9th CBSE Mathematics Mid Term Examination Question Paper (2019-20)
Time: 3 Hrs.
- All the questions are compulsory.
- The question paper consists of 40 questions divided into 5 sections.
- Section A consists of 16 questions of 1 mark each.
Section B consists of 3 questions of 2 marks each.
Section C consists of 8 questions of 3 marks each.
Section D consists of 6 questions of 4 marks each.
Section E consists of 7 questions of 3-D Dexture.
- There is no overall cchoice. However an internal choice has been provided.
- Use of calculator is not permitted.
9th Mathematics Mid Term: Section A
Fill in the blanks in Q 1 to Q 3
Q 1. There can be _______ many irrational numbers between two numbers on the number line.
Q 2. A polynomial of degree __________ is called constant polynomial.
Q 3. Co-ordinates of a point on the x-axis are of the form ________.
Choose the correct option in Q 4 to Q 6
Q 4. Find the rational number among the following numbers:
Q 5. The radius of a sphere i 2r, than the volume will be
- 4/3 πr³
- 32/3 πr³
Q 6. An exterior angle of a triangle is 105° and its two interior opposite angles are equal. Each of these equal angle is:
Objective type questions (Q 7 to Q 11)
Q 7. Three angles of a quadrilateral are 75°, 90° & 55°, find the fourth angle.
Q 8. Find the volume of sphere in terms of II whose diameter is 6 cm.
Q 9. Find the length of each side of an equilateral triangle having an area of 9√3 cm².
Q 10. In ΔPQR, PQ = PR and ∠Q = 65°, then find ∠R.
Q 11. Can a triangle have all the angles less than 60°? Give reason.
State whether the following statements are True or False in Q 12 to 16
Q 12. Zero is a rational number.
Q 13. x + 2√x + 1 is a polynomial.
Q 14. Two circle of same radii are congruent.
Q 15. Point (0, -7) lies in IV Quadrant.
Q 16. There cannot be more than one obtuse angle in a triangle.
Q 17. If (x + 1) is a factor of ax³ + 2x + 4a – 9. Find the value of a.
Q 18. Prove that each angle of an equilateral triangle is 60°.
In the given fig.
∠B < ∠A and ∠C < ∠D
Show that AD<BC
Q 19. The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many liters of water can it hold?
Q 20. Find the value of a and b.
7 + √5 / 7 – √5 – 7 – √5 / 7 + √5 = a + 7/11 √5b
(b) Locate √2 on a number line. [1½]
Q 21. If the polynomial az³ + 4z² + 3z – 4 and z³ – 4z + a leaves the same remainder when divided by z – 3, find the value of a.
Simplify: (a + b + c)² – (a – b – c)² + 4b² – 4c²
Q 22. In fig. if AB||CD,
CD||EF and y:z = 3:7
It is given that ∠XYZ = 64° and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects ∠ZYP find ∠XYQ and reflex ∠QYP.
Q.23. In figure, AB is a line segment and P is its mid point.
D and E are points on the same side of AB such
that ∠BAD = ∠ABE and ∠EPA = ∠DPB. Show that
- ΔDAP ≅ ΔEBP
- AD = BE
Q 24. A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non parallel sides are 14 m and 13 m. Find the area of the field.
Q.25. In figure, Diagonal AC of a parallelogram
ABCD bisect ∠A. Show that:
- It bisects ∠C also.
- ABCD is a rhombus.
Show that the diagonals of a rhombus are perpendicular to each other.
Q 26. Curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find
- radius of base
- Total surface area of the cone.
Q 27. A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?
9th CBSE Mathematics Mid Term Unsolved Paper 2019: Section D
Q 28. If a = 3 + 2√2, find the value of
Q 29. By actual division, find the quotient and remainder when 3x4 – 4x³ – 3x – 1 is divided by x + 1.
If a + b + c = 6 and and ab + bc + ca = 11, then find the value of a³ + b³ + c³ – 3abc
Q 30. Plot the points A (2,0), B(5,0) and C (5,3). Find the coordinates of the point D such that ABCD is a square. Find the area and perimeter of square.
Two side AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and OR and median PN of ΔPQR.
- ΔABM ≅ ΔPQN
- ΔABC ≅ ΔPQR
In fig., PR>PQ and PS bisects
∠QPR. Prove that ∠PSR > ∠PSQ.
Q 32. Twenty seven solid iron spheres each of radius r¹ and surface area S are melted to form a sphere with surface area S¹. Find the
- radius r¹ of the new sphere
- ratio of S and S¹
Volume of the two spheres are in the ratio 125:27. Find the ratio of their surface areas.
Q 33. ABC is a triangle right angled at C. A line through the mid point M of hypotenuse AB and parallel to BC intersect AC at D. Show that
- D is the mid point of AC
- CM = MA = ½ AB
9th Mathematics Mid Term: Section E (3D – Dexture) [1o]
Fill in the blanks in Q 34 and Q 35
Q 34. ________ 3D Printing technology was invented by Chuck Hull in 1983. 
Q 35. _________ 3D Printing technology used in our school. 
Choose the Correct option in Q 36 and Q 37
Q 36. Which of the following software we used in 3D printing? 
- Designing software
- Slicing software
- None of above
- both (a) and (b)
Q 37. The name of the material we use for 3D printing is 
- Acrylonitrile Butadirne Styrene
- Polylactic acid
- Poly carbonated acid
Q 38. Give a brief introduction of smart city? 
Q 39. What is the difference between alternating current and direct current? What is I.C. and write its full form. 
Question: What is the diameter of the filament you use in 3D Printer? What is the full form of FDM? 
What is alternating current? From where you obtained AC & DC?