Grade- 5
Mathematics
Chapter – 10 (Geometry)
• What kinds of figures are shown in the figures?
1) A
B
Ray AB
2) C
D
3)
•
Which kind of angle is shown in the figure?
1)
J
H
2)
J
I
3)
H
M
I
N
I
acute
•
Which kind of figure is given below ?
1)
2)
3)
4)
Square
•
Which kind of triangle according to sides ?
1) Equilateral
2)
• Name the polygon.
1)
Pentagon
4)
5)
3)
2)
3)
•
1)
2)
3)
4)
5)
6)
In the given figure ,name the following :
Diameter = GF
Centre
Chord
G
Radius
Arc
The longest chord
H
E
d
F
D
I
• Determine the perimeter?
1) A triangle whose sides are 4.8 cm, 5.1 cm , 6.5 cm .
Perimeter = sum of all sides
= 4.8 + 5.1 + 6.5
= 16.4 cm
2) An equilateral triangle whose side is 5.4 cm .
3) An isosceles triangle whose equal side = 4.8 cm and unequal side = 3.5 cm.
4) A square whose side is 6.9 cm.
5) A rectangle whose length is 4 cm and breadth is 3 cm .
Chapter – 11 Special angles
• Find the complement of the following angles
1) 29.7°
Complement of 29.7° = 90°- 29.7° = 60.3°
2) 11.6°
3) 49.1°
4) 22 °
• Find the supplement of the following angles .
1) 50°
Supplement of 50° = 180°- 50°= 130°
2) 105°
3) 80.7°
4) 95.2°
5) 161
• Find the angle :
1)
30°
?
The total of angles is straight angle = 180°
30° + ∠
= 180°
So ∠
= 180° - 30° = 150°
2)
3)
S
110
P
Q
P
?
L
R
?
48°
2 M
1)
C
D
78°
A
∴
∴
∴
∴
35
B
O
The sum of angle formed on line
∠ + ∠ + ∠
= 180°
35 + 78° + ∠
= 180°
113 + ∠
= 180°
∠
= 180° - 113°
= 67°
=
180
3) Find ∠
∠ = ∠ = ∠
2) Find
P
S
46
O
A
B
31°
R
C
D
E
Q
Find all the angles in the following figures.
1)
A
90
E
20°
B
C
O
•
F
∴
∴
∴
∴
∴
D
∠
= ∠ = 90°
(Vertically opp. )
∠ = ∠
= 20°
('()*+,--. /00. )
Sum of all angles at a line = 180°
∠
+ ∠ + ∠ = 180°
90 + ∠ + 20° = 180°
∠ + 110° = 180°
∠ = 180 – 110
= 70°
∠ = ∠ = 70°
(Vertically opp.)
2)
3)
70°
S
P
ᴗ
Z
ͻ
O
X
Y C
Q
50°
•
138°
R
60°
Find the size of angle marked with arcs.
1.
A
B
150°
ᴒ
O 140°
C
2.
A
B
40°
C
160°
80°
C
D
3.
P
S
Q
30 ᴒ O
70°
160°
R
The sum of angles at a
point = 360°
∠
+ ∠ + ∠
=360°
∴ 150 + 140 + ∠
= 360°
∴ 290 + ∠
= 360°
∴ ∠
= 360° - 290°
= 70°
Chapter-12 GEOMETRIC CONSTRUCTION
• Draw line segment.
1. 6cm
A
6cm
2. 7.4cm
3. 5.8cm
• Draw the circle with given radius.
a) r =
4cm
b) r =
5cm
c) r =
5.5cm
d) r =
6.2cm
• Draw the angle with protector and construct bisector.
B
1. 60°
30°
The sum of angles of triangle = 180°
∴ ∠ + ∠
+ ∠ = 180°
∴ 70° + 40° + ∠ = 180°
∴ 110 + ∠ = 180°
∴ ∠ = 180 – 110
∠ = 70
2. 140°
3. 42°
•
Draw any line segment per A
+ P Construct.
a) ∠123 = 60°
R
60°
P
b) ∠124 = 30°
c) ∠125 = 120°
Chapter-13
• Internal angles of polygon.
• Find the angle marked by small letter.
1.
2.
3.
Q
•
•
Find the sum of the angles of the following polygon.
1. Heptagon(7 sides)
The sum of the angles
=
(n – 2) × 180
=
(7 – 2) × 180
=
5
× 180
=
900°
b) Nonagon(9 sides)
c) Decagon(10 sides)
d) Dodecagon(12 sides)
Find the reaming angle.
1. Sum of the angle of hexagon is 630°
Ans: The sum of the angles of Hexagon
= ( 6 – 2 ) × 180
= 4 × 180
= 720°
∴ The reaming angle =
720° - 630°
=
90°
Chapter-14 UNITY METHOD
• Find the cost of 1.
1. 7 goats cost Rs. 630. Find the cost of 1 Goat.
Goat
Cost
7
630
1
?
Cost 1 goat
•
=
× 789
:
=
90°
2. 5 Chairs cost Rs. 630. Find the cost of 1 chair.
3. A carpenter earns Rs. 135 in 15 days. How much will he earn in 1 day.
4. 8 quintal of wheat cost Rs. 840 find the cost of 1 Quintal.
Find the given.
1. If 24 ball pen cost Rs. 56, find the cost of 18 such pens.
Pen
24
18
Cost of 18 pens
=
=
Cost
56
?
;7 ×<
==
42 Rs.
2. If a man earns Rs. 390 in 6 weeks, how much will he earn in 10 weeks.
3. If 3 litters of petrol costs Rs. 10.95. What will be cost of 8 litters?
4. 5 having blades costs Rs. 6.25 find the cost of 12 blades.
Chapter-15
DISTANCE, TIME AND SPEED
•
•
Find the distance.
1. A car travels at 45km/h. How far will it travel in 3 hours?
Ans:
Distance
=
speed ×time
=
45 × 3
=
135km
2. Harry runs at a speed of 12km/h. How far will he run in 2 hours.
3. A car travels at a speed 68 km/h. What distance does it travel in 4 hours?
Find the speed.
1. Anil runs 200 meters in 25 seconds. Find the speed.
Ans:
Speed =
?@ABCDEF
=
G@HF
99
;
= 8m/s
2. A van travelled 75km in 1 hours. Find its speed in km/h.
•
3. An aeroplane travelled 4320km in 6 hours. Find its speed.
Find the time.
1. A cyclist travels at 15km/h. How much time it take for 1 km?
Ans:
•
Time =
LH
;LH/N
=
;
hours.
LH
36
NOPQ
= 36×
;
<
= 10 m/s
2. 72 km per hour.
3. 14.4 km/h
Express in km/h.
1. 300 m is 15 sec.
Ans:
•
IJFFK
=
2. Subodh cycles at a speed of 32km/h. How long will he take to cycle 152km?
3. How long will a lorry take to travel 225km at a speed of 50km/h.
Convert into m/s.
1. 36 km per hour.
Ans:
•
?@ABCDEF
RH
Speed =
SOPQ
= 36×
2. 72 km per hour.
3. 14.4 km/h.
Express in km/h.
1. 300m is 15 sec.
899
Speed =
Now 20 m/s = 20 ×
<
;
;
= 72
;
<
= 10 m/s.
= 20
LH
NOPQ
2. 200 m is 36 sec.
3. 10 m/s.
8
Chapter-16
PERIMETER AND AREA
• Find the perimeter of square.
1. 14 cm. Perimeter of square
•
2. 6 mm
3. 4.7 m
4. 2.17 m
5. 0.19 m
Find the perimeter of rectangle.
1. l = 8 cm
b = 5 cm
Perimeter =
2 (a + b)
=
2 (8 + 5) cm
=
=
=
4 × side
4 × 14
56 cm
=
=
•
2 × 13 cm
26 cm.
2. l = 16 m
b = 14 m
Find the length or breadth.
1. L = 14 m
b =?
Perimeter = 58 m
b=
J
-l =
;<
3. l = 7 mm
b = 2.5 mm
- 14
= 29 – 14
=15m
2.
•
l =?
3. l = 20 mm
b = 8 cm
b =?
p = 34 cm
p = 50 mm
Find the length of side of square if perimeter is.
1. 12 cm
2. 10.4 cm 3. 36 m 4. 7.2 m
Side =
•
•
•
=
=
=
= 3cm
Find the area of rectangle.
1. 4 cm by 3 cm
Area
=
l×b
=
4 cm × 3 cm
=
12+U
2. 8 cm by 6 cm.
3. 20 cm by 15 cm.
4. 28 cm by 21 cm.
Find the area of a square.
1. 3 cm
Area of square
=
side × side
=
3 cm × 3 cm
=
9 cm2
2. 13 cm
3. 1.2 cm
4. 13.4 cm
Find the length or breadth.
1. Area = 320 cm b = 16 cm.
l=
•
T
WQFC
X
=
89
7
= 20cm
2. Area = 180cm b = 40 cm
3. Area = 187cm l = 17 cm
Find the area of shaded region:
1.
Area of outer rectangle
Area of inner rectangle
2.
= 9 cm × 6 cm
= 54 × cm
= 3 cm × 1 cm
=
3.
•
Find the area of given figures.
1.
Area of A = 4 × 5
= 20 m
Area of B = 4 × 5
= 60 m
Total area = A + B
= 20 + +0
= 80 m
2.
Area of A = 3 × 10
= 30m
Area of B = 4 × 3
= 12m
Total = A + B = 30 + 12 = 42
3.
19 cm
8 cm
8 cm
20 cm
15 cm
Chapter-17
VOLUME
• Find the volume of Cuboid.
1. l = 4 cm
b = 2 cm
h = 3 cm
Volume = l × b × h
=4×2×3
= 18 cm8
2. l = 0.05 cm
b = 3 cm
h = 4 cm
3. l = 10 cm
b = 2.5 cm
h = 2 cm.
•
•
Find the volume of cube.
1. Edge 4 cm.
Volume = side × side × side
= 4 cm × 4 cm × 4 cm
= 64 cm8
2. Edge 5 cm.
3. Edge 70 mm.
4. Edge 4.3 m.
Finding l or b or h if volume is given.
1. l = 2
b = 2 cm
h =?
Volume = 24 cm8
h=
YOZPHF
Z×X
=
=
= ×
=
=
<
= 3cm
2.
•
•
l=2
3. l = 8 cm
b = 70 mm
b=?
h = 5 mm
h = 0.5 cm
v = 2.4cm8
v = 2100 mm8
Find the volume if.
1. The end of a box has on area of 12 sq cm. If the box is 4 cm long. What is the
volume?
Ans: Volume
= Area × h
= 12 cm × 4 cm
= 48 cm8
2. A box has a base of area 136 cm. Its height is 2.5 cm what is the volume.
3. The area of the floor of a room is 180 m and height is 9 m. Find the volume.
Find the capacity in litters.
1. h = 3m, l = 6m, b = 4m.
Volume = l × b × h
= 6m × 4m × 3m
= 72 m8
8
Now 1m = 1000 l
∴ 72m8 = 72 × 1000
= 72000 m8
2. h = 1.5 m, l = 2 m, b = 3m.
3. h = 16 cm, l = 50 cm, b = 15 cm
Chapter-18 AVERAGE
• Find the average.
1. 3, 4 and 5
Average =
•
8[=[;
8
=
8
=4
2. 6, 8, 10, 12, 14, 16
3. 3.5, 5.9, 9.7, 8.3, 1.2, 4.6
Find the average.
1. The average of first 5 odd no. First five odd nos. Are
= 1, 3, 5, 7, 9
Average =
=
[8[;[:[\
;
;
;
=5
2. The average of first 10 counting no.
3. The average of first five multiples of 3.
Chapter-24 ROMAN NUMBER
• Write the following in roman numbers.
1. 3 = III
7. 210 =
2. 15 = XV
8. 907 =
3. 17 = XVII
9. 445 =
4. 28 =
10. 1231 =
5. 35 =
11. 1923 =
6. 105 =
12. 1040 =
• Write in the Hindu – Arabic.
1. IV
=4
6. L × X
=
2. IX
=9
7. L × IX
=
3. VII
=
8. MMCCC × XX =
4. XVII =
9. DCL × XVIII =
5. CCXII =
10. MCD × CII =
11. CCL × IV
=
• Write the Hindu – Arabic.
1. XL
= 40 × 1000
= 40000
2. VII D
= 7 × 1000 + 500
= 7000 + 500
= 7500
3. X DC IX
=
4. VII CM II
=
5. IX CM × IX
=
Chapter-25 ALGEBRA
• Write the Algebra form.
1. Five more than X.
X+5
2. Six less than Y.
Y–6
3. The product of 12 and t.
4. Square of a plus five times b.
5. The difference of 5 times m and 7.
• Find the volume.
If x = 6 and y = 2
1. 2x - 3y = 2 × 6 – 3 × 2
= 12 – 6
=6
2.
•
8
x + 4y
Solve the equation.
1. 3 + a = 5
∴ a=5–3
=2
2. x – 4 = 4
3. x – 6 = 5
4. 6 + a = 13
5. 3x = 12
6. 2x = 6
7.
8.
=
;
H
7
=4
=2
3.
:] ^_
]
4.
_[]
_^]
Chapter-27 DATA HANDLING
• Draw a pictograph for given data.
1.
Day
Sun
Mon
Tue
No. Of
4
1
2
stories
Take
= 1 story.
2.
Class
I
II
No. Of
15
20
students
Wed
3
Thu
1
III
10
IV
30
Fri
2
Sat
5
V
5
= 5 students
3.
Flavours
Vanilla
Chocolate
Strawberry
Boys
Girls
9
5
6
10
4
12
Butter
scotch
8
7