Mathematics Intervention Workbook Grade 7 2nd Term

The City School PAF Chapter Prep + Senior 1 Section Intervention workbook Mathematics (2nd Term)

Grade – 7

Q1 1.

Topic: Algebra 1 Encircle the correct option. A scarf y meters long is cut in two equal pieces. The length of each piece is a) 2y b)

2.

3.

4.

5.

𝐲 𝟐

c) y + 2 d) y + ½

Which expression represents "eight less than the product of five and a number"? a) 8 – 5n

c) 8 – (5 + n)

b) 8 – 5 + n

d) 5n – 8

The product of two numbers 2p and 7p is a) 2p x 7p

c) 14p

b) 2(p x 7)

d) (2 x 7) p

The days in n weeks can be represented as a) 7 + n

c) 7n

b) 7 x n

d)

𝑛 7

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

Q2

a) 2x + 16

c) 8x + 3

b) 6x + 9

d) 8x + 12

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

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

Q4

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

Q5

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.

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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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) c) $(y - 42) b) $(42 - y) 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b 2 ab b) mn a)

iii)

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

xy 5 xy b) 500 a)

iv)

ab mn am  bn d) mn c)

xy 20 x d) 20 y c)

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

c) 11

b) 10

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.

Q3

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

Q4

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.

Q5

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?

Q6

What are the four consecutive numbers whose sum is 50?

Q7

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?

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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Topic: Algebra 3 Q1 Write each phrase as an algebraic expression. a. b. c. d. e. f. g.

Seven increased by a number x 15 less than a number m The product of 13 and n Thirty-two divided by a number y Five more than twice a number Twice a number divide by 4 Three times a number decreased by 11

Q2 Choose the correct option i. Fifteen less than twice a number a) 15 – 2x b) 2x + 15

c) 2x – 15

ii. Three time a number, increased by seventeen a) 3(a + 17)

b) 3a + 17

c) (17 + 3)a

iii) The product of nine and a number, decreased by six a) 9(m – 6)

b) 6(9-m)

c)9m – 6

iv) Thirty divided by seven times a number a) 30 + 70n

7n

b)30

c) 30(7n)

v) Ali earns $30 in five days. Write an algebraic expression to represent the amount of money she will earn in x day. a) 30x Q3.A rectangle has a width of the perimeter of the rectangle.

b)

30 𝑥

c)30 + x

cm. The height is 3 cm less than the width. Write an expression for

Word problems on algebraic equation Remember to show all 5 parts. 1. Label the unknowns. 2. Set up the equation. 3. Solve the equation. 4. Find the value for the unknowns. 5. Check. The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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Work all problems in the space provided 1. Find two consecutive integers whose sum is 45.

2. Find three consecutive even integers whose sum is 72.

3. Find two consecutive odd integers whose sum is –88.

4. Find two consecutive even integers such that the sum of the larger and twice the smaller is 62.

5. Find three consecutive integers such that the sum of twice the smallest and 3 times the largest is 126.

6. Seven times a number is equal to 12 more than 3 times the number. Find the number.

7. Ten more than 6 times a number is 4 less than 4 times the number.

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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8. The second of two numbers is 4 times the first. Their sum is 50. Find the numbers.

9. The second of two numbers is 5 more than twice the first. Their sum is 80. Find the numbers.

10. The perimeter of a rectangle is 24 inches. Find the dimensions if its length is 3 inches greater than its width.

11. Find the measures of the angles of a triangle if the angles are represented by x, 4x, and 4x.

12. The perimeter of a triangle is 51 centimeters. The lengths of its sides are consecutive odd integers. Find the lengths of all three sides.

13. Two-thirds times a number plus 7 equals 7 minus the number. Find the number.

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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Topic: Inequalities Q1. Solve the following a. -3x ˂ 6 b. 1.5n ˃ 9 c.

3 8

v ˃ 15

d. 6(n + 10) ˂ 36 Q2. Of 8 pupils, there are 8 more girls than boys. How many girl pupils could there be? Solution: Assign letters:  

The number of girls: g The number of boys: b

We know that there are 8 pupils, so the: g + b = 8, which can be rearranged to b = 8-g We also know there are more girls than boys, so: g˃b We are being asked for the number of girl pupil: g Solve: Start with: g ˃ b b = 8 –g, so: g ˃ 8 – g Add g to both sides: g + g ˃ 8 Simplify: 2g ˃ 8 Divide both sides by 2 g˃4 so there could be 5,6,7 or 8 girls Now try it yourself Q3. A cab company charges $1.75 flat rate plus $0.65 a km. How far can Alice go if she only has $ 10 to spend at most?

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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Topic: Volume and Surface Area Q1

Encircle the correct option. a) 500 litres is same as A. 5,000 cm3

C. 500,000 cm3

B. 50,000 cm3

D. 500,0000 cm3

b) 1 ml is equivalent to

Q2

A. 0.1 cm3

C. 10 cm3

B. 1 cm3

D. 100 cm

Fill in the blanks. a) 1000 cm3=_____litres b) There are _________ cm3 in 1m3.

Q3

Express 3600 ml in mm3.

Q4

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

Q5

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:

Q7

a)

The volume of water in litres ;

b)

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

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

Q8

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.

Q9

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

Q1

Fill in the blanks.

Q3

a)

2.56 cm3

= _______________ liters

b)

673 liters

= _______________ m3

Do as directed.

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

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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___________________________________________________________________________ __________________________________________________________________________ Q4

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.

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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Topic: Statistics 1 Q1

Encircle the correct option. i)

The average of 2, 3, 4, 7 is A 4

ii)

B

16

C

64

D

7

270o

D

90o

The total number of degrees in a pie chart is A 180o

Q2

[2]

B

360o

C

Fill in the blanks. a) Mean is also known as _____________ b) The most suitable graph to show the data that change with time is called _________ graph. c) The relative quantities by areas of sectors of a circle is represented by ____________

Q3

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.

Q4

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

Doctors

Xᵒ

7xᵒ Nurses

200ᵒ Domestic Staff

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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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. ___________________________________________________________________________ Q5

Each student in a group of 240 was asked to choose his favourite subject from Mathematics, English and Geography. The result is represented by a pie chart given below.

120ᵒ Mathematics

2xᵒ

3xᵒ Geography

English

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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Calculate: a) the percentage of Mathematics ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ b) the number of pupils who chose Mathematics ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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Topic: Statistics 2 Q1 a)

Encircle the correct option. 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

b)

C. 1.8 miles D. 2.0 mile

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)

Which is the least popular pet among people? A. Rabbit B. Dog

Q2

C. Goldfish D. Cat

C. Goldfish D. Hamster

Fill in the blanks.

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.

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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Q3

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 ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ Q4

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. ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________

Q5

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

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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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? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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Topic: Statistics 3 Q1

Encircle the correct options. i) A graph in which different sectors represents various quantities are called? A. Histogram C. Bar graph B. Line 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 C. 8 B. 5 D. 2 & 5 both iii) What will be the mean of 7, 7, 8, 9?

iv)

a. 11.5 b. 15.5 Find median of 6 9 3 2 1 4 5 A. 3 B. 5

c. 10.5 d. 7.75 C. 4 D. 2

Q 2 Fill in the blanks. 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 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?

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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

Q6

Amphibians

Mammals

Birds

Fish

Reptiles

150

400

225

175

50

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 700 600 500 400 300 200 100 0 1989

1990

1991

1992

1993

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?

__________________

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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Topic: Miscellaneous Q1

Choose the correct option. The solution of 5 – 2y = 7 is

I.

a) 1

c) – 1

b) 2

d) – 3

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

II.

a) 70o

c) 50o

b) 60o

d) 40o

400 cm2 expressed in m2 is

III.

IV.

a) 4

c) 0.04

b) 0.4

d) 0.004

Order of rotational symmetry for a pentagon is

V.

a) 5

c) 15

b) 10

d) 20

A parallelogram has _____ lines of symmetry

VI.

a) 0

c) 2

b) 1

d) 4

Q3

The sum of four angles of a quadrilateral is a) 4500

c) 2800

b) 3600

d) 1800

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.

________________________________________________________________________ Q4

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?

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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Topic: Estimation and Approximation Q1. Estimate:

(a)

(b)

9.034 ×0.2106

(c)

0.0289 × 24.778

4.311 ×0.02916 3

981 ×0.0231

2905 × (0.512)3 0.004987

Q3. Complete the table:

Express

Correct to the number of significant figures indicated.

5003.583

4

37.87

2

18.1356

4

0.03256

3

19.64851

2

Q4. Estimate the value of the following and give your answer correct to one significant figure:

(a)

163.4 0.0818

(b) (398)2 × 0.062

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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Q5. Estimate, correct to one significant figure, the value of the following:

(a)

4.9 ×57 ×0.389

(b)

20.128

24.977 × 28.0349 19.897

Topic: Perimeter and Area of Simple Geometric Figures Q1. Complete the following table for each circle. Take π = 3.14. Space for calculations is provided at the end of the table. Radius

Diameter

Circumference

Area

4.2 cm 60 inches 132cm 78.5 𝑐𝑚2 2826 𝑚2 244.92 mm 56 cm 14 inches Q2. Complete the following table for each trapezium. Space for calculations is provided at the end of the table. Height

Parallel side 1

Parallel side 2

14 cm

8 cm

12 cm

45 m

75 m

6 inches

7 inches

Area

0.72 𝑚2 54 𝑖𝑛𝑐ℎ𝑒𝑠 2

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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Q3. Complete the following table for each parallelogram. Space for calculations is provided at the end of the table. Base

Height

18 cm

4.2 cm

Area

11.5 𝑚2

4.6 m 7 inches

8.4 𝑖𝑛𝑐ℎ𝑒𝑠 2

Q4. Find the area and perimeterof the following shaded parts:

Q5. Find the area of the following shaded parts:

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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Q6. Find the area of the following trapeziums:

In order to calculate the area and perimeter of strange figure like one given below: First of all identify all different shapes and find the perimeter and area of all the shapes separately and then add up all.

In this figure there is a rectangle, square, triangle and semi circle. Find the area of the given shape.

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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Topic: Angle properties of a polygon Q. find the unknown angles.

Q. Calculate the sum of the interior angles of the following polygons: a. a 16-gon

b. a 20-gon

Q. Calculate the angles:

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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Topic: Geometrical Construction Q1. Construct ABC such that AB = 10.5 cm , ABC =60◦ and BC = 7.5 cm. measure and write the length of AC.

The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class /Mathematics /Class – 7

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