Class IX - Mathematics Practice Paper - 3

Subject: Mathematics

Class IX – Mid Term Practice Paper

Time Allowed: 3 hours

Max. Marks: 80

General Instructions:

1. This question paper contains 39 questions divided into three parts A, B and C. All the questions are compulsory.

2. Part A consists of two sections – I and II. Section – I has 16 questions of 1 mark each and Section – II has 4 case-study based questions.

3. Part B consists of 8 objective type questions.

4. Part C consists of 11 questions carrying four questions of 2 marks and 3 marks each and three questions of 4 marks.

5. There is no overall choice. However internal choices are provided in some questions. You have to attempt only one of the alternatives in all such questions.

6. There is no negative marking.

7. Use of calculator is not permitted.

Part A

Section I

1.If AB = QR, BC = PR and CA = PQ in ∆ABC and ∆PQR, then

(A) ∆ABC ≅ ∆PQR

(B) ∆CBA ≅ ∆PRQ

(D) ∆BCA ≅ ∆PQR

2. A number is irrational if its decimal representation is:

(A) Non-terminating

(B) Non-terminating non-recurring

(D) Non-terminating recurring

Which of these is a correct way to convert below to an equivalent number whose denominator is a rational number?

3. A student recorded the population of some villages as shown below:

Village	Population
A	450
B	700
C	550
D	350
E	950

Then represented the data on the graph given below:

Which of the following scale was used on the y-axis?

(A) 1 unit = 10 people

(B) 1 unit = 50 people

(D) 1 unit = 500 people

4. In the given figure, the value of x is:

(A) 230°

(B) 100°

(D) 115°

5. Harish places two straws forming angles ‘a’ and ‘b’ as shown and moves straw N such that the value of ‘b’ gets three times of ‘a’. How does the value of ‘a’ change?

(A) The value of ‘a’ triples.

(B) The value of ‘a’ becomes less than ‘2b’

(D) The value of ‘a’ becomes 1/3 times

6. Some of the rational numbers between 7 and 11 can be expressed in the form m/6, where m belongs to a set of natural numbers. Which of the following statement is true?

(A) All possible values of m lie between 42 and 66

(B) All possible values of m lie between 42 and 77

(D) All possible values of m lie between 66 and 77

7. Ridhi’s work to represent √27 on a number line is shown. In the number line, arc DQ is drawn using OD as the radius. Looking at Ridhi’s work, Tina and Ajay made the following statements.

Tina: OA = 5 units, AB = BD = 1 unit

Ajay: OB = √26 units and AB = 1 unit

Who is correct?

(A) Only Tina

(B) Only Ajay

(D) Neither of them

8. x = 1, y = –1 is a solution of which of the following linear equation?

(A) x + y = 2

(B) x – y = 2

(D) 2x + y = 4

The coefficient of ‘y’ in the linear equation 5(2y – 4) + 3x – 4y – 7 = 0 is:

(A) -4

(B) 6

(D) 14

9. Two points having same ordinates but different abscissa lie:

(A) on x-axis

(B) on y-axis

(D) on a line parallel to y-axis

10. Two angles whose sum is equal to 180° are called:

(A) vertically opposite angle

(B) complementary angle

(D) supplementary angle

If one angle of a linear pair is acute then the other angle will be:

(A) right angle

(B) acute angle

(D) straight angle

11. The triangles made by two intersecting lines as shown in figure. What additional information is required to prove that ∆TOI ≅ ∆SOD?

(A) ∠DOS = ∠TOI

(B) ∠OTI = ∠ODI

(D) TI = DS

The given triangles ∆ XYZ and ∆ STU are congruent by which congruency rule?

(A) SSS

(B) RHS

(D) All of the above

12. Two triangles are shown. The perimeter of ∆ PUL is 30 cm. Are the triangles congruent?

(A) Yes, as on calculating the missing angle in each triangle it can be concluded that the triangles are congruent by AAA criteria.

(B) No, as the missing angle in each triangle cannot be calculated.

(D) The conclusion about the congruency of triangles can be made if length of the side MN, MQ or NQ of △MNQ is known.

13. The area of an equilateral triangle having altitude ‘a’ unit is:

If (s – a) = 10 cm, (s – b) = 20 cm, (s – c) = 30 cm, then the perimeter of the triangle is:

(A) 20 cm

(B) 30 cm

(D) 120 cm

14. The semi-perimeter of a triangle whose sides are 15 cm, 20 cm and 25 cm is:

(A) 60 cm

(B) 50 cm

(D) 20 cm

15. If on adding -8√2 to the expression 2(√k – 1) + √8 results in a rational number, what is the value of k?

(A) 6

(B) 12

(D) 36

16. The histogram below shows the number of visitors in a museum on different number of days:

Which of these is correct about the histogram?

(A) There were about 80 – 90 visitors for 12 days at the museum.

(B) There were about 60 – 70 visitors for 5 days at the museum.

(D) There were about 100 – 120 visitors for 26 days at the museum.

Section II

Q17-20 are case study based questions. Each case-study based questions have 5 sub-parts. You have to attempt only four out of five sub-parts. Each sub-parts is of 1 mark each

17. On her birthday, Srishti planned that this time she will celebrate her birthday in a small orphanage centre. She bought apples to give to children and adults living there. She gave 2 apples to each child and 3 apples to each adult along with Birthday cake. She distributed total 60 apples.

Based on the above information, answer the following questions:

(i) Taking the number of children as ‘x’ and the number of adults as ‘y’, the above situation can be represented in linear equation in two variables as:

(a) 2x + y = 60

(b) 2x + 3y = 60

(d) 3x + y = 60

(ii) If the number of children is 15, then find the number of adults.

(a) 10

(b) 15

(d) 25

(iii) If the number of adults is 12, then the number of children is:

(a) 8

(b) 10

(d) 14

(iv) If x = – 5 and y = 2 is a solution of the equation 3x + 5y = b then value of ‘b’ is:

(a) -5

(b) 5

(d) 2

(v) When 4y – x = 5 is written in the form of ax + by + c = 0, then the value of ‘a’ is:

(a) 1

(b) -1

(d) 4

18. A triangular park ABC has sides of 24 m, 32 m and 40m. A gardener has to put a fence all around it and also plant grass inside. A 3m wide space for a gate is left on one side.

Based on the above information, answer the following questions:

(i) What is the semi perimeter of the park?

(a) 40 m

(b) 42 m

(d) 48 m

(ii) What is the area of the park?

(a) 360 m²

(b) 384 m²

(d) 380 m²

(iii) The cost of planting grass at the rate of Rs 20 per m² is:

(a) Rs 7600

(b) Rs 7680

(d) Rs 7280

(iv) The cost of fencing it with barbed wire at the rate of Rs 30 per metre is:

(a) Rs 2880

(b) Rs 2700

(d) Rs 2810

(v) The length of altitude drawn to the shortest side of the park will be:

(a) 20 m

(b) 24 m

(d) 32 m

19. In a rural village, there was a big electricity pole PC as shown in the figure. This pole was tied strong wire of 10 m length. Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the help of a rope which the electricians carry on their bicycles. This time electrician need a stair case of 10 m so that it can reach at point P on the pole. The stair case makes an angle of 60⁰ with the line AC.

Based on the above information, answer the following questions:

(i) In ∆PAC and ∆PBC which side is common?

(a) PC

(b) AB

(d) BC

(ii) In the figure, ∆PAC and ∆PBC are congruent due to which criteria?

(a) RHS

(b) SAS

(d) ASA

(iii) In ∆PAC and ∆PBC which angles are equal?

(a) ∠A= ∠x

(b) ∠B = ∠ x

(d) ∠ACP = ∠BCP

(iv) What is the value of ∠BPC?

(a) 30°

(b) 45°

(d) 90°

(v) What is the value of ∠APC?

(a) 30°

(b) 45°

(d) 90°

20. Anil is a Mathematics teacher in a government school in New Delhi. After periodic test III, he collected the marks of all the students of class IX. He observed that the least marks and the highest marks scored by the students are 2 and 59 respectively. He prepares the frequency distribution table using the collected marks and draws the histogram using the table as shown in the adjoining figure.

(i) What is the width of the class?

(a) 5

(b) 10

(d) 20

(ii) What is the total number of students in histogram?

(a) 75

(b) 70

(d) 60

(iii) How many students scored 50% and above marks?

(a) 19

(b) 22

(d) 27

(iv) How many students scored less than 50% marks?

(a) 26

(b) 27

(d) 34

(v) What is the range of the collected marks?

(a) 57

(b) 59

(d) 65

Part B

21. Fill in the blanks:

(i) If a =2+√3, then the value of 1/a = __________________

(ii) The perpendicular distance of the point (-4,-3) from the x- axis is _____________

(iii) The _______________ is the largest side of a right-angled triangle.

(iv) According to Heron’s formula the area of a triangle is given by __________

22. State True or False:

(i) For two triangles to be congruent, any three parameters of the six (3 sides and 3 angles) should be equal.

(ii) The sum of 0.3 bar and 0.5 bar is 0.8 bar.

(iii) Every rational number can be represented as an integer

(iv) Lines which are parallel to the same line are parallel to each other.

Q 23 – 28 are very short answer type questions. Each question is of 1 mark.

23. Solve: 12^2/3 × 5^2/3

24. Find the value of x in given figure.

Find the value of ‘P’ in the given figure.

25. The graph of the linear equation 4x=6 is parallel to which axis?

At what point does the graph of 2x-y=6, cut the x-axis?

26. In ΔABC AB=BC and ∠B =40°. Find the value of ∠C.

Write the congruence criteria for ΔABC and ΔPQR where AB=QP, ∠B =∠P and BC=PR.

27. Find two irrational numbers between √2 and √3.

28. One of the angles of a linear pair is 65°. Find the measure of the other angle.

If two angles of a triangle are complementary, then what type of triangle will be formed?

Part C

Q 29 – 32 are very short answer type questions. Each question is of 2 mark.

29. Solve: –

If p = 5-2√6 then find the value of

30. Show that if the sum of the two angles of a triangle is equal to the third angle then the triangle is right angled triangle.

31. Find the area of isosceles triangle whose equal sides are of length 15cm each and third side is 12cm.

32. Find the coordinates of two points on x-axis and y-axis which are at equal distance from origin.

In which coordinate the following points lie?

a) (-4,6) b) (3,3)

Find (sum of abscissa) – (sum of ordinates) of both the points.

Q 33 – 36 are short answer type questions. Each question is of 3 mark.

33.

Show that

34. Find any three solutions of 2x + 5y = -1.

35. In the given figure if PQ=PR and MQ=MR then prove that ∠PQM = ∠PRM.

36. In figure, if ray OR bisects ∠POS and ray OT bisects ∠QOS and OR⊥OT then prove that P,O and Q are collinear.

Q 37 – 39 are long answer type questions. Each question is of 4 mark.

37. If both ‘a’ and ‘b’ are rational numbers, then find the values of ‘a’ and ‘b’:

38. The heights of employees in an office are as follows:

Draw a histogram for the above table.

39. Calculate the area of the shaded region

In an exhibition, an umbrella is made by stitching 10 triangular pieces of cloth with same message written on two triangular pieces. If each piece of cloth measures 60 cm, 60 cm and 20 cm, find how much cloth is required for each message.

Class IX – Mathematics Practice Paper – 3