Download VII - Maths (II SEM)

1
QUESTION BANK
MATHS
II - SEMESTER
STD VII
Chapter -1
Indices
I. Fill in the blanks
1) Repeated multiplication is written in _______________ form.
5
2)
3) a
4)
( )
5)
II. Choose the correct answer
1)
a) 5
2) ( )
3)
4)
5)
6)
7)
( )
( )
3
( ) =______
( ) =______
( ) =______
(( ) ) =______
b)11
a) 10
b)11
c)8
d)3
c)16
d)3
a) 10
b)a
c)16 d)7
a) 210
b)224
c)22
d)2-2
a) 86
b)8-1
c)81
d)85
a) pq+r
b)pq-r
c)pqr d)
a) 224
b)29
c)21
d)2-9
III. Solve (1m)
1) Read the exponent 83
2) Read the exponent 136
3) Read the exponent (-6)3
4) Read the exponent ( )
5) Write the expansion form of 38
6) Write the expansion form of ( )
7) Write the expansion form of ( )
8) Write the exponential form with positive index:- 3-5
9) Write the exponential form with positive index:- 10-7
10) Write the exponential form with positive index:- a-10
11) Write the exponential form with positive index:- x-12
12) Write the exponential form with negative index:- 54
13) Write the exponential form with negative index:- 1/34
14) Write the exponential form with negative index:- 27
15) Write the exponential form with negative index:- 1/x5
)
16) Simplify:- (
)
17) Simplify:- (
)
18) Simplify:- (
m
19) Write in (axb) form: 33 x 23
20) Simplify:- ( )
21) Simplify:- ( )
2
22) Simplify:- ( )
23) Simplify:- ( )
24) Write 236000 in scientific notation
25) Write 14567800000 in scientific notation
26) Write 0.00045213 in scientific notation
III. Solve (2m)
1) Write 125 in exponential form to base 5.
2) Write 256 in exponential form to base 4
3) Write 1331 in exponential form to base 11
4) Write exponential form of 1125.
5) Write exponential form of 324.
6) Simplify using law of exponents:7) Simplify using law of exponents:8) Simplify using law of exponents:- ( )
9) Simplify using law of exponents:10) Simplify using law of exponents:11) Simplify using law of exponents:12) Simplify using law of exponents:13) Simplify using law of exponents:- (
( )
)
14) Simplify using law of exponents:- ( )
15) Simplify using law of exponents:- ( )
16) Simplify using law of exponents:- ( )
(
)
( )
( )
( )
IV. Solve (3m)
1) convert into exponential form and apply 1st law of exponent:- 49 x 7
2) convert into exponential form and apply 1st law of exponent:- 27 x 81
3) convert into exponential form and apply 1st law of exponent:- 243 x 81
4) convert into exponential form and apply 1st law of exponent:- 1024 x 16
5) convert into exponential form and apply 2nd law of exponent:- 125 25
6) convert into exponential form and apply 2nd law of exponent:- 81 9
7) convert into exponential form and apply 2nd law of exponent:- 125 25
8) convert into exponential form and apply 2nd law of exponent:- 256 8
9) Which is greater?
or ( )
)
or (
or ( )
10) Which is greater?
11) Which is greater?
V. Solve (4m)
1) Simplify by reducing into exponential form:- 72x55x45
2) Simplify by reducing into exponential form:3) Simplify by reducing into exponential form:- 49
4) Simplify by reducing into exponential form:5) Simplify:-
(
) (
)
(
)
(
)
3
Chapter 5
Congruence
I. Fill in the blanks
1)
2)
3)
4)
Two geometrical figures are congruent if they have the same shape and ___________.
Line segments whose __________ are equal are congruent.
When two angles have ________________ they are congruent.
Congruent figures are always __________.
II. Choose the correct answer
1) The symbol of congruence is _______ a)
b)
c)
2) Which factor makes the figure congruent?
a) equal corresponding angles and same shape.
b) equal corresponding angles and same size.
c) same shape and size.
d) equal corresponding angles and same shape and size.
3) Two circles are congruent if they have
a) same radii
b) same centre
c) same centre and radii
d) same plane.
d)
III. Solve (1m)
1) Is the following figure congruent? Give reason.
2) Is the following figure congruent? Give reason.
3) Is the following figure congruent? Give reason.
4) Is the following figure congruent? Give reason.
IV. Solve (2m)
1) Draw a line segment AB=6cm. Draw 2 more line segments PQ and MN congruent to AB.
V. Solve (3m)
1) Write the corresponding vertices and corresponding sides in the following congruent
triangles.
4
K
L
P
M
R
Q
VI. Solve (4m)
1) Construct an angle of 120°. Construct another angle congruent to it.
2) Classify in to congruent or similar figures.
A
C
B
D
Chapter - 2
Ratio and Proportion
I. Choose the correct answer: (1M)
1) If a: b = c:d ,then a and d are called __________ .
( means, extremes , antecedents ,consequents )
2) If a:b = c:d ,then c and b are called _________ .
( means, extremes , antecedents ,consequents )
3) The simplest form of 5:15 is _________.
( 1:2 , 1:3 , 1:4 , 1:5 )
II. Fill in the blanks: (1M)
1) The comparison of two quantities of the same kind is called _______.
2) In the ratio a:b , a is ________ .
3) In the ratio a:b , a is ________
4) The inverse of a:b is ______
5)
= _________
III. Do as directed (1M)
1) Express the following in simplest form:
33:77
2) Express the following in simplest form:
5
3)
4)
5)
6)
7)
8)
25:125
Express the following in simplest form:
⅘:⅜
Express the following in simplest form:
1½:4½
Express the following in simplest form:
⅓:2
Express the following into their inverse form:
21:23
Express the following into their inverse form:
30:77
Fill in the blanks with appropriate numbers :
9) Fill in the blanks with appropriate numbers :
IV. Do as directed: (2M)
1) Express the following in simplest form:
100 g:500 g
2) Express the following in simplest form:
3 hours:6 hours
3) Express the following in simplest form:
500 g:1kg
4) Express the following in simplest form:
30 minutes:2 hours
5) Express the following in simplest form:
25cm:2m
6) Express the following in simplest form:
200ml:1litre
7) The total population of bandipur village is 54,000. 900 out of them are illiterate. Then
find out
(i)
The ratio of the total population to the number of illiterates.
(ii)
The ratio of the number of literates to number of illiterates.
V. Do as directed: (3M)
1) Solve the following & express the answer in their simplest form :
The population of Padnur village is 5880 .The ratio of number of females to number
of males is 10:11. Calculate the number of females and males in that village .
2) Solve :
In an alloy the ratio of Copper and Zinc is 5:3 by weight. Calculate the weight of
Copper and Zinc in 240g of the alloy.
3) Solve :
Distribute `642 among A,B and C in the ratio 1:2:3.
4) Check whether the following numbers are in proportion
5 , 6 , 10 , 12
6
5) Check whether the following numbers are in proportion
8 , 15 , 3 , 6
6) Check whether the following numbers are in proportion
1.5 , 4.5 , 2 , 6
VI. Do as directed (4M)
1) Solve the following on direct proportion :
The weight of 2m long iron rod is 6kg find the length of the iron rod if it weighs
15kg.
2)
Solve the following on direct proportion :
One kg of rice is enough for 8 people. Find the number of kgs of rice required for 200
people.
3) Solve
12 cows can graze a field for 10 days. In how many days will 20 cows graze the same
field.
4) Solve
30 people can complete a job in 12 days. How many days will 20 people take for
completing the same job ?
Chapter 6
Geometrical Constructions
I. Choose the correct answer: (1m)
1) Two lines are said to be __________ to each other if the angles formed at the point of
intersection are right angles. (equal, perpendicular, parallel, not equal)
2) _________ is a ray or line which divides the angle into two equal parts. (angle bisector,
perpendicular line, parallel line, line segment )
II. Fill in the blanks:
(1m)
1) One right angle = ________
2) If we bisect 90 ,we get _________
3) When you bisect 120 , using scale and compasses you will get ________
III. Do as directed:
(2m)
1) Draw a line segment of 6cm and draw a perpendicular bisector.
2) Draw a line segment of 7.4cm and draw a perpendicular bisector.
3) Draw a line segment PQ=10 cm. Divide it into four equal parts.
4) Construct 60 using a scale and compasses.
IV. Do as directed:
(3m)
1) Construct 110
2) Construct 132
3) Construct 30
4) Construct 45
5) Construct 90
V Solve:
using protractor and draw an angle bisector using a scale and compasses.
using protractor and draw an angle bisector using a scale and compasses.
using ruler (scale) and compasses.
using ruler (scale) and compasses.
using ruler (scale) and compasses.
(4m)
7
1) Draw a line
of length 10 cm. Mark a point P outside the line
perpendicular line passing through P.
2) Draw a line
of length 8cm.Mark a point A on the line
passing through A.
. Draw
. Draw perpendicular line
Chapter 3
Percentage
I. Fill in the blanks : (1m)
1) Profit = _________
2) Loss = __________
3) Percentage of profit = ________
4) Percentage of Loss = _________
II. Choose the correct answer:
(1m)
1) The extra money paid on the principal after a period of time is called ________
(Percentage, interest, profit, loss)
2) Amount = _________+ interest
(cost price, selling price, profit, principal )
3) Interest for every `100 for every year is known as _______ per annum.
(Principal, rate of interest, time, amount)
III Do as directed:
(1m)
1)
2)
3)
4)
5)
6)
7)
8)
Convert the following percentage into fraction: 50%
Convert the following percentage into fraction: 25%
Convert the following percentage into fraction: 87.5%
Convert the following percentage into fraction: 37.5%
Convert the following fraction into percentage: ½
Convert the following fraction into percentage: ¾
Convert the following fraction into percentage: 7/20
Convert the following fraction into percentage:
3/8
IV. Do as directed:
(2m)
1) There are 560 students in a school. 320 are boys. Find the percentage of girls in that
school
2) Find the simple interest for `3000 for 3 years at the rate of 12% .
3) Find the simple interest for `4500 for 2 years at the rate of 11% .
V. Do as directed:
(3m)
1) A computer shop owner bought a computer from the manufacturer for `12000. He sold it
for `15000. Find the profit percentage earned by him.
2) Rahul bought a mobile for `500 and sold it for `625 .Find the percentage of profit earned
by Rahul.
VI. Do as directed:
(4m)
8
1) A vegetable vender bought 20kg tomatoes for `200 out of which 5kg were rotten. He sold
the remaining tomatoes at `12 per kilogram. Find out the percentage of profit or loss
incurred to him.
2) Vasanth starts a Diary (milk) business by obtaining a loan of `25000 from a bank at the
rate of 15% per annum. Calculate the amount to be paid to the bank after 4 years.
Chapter - 7
Mensuration
I. Choose the correct answer:
(1m)
1) The length along the boundary of a closed figure is called __________
(Area , Perimeter , Length , breadth )
2) The surface enclosed by a closed figure in a plane is called __________
(Area , Perimeter , Length , Circumference)
3) A geometrical enclosed by two pairs of parallel lines is called _______
( Circle, Pentagon , Parallelogram , Hexagon)
4) A _________ is a locus of a point which moves in such a way that its distance from a fixed
point is constant.
( Circle, Square , Rectangle , Triangle)
5) Any line segment having its endpoints on the circle and passing through the centre of the
circle is called _______ of the circle.
( Radius, Circumference , Segment , Diameter )
6) A _________ is a closed geometrical figure in a plane having 3 sides .
( Pentagon, Square , Rectangle , Triangle)
II. Fill in the blanks :
(1m)
1) Perimeter of rectangle = _______.
2) Area of square = _________.
3) Perimeter of equilateral triangle= _______.
4) Circumference of a circle = _________.
5) Area of circle= ________.
6) Area of rectangular pathway = ________.
7) Area of circular pathway = __________.
8) Approximate value of ∏ = _______.
III. Solve
(2m)
1) Find the perimeter of the rectangle of the following measurements a) length = 8cm ,
breadth=6cm
b) length = 4.5m , breadth = 9.5m
2) Find the area of the rectangles of the following measurements a)length= 12.5m , breadth =
7m
b) length= 6.5m , breadth = 3.5m
3) Find the perimeter of the squares formed by the following measurements
a) side= 15m
b)side = 5.6cm
9
4) Find the area of the squares formed by the following measurements a)side= 12cm
b)side= 9.8cm
5) Find the perimeter of the following triangles .
6) Calculate the perimeter of the triangle whose sides are 6cm, 8cm and 6cm.
7) Find the perimeter of equilateral triangles with side : a) 11cm
8) Find the area of the triangle whose base is 14cm and the height is 7cm.
9) Find the area of parallelogram having base= 15m and height= 11m
10) Find circumference of the circle of the following radius : a) 21m
11) Find circumference of the circle of the following diameter : a) 49m
12) Find the area of the circle of the following radius : a) 10.5m
13) Find the area of the circle of the following diameter : a) 56m
IV. Solve:
(3m)
1)
A farmer has a field in the rectangular shape. The length of rectangular shaped field is
150m and its breadth is 100 m. Find out the cost of ploughing the field at the rate of `0.2
per m².
2)
What happens to the area of a rectangle when
3)
4)
5)
6)
7)
8)
9)
a) its length is doubled, breadth remaining the same?
b) its length is doubled, breadth is halved?
c) its length and breadth are doubled?
A garden is in the equilateral triangular shape. Its base is 22m and breadth is
18m. Find the cost of levelling the garden at ` 5 per m².
What happens to the area of triangle when
a) Its base is doubled , height remaining the same ?
b) Its base is doubled , height is halved?
c) Its base and height are doubled?
Find the altitude of the parallelogram shaped banner having base 12m and area
108
sq.m?
Find the diameter of a circle whose circumference is 1256 cm.(use ∏=3.14)
The diameter of a circular garden is 42m . What is the cost of fencing it at ` 25 per
metre ?
Find the cost of laminating decolam to a circular table of radius 1.4m , if the rate of
decolam is ` 50 per m².
Calculate the area of circular pathway formed by two concentric circles having the
following radii.
a) R= 20cm, r= 6cm
V. Solve:
(4m)
1) A door of length 2m and breadth 1m is fixed in a wall of 6m×4m.Find the cost of
painting only the wall, if the rate of painting the wall is `35 per m².
10
2) A lawn in a garden is in the shape of an equilateral triangle. If the length of one side of
the equilateral triangle is 75m, find the cost of fencing at the rate of `12 per metre.
3) The ratio of the base and height of a parallelogram is 3:2. If the area of the parallelogram
is 150 m², find base and height.
4) The circumference of the circle is 396 m. Find the area of the circle.
5) A slate is 30 cm long and 25 cm wide. It is surrounded by a wooden frame of width
2.5cm all around. John coloured the frame, need not consider the thickness of the frame.
Find the area of coloured frame.
6) The running track is enclosed between two concentric circles of radii 42m and 49m.
Find the cost of cementing the track at the rate of `25 per m².
Chapter – 4
Simple Linear Equations
I. Choose the correct answer:
(1m)
1) Which is the variable in the equation 2z+6=18 ?
( 2 , z , 6 , 18 )
2) Solution for the equation 2t=16 is _______
( t=8 , t=4 , t=16 , t=0)
3) Solution for the equation t-5=5 is ______
( t=0 , t=10 , t=5 , t= -10)
4) Solution for the equation 4=t+2 is ______
( t=2 , t=10 , t=6 , t=-2)
5) Which of the following is an equation ?
( 2x+3=8 , 2x+3<8 , 2x+3>8 , 2x+3 ≠8)
6) Which equation has y=4 as solution
( 2y+3=0 , y-7=2 , y+3=7 , y+4=0)
II. Fill in the blanks:
(1m)
1)
2)
3)
4)
5)
6)
L.H.S in the equation x-5=8 is _______
R.H.S in the equation 14-k = 2k+4 is ________
An equation containing only one variable with highest power one is called _________.
When 6 is added to a number we get 18, the equation is ________
When twice a number is multiplied by 5 we get 40, the equation is _______
When a number is divided by 10 we get quotient 4 leaving no remainder, the equation is
_______
7) Two algebraic expressions connected by the equal sign(=) is called an _______
III. Solve:
(2m)
8) Express the following statements in form of equations and solve
a) The sum of x and 9 is equal to 15
b) Twice a number decreased by 8 is equal to 18
c) When 22 is added to Megha’s age the sum is equal to 35
9) Solve the following equations
a) 5y-3=12
b) x-4=9
11
c) x/8=6
d)2k+6=0
e) k-½ = ¾
IV. Solve the following equations:
(4m)
10) Solve
a) 10-4x=26
b)6x-3=15
11) Solve
a) 3(x-7) = 24
b) 16-5x = 6
Chapter – 8
Data Handling
I. Fill in the blanks:
1)
2)
3)
4)
5)
(1m)
Arithmetic mean = ________
For the given data, the number of terms is an even number then, Median =_______
For the given data, the number of terms is an odd number then, Median =_______
The ______ is the value that occurs most frequently or most often .
Mean, Median and Mode which are representative values of the data is called _________.
II. Choose the correct answer:
(1m)
6) When we want to compare the same quantity between two different data, we use ________
(Bar graph , Double graph , Picto graph , Sector graph)
7) Arithmetic mean is obtained by the _____ of scores divided by the number of scores.
( Difference , Sum , Multiplication , Division )
III. Do as directed:
(2m)
8) The following are weights of 10 new born babies in a hospital on a particular day : (in Kg )
3.4 , 3.5 ,4.5, 3.9 ,4.2 ,3.8 ,4.4 ,4.5 ,3.6 and 4.1 respectively. Find the mean weight.
9) Find the missing numbers in each of the following data :
1. 21 , 25 , 29 , ____ , 31 , 33 and the mean is 28.
2. 41 , 43 , ____ , 47 , 49 , 51 and the mean is 46.
10) In a cricket match , 11 players scored runs as follows :
6 , 15 , 120 , 50 , 100 , 80 , 10 , 15 , 8 , 10 , 15 . Find the median
11) Find the mode of following data .
2 , 16 , 14 , 14 , 13 , 16 , 19 , 14 , 12 .
IV. Do as directed:
12) Find the mean of :
a) First nine prime numbers .
b) First eight natural numbers.
(3m)
12
13) The runs scored by two batsmen in the six matches are given below : Who performed
better ?
Batsman - 1
Batsman - 2
60
30
65
100
45
50
70
100
94
60
50
40
14) Find the median of the following data :
19 , 25 , 59 , 48 , 35 , 31 , 30 , 32 , 51.
If 25 is replaced by 52 then what will be the new Median ?
15) For what value of x the Mode of the following data is 18 ?
31 , 35 , 17 , 18 , 17 , 18 , 40 , x+12.
V. Do as directed :
(4m)
16) A survey of 100 school students regarding their favourite leisure time habits are given
below. Draw a bar graph to represent the above data.
HABIT
No. of students
Playing
35
Reading story books
10
Watching Television
20
Listening to the Music
5
Painting
30
17) The following table shows the educational level of Men and Women in Karnataka.
Represent it in suitable composite graph.
Education Level
Middle
Secondary
Higher Secondary
Graduate
No. of male
(in ten thousand)
No. of female
(in ten thousand)
95
20
45
30
92
10
30
25
Chapter – 9
Probability
I. Fill in the blanks :
(1m)
1) Experiments whose result is not controllable or predictable are called _______.
2) Probability = _________
II. Choose the correct answer:
(1m)
3) Sample space is denoted by the letter _________
(P,Q,R,S)
4) _______ of a random experiment is a particular outcome of the sample space denoted by
E.
13
(An event, Favourable outcomes, possible outcomes, Probability)
III. Do as directed:
(1m)
5) Toss two coins. Write all possible outcomes associated with this experiment. S= {
,
, ____ , ___ }
6) Five flash cards having odd numbers from 11 are shuffled well and one card is drawn from
it. Write the sample space.
IV. Do as directed:
(2m)
7) Write the possible outcomes of rolling a dice. Write the probability of getting the
following numbers
a) A prime number
8) Write the possible outcomes of rolling a dice. Write the probability of getting the
following numbers
a) A even number
9) Write the possible outcomes of rolling a dice. Write the probability of getting the
following numbers
a) A odd number
10) Write the possible outcomes of rolling a dice. Write the probability of getting the
following numbers
a) A number greater than 5.
V. Do as directed:
(4m)
11) A dice is divided 5 sectors and a pointer is placed in front of it. Then, it is spin for 75
times. Table given below shows the result that the position of the pointer against the
numbers. Draw a bar graph to represent the results.
Number of times dice is spin
75
The position of the pointer against
the numbers
1
6
2
14
3
26
4
19
5
10
Chapter - 10
Representation of Three Dimensional Objects in 2 Dimensional Figures
I. Fill in the blanks:
(1m)
1) Number of faces in a cuboid is ________.
2) Number of faces in a cube is ________.
3) Number of faces in a square based pyramid is ________.
4) Number of faces in a Triangular based prism is ________.
5) In a triangular based solid if all the faces are equilateral triangles then it is called
________.
14
II. Choose the correct answer:
(1m)
6) Tetrahedron has ________ edges.
(4, 5 , 6 , 7)
7) Number of vertices of a square based pyramid is _______.
(4, 5 , 6 , 7)
8) Number of edges of a triangular based prism is _______.
(6, 7, 8, 9)
III. Do as directed:
(1m)
9) Mention the number of curved surface, curved edge and vertices in a sphere.
IV. Do as directed:
(2m)
10) Write the number of faces and the number of vertices in the solid given below
a) Square based pyramid
b) Pentagonal based pyramid
11) Write the number of faces and the number of vertices in the solid given below
a) Hexagonal based pyramid
b) Cuboid
V. Do as directed:
(3m)
12) Mention the number of curved surface, curved edge and vertices in a
a) Cone
b) Cylinder