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Questions:

Generic 3

24 x 3 = 72

How many years are between 323 BC(BCE) and 1687 AD(CE)?

Madhan has to go to Karur from Coimbatore for an official visit. On his onward journey, he goes via Vellakoil to reach Karur. While returning to Coimbatore he travels via Erode. Both the routes travelled by him are given in the Fig Find the shortest route?

A school bus starts with full strength of 60 students. It drops some students at the first bus stop. At the second bus stop, twice the number of students get down from the bus. 6 students get down at the third bus stop and the number of students remaining in the bus is only 3. How many students got down at the first stop?

A person has Rs.960 in denominations of Rs.1, Rs.5 and Rs.10 notes. The number of notes in each denomination is equal. What is the total number of notes?

Are (–81) x [5 x (–2)] and [(–81) x 5] x (–2) equal? Mention the property.

Are (–42) x (–7) and (–7) x (–42) equal? Mention the property.

Prove that (–7) x (+8) is an integer and mention the property.

Browsing rates in an internet centre is Rs. 15 per hour. Nila works on the internet for 2 hours in a day for 5 days in a week. How much does she pay?

Find the value of :
(i) (-35)\(\times \) (-11)
(ii) 96\(\times \)(-20)
(iii) (-5)\(\times \)12
(iv) 15\(\times \) 5
(v) 999\(\times \)0

10.

Find the tetromino shapes found in the showcase given in Fig below. Form the same shape in the geoboard using rubberbands

11.

The collar of a shirt is in the form of isosceles trapezium whose parallel sides are 17 cm and 14 cm and the distance between them is 4 cm. Find the area of canvas that will be used to stitch the collar.

12.

The area of a trapezium is 828 sq. cm. If the lengths of its parallel sides are 19.6 cm and 16.4 cm, find the distance between them.

13.

Find the area of the trapezium whose height is 14 cm and the parallel sides are 18 cm and 9 cm of length

14.

Two angles are in the ratio 3:2. If they are linear pair, find them.

15.

Which of the following pair of adjacent angles will make a linear pair?
(i) 89°, 91°
(ii) 105°, 65°
(iii) 117°, 62°
(iv) 40°, 140°

16.

In Fig., find \(\angle \)AOC.

17.

Find the value of
(i) 3m + 2n
(ii) 2m − n
(iii) mn − 1, given that m = 2, n = − 1.

18.

Find the numerical co-efficient of the following terms. Also, find the co efficient of x and y in each of the term: 3x, - 5xy, - yz, 7xyz, y, 16yx.

19.

A parallelogram has adjacent sides 12 cm and 9 cm. If the distance between its shorter sides is 8 cm, find the distance between its longer side

20.

One of the sides and the corresponding height of the parallelogram are 12 m and 8 m respectively. Find the area of the parallelogram.

21.

Find the missing integers
(i) 0 + (2345) =______
(ii) 23479 + ______= 0

22.

From the ground floor a man went up six floors and came down six floors. In which floor is he now?

23.

A submarine is at 32 feet below the sea level. Then it moves up 8 feet. Find the depth of the submarine.

24.

Add
(i) (–40) and (30)
(ii) 60 and (–50)

Generic 5

1 x 5 = 5

25.

Ferozkhan collects Rs.1150 at the rate of Rs.25 per head from his classmates on account of the 'Flag Day' in his school and returns Rs.8 to each one of them, as instructed by his teacher. Find the amount handed over by him to his teacher.

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Answers Key:

Generic 3

24 x 3 = 72

Years in AD(CE) are taken as positive integers and BC(BCE) as negative integers.
Therefore, the difference is
= 1687 – (–323)
= 1687 + 323 = 2010 years

Distance travelled by Madhan from Coimbatore to Karur via Vellakoil = 131 km
Distance travelled by Madhan from Karur to Coimbatore via Erode = 66 + 101 = 167 km
Therefore, the route via Vellakoil is the shortest route.

Since we do not know the number of students who get down at the first stop, let us take the number as x. The number of students get down at the second bus stop is 2x.
x + 2x + 6 + 3 = 60
(1 + 2) x + 9 = 60
3x + 9 = 60
3x + 9 – 9 = 60 − 9 [Subtract 9 on both sides]
3x = 51
\(\frac { 3x }{ 3 } =\frac { 51 }{ 3 } \) [Divide by 3 on both sides]
Therefore, x = 17.
Thus, the number of students got down in the first bus stop is 17.

Let the number of notes in each denomination be x.
Then x + 5x + 10x = 960
(1 + 5 + 10) x = 960
16x = 960
Divide by 16 on both the sides,
\(\frac { 16x }{ 16 } =\frac { 960 }{ 16 } \) = 60
Therefore, x = 60
Thus, the number of notes in each denomination is 60.

Consider, (–81) x [5 x (–2)],(–81) x [5 x (–2)] = (–81) x (–10) = 810
Consider, [(–81) x [5 x (–2),[(–81) x 5] x (–2) = (–405) x (–2) = 810
Therefore, (–81) x [5 x (–2)] and [(–81) x 5] x (–2) are equal.
It is associative.

Consider, (–42) x (–7), (–42) x (–7) = +294
Consider, (–7) x (–42), (–7) x (–42) = +294
Therefore, (–42) x (–7) and (–7) x (–42) are equal.
It is commutative.

(–7) x (+8) = (–56)
Hence, –56 is an integer.
Therefore, (–7) x (+8) is closed under multiplicaton.

Number of hours spent on an internet for a day = 2 hrs
Therefore, number of hours spent on the internet for 5 days = 5 x 2 = 10 hrs
Cost of browsing per hour = Rs. 15
Cost of browsing for 10 hours = 15 x 10
Therefore, the amount paid by Nila for 5 days = Rs. 150

(i) (–35) x (–11) = 385
(ii) 96 x (–20) = – 1920
(iii) (–5) x 12 = –60
(iv) 15 x 5 = 75
(v) 999 x 0 = 0

10.

11.

Given height (h) = 4 cm
Parallel sides are (a) = 17 cm and (b) = 14 cm
Area of the trapezium = \(\cfrac { 1 }{ 2 } \times h\left( a+b \right) sq.units\)
= \(\cfrac { 1 }{ 2 } \times 4(17+14)\)
= \(\cfrac { 1 }{ 2 } \times 4(31)\)
= 62 sq. cm
Therefore, the area of canvas used is 62 sq. cm.

12.

Given, Area of the Trapezium = 828 cm²
\(\cfrac { 1 }{ 2 } \times h(a+b)=828\)
\(\cfrac { 1 }{ 2 } \times h(19.6+16.4)=828\)
\(\cfrac { 1 }{ 2 } \times h(36)=828\)
h (18) = 828
\(h=\cfrac { 828 }{ 18 } \)
h - = 46 m
Therefore, distance between the parallel sides = 46 cm

13.

Given, height (h) = 14 cm
parallel sides are (a) = 18 cm and (b) = 9 cm
Area of the trapezium = \(\cfrac { 1 }{ 2 } \times h(a+b)\)
= \(\cfrac { 1 }{ 2 } \times 14\left( 18+9 \right) \)
= 7(27)
= 189 sq. cm
Therefore, area of the trapezium is 189 sq. cm.

14.

Let the angles be 3x and 2x
Since they are linear pair of angles, their sum is 180°.
Therefore,

x = 36°
The angles are 3x = 3 x 36 = 108°
2x = 2 x 36 = 72°

15.

(i) Since 89° + 91° = 180°, this pair will be a linear pair.
(ii) Since 105° + 65° = 170° ≠ 180°, this pair cannot make a linear pair.
(iii) Since 117° + 62° = 179° ≠ 180°, this pair cannot make a linear pair.
(iv) Since 40° + 140° = 180°, this pair will be a linear pair.

16.

\(\angle \)AOC = \(\angle \)AOB + \(\angle \)BOC
= 46° + 51°
= 97°

17.

i) 3m + 2n = 3(2) + 2( −1) = 6 −2 = 4
ii) 2m − n = 2(2) − ( −1) = 4 + 1 = 5
iii) mn −1 = (2) ( −1) −1 = −2 −1 = –3

18.

Expression	Numerical co-efficient	Co-efficient of x	Co-efficient of y
3x	3	3	Not possible
-5xy	-5	-5y	-5x
-yz	-1	Not possible	-Z
7xyz	7	7yz	7xz
y	1	Not possible	1
16yx	16	16y	16x

19.

Given that the adjacent sides of parallelogram are 12 cm and 9 cm
If we choose the shorter side as base, that is b = 9 cm then distance between the shorter sides is height, that is h = 8 cm
Area of parallelogram = b x h sq.units = 9 x 8 = 72 sq. cm.
Again, if we choose longer side as base, that is b = 12 cm then distance between longer sides is height. Let it be 'h' units.

We know that, the area of the parellelogram = 72 sq.cm
b x h = 72
12 x h = 72
\(h=\cfrac { 72 }{ 12 } =6cm\)
Therefore, the distance between the longer sides = 6 cm.

20.

Given: b = 12 m, h = 8 m
Area of the parallelogram = b x h sq.units
= 12 x 8 = 96 sq.m
Therefore, Area of the parallelogram = 96 sq.m.

21.

(i) 0 + (-2345) = -2345
(ii) 23479 + (-23479) = 0
Therefore, additive inverse of 23479 is –23479

22.

Starting point = Ground floor
Number of floors climbed up = +6
Number of floors climbed down = –6
Now the landing point = +6 – 6 = 0 (ground floor)

23.

A submarine is 32 feet below sea level.
Therefore, it is represented by –32
Next it moves up 8 feet.
Moves above is represented as +8
The depth of the submarine = –32 + 8 = –24
Therefore, the submarine is located at 24 feet below the sea level.

24.

(i) (–40) and (30)
–40 + 30 = –10
(ii) 60 and (–50)
60 + (–50) = 60 – 50 = 10

Generic 5

1 x 5 = 5

25.

Ferozkhan collects Rs.1150 at the rate of Rs.25 per head from his classmates on account of the 'Flag Day'
Total amount collected = Rs.1150
Amount per head = Rs.25
Number of students = 1150 ÷ 25 = 46

Amount returned to each student is Rs.8
Amount returned to 46 students = 46 x 8 = Rs.368
Amount handed over to the class teacher = Rs.1150