DISTRICT COMMON EXAMINATION BOARD – KADAPA – YSR Dist.

Action Plan Model Question Paper 2019-2020

MATHEMATICS PAPER – II

(English Medium) Class: X (Max. Marks : 50) Time: 2.45 Hrs

Instructions:

1. Answer all the questions in a separate answer booklet. 2. The question paper consists of 4 sections and 33 questions. 3. There is internal choice in Section - IV. 4. Write answers neatly and legibly.

Section - Ⅰ

Note: 1. Answer all the Questions in one WORD or PHRASE. 2. Each Question carries ½ Mark. 12X ½ = 6

1. ∆PQR ~∆XYZ. If ∠P = 600, ∠Q = 500 then find ∠Z?

2. If BC2 + AC2 = AB2 then the vertex with right angle is.

3. The perimeters of two similar triangles are 30cm and 20cm respectively. If one side of first triangle is 12cm, determine the corresponding side of the second triangle. 4. The class mark of the class 5-b is 7.5. Then find the value of b ?

5. The data 1, 2, 3, 4, 5, 6, 7, 8, 9 has no mode. Give reason.

6. Are Rectangle and Square similar? Justify your answer.

7. Reduced and Enlarged photographs of an object are _____________

8. The size of the classes 1-5, 6-10, 11-15 is ____________

9. Write the converse of the statement “ In ∆ABC, if AB=AC, then ∠C= ∠B”

10. Which measure of central tendency do you consider to select class leader of your class?

11. The maps of Amaravathi in different atlases are [ ]

a) Similar b) Congruent c) Equal d) None of these

12. A man goes 9m towards east and then 12m towards North. Draw a rough diagram for this data to find the displacement from initial point to final point.

Section - Ⅱ

Note: 1. Answer all the Questions. 2. Each Question carries1 Mark. 8 X 1 = 8

13. ∆ABC~∆DEF and their areas are respectively 64cm2 and 121cm2. If EF = 15.4cm, then find BC?

14. ABC is an isosceles triangle right angled at C. Prove that AB2 = 2AC2

15. Find the Range of first 10 Prime numbers.

11-12-2029 . Day-09 Day

16E

16. Find the mean of 𝑎 -2, 𝑎 𝑎𝑛𝑑 𝑎 + 2.

17. Situation: 1. Average marks obtained by the students of a class.

Situation: 2 Marks obtained by most of the students.

a) What do we find in the first situation?

b) What do we find in the second situation?

18. When do we say that two polygons are similar?

19. Write S.A.S criterion for similarity of triangles.

20. From the adjacent figure, write the intersecting point of both ogives and find its median.

Section - Ⅲ

Note: 1. Answer all the Questions. 2. Each Question carries 2 Marks. 8 X 2= 16

21. A flag pole 4m tall casts a 6m shadow. At the same time, a nearby building casts a shadow of

24m. How tall is the building?

22. ∆ABC ~ ∆DEF. BC = 3cm, EF =4cm and area of ∆ABC=54cm2 . Determine the area of ∆DEF?

23. Find the mean of first 𝑛 natural numbers?

24. If the median of the data 4, 7, 𝑥 − 1, 𝑥 − 3, 16, 25 written in ascending order is 13. Then find the value of 𝑥 ?

25. D and E are points on the sides AB and AC respectively of 𝑎 ∆ABC. Check whether DEIIBC or not .

If AD=2.4cm, BD= 1.6cm, AE=7.2cm, EC=4.8cm.

26. Write the formula to find mode of grouped data and explain the terms in it.

27. Find the mean of the values of 𝑆𝑖𝑛0°, 𝐶𝑜𝑠 30°, 𝑡𝑎𝑛45°, 𝐶𝑜𝑡60°.

28. Draw the rough diagram for the following.

Construct a triangle shadow similar to the given ∆ABC, with its sides equal to 5

3 of the

corresponding sides of the triangle ABC.

Section - Ⅳ

Note: 1. Answer all the Questions. 5 X 4= 20 2. Each Question carries 4 Marks. 3.There is an internal choice for each question. 29. a) In ∆ABC, DE॥BC and

𝐴𝐷

𝐷𝐵=

3

5 AC =5.6cm find AE .

(Or)

b) In an equilateral triangle ABC, Dis a point on side BC such that BD = 1

3𝐵𝐶. Prove that 9AD2=7AB2

30. a) The table shows the daily expenditure on food of 25 householdes in a locality.

Daily Expenditure (in Rs) 100-150 150-200 200-250 250-300 300-350

Number of households 4 5 12 2 2

Find the mean daily expenditure on food by appropriate method? (Or)

b) The following table shows the ages of the patients admitted in a hospital during a month. Find the mode age of the patients.

Age ( in Years) 6-15 16-25 26-35 36-45 46-55 56-65

Number of patients 6 11 21 23 14 5

31. a)

(Or)

b) ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP=1cm and BP= 3cm,

AQ=1.5cm, CQ=4.5cm prove that ( Area of ∆APQ ) =1

16 ( Area of ∆ABC )

32. a) The following distribution shows the daily pocket allowance of children of a locality. The mean

pocket allowance is ₹18. Find the missing frequency 𝑓.

Daily pocket allowance (in Rupees)

11-13 13-15 15-17 17-19 19-21 21-23 23-25

Number of children 7 6 9 13 𝑓 5 4

(Or)

b) If the median of 60 observations, given below is 28.5. Find the values of 𝑥 𝑎𝑛𝑑 𝑦.

C.I 0-10 10-20 20-30 30-40 40-50 50-60

𝒇𝒓𝒆𝒆𝒒𝒖𝒆𝒏𝒄𝒚 5 𝑥 20 15 𝑦 5

33. a) Draw a triangle ABC in which AB=5cm, BC=6cm and ∠ABC = 600. Then, construct a triangle

similar to it, whose sides are 5

7 times the corresponding sides of ∆ABC.

(Or) b) The following distribution gives the daily income of 50 workers of factory.

Daily income (in Rs) 250-300 300-350 350-400 400-450 450-500

𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒘𝒐𝒓𝒌𝒆𝒓𝒔 12 14 8 6 10

Convert the distribution above to a less than type cumulative frequency distribution and draw its ogive.

AB, CD, PQ are Perpendicular to

BD. AB = 𝑥, CD= 𝑦 and 𝑃𝑄 = 𝑍.

Prove that 1

𝑥+

1

𝑦=

1

𝑧

Prepared by Sri D. VENKATA RAMANA, SA- Maths, ZPHS - Penagaluru