Class 9 Sample Paper Maths (Half Yearly)

SAMPLE
PAPER
Half Yearly Examination

Prepared For
NCERT BASED SYLLABUS
Applicable For
CBSE BOARD AND STATE BOARD USING NCERT

WWW.

HALF YEARLY EXAMINATION
SAMPLE QUESTION PAPER
Class - IX Subject – Mathematics
Time – 3 Hours Maximum Marks-80

GENERAL INSTRUCTIONS
1. This question paper consists of two parts A and B.
2. Part A has two sections- Section I and Section II.
a) Section I has 16 questions of 1 mark each.
b) Section II has 4 questions on case study. Each case study has 5 case based sub parts. An
examinee has to attempt any 4 out of 5 sub parts.
3. Part B has question number 21 to 26 of 2 marks each,
question number 27 to 33 of 3 marks each
and question number 34 to 36 of 5 marks each.
4. Internal choices have been provided where ever applicable.
5. Use of calculator or any other electronic device is not allowed.

1. If an angle is 16 more than its complement then find its measure.
OR
In ∆PQR, If ∠P=100 , PM bisects ∠P and PM ⊥ QR then find ∠Q.
2. Find one rational numbers between 3 and 4
OR
Express 0.6 in the form .
3. Find the remainder when 3 +7 is divided by 7+3
4. In which quadrant or axis do (-2,4) & (-1,0) lie ?
5. If the point (3, 4) lies on the graph of the equations 3y = a +7. Find a
6. State Euclid’s fifth postulate .
7. In an isosceles triangle, if the vertex angle is twice the sum of the base angle, calculate
vertex angle of the triangle.
8. The difference of two complementary angle is 40 , find the angle.
OR

If the angle of a triangle are in the ratio 2:3:4 . Determine the smallest angles.

9. Diagonal of quadrilateral ABCD bisect each other. If ∠A=35 , then find the value of ∠B.
OR
If ABCD is a trapezium in which AB∥ DC and ∠A=∠B = 45 find ∠C.

10. It is given that ∆ABC ≅ ∆FDE and AB=5cm, ∠ =40 and ∠ =80 . Find ∠
OR
If the altitude AD, BE and CF of a ∆ ABC are equal, then the triangle must be --------
triangle.
~1~

11. If the supplement of an angle is three times its complement, then find the angle.
12. D and E are mid-point of sides AB and AC respectively of ∆ ABC. If the perimeter of ∆
ABC is 38 cm. Find the perimeter of ∆ ADE.
13. ABCD is a parallelogram. If ∠A=65 . Find the value of ∠B+∠D.
14. The sum of two angles of a triangle is 85 and their difference is 25 . Find the third
angle.
15. In the given figure ∆ RST, find the value of x?

16. State RHS congruency criteria

Case Study Questions
17. On one day, Principal of a particular school visited the classroom. Class teacher was
teaching the concept of polynomial to students. He was very much impressed by her
way of teaching. To check, whether the students also understand the concept taught by
her or not, he asked various questions to students. Some of them are given below.
Answer them.
(i) Which one of the following is not a polynomial?
(a) 4x2 + 2x – 1
(b) y+ (3/y)
(c) x3 – 1
(d) y2 + 5y + 1
(ii) The polynomial of the type ax2 + bx + c, a ≠ 0 is called
(a) Linear polynomial
(b) Quadratic polynomial
(c) Cubic polynomial
(d) Biquadratic polynomial
(iii) The value of k, if (x – 1) is a factor of 4x3 + 3x2 – 4x + k, is
(a) 1
(b) –2
(c) –3
(d) None of these
(iv) If x + 2 is the factor of x3 – 2ax2 + 16, then value of a is
(a) –7
(b) 1
(c) –1
(d) None of these
(v) The number of zeroes of the polynomial x2 + 4x + 2 is

(a) 1
(b) 2
(c) 3
(d) None of these
~2~

18. OP, OQ, OR, OS, OT and OU are six roads and all join at a point O. These roads make
angles (∠ , ∠ , ∠ , ∠ , ∠ ) as shown in the figure. Roads OS and OT are
perpendicular to each other. PS and RU are straight lines and intersect each other at O.
∠ , ∠ , ∠ are in the ratio 1:2:3. A teacher showed this figure to a student of Mathematics
and asked the following questions.

(i) What is the angle between the roads OQ and OR?
(a) 20°
(b) 40°
(c) 60°
(d) 80°
(ii) What is the value of ∠ ?
(a) 30°
(b) 40°
(c) 60°
(d) 80°
(iii) Which of the following is a pair of complementary angles?
(a) ∠ , ∠
(b) ∠ , ∠
(c) ∠ , ∠
(d) ∠ , ∠
(iv) Which pair of angles do not form supplementary angles?
(a) ∠ ,∠
(b) ∠ ,∠
(c) ∠ ,∠
(d) ∠ ,∠
(v) The ∠ ∠ are called
(a) Vertically opposite angles
(b) Corresponding angles
(c) Adjacent angles
(d) None of the above
19. After summer vacation, Manit’s class teacher organised a small MCQ quiz, based on the
properties of quadrilaterals. During quiz, she asks different questions to students. Some
of the questions are listed below.
(i) Which of the following is/are the condition(s) for ABCD to be a quadrilateral?

(a) The four points A, B, C and D must be distinct and co-planar.
(b) No three of points A, B, C and D are collinear.
(c) Line segments i.e., AB, BC, CD, DA intersect at their end points only.
(d) All of these
~3~

(ii) Which of the following is wrong condition for a quadrilateral said to be a
parallelogram?
(a) Opposite sides are equal
(b) Opposite angles are equal
(c) Diagonal can’t bisect each other
(d) None of these
(iii) If AX and CY are the bisectors of the angles A and C of a parallelogram ABCD, then
(a) AX || CY
(b) AX || CD
(c) AX || AB
(d) None of these
(iv) ABCD and ABFG are two parallelograms. If ∠C = 63°, then determine ∠G.
(a) 63°
(b) 117°
(c) 90°
(d) None of these
(v) If angles of a quadrilateral are in ratio 3 : 5 : 5 : 7, then find all the angles.
(a) 54°, 80°, 80°, 146°
(b) 34°, 100°, 100°, 126°
(c) 54°, 90°, 90°, 126°
(d) None of these
20. To raise funds for cancer patients a charity race was organised on rectangular school
ground ABCD. Lines have been drawn with chalk powder at a distance of 1 m each. 100
flower pots have been placed at a distance of 1 m from each other along AD. Niharika
runs of the distance AD on the second line and posts a green flag. Preeti runs of the
distance AD on the 8th line and posts a red flag as shown in the given figure.

Answer the following questions based on above information.
(i) The coordinates of green flag are
(a) (25,2)
(b) (2,25)
(c) (4,25)
(d) (3,25)
(ii) The coordinates of red flag are

(a) (20,8)
(b) (20,7)
(c) (8,20)
(d) (7,20)
~4~

(iii) Coordinates of green flag and red flag lie in
(a) 1st and 2nd quadrant respectively
(b) 2nd and 1st quadrant respectively
(c) Both in 4th quadrant
(d) Both in 1st quadrant
(iv) The distance between the green flag and the red flag is
(a) 20 m
(b) √51m
(c) 45 m
(d) None of these
(v) If the position of green flag is P and that of red flag is Q, then find
( ) −( )
(a) 60
(b) 5
(c) 225
(d) None of these
21. Represent √6 an the number line
OR
Visualize the representation of 5.37 up to 4 place of decimal

22. Factories 8 - - 12
b + 6a
OR
Evaluate using suitable identity
105X104
23. Give the geometric representation of 2 +9=0 as an equation
i. In one variable
ii. In two variable
24. If a point C lies between two points A and B such that AC = BC, then prove that AC= AB.
25. It is given that ∠XYZ=64 and XY is produced to point P. If ray YQ bisects ∠ZYP. Find
∠XYQ
26. ABC is a right angled triangle in which ∠A=90 and AB=AC. Find ∠B and ∠C

27. If = and y = find +
√ √ √ √
√ √ √ √
28. Factories +2 -5y-6
29. In the figure AB∥ DE. Prove that ∠ABC+∠BCD=180 +∠CDE

OR
Prove that the angle between internal bisectors of one base angle and the external
bisector of the other base angle of a triangle is equal to one-half of the vertical angle
~5~

30. If the arms of one angle are respectively parallel to the arms of another angle, then show
that the two angles are either equal or supplementary.
31. The side AB and AC of triangle ABC are produced to point E and D respectively . If
bisectors BO and CO of ∠CBE and ∠BCD respectively meet at point O, then prove that:
∠BOC = 90 - ∠BAC
OR

In the given figure ∠Q is greater than ∠R, PA is the bisectors of ∠QPR and PM is
perpendicular to QR. Prove that ∠APM = (∠Q-∠R)

32. Triangle ABC and triangle DBC are two isosceles triangle on the same BC and vertices A
and D are on the same side of BC. If AD is extended to intersect BC at P, show that
i. ∆ABD ≅ ∆ ACD
ii. ∆ABP ≅ ∆ ACP
33. Show that the bisectors of angles of a parallelogram form a rectangle .
34. The parking charges of a car in a parking lot is Rs 30 for the first 2 hours and Rs 10 per
hour for subsequent hours. Taking the number of hours car is parked as x and the
parking charge as y, frame a linear equation in two variables for the given situation.
Taking number of hours car is parked along X axis and the parking charge along Y axis,
draw the graph for the linear equation framed. From the graph or algebraically find the
following:
i. The parking charge for 6 hours.
ii. The number of hours car is parked if the parking charge is Rs 50.

35. ABCD is a trapezium in which AB∥ CD and AD=BC. show that
i. ∠A=∠B
ii. ∠C=∠D
iii. ∆ ≅∆
iv. =
OR
State and Prove mid – point theorem . Using theorem solve the following:
In ∆ ABC, AD is the median through A and E is the mid point of AD. BE produced
meet AC in F. Prove that AF= AC

36. In right ∆ABC, right angle at C, M is the mid-point of hypotenuse AB, C is joined to M
and produced to a point D such that DM=CM . Point D is joined to point B. Prove that
i. ∆AMC≅ ∆BMD
ii. ∠DBC=90

iii. ∆DBC≅ ∆ACB
iv. = AB

~6~

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