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In this article you will get a collection of important 4 marks questions to prepare for the CBSE class 9 Mathematics annual exam 2018. All these questions have been provided with proper solutions.

In CBSE Class 9 Mathematics Exam 2018, Section - D will comprise 8 questions of 4 marks each.

Students must practice the questions given here as it will help them to not only assess their preparation level but also know the important topics which need to be prepared for the annual exam 2018.

**Given below are some sample questions from CBSE Class 9 Mathematics: Important 4 Marks Questions:**

**Q.** The polynomials a*x*^{3} – 3*x*^{2} +4 and 2*x*^{3 }– 5*x* +*a* when divided by (*x* – 2) leave the remainders *p* and *q* respectively. If *p* – 2*q* = 4, find the value of *a*.

**Sol.**

Let, *f*(*x*) = a*x*^{3} – 3*x*^{2} +4

And *g*(*x*) = 2*x*^{3 }– 5*x* +*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* = 8*a* – 12 + 4

**⟹**** ** *p* = 8*a* – 8 ....(i)

And *g*(2)= 2* *× 2^{3} – 5 × 2 + *a*

**⟹**** ** *q* = 16 – 10 + *a*

**⟹**** ** *q* = 6 + *a *....(ii)

But *p* – 2*q* = 4 (Given)

**⟹**** **8*a* – 8 – 2(6 + *a*) = 4 (Using equations (i) and (ii))

**⟹**** **8*a* – 8 – 12 − 2*a* = 4

**⟹**** **6*a* – 20 = 4** **

**⟹**** **6*a* = 24

**⟹**** ***a* = 24/6

**⟹**** ***a* = 4

**CBSE Class 9 Mathematics Exam 2018: Important 3 Marks Questions**

**Q. **Construct a ΔABC in which BC = 3.8 cm, ∠B = 45^{o}and AB + AC* *= 6.8cm.

**Sol.**

**Steps of Construction**

1. Draw BC = 38 cm.

2. Draw a ray BX making an ∠CBX = 45°.

3. From BX, cut off line segment BD equal to AB + BC i.e.,** **6.8 cm.

4. Join CD.

5. Draw the perpendicular bisector of CD meeting BD at A.

6. Join CA to obtain the required

**Justification:**

Clearly, A lies on the perpendicular bisector of CD.

∴ AC = AD

Now, BD = 6.8 cm

⟹ BA + AD = 6.8 cm

⟹ AB + AC = 6.8 cm

Hence, is the required triangle.

**CBSE Class 9 Mathematics Sample Paper: 2017-2018**

**Q.** If *a* + *b* + *c* = 6 and *ab* + *bc* + *ca* = 11, find the value of *a*^{3 }+*b*^{3 }+*c*^{3 }− 3*abc*.

**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 }− 3*abc* =(* a* + *b* + *c*)[* a*^{2 }+ *b*^{2} +*c*^{2} −(*ab *+ *bc *+ *ca*)]

= 6 × (14 − 11)

= 6 × 3 = 18

**To get the complete set of questions, click on the following link:**

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