.
A.
(2, 3)
B.
(2.67, 3.33)
C.
(2.5, 3.5)
D.
(3, 4)
Show solution
Solution
Using the section formula: P(x, y) = ((2*3 + 1*1)/(2+1), (2*4 + 1*2)/(2+1)) = (2.67, 3.33).
Correct Answer:
B
— (2.67, 3.33)
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Q. Find the coordinates of the point that divides the segment joining (1, 2) and (3, 8) in the ratio 1:3.
A.
(2, 6)
B.
(2.5, 5)
C.
(2, 5)
D.
(3, 5)
Show solution
Solution
Using the section formula: (mx2 + nx1)/(m+n), (my2 + ny1)/(m+n) where m=1, n=3. Coordinates = ((1*3 + 3*1)/(1+3), (1*8 + 3*2)/(1+3)) = (2, 6).
Correct Answer:
A
— (2, 6)
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Q. Find the coordinates of the point that divides the segment joining (1, 2) and (5, 6) in the ratio 2:1.
A.
(3, 4)
B.
(4, 5)
C.
(2, 3)
D.
(5, 5)
Show solution
Solution
Using the section formula: P = ((2*5 + 1*1)/(2+1), (2*6 + 1*2)/(2+1)) = (3, 4).
Correct Answer:
A
— (3, 4)
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