CBSE Class 9 Maths Important Questions (with Solutions) for Annual Exam 2021
Here you will get the important questions for the CBSE Class 9 Mathematics Exam 2021. All questions are provided with appropriate and simple solutions to help you with easy preparations for the exam.
All the questions provided here have been prepared according to the trends followed in past years' exams and are based on the complete syllabus of Class 9 Maths. Moreover, detailed and appropriate solutions have been provided for all the questions. This will help students save their time by not searching for solutions in different books or surfing online. They will also get an idea about how to write perfect solutions in exams to score full marks. This way they can make a quick but effective preparation for their CBSE Class 9 Maths Exam 2021.
Find below the important questions for CBSE Class 9 Mathematics Annual Exam 2021:
Important 1 Mark Questions
Here we provide a set of questions that should be prepared for the 1 mark questions to be asked in CBSE Class 9 Maths Paper 2021.
Questions and answers provided below will help to acquaint the important concepts which can be tested in Section A of Class 9 Maths paper.
Some sample questions from the set of Important 1 Mark Questions for CBSE Class 9 Mathematics Exam, are given below:
Q. If (1, −2) is a solution of the equation 2x – y = p, then find the value of p.
Sol.
2x − y = p
Putting x = 1, y = −2, in above equation, we get:
2(1) – (−2) = p
⟹ p = 4
Q. If the graph of equation 2x + ky = 10k, intersect x-axis at point (2, 0) then find value of k.
Sol.
Here, 2x + ky = 10k ...(i)
At point (2, 0), equation (i) becomes:
2(2) + k(0) = 10k
⟹ 4 = 10k
⟹ k = 10/4 = 0.4
CBSE Class 9 Mathematics Syllabus 2019-2020
Q. Find the radius of largest sphere that is carved out of the cube of side 8 cm.
Sol.
The largest sphere can be carved out from a cube, if we take diameter of the sphere equal to edge of the cube.
∴ Diameter of the sphere = 8 cm
Thus, radius of the sphere = 8/2 = 4 cm
Get here the complete set of CBSE Class 9 Mathematics: Important 1 Mark Questions |
Also, Check Important MCQs for CBSE Class 9 Science Exam 2021
Important 2 Marks Questions
Here you will get important 2 marks questions which might be asked in CBSE class 9 Mathematics paper.
Some sample questions from the set of Important 2 Marks Questions for CBSE Class 9 Mathematics Exam, are given below:
Q. Find the total surface area of a cube, whose volume is 3√3a^{3} cubic units.
Sol.
Since volume of a cube = 3√3a^{3}
⟹ (side)^{3 }= 3√3a^{3}
⟹ (side)^{3 }= √3 × √3 × √3 × a^{3}
⟹ (side)^{3 }= (√3a)^{3}
⟹ side= √3a
Now, total surface area of cube =6 (side)^{2 }
= 6(√3a)^{2}
= 18a^{2} sq. units
Q. If two opposite angles of a parallelogram are (63 − 3x)° and (4x − 7)°. Find all the angles of the parallelogram.
Sol.
In a parallelogram, the opposite angles are equal.
∴ (63 − 3x)° = (4x − 7)°
⟹ 4x + 3x = 63 +7
⟹ 7x = 70
⟹ x = 10
(63 − 3x)° = 33°
(4x − 7)° = 33°
Now, sum of all interior angles of a parallelogram = 360°
∴ Sum of the other two opposite angles = 360° − (33° + 33°) = 360° − 66° = 294°
∴ Each of the other two opposite angles = 294/2 = 147°
Hence the four angles of a parallelogram are 33°, 147°, 33°, 147°
Get here the complete set of CBSE Class 9 Mathematics: Important 2 Marks Questions |
Important 3 Marks Questions
Get here a collection of important 3 marks questions which students must practice to make an effective preparation for the CBSE Class 9 Mathematics Paper 2021.
Some sample questions from the set of Important 3 Marks Questions for CBSE Class 9 Mathematics Exam are given below:
Q. Suman spins two spinners, one of which is labeled 1, 2 and 3 and the other are labeled A, B, C and D. Find the probability of:
(i) Stopping at 2 and C.
(ii) Stopping at 3 and either B or D
(iii) Stopping at any number and A
Sol.
Sample space = {A1, A2, A3, B1, B2, B3, C1, C2, C3, D1, D2, D3}
Total possible outcome = 12
Probability of stopping at 2 and C = 1/12
Probability of stopping at 3 and either B or D = 2/12 = 1/6
Probability of stopping at any number and A = 3/12 = 1/4
Q. Construct an angle of 135^{o} at the initial point of a given ray and justify the construction.
Sol.
Steps of construction:
1. Draw a ray OA.
2. With its initial point O as centre and any radius, draw an arc BE, cutting OA and its produced part at C and E respectively.
3. With centre B and same radius (as in step 2), draw an arc, cutting the arc BE at C.
4. With C as centre and the same radius, draw an arc cutting the arc BE at D.
5. With C and D as centres, and any convenient radius (more than 1/2 CD), draw two arcs intersecting at P.
6. Join OP.
Then ∠AOP = ∠EOP = 90^{o}
7. Draw OQ as the bisector of ∠EOP.
Then, ∠AOQ =135^{o}
Justification :
By construction ∠AOP = 90^{o}
Thus, ∠AOP = ∠EOP = 90^{o}
Also, OQ is drawn as the bisector of ∠EOP
Therefore, ∠POQ =1/2∠EOP =1/2 × 90^{o} = 45^{o}
Thus, ∠AOQ = ∠AOP + ∠POQ = 90^{o} + 45^{o} = 135^{o}
Hence justified.
Get here the complete set of CBSE Class 9 Mathematics: Important 3 Marks Questions |
Important Long Answer Type Questions
Here you will get a set of important long answer type questions that can be asked for 5 marks in CBSE Class 9 Mathematics Paper 2021.
Some sample questions from the set of Important 4 Marks Questions for CBSE Class 9 Mathematics Exam, are given below:
Q. Q. If a + b + c = 6 and ab + bc + ca = 11, find the value of a^{3 }+b^{3 }+c^{3 }− 3abc.
Sol.
(a + b + c)^{2} = a^{2 }+ b^{2} +c^{2} +2(ab + bc + ca)
(6)^{2 }= a^{2 }+ b^{2} +c^{2} + 2 × 11
a^{2 }+ b^{2} +c^{2} = 36 – 22 = 14
a^{3 }+b^{3 }+c^{3 }− 3abc = ( a + b + c)[ a^{2 }+ b^{2} +c^{2} −(ab + bc + ca)]
= 6 × (14 − 11)
= 6 × 3 = 18
Q. The polynomials ax^{3} – 3x^{2} +4 and 2x^{3 }– 5x +a when divided by (x – 2) leave the remainders pand q respectively. If p – 2q = 4, find the value of a.
Sol.
Let, f(x) = ax^{3} – 3x^{2} +4
And g(x) = 2x^{3 }– 5x +a
When f(x) and g(x) are divided by (x – 2) the remainders are p and q respectively.
⟹ f(2) = p and g(2) = q
⟹ f(2) = a × 2^{3} – 3 × 2^{2} + 4
⟹ p = 8a – 12 + 4
⟹ p = 8a – 8 ....(i)
And g(2)= 2 × 2^{3} – 5 × 2 + a
⟹ q = 16 – 10 + a
⟹ q = 6 + a ....(ii)
But p – 2q = 4 (Given)
⟹ 8a – 8 – 2(6 + a) = 4 (Using equations (i) and (ii))
⟹ 8a – 8 – 12 − 2a = 4
⟹ 6a – 20 = 4
⟹ 6a = 24
⟹ a = 24/6
⟹ a = 4
Get here the complete set of CBSE Class 9 Mathematics: Important Long Answer Type Questions |
CBSE Class 9 students are suggested to solve the Mathematics important questions given here and then check their solutions. This will help them to assess their preparation level hence making an effective preparation for the annual exam.
Important* CBSE Class 9 Maths Complete Study Material & Preparation Guide for Annual Exam 2021