Math

1. SSC-2015 Final Model Test Examination
Subject: Mathematics/ Full Marks-100[Creative-
60/ MCQ-40]/Sub. Code: 10/SET-𝜷
Group-A (Algebra)
Answer any two questions:-
1. 𝑃 = 𝑎2
+
1
𝑎2 − 2 − 2𝑎 +
2
𝑎
𝑎𝑛𝑑 𝑄 = 4𝑎2
+
1
4𝑎2 − 2 − 4𝑎 +
1
𝑎
a. Resolve P into factors.
b. If Q=0, Find the value of a.
c. If P=0 what is the value of 𝑎2
+
1
𝑎2?
2. 7x-3y=31 and 9x-5y=41
a. What type of equation are the given equations?
b. Solve the equations by the method of cross-multiplication.
c. Solve the equations graphically.
3. The 5th term of a geometric series is
9
32
and 10th term is
81
28
,
a. Find the common ratio.
b. Find the third term of the series.
c. Find the sum of first four terms.
Group-B (Geometry)
Answer any two questions:-
4. The length of PQ=10 cm.
a. Divide PQ into five equal parts.
b. Construct an equilateral triangle whose perimeter is equal
to PQ.
c. Construct a triangle when the two base adjacent angles
∠X = 450
and ∠Y = 600
and the length of the perpendicular
from the vertex is half of PQ to the base are given.
5. The centre of the circles CDL and CKJ are A and B. EF and GH are
the tangents of the circles CDL and CKJ through the point of contacts D
and C respectively. Again IJ and IK are the tangents to the circles CKJ
through the point of contacts J and K respectively from a outside point I.
Both circles touch each other at C.
a. Prove that 𝐸𝐹 ⊥ 𝐴𝐷.
b. Using ‘a’ prove that A,C and B are collinear.
c. Using ‘a’ prove that IJ=IK.
6. If the chord AB = z cm and OD ⊥ AB, are in the circle ABC with centre
O use the adjoint figure to answer the following questions:
a. Find the area of the semi-circle.
b. Show that D is the midpoint of AB.
c. If OD = (
𝑧
2
− 2) cm, determine z.
Group-C (Trigonometry and Mensuration)
Answer any one question:-
7. The length of the shadow of the Minar AB is BO when the
angle of elevation of the sun is 600.
a. Find the length of OA.
b. What is the height of the Minar?
c. Show that, tan2A =
2 tan A
1 – tan2 A
8. A horse turned around a circular field with a speed of 66 m per minute
in 1
1
2
minute.
a. Determine the diameter of the field.
b. What is the area of the field?
c. The area of a square is equal to the area of the circular field.
What is the length of the square?
Group-D (Statistics)
Answer the question:-
9. Frequency distribution table of the marks obtained in mathematics of
50 students are given below:
Class
Interval
31-40 41-50 51-60 61-70 71-80 81-90 91-
100
Frequency 6 8 10 12 5 7 2
(a) Write cumulative frequency distribution table?
(b) Find the median of the data.
(c) Find the mode of the data.

2. SSC-2015 Final Model Test Examination
Subject: Mathematics/ Full Marks-100[Creative-
60/ MCQ-40]/Sub. Code: 10/SET-𝜷
1. (i) Sin2
A=1-Cos2
A (ii) Sec2
A=1+tan2
A (iii) Cot2
A=1-tan2
A
Which one ofthe followingis correct in accordance withthe above statements?
(a) (i) and(ii) (b) (i) and(iii) (c) (ii) and(iii) (d) (i),(ii) and(iii)
2. If CotA=
2
3
, which oneis the value oftan2
A?
(a)
2
3
(b)
3
2
(c)
4
9
(d)
9
4
3. SecA=5, which one is the value oftan2
A?
(a) 20 (b) 24 (c) 25 (d)26
4. The Symbol of sin𝜃 means-the multiplication of sin and 𝜃.
(a) the multiplication of sin and 𝜃. (b) the ratioofsine of the angle 𝜃 (c) Both (d) None of them
5. CosecA (Cosectant ofangle A)=?
(a)
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑆𝑖𝑑𝑒
𝐻𝑦𝑝𝑡𝑒𝑛𝑢𝑠𝑒
(b)
𝐻𝑦𝑝𝑡𝑒𝑛𝑢𝑠𝑒
𝑂𝑝𝑝𝑜 𝑠𝑖𝑡𝑒 𝑆𝑖𝑑𝑒
(c)
𝐻𝑦𝑝𝑡𝑒𝑛𝑢𝑠𝑒
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑆𝑖𝑑𝑒
(d)
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑆𝑖𝑑𝑒
6. tanA(tangent of angle A)=?
(a)
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑆𝑖𝑑𝑒
𝐻𝑦𝑝𝑡𝑒𝑛𝑢𝑠𝑒
(b)
𝐻𝑦𝑝𝑡𝑒𝑛𝑢𝑠𝑒
𝑂𝑝𝑝𝑜 𝑠𝑖𝑡𝑒 𝑆𝑖𝑑𝑒
(c)
𝑂𝑝𝑝𝑜 𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑆𝑖𝑑𝑒
(d)
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑆𝑖𝑑𝑒
7. Which one of thefollowingis correct for CotA.
(a)
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒
𝑂𝑝𝑝𝑜 𝑠𝑖𝑡𝑒 𝑆𝑖𝑑𝑒
(b)
1
𝑡𝑎𝑛𝐴
(c)
𝐶𝑜𝑠𝐴
𝑆𝑖𝑛𝐴
(d) All
8. If SinA=
2
3
andCos A=
2
3
, what is the value of Cot2
A?
(a) 1 (b) 2 (c) 3 (d) 4
Answer of questions 9 and10 onthe basis of thefigure:
9. What is thevalue of sin 𝜃
(a)
3
4
(b)
4
3
(c)
3
5
(d)
4
5
10. What is the value of cot 𝜃
(a)
3
4
(b)
4
5
(c)
3
5
(d)
4
3
11. The lengthofthe circle is called-
a. Perimeter b. Circumferencec. Both d. None.
12. Circumference=?
a. 𝜋𝑟 b. 𝜋𝑟2
c. 2 𝜋𝑟 d. 2𝜋𝑟2
.
13. Perimeterof the circle=?
a. 𝜋𝑟 b. 𝜋𝑟2
c. 2 𝜋𝑟 d. 2𝜋𝑟2
.
14. 𝜋 =?
a. 3.14159265 b. 3.14159265….. c. 3.1416 d. None
15. The diameter ofthe circle is 26 cm. What is its circumference?
a. 71.68 b. 81.68 c. 71.68 cm. d. 81.68 .cm
16. Total angle producedat the centreof the circle=?
a. 1800
b.2700
c. 3600
d. None
17. An arc s produces angle 𝜃0
at thecentre of a circlewith radius r. Then s=?
a.
𝜋𝑟
360
b.
𝜋𝑟𝜃
360
c.
𝑟𝜃
360
d.
𝜋𝑟𝜃
390
18 .Area of a triangle with sides 3cm,4cm, 5cmis ____
a)6sqcm b)2sqcm c)3sqcm d) 4sqcm
19. Area of a right triangle whose perpendicular sides are 15cm, 10cmis
a) 150 sqcm b)75 sqcm c) 54sqcm d) 34sqcm.
20. Perimeterof a right triangle withbase 3cm andhypotenuse 5cmis
a)11 cm b) 13cm c) 12cm d)14cm.
21. Area of an isosceles right triangle havingone ofthe equal sides 4cm is
a) 3sqcm b) 4sqcm c) 5sqcm d) 8sq cm
22. Area of an equilateral triangle of side 6cmis _______
a)9√3sqcm b)3sqcm c)4sqcm d)5sqcm.
23 .If the areaof an equilateral triangle is 25√3sqcm, then its side is
a)8cm b)10cm c)9cm d)12cm.
24. Perimeterof a rectangle of sides 7cm and3cmis _________
a) 18cm b)32cm c)20cm d) 23cm
25. Area of a rectangle with dimensions 5cm, 4cmis _________
a)54cm b)21sqcm c) 13sqcm d)20sqcm
26. Howmuch taka will be the total cost for decoratingthefloor withmosaicat Tk. 900per square metre
when Length of thefloor ofa rectangular room is 2 metres more thanits breadthandperimeterof thefloor is
20 metres?
a. 72000 b. 43200 c. 28800 d. 21600
27. (10
2
3)
3
4
=?
(a) 10 (b) √10 (c) √103
(d) √104
28.
√72. √24014
3
√3433
=?
(a) 1 (b) 2 (c) 5 (d) 7
29. If 22x+1
= 128 thenwhat is the value ofx?
(a) 2 (b) 3 (c) 4 (d)5
30.In arithmetic, which numbers are used?
a. Only positive b. Only negative
c. Both d. None
31. The lengthandwidth of two adjacent sides of a parallelogramare 7 cm.and5cm.respectively. What is
the half of its perimeterin cm.?
(a) 12 (b) 20 (c) 24(d) 28
32. The lengthofthe side of an equilateral triangle is 6 cm. What is its area (cm2)?
(a) 3 √3 (b) 4 √3 (c) 6 √3 (d) 9 √3
33. If the height of a trapeziumis 8 cm. andthelengths ofthe parallel sides are 9 cm.
and7 cm. respectively, what is its area (cm2)?
(a) 24 (b) 64 (c) 96(d) 504
34. Followthe informationgivenbelow:
(i) A square stone with the side of 4 cm.has 16 cm. perimeter. (ii) The area of circular sheet withthe radius 3
cm.is 3πcm2. (iii) The volume ofa cylinderwith height of 5cm. andtheradius of 2 cm. is 20π cm3.
Accordingto the information above, whichoneof the followingis correct?
(a) i andii (b) i andiii (c) ii andiii (d) i , ii andiii
35. Of the following, which one is class interval ?
(a) The difference betweenthe highest andthe lowest data
(b) The difference between the first andthe last data
(c) The difference betweenthe highest andthe lowest number of each class
(d) The sum of thehighest andthe lowest numbers of eachclass.
36. Whichone indicates the dataincludedin each class when the data are classified?
(a) Class limit (b) Mid-point of theclass
(c) Numbers of classes (d) Class frequency
37. If the disorganizeddataof statistics are arrangedaccordingtothe value, the data clusterroundnear any
central value.This tendencyof datais called
(a) mode (b) cetral tendency(c)mean(d) median
In winter, the statistics of temperatures (incelsius) of a region in Bangladesh is 100,90,80,60,110, 120, 70,
130, 140, 50. In thecontext of this statistics, answer the questions from(38 – 40).
38.Which is themode ofthe above numerical data ?
(a) 120 (b) 50 (c)140(d) no mode
39. Whichone is the mean oftemperature of theabovenumerical data?
(a) 80 (b) 8.50 (c)9.50(d) 90
40. Whichone is the medianof thedata ?
(a) 9.50 (b) 90 (c)8.50(d) 80