Worksheet 1 - The Air Force School

SUMMITIVE ASSESMENTMATHS
THE AIR FORCE SCHOOL
REAL NUMBERS
WORKSHEET-1
Q.1. The LCM of two numbers is 1200. Which of the following cannot be
their HCF?
(a) 600
(b)500
(c)400 (d)200
Q.2. If the LCM of a and 18 is 36 and the HCF of a and 18 is 2, then a=
(a)2 (b)3 (c)4 (d)1
Q.3. If HCF of (26, 169) = 13, then LCM (26, 169) =
(a)26
(b)52 (c)338
(d)13
Q.4. 3.27 is(a)an integer
(b)a rational no.
(c)a natural no.
(d)a irrational no.
Q.5. The LCM and HCF of two rational no. areequal, then the number must
be –
(a)Prime (b)Co prime (c)Composite
(d)Equal
Q.6. Explain why 7X11X13+13 and 7X6X5X4X3X2X1+5 are composite
number
Q.7. Check whether 6n can end with the digit 0 for any natural no. n.
Q.8. The HCF of two numbers is 16 and their product is 3072 find their
LCM.
Q.9. Prove that √3 is an irrational no.
Q.10. Prove that 3√2 is an irrational no.
Q.11. what can you say about the prime factorization of following rational
no.
(i)34.12345
(ii)34.5678
Q.12. is the rational no. 441/2 5 ×57 ×72 is a terminating or non terminating
decimal representation .
THE AIR FORCE SCHOOL
POLYNOMIALS
WORKSHEET-2
Q.1. If α, β are the zeros of polynomial 4x2 + 3x + 7 then 1/α + 1/β is =
(a) 7/3
(b) -7/3
(c) 3/7
(d) -3/7
Q.2. If one zero of the quadratic polynomial 4x2 - 8kx - 9 is negative of the
other, find the value of k.
Q.3. If α, β are zeros of polynomial 2x2 + 5x + k satisfying relation
α2 + β2 + 2β = 21/4 then find the value of k this to be possible.
Q.4. If α and β are the zeros of quadratic polynomial ax2 + bx + c then
evaluate
(i) α – β
(ii) α4 + β4
(iii) 1/α - 1/β
Q.5. divide the polynomial 3x2 – x3 – 3x + 5 by the polynomial x – 1 – x2
And verify the division algorithm.
Q.6. Find all the zeros of the polynomial 2x4 – 3x3 – 3x2 + 6x – 2 if two of its
zeros are √2 and -√2.
Q.7. If the polynomial 6x4 + 8x3 + 17x2 + 21x + 7is divided by another
polynomial 3x2 + 4x + 1 then the reminder comes out to be ax + b then find
a and b.
THE AIR FORCE SCHOOL
PAIR OF LINEAR EQUATION
IN TWO VARIABLE
WORKSHEET-3
Q.1.the value of k for which the system of number kx – y =2 & 6x – 2y = 3
has a unique solution, is
(a) =3
(b) ≠3
(c) ≠0
(d) =0
Q.2.The value of k for which the system of equation x+ 2y – 3 =0 &
5x + ky + 7 = 0 has no solution, is
(a) 10
(b) 6
(c) 3
(d) 1
Q.3. If am ≠ bl then the system of equation ax + by = c & lx + my = n
(a) has a uniue solution
(b) has no solution
(c) has infinitely many
solution
(d) may or may not have a solution
Q.4. the value of k for which the system of equation x +2y = 5 &
3x + ky + 15 = 0 has no solution
(a) 6
(b) -6
(c) 3/2
(d) none of these
Q.5.If the system of equation 2x + 3y = 5 & 4x + ky = 10 has infinitely many
solution, the value of k is
(a) 1
(b) ½
(c) 3
(d) 6
Q.6. The some of two digit number and the number obtained by reversing
the order of the digit is 121, and the two digit differ by 3. Find the number.
Q.7. The difference between two numbers in 26 and one number is twice
the product of the digit. Find the number.
Q.8. A two diit number is such that the product of its digit is 20. If 9 is added
to the number, the digit interchange their place. Find the place.
Q.9. A father is three time as old as his son. In 12 years of time, he will be
twice as old as his son. Find the present age of father and son.
Q.10. A boat covers 32 km upwards stream and 36 km downwards stream
in 7 hours. Also it covers 40 km upwards stream and 48 km downwards
stream in 9 hours. Find the speed of the boat in the still water and that of
the stream.
THE AIR FORCE SCHOOL
TRIANGLE
WORK SHEET-4
Q.1. A vertical stick 20m long casts shadow 10m long on the ground. At the
same time, a tower casts a shadow 50m long on the ground. The height of
the tower is:
(a)100m
(b)120m
(c)25m
(d)200m
Q.2. Two poles of height 6m and 11m stand vertically upright on the plane
ground. If the distance between their foot is 12m, the distance between
their tops is:
(a)12m
(b)14m
(c)13m
(d)11m
Q.3.If D, E, F are mid-point of side BC, CA and AB respectively of
ABC,
then the ratio of the areas of triangle DEF and ABC is:
(a)1:4
(b)1:2
(c)2:3
(d)4:5
Q.4. The areas of two similar triangle,
ABC and
81cm2 respectively. If the largest side of larger
DEF are 144cm2 and
ABC be 36cm, then the
largest side of the smaller triangle DEF is:
(a)20cm
(b)26cm
(c)27cm
(d)30cm
Q.4. A man goes 24m due west and then 7m due north. How far is he from
the starting point?
(a)31m
(b)17m
(c)25m
(d)26m
Q.5. If a line is drawn parallel to one side of a triangle intersecting the other
two side , then it divide the two side in the same ratio.(basic proportionality
theorem)
Q.6.In
triangle
ABC
&
ADC,
PQIIBC
and
PRIICD.
Prove
that
(i)AR/AD=AQ/AB (ii) QB/AQ=DR/AR.
Q.8.In triangle ABC, DEIIBC and CDIIEF. Prove that AD2 =AB × AF
Q.9.In triangle ABC, if D is a point on BC such that BD/DC=AB/AC, prove
that AD is the bisector of angleA.
Q.10.in the given figure, ad is the bisector of
AB=6cm, determine AC
A. If BD=4cm, DC=3cm and
A
6cm
B
C
4cm
D
3cm
Q.11. If the bisector of an angle of a triangle bisects the opposite side,
prove that the triangle is isosceles.
Q.12. In
ABC, if
BAD= CAD, prove that AB/AC=BD/DC.
A
B
C
D
Q.13.If the diagonal of a quadrilateral divide each other proportionally, then
it is a trapezium.
Q.14. In the trapezium, ABIICD. If OA=3x-19, OB=x-4, OC=x-3 and OD=4,
find x.
Q.15. In a trapezium, AO/OC=BO/OD=1/2 and AB=5cm. find the value of
DC.
Q.16. The area of two similar triangles are in the same ratio of the square
of the corresponding altitudes.
Q.17. A ladder 15cm long reaches a window which is 9m above the ground
on one side of a street. Keeping its foot at the same point, the ladder
is turned to the other side of the street to reach the window 12m high.
the width of the street.
THE AIR FORCE SCHOOL
TRIGONOMETRY
WORK SHEET-5
Q.1.if θ is an acute angle such that cosθ = 3/5, then sinθ tanθ -1
2tan2θ
(i)16/625
(ii)1/36
(iii)3/160
(iv)160/3
Q.2.If tanθ = 1/√7 then cosec2θ – sec2θ
Cosec2θ + sec2θ
(i)7/25
(ii)1
(iii)-7/25
(iv)4/25
Q.3. the value of cos320 - cos370
Sin370 - sin320
(i)1/2
(ii)1/√2
(iii)1
(iv)0
Q.4. If x tan45 cos60 =sin60 cot60 , then x is equal to
(i)1
(ii)√3
(iii)1/2
(iv)1/√2
Q.5. 1- tan245 is equel to
1+ tan245
(i)tan90
(ii)1
(iii)sin45
(iv)sin60
Q.6. In a
ABC, right angle at B, AB=4 and BC=3, find all trigonometric
ratio of A.
Q.7.If sin A =3/4, find sin A and cos A.
Q.8.If cosec A =
10, find other five trigonometric ratio.
Q.9.If sin A =1/3, evaluate cos A cosec A +tan A sec A.
Q.10. If tan A =1 and tan B = √3 , evaluate cos A cos B – sin A sin B.
Q.11. If tanθ + 1/tanθ = 2, find tan2θ + 1/tan2θ.
Q.12.Show that 2(cos2 45 + tan2 60 ) – 6(sin2 45 + tan2 30 ) = 6
Q.13.Evaluate each of the following:
(i) sin2 45 + cos2 45
tan 2 60
(ii) 5 sin2 30 + cos2 45 - 4 tan2 30
2sin30 cos30 + tan45
Q.14. √3 sin x = cos x
Q.15. Evaluate the following
(i) sin39 - cos51
(ii) sin36 - sin54
cos54 cos36
Q.16. Prove √1 + cosθ = cosecθ + cotθ
√1- cosθ
Q.17. Prove
sinθ + tanθ
= secθ cosecθ + cotθ
1-cosθ 1+cosθ
Q.18. Prove cosA + sinA = cosA + sinA
1-tanA 1-cotA
Q.19.If cosθ + sinθ =√2 cosθ, show that cosθ – sinθ = √2 sinθ.
THE AIR FORCE SCHOOL
STATISTIC
WORKSHEET-6
Q.1.The arithmetic mean of 1, 2, 3,…., n is
(a) n+1/2
(b) n-1/2
(c) n/2
(d) n/2+1
Q.2.for the frequency distribution, mean, median and mode are connected
by the relation
(a) mode = 3mean – 2median
(b) mode = 2median + 3mean
(c) mode = 3median + 2mean
(d) mode = 3median + 2mean
Q.3. Which of these can’t be determined graphically?
(a) mean
(b) median
(c) mode
(d) none of these
Q.4. If the mode of the data 16, 15, 17, 16, 15, x, 19, 17, 14 is 15 then x =
(a)15
(b) 16
(c) 17
(d) 19
Q.5. if the mean of 6, 7, x, y, 17 is 9 then
(a) x + y = 21
(b) x + y = 19
(c) x – y = 19
(d) x – y = 21
Q.6. If the mean of of the following data is 6 then find the value of p
x: 2
4
6
10
p+5
f : 3
2
3
1
2
Q.7. Find the missing frequency in the following frequency distribution if it is
known that the mean of the distribution is 1.46.
Number of accidents(x): 0
1
2
3
4
5
total
Frequence(f):
46 ?
?
25 10
5
200
Q.8.The following gives the number of children 150 families in the village
No. of children(x):
0
1
2
3
4
5
No. of families(f):
10
21 55
42
15
7
Q.9. the following gives the distribution of total household expenditure (in
rupees) of manual workers in the city.
Expenditure: 100-150
Frequency:
24
150-200 200-250
40
33
250-300
28
300-350 350-400
30
22
Q.10 find the mean marks of the student from the folloeing cumulative
frequency distribution
Marks – below10 below20 below30 below40 below50 below60 below70 below80 below90
No.of - 5
9
17
29
45
60
70
78
85
students
Q.11. the following are the marks of the student in the class. Find the
median. 34, 32, 48, 38, 24, 30, 27, 21, 35
Q.12.If the median of the following frequency distribution is 46 find the
missing frequency.
Variable : 10-20 20-30 30-40 40-50 50-60 60-70 70-80
total
Frequency : 12
30
?
65
?
25
18
229
Q.13. Find the mean , median , mode of the following data:
Classes
: 0-20 20-40 40-60 60-80 80-100 100-120 120-140
Frequency : 6
8
10
12
6
5
3
Q.14. Draw an ogive and the cumulative frequency polygon for the
following data
Marks
: 0-10 10-20 20-30 30-40 40-50 50-60
No. of students : 7
10
23
51
6
3
Q.15. a student noted the number of cars passing through a spot on a road
for 100 periods each of 30 minutes and summarized it in the table given
below. Find the mode of the data:
No. of cars : 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Frequency : 7
14
13
12
20
11
15
8
Q.16.the frequency distribution of scores obtained by 230 candidate in a
median entrance test is as follows.
Scores
: 400-450 450-500 500-550 550-600 600-650 650-700 700-750 750-800
No. of
Candidates : 20
35
40
32
24
27
18
24
Q.17. draw a cumulative frequency curve and cumulative frequency
polygon for the following frequency distribution by less than method.
Age
: 0-9 10-19 20-29 30-39 40-49 50-59 60-69
No. of person : 5
15
20
23
17
11
9
Q.18. Following is the age distribution of the group of student. Draw the
cumulative frequency polygon, cumulative frequency curve(less than type)
and hence obtain the median value.
AGE
5-6
6-7
7-8
8-9
9-10
10-11
FREQUENCY
40
56
60
66
84
96
AGE
11-12
12-13
13-14
14-15
15-16
16-17
FREQUENCY
92
80
64
44
20
8