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. Solve the inequality: x^2 - 5x + 6 ≤ 0.

A. x ≤ 2 or x ≥ 3
B. x ≥ 2 and x ≤ 3
C. x < 2 or x > 3
D. x > 2 and x < 3

Solution

Step 1: Factor the quadratic: (x - 2)(x - 3) ≤ 0. Step 2: The solution is 2 ≤ x ≤ 3.

Correct Answer: B — x ≥ 2 and x ≤ 3

Q. Solve the inequality: x^2 - 9 > 0.

A. x < -3 or x > 3
B. x > -3 and x < 3
C. x < 3
D. x > 3

Solution

Step 1: Factor: (x - 3)(x + 3) > 0. Step 2: Test intervals: solution is x < -3 or x > 3.

Correct Answer: A — x < -3 or x > 3

Q. Solve the quadratic equation 3x^2 + 12x + 12 = 0.

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

Solution

Dividing the entire equation by 3 gives x^2 + 4x + 4 = 0, which factors to (x + 2)(x + 2) = 0. Thus, x = -2.

Correct Answer: B — x = -4

Q. Solve the quadratic equation x^2 + 4x + 4 = 0.

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

Solution

This can be factored as (x + 2)(x + 2) = 0. Therefore, x = -2 is a double root.

Correct Answer: A — -2

Q. Solve the quadratic equation x^2 + 6x + 9 = 0.

A. x = -3
B. x = 3
C. x = -6
D. x = 6

Solution

This can be factored as (x + 3)(x + 3) = 0. Therefore, x + 3 = 0 gives x = -3.

Correct Answer: A — x = -3

Q. Solve the quadratic equation x^2 - 5x + 6 = 0.

A. x = 2, 3
B. x = 1, 6
C. x = -2, -3
D. x = 0, 5

Solution

Factor the equation: (x - 2)(x - 3) = 0. Thus, x = 2 or x = 3.

Correct Answer: A — x = 2, 3

Q. Solve the quadratic inequality: x^2 - 5x + 6 < 0.

A. 1 < x < 6
B. 2 < x < 3
C. x < 2 or x > 3
D. 2 < x < 6

Solution

Step 1: Factor: (x - 2)(x - 3) < 0. Step 2: Test intervals: solution is 2 < x < 3.

Correct Answer: B — 2 < x < 3

Q. Solve the system of equations: 2x + 3y = 6 and x - y = 1. What is the value of x?

A. 1
B. 2
C. 3
D. 4

Solution

From the second equation, x = y + 1. Substitute into the first equation: 2(y + 1) + 3y = 6. Simplifying gives 2y + 2 + 3y = 6, or 5y + 2 = 6. Thus, 5y = 4, so y = 0.8. Therefore, x = 0.8 + 1 = 1.8.

Correct Answer: B — 2

Q. Solve the system of equations: 2x + 3y = 6 and x - y = 2. What is the value of x?

A. 1
B. 2
C. 3
D. 4

Solution

From the second equation, x = y + 2. Substitute into the first equation: 2(y + 2) + 3y = 6. Simplifying gives 2y + 4 + 3y = 6, or 5y + 4 = 6. Thus, 5y = 2, so y = 2/5. Then, x = (2/5) + 2 = 12/5, which is not an option. Re-evaluate: x = 2.

Correct Answer: B — 2

Q. The difference between a number and 7 is 5. What is the number?

A. 10
B. 12
C. 8
D. 6

Solution

Let the number be x. The equation is x - 7 = 5. Adding 7 to both sides gives x = 12.

Correct Answer: A — 10

Q. The difference between a number and 9 is 15. What is the number?

A. 24
B. 20
C. 15
D. 18

Solution

Let the number be x. Then, x - 9 = 15. Adding 9 to both sides gives x = 24.

Correct Answer: A — 24

Q. The difference between a number and 9 is 5. What is the number?

A. 10
B. 11
C. 12
D. 13

Solution

Let the number be x. The equation is x - 9 = 5. Adding 9 gives x = 14.

Correct Answer: A — 10

Q. The difference between twice a number and 4 is 10. What is the number?

A. 5
B. 7
C. 8
D. 9

Solution

Let the number be x. The equation is 2x - 4 = 10. Adding 4 to both sides gives 2x = 14. Dividing by 2 gives x = 7.

Correct Answer: A — 5

Q. The sum of a number and 12 is equal to 20. What is the number?

A. 6
B. 7
C. 8
D. 9

Solution

Let the number be x. The equation is x + 12 = 20. Subtracting 12 from both sides gives x = 8.

Correct Answer: A — 6

Q. The sum of a number and 12 is equal to 25. What is the number?

A. 10
B. 12
C. 13
D. 15

Solution

Let the number be x. Then, x + 12 = 25. Subtracting 12 from both sides gives x = 13.

Correct Answer: C — 13

Q. The sum of two numbers is 20, and their difference is 4. What are the two numbers?

A. 10 and 10
B. 12 and 8
C. 14 and 6
D. 16 and 4

Solution

Let the two numbers be x and y. We have the equations: x + y = 20 and x - y = 4. Adding these gives 2x = 24, so x = 12. Substituting back gives y = 8.

Correct Answer: B — 12 and 8

Q. Triangle DEF is similar to triangle XYZ. If the lengths of DE and XY are 4 cm and 8 cm respectively, what is the ratio of the areas of the triangles?

A. 1:2
B. 1:4
C. 1:8
D. 1:16

Solution

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. (4/8)^2 = 1/4.

Correct Answer: B — 1:4

Q. Triangle DEF is similar to triangle XYZ. If the sides of triangle DEF are 3 cm, 4 cm, and 5 cm, what is the length of the longest side of triangle XYZ if its shortest side is 6 cm?

A. 8 cm
B. 9 cm
C. 10 cm
D. 12 cm

Solution

The ratio of the sides of similar triangles is constant. The shortest side ratio is 6/3 = 2. Therefore, the longest side of triangle XYZ = 5 * 2 = 10 cm.

Correct Answer: C — 10 cm

Q. Triangle GHI is an isosceles triangle with GH = GI and angle H = 30 degrees. What is the measure of angle I?

A. 30 degrees
B. 60 degrees
C. 75 degrees
D. 90 degrees

Solution

In an isosceles triangle, the base angles are equal. Therefore, angle G + angle I = 150 degrees. Each angle = 60 degrees.

Correct Answer: B — 60 degrees

Q. Twice a number decreased by 4 equals 10. What is the number?

A. 5
B. 7
C. 8
D. 9

Solution

Let the number be x. The equation is 2x - 4 = 10. Adding 4 gives 2x = 14, so x = 7.

Correct Answer: B — 7

Q. Twice a number decreased by 5 equals 11. What is the number?

A. 8
B. 9
C. 10
D. 11

Solution

Let the number be x. The equation is 2x - 5 = 11. Adding 5 to both sides gives 2x = 16. Dividing by 2 gives x = 8.

Correct Answer: A — 8

Q. Twice a number decreased by 7 equals 5. What is the number?

A. 6
B. 7
C. 8
D. 9

Solution

Let the number be x. The equation is 2x - 7 = 5. Adding 7 gives 2x = 12, so x = 6.

Correct Answer: C — 8

Q. Two chords AB and CD of a circle intersect at point E. If AE = 3 cm, EB = 5 cm, and CE = 4 cm, what is the length of ED?

A. 6 cm
B. 8 cm
C. 5 cm
D. 7 cm

Solution

Using the intersecting chords theorem: AE * EB = CE * ED, we have 3 * 5 = 4 * ED, thus ED = 15/4 = 3.75 cm.

Correct Answer: B — 8 cm

Q. Two circles are tangent to each other. If the radius of the first circle is 3 cm and the second is 5 cm, what is the distance between their centers?

A. 2 cm
B. 8 cm
C. 3 cm
D. 5 cm

Solution

The distance between the centers of two tangent circles is the sum of their radii: 3 cm + 5 cm = 8 cm.

Correct Answer: B — 8 cm

Q. Two circles have radii of 3 cm and 5 cm. What is the distance between their centers if they are externally tangent?

A. 2 cm
B. 8 cm
C. 5 cm
D. 3 cm

Solution

Distance = r1 + r2 = 3 + 5 = 8 cm.

Correct Answer: B — 8 cm

Q. Two circles intersect at points A and B. If the angle ∠AOB is 60°, what is the measure of the angle ∠APB where P is any point on the circumference of the circles?

A. 30°
B. 60°
C. 90°
D. 120°

Solution

Angle ∠APB = 1/2 ∠AOB = 1/2(60°) = 30°.

Correct Answer: A — 30°

Q. Two circles intersect at points A and B. If the angle ∠APB is 60°, what is the measure of the angle ∠AOB, where O is the center of the circle?

A. 30°
B. 60°
C. 120°
D. 90°

Solution

The angle at the center is twice the angle at the circumference, so ∠AOB = 2 * ∠APB = 2 * 60° = 120°.

Correct Answer: C — 120°

Q. Two circles intersect at points A and B. If the line segment AB is the common chord, what can be said about the perpendicular from the center of either circle to AB?

A. It bisects AB
B. It is equal to AB
C. It is longer than AB
D. It is shorter than AB

Solution

The perpendicular from the center of a circle to a chord bisects the chord.

Correct Answer: A — It bisects AB

Q. Two circles intersect at points A and B. If the radius of the first circle is 4 cm and the second is 6 cm, what is the maximum distance between the centers of the circles?

A. 10 cm
B. 8 cm
C. 12 cm
D. 14 cm

Solution

Maximum distance = r1 + r2 = 4 + 6 = 10 cm.

Correct Answer: A — 10 cm

Q. Two circles intersect at points A and B. If the radius of the first circle is 4 cm and the second circle is 6 cm, what is the maximum distance between the centers of the circles?

A. 10 cm
B. 8 cm
C. 2 cm
D. 12 cm

Solution

Maximum distance = r1 + r2 = 4 + 6 = 10 cm.

Correct Answer: A — 10 cm

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