Mathematics (School)

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Mathematics (School)

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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!

Algebra (Secondary) Arithmetic (Primary) Geometry Statistics & Probability Trigonometry

Q. If angle A and angle B are alternate exterior angles formed by two parallel lines cut by a transversal, and angle A measures 120 degrees, what is the measure of angle B?

A. 60 degrees
B. 120 degrees
C. 180 degrees
D. 90 degrees

Solution

Alternate exterior angles are equal, so angle B also measures 120 degrees.

Correct Answer: B — 120 degrees

Q. If angle A and angle B are alternate exterior angles formed by two parallel lines and a transversal, and angle A measures 45 degrees, what is the measure of angle B?

A. 45 degrees
B. 135 degrees
C. 90 degrees
D. 180 degrees

Solution

Alternate exterior angles are equal, so angle B = 45 degrees.

Correct Answer: A — 45 degrees

Q. If angle A and angle B are alternate interior angles formed by a transversal intersecting two parallel lines, and angle A measures 75 degrees, what is the measure of angle B?

A. 75 degrees
B. 105 degrees
C. 90 degrees
D. 180 degrees

Solution

Alternate interior angles are equal, so angle B also measures 75 degrees.

Correct Answer: A — 75 degrees

Q. If angle A and angle B are corresponding angles formed by a transversal intersecting two parallel lines, what can be said about their measures?

A. Angle A is greater than angle B.
B. Angle A is less than angle B.
C. Angle A is equal to angle B.
D. Angle A and angle B are supplementary.

Solution

Corresponding angles are equal when two parallel lines are cut by a transversal.

Correct Answer: C — Angle A is equal to angle B.

Q. If angle A and angle B are same-side interior angles formed by a transversal cutting two parallel lines, what is their relationship?

A. They are equal.
B. They are complementary.
C. They are supplementary.
D. They are adjacent.

Solution

Same-side interior angles are supplementary when two parallel lines are cut by a transversal.

Correct Answer: C — They are supplementary.

Q. If angle A and angle B are same-side interior angles formed by a transversal cutting two parallel lines, and angle A measures 75 degrees, what is the measure of angle B?

A. 75 degrees
B. 105 degrees
C. 90 degrees
D. 180 degrees

Solution

Same-side interior angles are supplementary, so angle B = 180 - 75 = 105 degrees.

Correct Answer: B — 105 degrees

Q. If angle A and angle B are same-side interior angles formed by a transversal intersecting two parallel lines, and angle A measures 65 degrees, what is the measure of angle B?

A. 115 degrees
B. 65 degrees
C. 180 degrees
D. 90 degrees

Solution

Same-side interior angles are supplementary. Therefore, angle B = 180 - 65 = 115 degrees.

Correct Answer: A — 115 degrees

Q. If angle C is 30 degrees and is an interior angle on the same side of the transversal as angle D, what is the measure of angle D if the lines are parallel?

A. 30 degrees
B. 150 degrees
C. 90 degrees
D. 180 degrees

Solution

Since angle C and angle D are interior angles on the same side of the transversal, they are supplementary. Therefore, angle D = 180 - 30 = 150 degrees.

Correct Answer: B — 150 degrees

Q. If angle C is 30 degrees and is one of the corresponding angles formed by a transversal intersecting two parallel lines, what is the measure of the other corresponding angle?

A. 30 degrees
B. 150 degrees
C. 90 degrees
D. 60 degrees

Solution

Corresponding angles are equal when a transversal intersects two parallel lines. Therefore, the other corresponding angle also measures 30 degrees.

Correct Answer: A — 30 degrees

Q. If angle C is a corresponding angle to angle D and angle D measures 85 degrees, what is the measure of angle C?

A. 85 degrees
B. 95 degrees
C. 75 degrees
D. 180 degrees

Solution

Corresponding angles are equal, so angle C also measures 85 degrees.

Correct Answer: A — 85 degrees

Q. If angle X and angle Y are complementary and angle X measures 35°, what is the measure of angle Y?

A. 45°
B. 55°
C. 65°
D. 75°

Solution

Complementary angles sum to 90°. Therefore, angle Y = 90° - 35° = 55°.

Correct Answer: B — 55°

Q. If cos(θ) = 0.6, what is sin(θ) using the Pythagorean identity?

A. 0.8
B. 0.6
C. 0.4
D. 0.2

Solution

Using sin²θ + cos²θ = 1, sin²θ = 1 - 0.6² = 0.64, so sin(θ) = 0.8.

Correct Answer: A — 0.8

Q. If cos(θ) = 0.8, what is the value of θ in degrees (to the nearest degree)?

A. 36
B. 45
C. 60
D. 64

Solution

θ = arccos(0.8) ≈ 36.87°, rounded to 37°

Correct Answer: D — 64

Q. If f(x) = 2x^2 - 8x + 6, what is f(3)?

A. 0
B. 2
C. 6
D. 12

Solution

Substituting x = 3 into the function: f(3) = 2(3)^2 - 8(3) + 6 = 18 - 24 + 6 = 0.

Correct Answer: B — 2

Q. If f(x) = 3x^2 - 12x + 9, what is f(2)?

A. 0
B. 3
C. 9
D. 6

Solution

Substitute x = 2 into the function: f(2) = 3(2)^2 - 12(2) + 9 = 12 - 24 + 9 = -3.

Correct Answer: A — 0

Q. If f(x) = x^2 - 4, what are the roots of the polynomial?

A. -2 and 2
B. 0 and 4
C. 1 and -1
D. 2 and 4

Solution

The polynomial can be factored as (x - 2)(x + 2). Setting each factor to zero gives us x - 2 = 0 or x + 2 = 0, so the roots are x = -2 and x = 2.

Correct Answer: A — -2 and 2

Q. If f(x) = x^2 - 4x + 4, what is f(2)?

A. 0
B. 1
C. 2
D. 4

Solution

Substituting x = 2 into the function gives f(2) = 2^2 - 4(2) + 4 = 0.

Correct Answer: A — 0

Q. If f(x) = x^2 - 6x + 8, what are the roots of f(x)?

A. 2 and 4
B. 1 and 8
C. 3 and 5
D. 0 and 6

Solution

Factoring gives f(x) = (x - 2)(x - 4). Setting each factor to zero gives the roots x = 2 and x = 4.

Correct Answer: A — 2 and 4

Q. If f(x) = x^2 - 6x + 9, what is f(3)?

A. 0
B. 3
C. 6
D. 9

Solution

Substituting x = 3 into the function: f(3) = 3^2 - 6(3) + 9 = 9 - 18 + 9 = 0.

Correct Answer: A — 0

Q. If f(x) = x^2 - 9, what are the roots of the polynomial?

A. -3 and 3
B. 0 and 9
C. 3 and 9
D. 1 and -1

Solution

We can factor the polynomial as f(x) = (x - 3)(x + 3). Setting each factor to zero gives us the roots x = -3 and x = 3.

Correct Answer: A — -3 and 3

Q. If line A has a slope of 4 and line B is perpendicular to line A, what is the slope of line B?

A. -1/4
B. 1/4
C. -4
D. 4

Solution

The slopes of perpendicular lines are negative reciprocals. The negative reciprocal of 4 is -1/4.

Correct Answer: A — -1/4

Q. If one angle of a triangle is 50 degrees and another is 60 degrees, what is the measure of the third angle?

A. 70 degrees
B. 80 degrees
C. 90 degrees
D. 100 degrees

Solution

The third angle can be found by subtracting the sum of the other two angles from 180 degrees: 180 - (50 + 60) = 70 degrees.

Correct Answer: A — 70 degrees

Q. If one angle of a triangle is 90 degrees and the other two angles are equal, what are the measures of the other two angles?

A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 75 degrees

Solution

In a triangle, the sum of the angles is 180 degrees. If one angle is 90 degrees, the remaining two angles must sum to 90 degrees. Since they are equal, each must be 45 degrees.

Correct Answer: B — 45 degrees

Q. If one root of the equation x^2 + px + 6 = 0 is 2, what is the value of p?

A. -8
B. -4
C. 4
D. 8

Solution

If one root is 2, then the other root can be found using the product of the roots: 2 * r = 6, so r = 3. The sum of the roots is 2 + 3 = -p, thus p = -5.

Correct Answer: B — -4

Q. If one root of the equation x^2 + px + q = 0 is 3, what is the value of p if the other root is 1?

A. -4
B. -6
C. 4
D. 6

Solution

Using the sum of the roots, p = -(3 + 1) = -4. The product of the roots gives q = 3 * 1 = 3.

Correct Answer: B — -6

Q. If point A is at (1, 2) and point B is at (4, 6), what is the section formula for point P that divides AB in the ratio 1:2?

A. (2, 3)
B. (3, 4)
C. (1.5, 2.5)
D. (2.5, 3.5)

Solution

Using the section formula: P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) = ((1*4 + 2*1)/(1+2), (1*6 + 2*2)/(1+2)) = (3, 4).

Correct Answer: B — (3, 4)

Q. If point A is at (1, 2) and point B is at (4, 6), what is the section formula for point C that divides AB in the ratio 1:2?

A. (2, 3)
B. (3, 4)
C. (2.5, 4)
D. (3.5, 5)

Solution

Using the section formula: C = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) where m=1, n=2. C = ((1*4 + 2*1)/(1+2), (1*6 + 2*2)/(1+2)) = (3, 4).

Correct Answer: B — (3, 4)

Q. If point A is at (1, 2) and point B is at (4, 6), what is the section formula ratio if point C divides AB in the ratio 1:2?

A. (2, 4)
B. (3, 5)
C. (2.5, 4)
D. (3, 4)

Solution

Using the section formula: C = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) where m=1, n=2. C = ((1*4 + 2*1)/(1+2), (1*6 + 2*2)/(1+2)) = (2.67, 4).

Correct Answer: B — (3, 5)

Q. If point A is at (1, 2) and point B is at (4, 6), what is the section formula to find point C that divides AB in the ratio 1:2?

A. (2, 4)
B. (3, 5)
C. (2.5, 4)
D. (3.5, 5)

Solution

Using the section formula: C = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) = ((1*4 + 2*1)/(1+2), (1*6 + 2*2)/(1+2)) = (3, 5).

Correct Answer: B — (3, 5)

Q. If point A is at (2, 3) and point B is at (8, 7), what is the midpoint M of segment AB?

A. (5, 5)
B. (4, 5)
C. (6, 5)
D. (5, 4)

Solution

Midpoint M = ((x1 + x2)/2, (y1 + y2)/2) = ((2 + 8)/2, (3 + 7)/2) = (5, 5).

Correct Answer: A — (5, 5)

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