STMARY’SANGLO-INDIANHIGHERSECONDARYSCHOOL,CHENNAI-1

TESTDATE28May2020STUDYMATERIALFORHOMEPRACTICETESTSERIES-5XSTD

Home Practice Test Series 5 - Instructions Portions for the test on 28 May 2020 Only 2 mark questions from the following topics are included for the test.

(i) Coordinate Geometry (Fully), (ii) Mensuration (Fully) (iii) Trigonometry (Fully) Only 8 mark questions from the following topics are included for the test.

(iv) Practical Geometry (Fully) (v) Graph (Fully) To facilitate you to study, some of the important 2 Mark Questions with Answers are shortlisted in this study material, first prepare this study material before you can prepare the other questions in the above-mentioned topics. Blueprint: Section I – 12 x 2 = 24 Section II – 2 x 8 = 16 Maximum Marks – 40 Marks Time – 1 Hr. 15 min. Note: • Question paper will be uploaded in the school website on

Thursday (28 May 2020) at 11:45 am. • Question paper has to be answered before 4:00 pm under the

supervision of the parent. • The answer key will be uploaded in the website in the evening at

7:00 pm. • The parent has to assess the answer script by referring to the

Answer Key. • Answer papers should be kept under your safe custody and

produced at the time of your XI std. admission. For, this is also a way of checking a student’s sense of responsibility.

• Since the Exam dates are announced and your time is ticking prepare for the test to the best of your ability

STMARY’SANGLO-INDIANHR.SEC.SCHOOL,CHENNAI-1

FL\0528May2020HOMEPRACTICETESTSERIES–5STUDYMATERIALXSTD MATHEMATICS1. If three points (3 , -1) , (a , 3) and (1 , -3) are collinear, find the value of ‘a’.

2. Find the equation of a straight-line parallel to Y axis and passing through the point of intersection of the lines 4x + 5y = 13 and x - 8y + 9 = 0

3. The area of a triangle is 5 sq. units. Two of its vertices are (4,1) and (5, –3). The third vertex is (x, y) where y = x + 2. Find the coordinates of the third vertex. The area of triangle = 5 !

" 𝑥! 𝑥" 𝑥%𝑦! 𝑦" 𝑦%

𝑥!𝑦! = 5

!" 4 5 𝑥1 −3 𝑦

41 = 5

!"– 12– 5 + 5y + 3𝑥 + 𝑥 − 4𝑦 = 5

4x+y–17=5x"!

4x+x+2=10+175x=25x=5y=x+2=5+2=7 Therefore, the third vertex = (5 , 7)

4. If the points A(2 , 1), B(3 , -2) and C(a , b) are collinear, then prove that 3a + b = 7. Since the points are collinear, the area of triangle = 0 !

" 𝑥! 𝑥" 𝑥%𝑦! 𝑦" 𝑦%

𝑥!𝑦! = 0

!" 2 3 𝑎1 −2 𝑏

21 = 0

!"– 4– 3 + 3b + 2𝑎 + 𝑎 − 2𝑏 = 0 3a+b–7=0x"

!

3a+b=7

5. Prove that the points A(4 , 4), B(3 , 5) and C(-1 , -1) form a right angled triangle.

Slope = 3453674576

Slope of AB = 89:%9:

= !9!

= -1

Slope of BC = 9!989!9%

= 9;9:

= %"

Slope of AC = 9!9:9!9:

= 9898

= 1

Slope of AB x Slope of AC = -1 x 1= -1 Therefore, side AB is perpendicular to AC This proves that triangle ABC forms a right-angled triangle. 6. Find the equation of the line which passes through the points (0 , -a) and (b , 0)

Equation of the straight line which passes through two points is: 393634536

= 797674576

3?9>

3= = 7

?

ax = by ax – by = 0

7. Prove that the condition required for the lines a1x+b1y+c1=0 and a2x+b2y+c2=0 to be perpendicular is a1a2+ b1b2 = 0 a1x+b1y+c1=0 ---------------------- (1) a2x+b2y+c2=0 ---------------------- (2) Slope of line (1) = 9@ABCCD@DBEFAC7

@ABCCD@DBEFAC3= 9=6

?6

Slope of line (2) = 9=4?4

m1 x m2 = -1

9=6?6

x 9=4?4

= - 1 ⟹ =6=4?6?4

= - 1

𝑎!𝑎" = - 𝑏!𝑏" ⟹ a1a2+ b1b2 = 0

8. Find the equation of the straight line passing through the points (a , b) and (a+b , a-b) Sol:

9. Find the equation of the line passing through (1 , 2) and making an angle of 30° with y-axis.

10. A line passing through the points (a , 2a) and (-2 , 3) is perpendicular to the line 4x + 3y + 5 = 0, find the value of a.

Slope of the line 4x + 3y + 5 = 0 is = 9@ABCCD@DBEFAC7@ABCCD@DBEFAC3

= 9:%

Slope of the line joining the points (a , 2a) and (-2 , 3) = 3453674576

= %9"=9"9=

9:%

x %9"=9"9=

= - 1 [ Since the lines are perpendicular]

9!"

11.Findtheequationofthestraightlineswhichpassesthrough(4,3)andarerespectivelyparallelandperpendiculartotheX-axis. 12. If the straight line y = mx + c passes through the points (2 , 4) and (-3 , 6). Find the values of m and c. Sol: Since y = mx + c passes through (2 , 4) it becomes, 2m + c = 4 ------------- (1) Since y = mx + c passes through (-3 , 6) it becomes, -3m + c = 6 ------------- (2) (1)–(2)⟹5m=-2⟹m=9"

8

Substitutingm=9"8inequation(1)weget,2 9"

8+c=4

9:8+c=4

c=4+:8

c=":8

13. The slant height of a frustum of a cone is 4 m and the perimeter of circular ends are 18 m and 16 m. Find the cost of painting its curved surface area at Rs 100 per sq. m. Therefore,thecostofpaintingCSAofthefrustumofcone=68x100=Rs6800

14. A hemi-spherical hollow bowl has material of volume 𝟒𝟑𝟔𝝅

𝟑 cubic cm. Its external

diameter is 14 cm. Find its thickness.

15. How many metres of cloth of 2.5 m width will be require to make a conical tent whose radius is 7 m and height is 24 m. 16. The CSA and volume of a cylindrical pillar 264 m2 and 924 m3. Then find its diameter. 17. If the volume of a sphere is 38808 cm3, then find its surface area.

18. A copper sphere of diameter 18 cm is drawn into a wire of diameter 4 mm. Find the length of the wire made. Radius of sphere (R) = 9 cm

Radius of wire (r) = 2 mm = 0.2 cm = "!>

cm

Volume of sphere = Volume of wire (Cylinder)

:%𝜋𝑅% = 𝜋𝑟"h

:% x 𝜋x9x9x9 = 𝜋x "

!>𝑥 "!>

x h

h = :7%7Q7Q7!>7!>:

= 24300 cm = ":%>>!>>

m = 243 m

19. A hemispherical bowl of internal radius 9 cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 3 cm and height 4 cm. How many bottles will be needed to transfer all the liquid into bottles from the hemispherical container. 20. The radius of a cone is 20 cm. If the volume is 8800 cm3, find it’s height. 21. The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white washing it’s CSA at the rate of Rs 210 per 100 sq m.

22. The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface areas.

23. A right angled triangle ABC with sides 5 cm, 12 cm and 13 cm is made to revolve around the side of 12 cm. Find the volume generated by it. = 100 x 3.142 = 314.2 cm3 (approx.) 24. If sec 𝜽 + tan 𝜽 = 𝒙, then prove that sec 𝜽= 𝐱

𝟐

25. If sin 𝜽 + sin2 𝜽 = 𝟏, then cos2 𝜽 + cos4 𝜽 = 1 26. Prove that 𝒕𝒂𝒏𝜽

28. The angle of depression of a car standing on the ground from the top of a 75 m tower is 30°. Find the distance of the car from the base of the tower. 29. A tower is 100 𝟑 m high. Find the angle of elevation of its top from a point 100 m away from it foot.

30. A kite is flying at a height of 60 m above the ground. The inclination of the string with the ground is 60°. Find the length of the string.