Mathematics Reinforcement Worksheets (Grade 7)

Transcription

1 Mathematics Reinforcement Worksheets (Grade 7)

2 Q 1. Worksheet 1 Topic: Percentage, Rate, Ratio and Proportion 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 C. Twice the total number of seats B. ½ of 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. 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. Q6. Express the following in simplest ratios. i) 4 hours to 100 minutes ii) Divide 72 in the ratio 1:2. Q7. Find the cost of 8 books when 6 books cost $48. Q8. Find cost of 10kg of tea when 3kg of tea cost $18

3 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. Q10. The cost of 5 meters of a particular quality of cloth is Rs Find the cost of 15 metres of cloth of the same type. Q11. 8 workers can paint a building in 24 days. How many days will 18 workers take to paint the same building? Q12. A loaded truck travels 14 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours? Q 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 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? Q 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?

4 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 c) 8 - (5 + n) b) n d) 5n 8 ii. iii. iv. The product of two numbers 2p and 7p is a) 2p x 7p b) 2(p x 7) The days in n weeks can be represented as a) 7 + n b) 7 x n c) 14p d) (2 x 7) p c) 7n 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 d) c) 8x + 3 d) 8x + 12 v. Lame and Jane have $42 altogether. If Lame has $y, then Jane has vi. vii. viii. a) $(42 + y) b) $(42 - y) c) $(y - 42) d) $(42 y) 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) a b 2 a b m n ab c) mn am bn d) m n If 5 pencils cost x cents, then the cost of y similar pencils in $ is. a) b) xy 5 xy 500 xy c) 20 x d) 20y 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.

5 Q3. The sum of three consecutive even numbers is 210. Find the largest of these numbers. Q4. The sum of three consecutive odd numbers is 243. Find the three numbers. Q5. If S = 4 r 2, find S when r = 10 ½ and = 22/7 Q6. If x + 3 =, find x when y = 8 and z = 2 Q7. When a number is doubled and 5 is subtracted from the result, the answer is 37. What is the number? Q8. The sum of two numbers is 120. If the larger number is four times the smaller number, what are the two numbers? 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. Q10. If the current temperature is 9 o. 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.

6 xy Q12. If x y, find x, when y = 3, p = 2 and q = 4. p q 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? Q14. What are the four consecutive numbers whose sum is 50? 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? 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? 2 3 Q17. If the product of two numbers is 2. If one number is, find their sum. 3 5

7 Worksheet 3 Topic: Volume and Surface Area Q1. Encircle the correct option. i. 500 litres is same as a) 5,000 cm 3 c) 500,000 cm 3 b) 50,000 cm 3 d) 500,0000 cm 3 ii. 1 ml is equivalent to a) 0.1 cm 3 c) 10 cm 3 b) 1 cm 3 d) 100 cm 3 iii. In what ratio 30m 3 must be decreased to become 15m 3? a) 2:1 c) 1:2 b) 3:6 iv. The cost of mutton increases from $15 to $45. The increased ratio is a) 15:45 c) 5:1 b) 45:15 Q2. Fill in the blanks. a) 1000 cm 3 = litres b) 2.56 cm 3 = liters c) 673 liters = m 3 d) 11% of $ 400 = $ Q3. Find the width of a cuboid, if volume is 64cm 3, length is 2cm and height is 8cm. Q4. If the surface area of a cube is 24cm 2, find length of a cube. 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 cm 2 of a cuboid. Find; a) the volume and b) height

8 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 cm 3. Q9. Do as directed. a) The Volume of a cube is 343m 3. 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.

9 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 ii) Number of line/s of symmetry in a parallelogram. a) 0 b) 1 c) 3 d) 0 c) 2 d) 4 iii) If 4cm on map represent 20m in actual. What is the scale of the map? a) 4:20 c) 2:10 b) 1:5 d) 4:5 iv) Which of the following can be true for an equilateral triangle a) Each angel is less than 60 o c) Each angle is equal to 60 o b) Each angle is greater than 60 o v) Sum of interior angles in a triangle is a) 90 o c) 360 o b) 180 o d) 270 o vi) Sum of angles on a straight line is a) 90 o c) 180 o b) 270 o d) 360 o vii) In isosceles triangle the angles on the base are a) Equal b) 90 viii) d) 2 angles are obtuse angles c) Different d) None of the above In a right angle triangle, one of the angles is 32 o, which of the following can be another of the angles in the triangle a) 148 o c) 58 o b) 57 o d) 59 o 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

10 Q4. Find the unknown angles marked in the following figures a) b) c) d) e)

11 f) g) h) i) j) k)

12 l) Q5. A road sign shows that it is 162km to the town of Hwange. HWANGE 162km a) Which letters have symmetry lines in HWANGE? b) Which letters have 2 order of rotational symmetry? c) How long would it take to reach Hwange at the speed of 72km/h?

13 Q1. Encircle the correct option. i) The average of 2, 3, 4, 7 is a) 4 b) 16 Worksheet 5 Topic: Graphs and Statistics c) 64 d) 7 ii) The total number of degrees in a pie chart is a) 180 o c) 270 o b) 360 o d) 90 o 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 v) Which is the least popular pet among people? a) Rabbit b) Dog c) Goldfish d) Cat c) Goldfish d) Hamster vi) A graph in which different sectors represents various quantities are called? a) Histogram c) Bar graph b) Line 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 c) 8 b) 5 d) 5 & 8 both viii) What will be the mean of 7, 7, 8, 9? a) 11.5 b) 15.5 ix) Find median of 6, 9, 3, 2, 1, 4, 5 a) 3 b) 5 c) 10.5 d) 7.75 c) 4 d) 2

14 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 a) Use the data to calculate i. Mode ii. Mean Q4. The pie chart shows the number of doctors, domestic staff and nurses in a certain hospital. Doctors Xᵒ s Nurses 7xᵒ 200ᵒ Domestic Staff 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?

15 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 English 3xᵒ Geography Calculate a) the percentage of Mathematics b) the number of pupils who chose Mathematics 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 c) median

16 Q7. A sample of six students were randomly selected and asked, "How many times did you check your yesterday?" The numbers were: 3, 0, 8, 2, 6, 2. Find the mean and mode. 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? 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? 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

17 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? 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?

18 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. A B C

19 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. iv. 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 c. the size of each interior angle b. the size of each exterior angle Find the sum of interior angles of the following regular polygons: a. 18-gon c. 14-gon b. 9-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 Find the gradient of the line passing through the following points: a. (-5, 2), (7, -6) c. (7, 11), (9, 2) b. (0, 5), (3, -2) d. (4, -3), (2, -5