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. Find the value of x in the equation x^2 - 9 = 0.

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

Solution

Factoring gives (x - 3)(x + 3) = 0. Thus, the solutions are x = 3 and x = -3.

Correct Answer: A — 3

Q. Find the value of x in the inequality 3x - 5 < 4.

A. x < 3
B. x > 3
C. x < 1
D. x > 1

Solution

Add 5 to both sides: 3x < 9. Divide by 3: x < 3.

Correct Answer: A — x < 3

Q. Find the x-intercepts of the equation 3x^2 + 12x + 12 = 0.

A. x = -2
B. x = -4
C. x = 0
D. x = -6

Solution

Using the quadratic formula: a = 3, b = 12, c = 12. Discriminant = 12² - 4(3)(12) = 144 - 144 = 0. x = -b / 2a = -12 / 6 = -2.

Correct Answer: B — x = -4

Q. Find 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

Solution

Set y = 0: 0 = x^2 - 4. This factors to (x - 2)(x + 2) = 0, giving x = 2 and x = -2.

Correct Answer: A — x = 2, -2

Q. Find x if 2(x + 3) = 14.

A. x = 4
B. x = 5
C. x = 6
D. x = 7

Solution

Step 1: Divide both sides by 2: x + 3 = 7. Step 2: Subtract 3 from both sides: x = 4.

Correct Answer: A — x = 4

Q. Find x if 2(x + 3) = 16.

A. x = 4
B. x = 5
C. x = 6
D. x = 7

Solution

Step 1: Divide both sides by 2: x + 3 = 8. Step 2: Subtract 3 from both sides: x = 5.

Correct Answer: A — x = 4

Q. Find x if 2(x - 3) = 10.

A. x = 5
B. x = 8
C. x = 10
D. x = 13

Solution

Step 1: Divide both sides by 2: x - 3 = 5. Step 2: Add 3 to both sides: x = 8.

Correct Answer: B — x = 8

Q. Find x if 7x + 2 = 23.

A. x = 2
B. x = 3
C. x = 4
D. x = 5

Solution

Step 1: Subtract 2 from both sides: 7x = 21. Step 2: Divide both sides by 7: x = 3.

Correct Answer: C — x = 4

Q. Find x in the equation 2(x + 3) = 16.

A. x = 4
B. x = 5
C. x = 6
D. x = 7

Solution

Step 1: Divide both sides by 2: x + 3 = 8. Step 2: Subtract 3 from both sides: x = 5.

Correct Answer: C — x = 6

Q. Find x in the equation 3(x - 2) = 12.

A. x = 4
B. x = 6
C. x = 8
D. x = 10

Solution

Step 1: Divide both sides by 3: x - 2 = 4. Step 2: Add 2 to both sides: x = 6.

Correct Answer: B — x = 6

Q. Find x in the equation 4(x - 2) = 12.

A. x = 2
B. x = 4
C. x = 6
D. x = 8

Solution

Step 1: Divide both sides by 4: x - 2 = 3. Step 2: Add 2 to both sides: x = 5.

Correct Answer: C — x = 6

Q. For the data set 1, 2, 3, 4, 5, what is the median?

A. 2
B. 3
C. 4
D. 5

Solution

Median is the middle value. The sorted data is 1, 2, 3, 4, 5. Median = 3.

Correct Answer: B — 3

Q. For the data set 10, 20, 30, 40, 50, what is the median?

A. 20
B. 30
C. 25
D. 40

Solution

Median = (30 + 40) / 2 = 35, since there are 5 numbers.

Correct Answer: B — 30

Q. For the data set 12, 15, 12, 18, 20, what is the median?

A. 15
B. 16
C. 17
D. 18

Solution

Median = 15, as the sorted data is 12, 12, 15, 18, 20.

Correct Answer: A — 15

Q. For the data set 3, 7, 8, 12, what is the median?

A. 7
B. 8
C. 10
D. 12

Solution

Median is the average of 7 and 8, which is 7.5.

Correct Answer: B — 8

Q. For the dataset: 12, 15, 20, 22, 25, what is the median?

A. 15
B. 20
C. 22
D. 25

Solution

To find the median, arrange the numbers: 12, 15, 20, 22, 25. The median is the middle value, which is 20.

Correct Answer: B — 20

Q. For the dataset: 4, 8, 6, 5, 3, what is the median?

A. 4
B. 5
C. 6
D. 8

Solution

First, arrange the numbers in ascending order: 3, 4, 5, 6, 8. The median is the middle value, which is 5.

Correct Answer: B — 5

Q. For the following set of numbers: 5, 7, 9, 11, 13, what is the median?

A. 7
B. 9
C. 11
D. 13

Solution

The median is the middle value, which is 9.

Correct Answer: B — 9

Q. For the function y = sin(3x), what is the period?

A. π
B. 2π
C. 3π
D. 6π

Solution

The period is calculated as 2π divided by the coefficient of x, which is 3, giving a period of 2π/3.

Correct Answer: A — π

Q. For the numbers: 3, 3, 4, 5, 5, 5, 6, what is the mean?

A. 4
B. 5
C. 5.5
D. 6

Solution

Mean = (3 + 3 + 4 + 5 + 5 + 5 + 6) / 7 = 31 / 7 ≈ 4.43.

Correct Answer: B — 5

Q. From a point 25 meters away from the base of a building, the angle of elevation to the top of the building is 30 degrees. What is the height of the building?

A. 25/√3 meters
B. 15 meters
C. 20 meters
D. 10 meters

Solution

Using tan(30) = height / 25, height = 25 * tan(30) = 25 * (1/√3) = 25/√3 meters.

Correct Answer: A — 25/√3 meters

Q. From a point 30 meters away from the base of a tower, the angle of elevation to the top of the tower is 45 degrees. What is the height of the tower?

A. 30 meters
B. 45 meters
C. 60 meters
D. 15 meters

Solution

Using tan(45) = height / 30, we have height = 30 * tan(45) = 30 * 1 = 30 meters.

Correct Answer: A — 30 meters

Q. From a point on the ground, the angle of elevation to the top of a 15-meter tall building is 45 degrees. How far is the point from the base of the building?

A. 15 meters
B. 30 meters
C. 10 meters
D. 20 meters

Solution

Using tan(45°) = height/distance, distance = height/tan(45°) = 15/1 = 15 meters.

Correct Answer: A — 15 meters

Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the point is 50 meters away from the base of the hill, what is the height of the hill?

A. 50 meters
B. 25 meters
C. 70 meters
D. 45 meters

Solution

Using tan(45°) = height/50, height = 50 * tan(45°) = 50 meters.

Correct Answer: A — 50 meters

Q. Given the following set of numbers: 3, 7, 7, 2, 5, what is the mode?

A. 2
B. 3
C. 5
D. 7

Solution

The mode is the number that appears most frequently. Here, 7 appears twice, which is more than any other number.

Correct Answer: D — 7

Q. Given the numbers: 5, 7, 7, 8, 10, what is the mode?

A. 5
B. 7
C. 8
D. 10

Solution

The mode is the number that appears most frequently. Here, 7 appears twice.

Correct Answer: B — 7

Q. Given two parallel lines and a transversal, if one of the alternate exterior angles is 120 degrees, what is the measure of the other alternate exterior angle?

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

Solution

Alternate exterior angles are equal when two parallel lines are cut by a transversal. Therefore, the other alternate exterior angle also measures 120 degrees.

Correct Answer: B — 120 degrees

Q. Given two parallel lines and a transversal, if one of the interior angles measures 40 degrees, what is the measure of the corresponding angle?

A. 40 degrees
B. 140 degrees
C. 180 degrees
D. 90 degrees

Solution

Corresponding angles are equal when two parallel lines are cut by a transversal. Therefore, the corresponding angle also measures 40 degrees.

Correct Answer: A — 40 degrees

Q. Given two parallel lines and a transversal, if one of the same-side interior angles is 40 degrees, what is the measure of the other same-side interior angle?

A. 40 degrees
B. 140 degrees
C. 180 degrees
D. 90 degrees

Solution

Same-side interior angles are supplementary. Therefore, if one angle is 40 degrees, the other must be 180 - 40 = 140 degrees.

Correct Answer: B — 140 degrees

Q. Given two parallel lines cut by a transversal, if one of the alternate exterior angles is 120 degrees, what is the measure of the other alternate exterior angle?

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

Solution

Alternate exterior angles are equal when two parallel lines are cut by a transversal. Thus, the other alternate exterior angle also measures 120 degrees.

Correct Answer: B — 120 degrees

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