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
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
Important 2 Marks Questions
Here you will get important 2 marks questions which might be asked in CBSE class 9 Mathematics paper.
In CBSE class 9 Mathematics exam 2019, Section-B will contain 6 questions of 2 marks each.
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√3a3 cubic units.
Sol.
Since volume of a cube = 3√3a3
⟹ (side)3 = 3√3a3
⟹ (side)3 = √3 × √3 × √3 × a3
⟹ (side)3 = (√3a)3
⟹ side= √3a
Now, total surface area of cube =6 (side)2
= 6(√3a)2
= 18a2 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°
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 2019.
In CBSE class 9 Mathematics exam 2019, Section-C will contain 10 questions of 3 marks each
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 135o 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 = 90o
7. Draw OQ as the bisector of ∠EOP.
Then, ∠AOQ =135o
Justification :
By construction ∠AOP = 90o
Thus, ∠AOP = ∠EOP = 90o
Also, OQ is drawn as the bisector of ∠EOP
Therefore, ∠POQ =1/2∠EOP =1/2 × 90o = 45o
Thus, ∠AOQ = ∠AOP + ∠POQ = 90o + 45o = 135o
Hence justified.
Important 4 Marks Questions
Here you will get a set of important 4 marks questions to prepare for the CBSE Class 9 Mathematics Paper 2019.
In CBSE class 9 Mathematics exam 2018, Section-D will contain 8 questions of 3 marks each
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 a3 +b3 +c3 − 3abc.
Sol.
(a + b + c)2 = a2 + b2 +c2 +2(ab + bc + ca)
(6)2 = a2 + b2 +c2 + 2 × 11
a2 + b2 +c2 = 36 – 22 = 14
a3 +b3 +c3 − 3abc = ( a + b + c)[ a2 + b2 +c2 −(ab + bc + ca)]
= 6 × (14 − 11)
= 6 × 3 = 18
Q. The polynomials ax3 – 3x2 +4 and 2x3 – 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) = ax3 – 3x2 +4
And g(x) = 2x3 – 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 × 23 – 3 × 22 + 4
⟹ p = 8a – 12 + 4
⟹ p = 8a – 8 ....(i)
And g(2)= 2 × 23 – 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
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.
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