## 9th CBSE Mathematics Pre-Mid Examination Question Paper (2019-20)

**School Name: Himalayan Public School**, Sector 13, Rohini,

**Delhi**110085

**India**

**Time:**3 hr

**M.M.**80 marks

**Date: 24/06/2019**

**Class:**IX

**Subject: Mathematics**

**General Introductions:**

- All questions are compulsory.
- This question paper consists of 40 questions divided into five sections – A, B, C, D and 3-D DEXTER.
- Section-A contains 16 questions of 1 mark each.

Section-B contains 3 questions of 2 mark each.

Section-C contains 8 questions of 3 mark each.

Section-D contains 6 questions of 4 mark each.

3-D DEXTER contains 4 questions of 1 mark each and 3 questions of 2 marks each. - Use of Calculators is not permitted.

## Section A: 9th Mathematics Pre-Mid Exam

#### Question: 1. Give an example of two irrational number whose product is rational.

#### Question: 2.

#### Question: 3.

#### Question: 4. Find the value of (3√2 – 5) (3√2 + 5)

#### Question: 5. What is the degree of the polynomial p(x) = 3?

#### Question: 6. Find the coefficient of x in (5 – *x *)².

#### Question: 7. Find the zero of the polynomial p(x) = 2x + 9.

#### Question: 8. If *p*(*x*) = *x*² – 2√2*x* + 1, find *p*(2√2)

#### Question: 9. Find the reminder when *x*¹¹ + 101 is divided by *x* + 1.

#### Question: 10. Find the value of 103² using a suitable Identity.

#### Question: 11. Where does the point (-2, 7) lie in the coordinate plane?

#### Question: 12. If two complementary angles are in the ratio 4:5, then find the angles.

#### Question: 13. The angles of a triangle are (3*x* + 40°), (4*x* + 10°) and (3*x* + 50°). Find the value of *x*.

#### Question: 14. What are the coordinates of a point whose abscissa is -2 and lies on *x* – axis?

#### Question: 15. Find the measure of an angle whose supplement is equal to the angle itself.

#### Question: 16. An exterior angle of a triangle is 80° and the two interior opposite angle are equal. Find the measure of each interior opposite angle.

**Section B: 9th Mathematics Pre-Mid Exam**

#### Question: 17.

#### Question: 18. If the area of an equilateral triangle is 81√3 cm², find its perimeter.

#### Question: 19. In figure, lines PQ and RS intersect at a point T, such that ∠PRT = 40°, ∠RPT = 95° and

∠TSQ = 75°, find ∠SQT.

**Section C: 9th Mathematics Pre-Mid Exam**

#### Question: 20.

#### Question: 21.

#### Question: 22. If *x* – 2y = 6, find the value of *x*³ – 8y³ – 36*x*y – 216.

#### Question: 23. Factorise: 8*x*³ – 27y³ – 36*x*²y + 54*x*y²

#### Question: 24. Find:

- mirror image of P(-1, 4) in x – axis.
- perpendicular distance of Q(-2, -4) from x axis.
- abscissa of the point R(3, 0).

#### Question: 25. In figure, AB || EF and CD || EF. Also EA ⊥ AB. If ∠BEF = 40°, then find *x*, y and *z*.

#### Question: 26. In figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between OP and OR.

#### Prove that ∠ROS = ½ (∠QOS – ∠POS).

#### Question: 27. Side of a triangle are in the ratio 13:14:15 and its perimeter is 84 cm. Find its area.

**Section D**

#### Question: 28.

#### Question: 29. If p(*x*) = a*x*³ – 3*x*² + 4 and g(*x*) = 2*x*³ – 5*x* + a, when divided by *x* – 2 leaves reminder p abd q respectively and if p – 2q = 4, find the value of a.

#### Question: 30. Factorise p(*x*) = *x*³ + 13*x*² + 32*x* + 20

#### Question: 31. Three vertex of a square PQRS and P(1,0), Q(5,0) and R(5,4). Then

(a) plot the point P, Q and R on graph.

(b) find the coordinates of the missing vertex S.

(c) find the area and perimeter of PQRS.

#### Question: 32. In ΔABC, the side AB and AC of triangle are produced to points E and D respectively. If bisectrs BO and CO of ∠CBE and ∠BCD respectively meet at point O, then prove that ∠BOC = 90° – ½ ∠A.

#### Question: 33. ABC is an equilateral triangle with side ‘a’.

- Find the area of ΔABC using Heron’s formula.
- If its perimeter is 180 cm, what will be the area of the triangle.

**3-D DEXTER**

#### Question: 34. Who invented 3D printing? [1]

#### Question: 35. What is the full form of ABS? [1]

#### Question: 36. At what temperature PLA melts? [1]

#### Question: 37. How many motors does 3D printer has? [1]

#### Question: 38. Explain the process of printer a cube. [2]

#### Question: 39. What is design thinking? What are 5 stages of the design thinking? [2]

#### Question: 40. Write shortcuts of the following: [2]

- Rectangle tool
- Offset tool
- Rotate tool
- Push Pull