mathematics reinforcement worksheets (grade 7) · pdf fileworksheet 1 topic: percentage, rate,...
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Mathematics Reinforcement Worksheets
(Grade 7)
Worksheet 1
Topic: Percentage, Rate, Ratio and 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
Q2. 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. __________________.
d) 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.
e) Each truck can carry 3 boxes. Write this ratio as a fraction. ___________.
f) If a car travels 81 km in 3 hours, then it can travel __________ km in one hour.
g) In inverse proportion, when one quantity increases the other quantity __________.
Q3. 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. ___________
Q4. The height of a tree was 4.8m. After one year the height of the tree was increased by 125%, find
the new height.
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Q5. The workers of an electronic company were given an increase amounting to 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.
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Q6. Express the following in simplest ratios.
i) 4 hours to 100 minutes
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ii) Divide 72 in the ratio 1:2.
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Q7. Find the cost of 8 books when 6 books cost $48.
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Q8. Find cost of 10kg of tea when 3kg of tea cost $18
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Q9. A truck needs 54 litres of diesel for covering a distance of 297 kilometers. How much diesel required for the
truck to cover the distance of 550 kilometer.
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Q10. The cost of 5 meters of a particular quality of cloth is Rs. 210. Find the cost of 15 metres of cloth of the same
type.
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Q11. 8 workers can paint a building in 24 days. How many days will 18 workers take to paint the same building?
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Q12. A loaded truck travels 14 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours?
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Q13. 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
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Q14. If 270 kg of corn would feed 42 horses for 21 days, for how many days would 360 kg of it feed 21
horses?
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Q15. 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?
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Worksheet 2 Topic: Algebra
Q1. Encircle the correct option. i. 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
ii. 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
iii. The days in n weeks can be represented as
a) 7 + n
b) 7 x n
c) 7n
d)
iv. 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
v. 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)
vi. 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
vii. 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
viii. 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 with an appropriate answer.
a) 5a and 5b are ___________ terms.
b) How many minutes are there in m hours? _______________
c) Sum of 2q and 7p is _______________.
d) Construct a formula for the given statement. The cost of m eggs at 12 cents each. _________.
e) In the term 3n, n is the ___________ and 3 attached to it is called ________ of the term.
f) Sum of two consecutive numbers is 100. If first number is x, second number will be __________.
g) Open sentences which use the symbol “=” are called _____________.
h) Mr. Ghazi is three times as tall as his son, Ali. If Ali is x m tall, then Mr. Ghazi is ________ m tall.
i) There are _________ days in n weeks.
j) If x = 3 and y = 4, the value of 3xy is ___________.
Q3. The sum of three consecutive even numbers is 210. Find the largest of these numbers.
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Q4. The sum of three consecutive odd numbers is 243. Find the three numbers.
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Q5. If S = 4r2, find S when r = 10 ½ and = 22/7
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Q6. If x –
+ 3 –
=
, find x when y = 8 and z = 2
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Q7. When a number is doubled and 5 is subtracted from the result, the answer is 37. What is the
number?
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Q8. The sum of two numbers is 120. If the larger number is four times the smaller number, what are
the two numbers?
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Q9. 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.
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Q10. 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 _____________________________________________
Q11. Find a, as the sum of 2a and 15 is divided by 7, the result is 11.
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Q12. If qp
xyyx
, find x, when y = 3, p = 2 and q = 4.
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Q13. 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?
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Q14. What are the four consecutive numbers whose sum is 50?
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Q15. 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?
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Q16. 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?
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Q17. If the product of two numbers is 3
22 . If one number is
5
3, find their sum.
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Worksheet 3
Topic: Volume and Surface Area
Q1. Encircle the correct option. i. 500 litres is same as
a) 5,000 cm3 b) 50,000 cm3
c) 500,000 cm3 d) 500,0000 cm3
ii. 1 ml is equivalent to a) 0.1 cm3 b) 1 cm3
c) 10 cm3 d) 100 cm3
iii. In what ratio 30m3 must be decreased to become 15m3? a) 2:1 b) 3:6
c) 1:2
iv. The cost of mutton increases from $15 to $45. The increased ratio is a) 15:45 b) 45:15
c) 5:1
Q2. Fill in the blanks.
a) 1000 cm3=_____litres b) 2.56 cm3 = _______________ liters c) 673 liters = _______________ m3 d) 11% of $ 400 = $_____________
Q3. Find the width of a cuboid, if volume is 64cm3, length is 2cm and height is 8cm. _________________________________________________________________________________
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Q4. If the surface area of a cube is 24cm2, find length of a cube.
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Q5. 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.
_________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ Q6. 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 _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________
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Q7. 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. _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________
Q8. Find the total surface area of a solid cube of volume 125 cm3. _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ Q9. 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 21 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 a ratio in its simplest form. ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Q10. 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. ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Worksheet 4
Topic: Angle properties and Symmetry
Q1. Encircle the correct option. i) Number of line/s of symmetry in an isosceles triangle.
a) 1 b) 2
c) 3 d) 0
ii) Number of line/s of symmetry in a parallelogram. a) 0 b) 1
c) 2 d) 4
iii) If 4cm on map represent 20m in actual. What is the scale of the map? a) 4:20 b) 1:5
c) 2:10 d) 4:5
iv) Which of the following can be true for an equilateral triangle a) Each angel is less than 60o b) Each angle is greater than 60 o
c) Each angle is equal to 60 o d) 2 angles are obtuse angles
v) Sum of interior angles in a triangle is a) 90 o b) 180 o
c) 360 o d) 270 o
vi) Sum of angles on a straight line is a) 90 o b) 270 o
c) 180 o d) 360 o
vii) In isosceles triangle the angles on the base are a) Equal b) 90
c) Different d) None of the above
viii) In a right angle triangle, one of the angles is 32o, which of the following can be another of the angles in the triangle a) 148o b) 57o
c) 58o d) 59o
Q2. Fill in the blanks with the correct answer.
a) In ∆PQR, if <p =48° and <Q =59° then <R =________. b) A scalene triangle is one which has no ________ sides and no _______ angles. c) If two of the interior angles of a triangle are equal, the triangle is _____________. d) The sum of adjacent angles on a straight line is ______.
Q3. Draw lines of symmetry in the following shapes. i) ii)
Number of lines of symmetry ______ Number of lines of symmetry ______
Q4. Find the unknown angles marked in the following figures
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
Q5. 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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HWANGE 162km
Worksheet 5
Topic: Graphs and Statistics Q1. Encircle the correct option.
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) 360o
c) 270o
d) 90o
iii) 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
iv) 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
v) Which is the least popular pet among people?
a) Rabbit
b) Dog
c) Goldfish
d) Hamster
vi) A graph in which different sectors represents various quantities are called?
a) Histogram
b) Line graph
c) Bar graph
d) Pie chart
vii) 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) 5 & 8 both
viii) What will be the mean of 7, 7, 8, 9?
a) 11.5
b) 15.5
c) 10.5
d) 7.75
ix) Find median of 6, 9, 3, 2, 1, 4, 5
a) 3 b) 5
c) 4 d) 2
Domestic Staff
Nurses
Doctors
200ᵒ
Xᵒ
7xᵒ
Q2. Fill in the blanks.
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 ____________.
d) Ann wore following color of shoes in a particular week: Blue, red, green, blue, black, brown, blue.
Ann wore __________ colored shoes most frequently.
e) 2, 5, 4, 6, 2, 3, 4, 4, 1
The mean, median and mode for the above data will be _______ , _______ , _______ respectively.
f) In a pie chart ,all the angles of sectors add up to ____________ g) Median is ________ value of the date. h) The median of first ten odd numbers is ___________. i) A _____________ graph uses pictures to represent statistics. j) The mean of the first five whole numbers is _______. k) If the mean of six numbers is 51, then the sum of these six numbers is ____________.
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
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Q4. The pie chart shows the number of doctors, domestic staff and nurses in a certain hospital.
s
a) Calculate the value of x.
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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? _________________________________________________________________________________
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Geography
English
Mathematics 3xᵒ
120ᵒ
2xᵒ
c) Calculate the percentage of domestic staff.
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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.
Calculate
a) the percentage of Mathematics
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b) the number of pupils who chose Mathematics
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Q6. 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
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c) median
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Q7. 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.
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Q8. The pie chart below shows the students attendance at Central Middle School Fall Festival.
a) What percent of Grade 7 Girls attended the festival?
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b) Find the angle subtended by the sector of Grade 7 boys?
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c) There were 32 girls of Grade 7 who attended the festival. What was the total number of students who
attended the festival?
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d) Hence, find the number of Grade 6 and Grade 8 boys who attended the festival?
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Q9. 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
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0
100
200
300
400
500
600
700
1989 1990 1991 1992 1993
Q10. 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?
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Q11. 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? __________________
Worksheet: 06
Topic: Time & Construction
2. In the following triangle ABC, Construct an angle bisector at C and construct a perpendicular
bisector of AB. Mark as X , the point of intersection of both the bisectors.
C B
A
Worksheet: 07
Topic: Angle properties of polygons and graphs
1. Do as directed:
i. Find the number of sides of a regular polygon if each of its exterior angles is:
a. 20⁰ b. 60⁰
c. 120⁰ d. 40⁰
ii. Find the size of an exterior angle of a polygon of:
a. 5 sides b. 9 sides
c. 15 sides d. 19 sides
iii. The sum of interior angles of a regular polygon is five times the sum of its exterior angles. Find:
a. the number of sides of the polygon b. the size of each exterior angle
c. the size of each interior angle
iv. Find the sum of interior angles of the following regular polygons:
a. 18-gon b. 9-gon
c. 14-gon d. 20-gon
v. Find the size of each interior angle of the following regular polygons of:
a. 7 sides b. 12 sides
c. 8 sides d. 22 sides
2. Fill in the blanks:
a. The general form of the equation of a straight line is ____________________________. b. If a line is passing through the origin, the value of c (y-intercept) is ___________. c. If the value of m (gradient) of a straight line is negative, the line will pass from the ________ to
the ________ quadrant. d. If the value of m of a straight line is positive, the line will pass from the ________ to the
________ quadrant. e. If the equation of a straight line is y = -2x – 3, the value of m is ________. f. If a straight line is touching the y-axis at (0, 3), the value of c is ________. g. If the equation of a straight line is y = 7x – 6, the value of c is ________.
3. Plot the graphs of the following equations:
a. 2y = 4x – 6 b. y = x + 7 c. y = -3x – 2 4. Find the gradient of the following lines:
a. 2y = 3x – 5 b. 3y = 12x – 6 c. 5y = -4x + 2
5. Find the gradient of the line passing through the following points: a. (-5, 2), (7, -6)
b. (0, 5), (3, -2)
c. (7, 11), (9, 2)
d. (4, -3), (2, -5