1

THE CITY SCHOOL

P A F CHAPTER

PREP SECTION

MATHEMATICS

WORK BOOK

CLASS – 7

2nd

term

PREPARED BY:

Adnan saleem

Samina javed

Uzma habib

Amna chinoy

2

TASK # 1

Take the value of as 3

, where necessary.

Q1. Find the unknown value in each case.

If =15,find .

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If ,find .

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if

3

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If

and

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if ,

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4

TASK # 2

Q1. Construct the formula.

A number decrease another by four and their sum is 32.

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When a number is trebled and four is subtracted from the result,the answer is 22.

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The sum of two numbers is 118.If the larger number is

Four times the smaller number.What are the two numbers.

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The sum of three consecutive even numbers is 441.

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The sum of three consecutive odd numbers is 171.

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When a number is divided by three and has two

subtracted from it, the result is 1/4 of the number.

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Jack is thrice as old as Roy.Roy is seven year

younger than John. If the sum of their ages is 27.

5

TASK# 3

Q1.Simplify these ratios:

15:18:60

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618:202

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1.36:0.18

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Q2.Express the following ratios in their simplest forms.

644:476:150

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1015:350:555

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8

: 3

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Q3.Express the first quantity to the second quantity as a ratio in its lowest terms.

45min,1h

6

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0.25 km,65m

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5.5h,75min

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0.4cm,1.6

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Q4.A sum of money is divided in the ratio 5:7:11.Calculate the shmallest share.

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Q5.In what ratio must 244kg be decreased to become 102kg?

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Q6.If light can travel 23 times around the world in 4 seconds,how many times can it circle the

world in 12 second.

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7

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Q7.My car travels 148 km on 16 ;litres of petrol.How far do I expect it to travel on a full tank of

40 litres?

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_

Q8.It takes a cyclist 88 minutes to cycle a distance of 22km,how long will it take him to cycle a

distance of 11 km?

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8

Facts to remember

Pie chart

A pie chart is a representation of numerical data, by inserting sectors of different angles into the

circle corresponding to the data.

Bar chart

A bar chart is a representation of numeric data, by making vertical or horizontal bars

corresponding to the given data.

Histogram

A histogram is similar to bar chart, the only difference is that while bar charts have gaps between

the bars, in histogram there are no gaps between the bars.

Mean

Mean is the average of the available data

Median

Median is the middle term of the whole data when the data is arranged in the ascending order.

Mode

Mode is the most popular, most frequent or the most repeated term.

9

TASK # 4

Question 1

Visitors to a National Park were asked to vote for their favourite animal. The results are shown

on the given pie chart.

a) Calculate the value of

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b) Calculate the percentage of visitors who voted for the giraffes.

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Lion

Giraffe

Elephant

Others

120°

135°

𝔁°

10

Question 2

Results of a test are illustrated in the given pie chart. If the total number of students is 18,

a) Find

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b) Find the number of students getting each grade.

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A

[CATEGORY NAME]

[CATEGORY NAME]

[CATEGORY NAME]

𝔁°

120°

3𝔁°

80°

11

Question 3

Each pupil in a class was asked to measure the length of the pencil he was using. The result is

shown in the bar graph

a) What is the shortest length of pencil? How many pupils are using pencil of this length?

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b) What is the most common length?

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c) What fraction of class is using pencils of 8cm long?

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d) Find the percentage of pupil using pencils shorter then 6cm.

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0

1

2

3

4

5

6

7

8

9

10

2 4 6 8 10 12 14

Freq

uen

cy

Length of pencils (in cms)

12

Question 4

The marks scored by eleven children in a spelling test are as follows:

9, 1, 4, 8, 7, 8, 4, 2, 10, 9, 4

Find:

a) Mode

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b) Median

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c) Mean

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Question 5

The students will take a survey of a class and find out the favorite subject of the students. The

data will be collected and represented in a bar graph.

13

Question 6

For the distribution 5, 8, 12, 10, 5, 3, 7, 5, 20, 10.

Find:

a) Mean

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b) Median

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c) Mode

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14

TASK # 5

Q1.Write direct or inverse proportion against the following statements:

The number of pencils bought and their cost.__________

The number of men on a job and the days required to complete it.__________

The speed of a car and the time taken to cover a given distance.__________

The distance covered and the time taken by a car moving at constant

speed.__________

Q2.The total cost of 10 lottery tickets is $20.Find the cost of 25 such tickets.

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Q3.If 8 men can do a job in 12 days. How long will 24 men take to complete it?

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15

Q4.Find the value of in each of the following.

X : 12 = 6: 12

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20 :a=5:25-

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4:8=12:p

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16

TASK # 6

Q1.Fill in the blanks.

If ∆ ABC ≡ ∆PQR then AC=__________________________

If ∆ XYZ ≡∆ABC then angle xzy=_____________________

If R.F of a map is 1:30000 then the scale of the map

is_______________________

The scale of a map is 1 cm to 5km then R.F of the map

is_____________________

Q2.Select true or false.

If ABCD ≡ WXYZ then BD=YZ_______________________

If ABCD≡PQRS then angle ADC=PRS_________________

If R.F of a map is 1:200000 then the scale is 1cm to 2km______________________

If the scale of a map is 1cm to 3m then R.F of the map is 1:300________________

17

Q3.If the scale of a map is 2 cm to 5km then what is the R.F of the map?

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Q4.The scale of a map is 1cm to 3km. Find the distance on the map between two towns if the are

actually 24 km apart.

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Q5.If ABC ≡ ∆ PQR, mention all the corresponding sides and angles. Hence if AB =3cm, AC=

2cm, angle ABC = 75°.Find PQ , PR and angle PQR.

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Q6.The model of an aircraft is in the scale 1:80. If the wing span of the model is 25 cm. What is the

wingspan of the actual aircraft in meter?

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18

TASK # 7

The above diagram tents to explain all angle properties made with parallel lines.With

reference to the diagram the following concept is conveyed.

Angle a + Angle b = 180°(Interior angles)

Angle a + Angle e = 180°(Adjacent angles)

Angle b = Angle c (Vertically opposite angles)

Angle e = Angle c (Corresponding angles)

Angle a = Angle d (Alternate angles)

Angle e = Angle b (Alternate angles)

Note:

When two lines are parallel, their interior angles are supplementary i.e. 180°

Sum of adjacent angles on a straight line are always supplementary i.e. 180°

Whenever two lines intersect, they form vertically opposite angles. Vertically opposite

angles are always equal.

When two line are parallel, alternate angles are always equal.

When two lines are parallel, corresponding angles are always equal.

19

Question 1

Find the unknown angles marked in the following figures

a)

b)

c)

20

d)

e)

f)

g)

21

h)

i)

j)

k)

22

l)

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TASK#8

Line of symmetry and rotational symmetry in polygons

A line of symmetry is a line that divides a polygon into two equal halves, so that the divided

polygon is congruent to its other half.

The rotational symmetry exists in geometrical figure if the figure can map onto itself after being

rotated about a fixed point through a certain angle. The fixed point about which the figure is

being rotated is called the center of rotational symmetry.

Some geometrical figures along with their lines of symmetry and order of their rotational

symmetry are given below.

Figure Number of lines of

symmetry

Order of rotational

symmetry

Scalene triangle 0 1

Isosceles triangle 1 1

Equilateral triangle 3 3

Trapezium 1 1

Kite 1 1

Parallelogram 0 2

Rhombus 2 2

Rectangle 2 2

Square 4 4

Irregular quadrilateral 0 1

Regular pentagon 5 5

Regular hexagon 6 6

Regular heptagon 7 7

Regular octagon 8 8

Regular nonagon 9 9

Regular decagon 10 10

n-sided polygon n n

Semi-circle 1 1

Circle Infinity Infinity

24

Question 1

Identify the following shapes and diagram to identify lines of symmetry.

a)

b)

c)

25

26

Question 2

A road sign shows that it is 162km to the town of Hwange.

a) Which letters have symmetry lines in HWANGE?

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b) Which letters have 2 order of rotational symmetry?

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c) How long would it take to reach Hwange at the speed of 72km/h?

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HWANGE162km

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TASK # 9

Choose the correct answer.

1. The ratio of boys to girls in a school is 7:9. If the enrolment of the school is 786, how many

boys are there?

a) 48

b) 336

c) 96

d) 432

2. Judy and Daniel shared some pencils in the ratio 3:2. If Judy receives 15 pencils, how many

pencils did Daniel receive?

a) 1. 6

b) 2. 9

c) 3. 10

d) 4. 15

3. The ratio of the 3 sides of a triangle is 1:3:5. If the length of the shortest side is 15 cm, find the

perimeter of triangle,.

a) 1. 135 cm

b) 2. 75 cm

c) 3. 45 cm

d) 4. 21 cm

4.

=

5.

=

:2 = 1 :

: 5 = : 20

8. 2 kg to 1 kg 500 g = ____ : ____

9. 3 wk 3 days to 1 wk 5 days = ____ : ____

10. If a printing press is printing 600 sheets of paper in one hour, rate of typing is _____ sheets

per minute.

28

TASK# 10

Question 1

In a rectangle, the ratio of the length to its breadth is 5:3. If its perimeter is 96 cm, what is its

length?

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Question 2

In a school, the ratio of the number of boys to the number of girls in an Art Club is 5:3

respectively. If there are 24 more boys than girls, what is the total number of children in the

Club?

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Question 3

A cake is cut into 3 pieces in the proportion of 1:2:3. Find the weight of the whole cake, if the

largest piece weighs 600 g.

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Question 4

Share Rs 150 between Khalid, Tariq and Ali in the ration 1:3:6.

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Question 5

There are 250 boys and 150 girls in a school. 24 prefects are to be chosen. Find the no. of boys

and girls chosen, if the no. chosen are to be in proportion to the number of boys and girls in

school.

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Question 6

Sana is 2 years old. Fahad is 3 years 6 months old; express the ratio of Sana’s age to Fahad’s age.

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Question 7

Find a pair of equivalent ratios from the following:

1:3, 4:8, 2/3:2

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Question 8

Cheryl and Daryl shared 84 marbles in the ratio 3:4. How many marbles must Daryl give to

Cheryl so that they both share equal no. of marbles?

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Question 9

Find the ratio of the weight of a Japanese car weighing 4200kg to that of a German car weighing

7200kg.

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Question 10

Four people contributed sums of money to the charity in the ratio 2:3:5:8. If the largest amount

contributed is $24. Calculate the total amount contributed by the four people.

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31

TASK # 11

Find the value of the following:

of 500 kg is

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of 60 cm

is____________________________________________________________________

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If you increase 40 by 125%; the result

is___________________________________________________

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If you decrease 250 by 40% the result is

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original cost ($) Percentage

change

Working New Cost ($)

Petrol 125 +8%

Cement 420 -20%

Paper 200 +3%

32

Fiber 120 144

Gas 60 27

TASK#12

Question 1

In a factory there are 900 employees. On a particular day 3% of them were late for work. How

many employees were late to work?

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Question 2

During winter the price of a sweater increased from $8.5 to $10. What is the percentage

increase?

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Question 3

A property costs 25% more today than when it was built. If the original cost of the property was

$95000, find its price today.

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33

Question 4

The new microwave oven takes 20 seconds less to defrost frozen dinner. If the old oven took

1min 40secs. What is the percentage decrease in the time to defrost?

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Question 5

After 3% surcharge the electricity bill amounted to $412. What was the original bill?

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Question 6

A toy shop sold 60% more toys during December than in November because of the Christmas

season. If the shop sold 4800 toys in December, calculate how many toys it sold in November.

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Question 7

A new cell phone at its launch cost $. After 1 year its value decreased by 15%. For the second

year its value further decreased by 10%. What is the value of the cell phone after 2 years?

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Question 8

As part of the annual increment the employees of ABC Ltd were given an increase of 6% in their

monthly salaries.

(a) Jane earns $2000 per month. What is her increased salary?

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(b) Harry’s increased salary for the month amounted to $1378. What was his original salary?

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Question 9

The costs of manufacturing a batch of certain medicine are:

Raw materials: $ 800

Labor: $500

Overheads: $200

If the cost of raw materials increased by 6%, labor by 7% and overheads by 4%, find the

percentage increase in the cost of producing one batch of this medicine.

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Question 10

The heights of three buildings were compared. Building A was 5% taller than building B and

building C was 15% shorter than building C. By what percentage is building A taller than

building C?

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36

TASK#13

1. What is the volume of a cuboid with length width and

height

a.

b.

c.

d.

2. How much water is needed to fill a tank 12cm by 10cm by 4 cm?

a. 800

b. 400

c. 840

d. 480

3. The length of a rectangular tank is 18cm. Its width is 7cm and its

height is 10cm. It is 2/5 filled with water. How much water is there

in the tank?

a. 504

b. 840

c. 560

d. 1260

4. A rectangular tank has a length of 15cm, width of 8cm and depth

of 5cm. Three-fourth of it is filled with water. How much more

water is needed to fill the tank?

a. 600

b. 150

c. 450

d. 540

5. How much water is required to fill a tank which has a capacity of

9liters when 3500ml is already there in the tank?

a. 5000 ml

b. 5.5liters

c. 5 liters

d. 2500 ml

37

6. How many 0.5 litres containers can be filled with water from a 5

litre tank?

a. 5

b. 15

c. 10

d. 2.5

7. If the volume of a cuboid 6.9cm by 4cm is 82.8 , what is the

height of the cuboid?

a. 12

b. 20.7

c. 3

d. 27.6

8. A rectangular tank 40cm by 30cm by 10cm contained water to a

depth of 6cm. find the amount of water required to make it full.

a. 12000

b. 7200

c. 4800

d. 1800

9. A cube has a volume of 343 . What is the total surface area of

the cube?

a. 49

b. 294

c. 147

d. 14

10. A bottle can hold

litre of orange juice. How many bottles are

needed to hold 8 litres of orange juice?

a. 2

b. 4

c. 16

d. 32

38

TASK#14

1.Find the total surface area of a solid cube of volume .

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2.A container measures 15cm by 10cm by 5cm. Find its volume.

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3.What is the volume of petrol in a tank which is 10m by 5m by 3m

when two-thirds of it is filled?

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4.A tank measuring 20 by 10m by 5m is 60% filled with water. If 50000

liters of water are drawn out of it, how many liter of water are left in

the tank?

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5.

of water is poured into a rectangular container measuring

20cm by 10cm by 8cm. Find the amount of water that will over flow?

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6. A tank with length 18cm breadth 9cm and depth 6cm is

filled with

water. How much more water is required to fill the tank to its brim?

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39

7.A rectangular tank 60cm long, 30cm wide and 12cm high is

filled

with water. A brick 18cm long, 10cm wide and 6cm high is put into it.

What is the depth of the water in the tank now?

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8.A tank 20cm by 15cm by 16cm contains a certain number of metal

balls of the same volume. Water is then poured into the tank till it is

full. When the metal balls are removed, the water left is 2100 . How many metal balls are there in the tank at first if each ball has a

volume of 90 ?

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9.A tank measuring 60cm by 15cm by 12cm is

filled with water. After

5 stones are placed into the tank, the water level rises by 6cm.

(a) How many liters of water is there in the tank?

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(b) Find the volume of one such stone.

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