Class 9 practice
Class 9 maths questions.
Maths questions for Class 9, at the level of students aged 12–14, each with its answer and a short explanation. Try each one before opening the answer.
Ananya scored 85% in a test of 400 marks. In a second test, she scored 70%. If her combined score across both tests was 76%, what was the maximum possible marks of the second test?
Level 4 of 5Show the answer
Answer: 600
Let the second test total be M. Then 340 + 0.70M = 0.76(400 + M), simplifying to 340 + 0.70M = 304 + 0.76M. Thus, 0.06M = 36, so M = 600 marks.
A metallic sphere of radius 3 cm is melted and recast into small cones of radius 1 cm and height 3 cm. How many such cones can be formed?
Level 4 of 5Show the answer
Answer: 36
Volume of sphere = (4/3) * pi * 3^3 = 36 * pi. Volume of one cone = (1/3) * pi * 1^2 * 3 = pi. Number of cones = (36 * pi) / pi = 36.
The average score of 24 students in a math test is 56. When the teacher's score is included, the average increases by 1. What is the teacher's score?
Level 4 of 5Show the answer
Answer: 81
Total score for 25 people = 25 * 57 = 1425. Total score for 24 students = 24 * 56 = 1344. Teacher's score = 1425 - 1344 = 81.
Each interior angle of a regular polygon measures 140 degrees. How many sides does this polygon have?
Level 4 of 5Show the answer
Answer: 9
Each exterior angle equals 180 - 140 = 40 degrees. Since the sum of exterior angles is always 360 degrees, the number of sides is 360 / 40 = 9.
A bag contains 5 green marbles, 7 blue marbles, and 8 yellow marbles. What is the probability of drawing a marble that is either green or blue?
Level 4 of 5Show the answer
Answer: 3/5
The total number of marbles is 5 + 7 + 8 = 20. Favorable marbles equal 5 + 7 = 12. Therefore, the probability is 12/20 = 3/5.
A solid metallic cuboid measuring 16 cm by 8 cm by 4 cm is melted down and recast into a single cube. What is the side length of this new cube?
Level 4 of 5Show the answer
Answer: 8 cm
The volume of the cuboid is 16 × 8 × 4 = 512 cm³. Since volume is conserved during melting, the cube's side length is the cube root of 512, which is 8 cm.
A cloth pouch contains 5 green marbles, 7 red marbles, and 8 blue marbles. Tarun picks one marble without looking. What is the probability that it is red?
Level 4 of 5Show the answer
Answer: 7/20
Total number of outcomes = 5 + 7 + 8 = 20 marbles. The number of red marbles is 7. Therefore, the probability is 7/20.
Rohan bought a book at a 20% discount on its marked price. He then sold it for ₹960, making a profit of 20%. What was the original marked price of the book?
Level 4 of 5Show the answer
Answer: ₹1,000
Cost price = 960 / 1.2 = ₹800. Since the cost was 20% below the marked price, marked price = 800 / 0.8 = ₹1,000.
Priya travels from her house to school at 12 km/h and returns along the same route at 18 km/h. What is her average speed for the entire journey?
Level 4 of 5Show the answer
Answer: 14.4 km/h
For equal distances, the average speed is given by (2 × v1 × v2) / (v1 + v2). Here, (2 × 12 × 18) / (12 + 18) = 432 / 30 = 14.4 km/h.
- True or false?
Doubling the radius of a circular flowerbed increases its total area by a factor of four.
Level 4 of 5Show the answer
Answer: True
The area of a circle is proportional to the square of its radius. Replacing radius r with 2r results in four times the original area.
- Fill in the blank.
If 4 raised to the power of x equals 64 squared, the value of x is ___.
Level 4 of 5Show the answer
Answer: 6
Since 64 equals 4 cubed, 64 squared is (4³)² = 4⁶. Equating exponents gives x = 6.
- Fill in the blank.
When 3 times a number is subtracted from 75, the result equals twice that number, making the number ___.
Level 4 of 5Show the answer
Answer: 15
Setting up the linear equation 75 - 3x = 2x gives 5x = 75. Dividing both sides by 5 yields x = 15.
- Fill in the blank.
After scoring 88, 92, and 84, Priya needs a final score of ___ to achieve a four-round mean of 90.
Level 4 of 5Show the answer
Answer: 96
The total score required for a mean of 90 across four rounds is 4 × 90 = 360. Subtracting the existing sum (264) gives 96.
Which fraction is the odd one out?
Level 4 of 5Show the answer
Answer: 7/75
The other three fractions produce terminating decimals because their denominators have only 2 and 5 as prime factors. The fraction 7/75 produces a repeating decimal because 75 contains the factor 3.
Devika marks an article 40% above its cost price. She then offers a discount of 25% on the marked price. What is her net profit percentage?
Level 5 of 5Show the answer
Answer: 5%
If the cost price is ₹100, the marked price is ₹140. A 25% discount on ₹140 equals ₹35, leaving a selling price of ₹105, which is 5% profit.
Two standard six-sided dice are rolled simultaneously. What is the probability that the product of the two numbers obtained is a multiple of 6?
Level 5 of 5Show the answer
Answer: 5/12
Out of 36 pairs, products are multiples of 6 if one number is 6 (11 pairs), or from (2,3), (3,2), (4,3), (3,4) (4 pairs). Total favorable = 15; 15/36 = 5/12.
If 2 raised to the power (x - 1) plus 2 raised to the power (x + 1) equals 320, find the value of x.
Level 5 of 5Show the answer
Answer: 7
Factoring out 2^x gives 2^x * (1/2 + 2) = 320. Thus, 2^x * (5/2) = 320, so 2^x = 128. Since 2^7 = 128, x = 7.
- True or false?
If a natural number is divisible by both 4 and 6, it must be divisible by 24.
Level 5 of 5Show the answer
Answer: False
The lowest common multiple of 4 and 6 is 12. Numbers such as 12, 36, and 60 are divisible by both 4 and 6, yet leave remainders when divided by 24.
- True or false?
A convex polyhedron with exactly 8 vertices and 12 edges has 6 faces.
Level 5 of 5Show the answer
Answer: True
According to Euler's formula, Faces + Vertices - Edges = 2. Substituting 8 vertices and 12 edges gives Faces + 8 - 12 = 2, so the number of faces equals 6.
Which set of side lengths is the odd one out?
Level 5 of 5Show the answer
Answer: 16 cm, 63 cm, 67 cm
The other three sets are Pythagorean triplets satisfying a² + b² = c² to form right triangles. However, 16² + 63² = 4225 = 65², not 67².
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