The City School · · 2018-01-07... Direct and Inverse Proportion Q 1 If a class has 44 seats in...

The City School

PAF Chapter

Prep Section

Mathematics

Class – 7

Worksheets for Intervention Classes

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Topic: Algebra 1

Q1 Encircle the correct option.

1. A scarf y meters long is cut in two equal pieces. The length of each piece is

a) 2y

b)

c) y + 2

d) y + ½

2. Which expression represents "eight less than the product of five and a number"?

a) 8 – 5n

b) 8 – 5 + n

c) 8 – (5 + n)

d) 5n – 8

3. The product of two numbers 2p and 7p is

a) 2p x 7p

b) 2(p x 7)

c) 14p

d) (2 x 7) p

4. The days in n weeks can be represented as

a) 7 + n

b) 7 x n

c) 7n

d)

5. The length of a side of square is given as 2x + 3. Which expression represents the perimeter

of the square?

a) 2x + 16

b) 6x + 9

c) 8x + 3

d) 8x + 12


Q2 Fill in the blanks with an appropriate answer.

a) The speed of car is 55 km/hrs. The distance covered in y hours can be represented in

algebraic expression as ___________________.

b) 5a and 5b are ___________ terms.

c) How many minutes are there in m hours? _______________

d) Sum of 2q and 7p is _______________.

e) Construct a formula for the given statement. The cost of m eggs at 12 cents each.

_________

Q3 If S = 4r2, find S when r = 10 ½ and = 3.142

Q4 If x –

+ 3 –

=

, find x when y = 8 and z = 2

Q5 When a number is doubled and 5 is subtracted from the result, the answer is 37. What is the number?

Q6 The sum of two numbers is 120. If the larger number is four times the smaller number, what are the

two numbers?

Q7 When loaded with bricks, a lorry weighs 11,600 kg. If the bricks are three times as heavy as the

empty lorry, find the weight of the bricks.


Topic: Algebra 2

Q1. Encircle the correct option.

i) Lame and Jane have $42 altogether. If Lame has $y, then Jane has

a) $(42 + y)

b) $(42 - y)

c) $(y - 42)

d) $(42 y)

ii) In a class, the average age of m boys is a years and n girls b years. The average age of class is

_____.

a) 2

ba

b) nm

ba

c) mn

ab

d) nm

bnam

iii) If 5 pencils cost x cents, then the cost of y similar pencils in $ is _________.

a) 5

xy

b) 500

xy

c) 20

xy

d) y

x

20

iv) The sum of the ages of two brothers is 11. Elder brother is 10 years older than younger

brother. The younger brother is ______ years old.

a) 1

b) 10

c) 11

d) 21


Q2. Fill in the blanks.

a) In the term 3n, n is the ___________ and 3 attached to it is called ________ of the term.

b) Sum of two consecutive numbers is 100. If first number is x, second number will be

__________.

c) Open sentences which use the symbol “=” are called _____________.

d) Mr. Ghazi is three times as tall as his son, Ali. If Ali is x m tall, then Mr. Ghazi is

________ m tall.

e) There are _________ days in n weeks.

f) If x = 3 and y = 4, the value of 3xy is ___________.

Q3 If the current temperature is – 9o. Write a simple equation to find the new temperature? If the

temperature:

a) falls by 5 degrees _____________________________________________

b) rises by 5 degrees _____________________________________________

c) decreases by y degrees _____________________________________________

d) increases by z degrees _____________________________________________

Q4 Find a, as the sum of 2a and 15 is divided by 7, the result is 11.

Q5 A man buys r shirts at $p each and sells them at $q each. What is the profit? Give your

answer in terms of p, q and r.

Q6 If qp

xyyx

, find x, when y = 3, p = 2 and q = 4.

Q7 A class of 44 pupils sat for a test in a Mathematics. If the number of pupils who passed the

test is three times the number of pupils who failed, find the number of pupil who passed the

test?

Q8 What are the four consecutive numbers whose sum is 50?

Q9 Susan is 10 years older than her brother. In three years time, she will be twice as old her

brother. What are their present ages?

Q10 The length of the rectangular field is 7cm longer then its width. If the perimeter of the

rectangle is 74cm, find the length and area of the rectangle?

Q11 If the product of two numbers is3

22 . If one number is

5

3, find their sum.


Topic: Ratio and percentage

Q 1 Fill in the blanks.

a) After 6% deduction in bill, $282 still remains to be paid. The original bill was

_____________.

b) 80% of 15 is _____________.

c) Express 15 as percentage of 80. __________________.

Q 2 The height of a tree was 4.8m. After one year the height of the tree was increased by 125%,

find the new height.

Q 3 The workers of an electronic company were given an increment of 8% in their monthly

salaries:

a) If Peter earned $1800 per month originally find his monthly salary after the increment

b) If Paul’s monthly salary after the increment is $1728, find his original monthly salary.

Q 4 Express the following in simplest ratios.

i) 4 hours to 100 minutes

ii) Divide 72 in the ratio 1:2.


Topic: Direct and Inverse Proportion

Q 1 If a class has 44 seats in 4 rows then how many seats will it have it 2 rows?

A. ¼ of the total number of seats

B. ½ of the total number of seats

C. Twice the total number of seats

D. 1/3 of the total number of seats


a) Two quantities x and y are said to be in ___________ if they increase (decrease) together

in such a manner that the ratio of their corresponding values remains constant.

b) Each truck can carry 3 boxes. Write this ratio as a fraction. ___________

c) In inverse proportion, when one quantity increases the other quantity __________.

Q 3 State whether the statements are True or False.

a) The number of workers and the speed to complete a job is a case of direct proportion.

__________

b) Length of a square and its area vary directly with each other. ____________

c) If a car is travelling 216 miles in 1 hour then it will cover 108 miles in 2 hours. ___________

Q 4 Find the cost of 8 books when 6 books cost $48.

Q 5 Find the cost of 10 kg of tea when 3kg of tea cost $18

Q 6 A truck needs 54 litres of diesel for covering a distance of 297 kilometers. The diesel

required for the truck to cover the distance of 550 kilometer is

Q 7 The cost of 5 meters of a particular quality of cloth is Rs. 210. Find the cost of 15 meters of

cloth of the same type.

Q 8 8 workers can paint a building in 24 days. How many days will 18 workers take to paint the

same building?

Q 9 A loaded truck travels 14 km in 25 minutes. If the speed remains the same, how far can it

travel in 5 hours?

Q 10 Ahmed takes 175 minutes to drive home at 80 km/hr. How long will it take to drive home at

100 km/hr?

Q 11 28 shirts and 24 pants are there in the cupboard. Find the

a) ratio of shirts to pants

b) ratio of pants to the total items in the cupboard

c) ratio of shirts to the total items in the cupboard

Q 12 If 270 kg of corn would feed 42 horses for 21 days, for how many days would 360 kg of it

feed 21 horses?

Q 13 50 kg of grade A coffee beans is mixed with 100 kg of grade B coffee beans. What will be

the weight in kg of grade B coffee beans in 60 kg of the mixture?


Topic: Volume and Surface Area

Q1 Encircle the correct option.

a) 500 litres is same as

A. 5,000 cm3

B. 50,000 cm3

C. 500,000 cm3

D. 500,0000 cm3

b) 1 ml is equivalent to

A. 0.1 cm3

B. 1 cm3

C. 10 cm3

D. 100 cm3


a) 1000 cm3=_____litres

b) There are _________ cm3

in a m3.

Q 3 Express 3600 ml in mm3.

Q 4 Find the width of a cuboid, if volume is 64cm3, length is 2cm and height is 8cm.

Q 5 If the surface area of a cube is 24cm2, find length of a cube.

Q 6 An open rectangular tank of length 12 cm, width 8 cm and height 16 cm contains water up to a

height of 8 cm. Calculate:

a) The volume of water in litres ;

b) The total surface area of the tank that is in contact with the water.

Q 7 The length is 8 cm, width is 12 cm and surface area is 426 cm2 of a cuboid. Find;

a) the volume and

b) height

Q 8 Find the capacity in litres of a rectangular tank if the height of the tank is 0.15 m, length is

0.24 m and width is 0.19 m.

Q 9 Find the total surface area of a solid cube of volume 125 cm3


Topic: Statistics 1

Q 1 Encircle the correct option. [2]

i) The average of 2, 3, 4, 7 is

A 4 B 16 C 64 D 7

ii) The total number of degrees in a pie chart is

A 180o B 360

o C 270

o D 90

o


a) Mean is also known as _____________

b) The most suitable graph to show the data that changes with time is called _________

graph.

c) The relative quantities by areas of sectors of a circle is represented by ____________

Q 3 The number of new cars sold per month is given below

Months Jan Feb Mar Apr May June July

No. Cars 23 15 48 28 17 28 16

a) Use the data to calculate

i. Mode ________________

ii. Mean

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

b) Illustrate the information on a bar graph.


Domestic Staff

Nurses

Doctors

200ᵒ

Xᵒ

7xᵒ

Q 4 The pie chart shows the number of doctors, domestic staff and nurses in a certain hospital.

a) Calculate the value of x.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

b) If there are 35 doctors in the hospital, how many

i. nurses are there in the hospital?

ii. domestic staff is in the hospital?

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

c) Calculate the percentage of domestic staff.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________


Geography

English

Mathematics 3xᵒ

120ᵒ

2xᵒ

Q 5 Each student in a group of 240 was asked to choose his favourite subject from Mathematics,

English, Geography. The result is represented by a pie chart given below.

Calculate:

a) the percentage of Mathematics

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

b) the number of pupils who chose Mathematics

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________


Topic: Statistics 2

Name: _________________________ Section: _____ Date: __________

Time: ___________

Q 1 Encircle the correct option.

a) The list shows the number of miles Sana hiked on each of 7days, 1.6, 3.1, 1.5, 2.0, 1.1, 1.8, 1.5. What

was the mean number of miles she hiked each day?

A. 1.5 miles

B. 1.6 miles

C. 1.8 miles

D. 2.0 miles

b) The following bar graph shows different kinds of pet owned by people in a certain area.

Which is the most popular pet among the people?

A. Rabbit

B. Dog

C. Goldfish

D. Cat


c) Which is the least popular pet among people?

A. Rabbit

B. Dog

C. Goldfish

D. Hamster


a) Ann wore following color of shoes in a particular week: Blue, red, green, blue, black, brown,

blue.

Ann wore __________ colored shoes most frequently.

b) 2, 5, 4, 6, 2, 3, 4, 4, 1

The mean, median and mode for the above data will be _______ , _______ , _______

respectively.

Q 3 The weekly salaries of six employees at McDonalds are $140, $220, $90, $180, $140, $200. For these

six salaries, find the:

a) mode

_____________________________________________________________

b) mean

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

c) median

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

Q 4 A sample of six students were randomly selected and asked, "How many times did you check your

email yesterday?" The numbers were: 3, 0, 8, 2, 6, 2. Find the mean and mode.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________


Q 5 The pie chart below shows the students attendance at Central Middle School Fall Festival.

a) What percent of Grade 7 Girls attended the festival?

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

b) Find the angle subtended by the sector of Grade 7 boys?

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

c) There were 32 girls of Grade 7 who attended the festival. What was the total number of

students who attended the festival?

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

d) Hence, find the number of Grade 6 and Grade 8 boys who attended the festival?

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________


Topic: Statistics 3

Q 1 Encircle the correct options.

i) A graph in which different sectors represents various quantities are called?

A. Histogram

B. Line graph

C. Bar graph

D. Pie chart

ii) The mode of the data 2 , 2 , 2 , 3 , 3 , 4 , 5 , 5 , 5, 6 , 6 , 8 is

A. 2

B. 5

C. 8

D. 2 & 5 both

iii) What will be the mean of 7, 7, 8, 9?

A 11.5

B 15.5

C 10.5

D 7.75

iv) Find median of 6 9 3 2 1 4 5

A 3

B 5

C 4

D 2


a) In a pie chart ,all the angles of sectors add up to ____________

b) Median is ________ value of the date.

c) The median of first ten odd numbers is ___________.

d) A _____________ graph uses pictures to represent statistics.

e) The mean of the first five whole numbers is _______.

f) If the mean of six numbers is 51, then the sum of these six numbers is ____________

Q 3 The following are the heights (in meters) of a group of basketball players. Find the

1.8, 1.8, 1.9, 2.0, 1.7, 1.8, 1.9, 1.6, 2.0, 1.8, 1.9,1.2

a) mean height of the group, correct to one decimal place

b) median of the given data

c) mode of the data


0

100

200

300

400

500

600

700

1989 1990 1991 1992 1993

Q 4 The following pie chart shows a survey of the number of cars, buses and motorcycles that pass a

particular junction. There were 150 buses in the survey.

a) Calculate the total number of vehicles in the survey.

b) What percentage of vehicles passing by the junction were cars?

c) How many cars were in the survey?

Q 5 In a Zoological Park there are 1000 creatures as per the following table given below. Represent the

above data by a histogram.

Q 6 Read the following bar graph which shows the number of books sold by a bookstore during five

consecutive years and answers the question given bellow

a) How many books were sold in 1989? __________________

b) In which year were 600 books sold? __________________

c) In which year fewer than 200 books were sold? __________________

d) How many books were sold from 1989 to 1991? __________________

Amphibians Mammals Birds Fish Reptiles

150 400 225 175 50


Topic: Ratio and Volume

Q 1 Choose the correct answer.

i) In what ratio 30m3 must be decreased to become 15m3?

a) 2:1

b) 3:6

c) 1:2

ii) The cost of mutton increases from $15 to $45. The increased ratio is

a) 15:45

b) 45:15

c) 5:1


a) 2.56 cm3 = _______________ liters

b) 673 liters = _______________ m3

c) 11% of $ 400 = _______________

Q 3 Do as directed.

a) The Volume of a cube is 343m3. Find the side of a cube.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

b) The regular selling price of an item at Shop is $32. The shopkeeper increases

the price in the ratio 5: 4. Find the increased price.

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

c) If it takes7 hours to fill 3 gallons. How many gallons can be filled in 20 hours?

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________


d) The school has increased its student body from 150 students to 240 from last year. Find the

increased percent.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

e) Express 0.75m, 25km as ratio in its simplest form.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

Q 4 An open rectangular tank of length 4m, width 9m and height 7m contains water up to a height 3m.

Calculate:

a) The volume of water in liters.

b) The total Surface area of the tank that is in contact with the water.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________


Topic: Miscellaneous

Q 1 Choose the correct option.

I. The solution of 5 – 2y = 7 is

a) 1

b) 2

c) – 1

d) – 3

II. Base angle in the given isosceles triangle is 70O, third angle is

a) 70o

b) 60o

c) 50o

d) 40o

III. 400 cm2 expressed in m2 is

a) 4

b) 0.4

c) 0.04

d) 0.004

IV. The ratio of 0.4 to 2 in simplified form is

a) 0.2 : 1

b) 4 : 20

c) 2 : 10

d) 1 : 5

V. If a typist types 900 words in 1 hour, his rate of typing in words per minute is

a) 30

b) 15

c) 10

d) 5


VI. Order of rotational symmetry for a pentagon is

a) 5

b) 10

c) 15

d) 20

VII. In the given right triangle, value of missing angle x is

a) 35o

b) 45o

c) 55o x

d) 65o 155o

VIII. A parallelogram has _____ lines of symmetry

a) 0

b) 1

c) 2

d) 4

IX. The sum of four angles of a quadrilateral is

a) 4500

b) 3600

c) 2800

d) 1800

Q 2 Find the percentage increase if cost price is raised from $600 to $624

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________


Q 3 Write an algebraic expression involving x for each of the following:

i. Six times of a certain number is 16 more than twice the number.

________________________________________________________________________

ii. When a number is decreased by 2 and the result multiplied by 3, the final result is 24.

________________________________________________________________________

iii. The sum of two consecutive odd numbers is 64.

________________________________________________________________________

Q 4. If V= 1/3 Ah, find A when V= 42 and h= 6.

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

The City School · · 2018-01-07... Direct and Inverse Proportion Q 1 If a class has 44 seats in...

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