BRAIN INTERNATIONAL SCHOOL

TERM I CLASS-VIII 2021-22

SUBJECT: – MATHEMATICS REVISION SHEET

RATIONAL NUMBERS

1. Is -0.4 a rational number?

(a) No, because it cannot be written in the form of 𝑝

𝑞 .

(b) Yes, because it can be written in the form of 𝑝

𝑞.

(c) Yes, because it is a negative number.

(d) No, because it is a decimal number.

2. If the multiplicative identity of rational number 𝑝

𝑞 is x, what could be the value of x ?

(a) 𝑝

𝑞 (b)

𝑞

𝑝 (c) 0 (d) 1

3. Which of these letters on the given number line represents 5

3 ?

(a) E (b) F (c) G (d) H

4. How many integers and rational numbers are there between -3 and 3?

(a) 7, 5 (b) 5, infinite (c) 7, infinite (d) infinite, infinite

5. The two rational numbers whose multiplicative inverse is same as they are.

(a) 0,1 (b) 0, -1 (c) 1 ,-1 (d) do not exist

6. If a = , b = , verify the following:

(i) a × b = b × a (ii) a + b = b + a

7. Find the reciprocal of the product of −16

11 and −

2

44 .

8. Find 5 rational numbers between −2

5 and

7

9

9. Represent the following rational numbers on number lines.

(a) −2

3 (b)

3

4 (c)

3

2

10. Find:

11. Show that:

12. If x = 1

2 y =

−2

3 and z =

1

4 , verify that x × (y × z) = (x × y) × z.

13. The product of two rational numbers is 25

58. If one of the numbers is

−35

29, find the other.

14. At a fruit shop, 21

4 kg bag of apples cost ₹ 90. At this rate what is the cost of 750 g of apples in terms of

paisa.

15. The sum of the two rational numbers is1

3 . If one of the numbers is

−5

48 , then find the other.

16. What number should be subtracted from −5

36 to get

−7

12 ?

LINEAR EQUATIONS IN ONE VARIABLE

1. Which of the following is a solution of the equation 2 (x-9) = -14?

(a) x =0 (b) x= 1 (c) x=2 (d) x = 3

2. Anita has ₹ 1800 and saves ₹ 600 each week to buy a new guitar that costs ₹ 12000. If n represents the number

of additional weeks, she needs to save to buy the guitar, which equation represents the situation and what will

be the value of n?

(a) 1800 + 600 n = 12000 ; n = 23

(b) 1800 + 600 n = 12000 ; n = 17

(c) 1800 n + 600 = 12000 ; n = 6

(d) 1800 n + 600 = 12000 ; n = 7

3. If x = a, then which of the following is not always true for an integer k.

(a) kx = ak

(b) 𝑥

𝑘 =

𝑎

𝑘

(c) x – k = a – k

(d) x + k = a + k

4. Four-fifths of a number is greater than three -fourths of the number by 4. The number is

(a) 12 (b) 64 (c) 80 (d) 102

5. The ages of A and B are in the ratio 5:7. Four years from now the ratio of their ages will be 3:4. The present age

of B is

(a) 20 years (b) 28 years (c) 15 years (d) 21 years

6. Sum of two numbers is 95. If one exceeds the other by 3, find the numbers.

7. If five times Ritu‟s money is ₹ 80, then find the amount she has.

8.The two numbers are in the ratio 4:3. If they differ by 18, find the numbers.

9. Three consecutive integers add up to 57. What are these integers?

10. When 4 is subtracted from three times a number and the result is divided by 3 more than the number, we get 2

5.

Find the number.

11. Solve the following linear equations:

(a) 𝑥

2 -10 =

1

2

(b) 3−𝑥

2𝑥−3 =

−1

2

(c) 𝑥−7

3 =

𝑥−1

5

(d) 11 – 5x + 3x + 4x =18

(e) (2x-2) +(3x-3) +(9x-9) = 1

12. The perimeter of a rectangular swimming pool is 154 meters. Its length is 2m more than twice its breadth. Find

its dimensions.

13. Convert the following statements into equations:

(a) 2 subtracted from a number is equal to 15.

(b) 3 times a number decreased by 2 is 4.

(c) 2 times the sum of the number x and 7 is 13.

14. A number is 12 more than the other. Find the numbers if their sum is 48.

15. A sum of ₹2700 is to be given in the form of 63 prizes. If the prize is of either ₹100 or ₹25, find the number of

prizes of each type.

16. If 40% of a number is added to 42 then result is the number itself. Find the number.

17. The sum of a two-digit number and the number obtained by reversing its digits is 121. Find the number if its

unit place digit is 5.

UNDERSTANDING QUADRILATERALS

1. Rajat constructs a parallelogram ABCD. What additional information does he need to convert it into a

rectangle?

(a) ∠ D = 90° and AB=CD

(b) AC = BD and AB = CD

(c) ∠ D = 90° and AC = BD

(d) AB = BC and CD = DA

2. From each vertex of a polygon, all diagonals are drawn. If exactly nine diagonals are drawn, which polygon is

drawn?

(a) Heptagon (b) Hexagon (c) Octagon (d) Pentagon

3. Consider a hexagon shown. What is the measure of ∠ 𝑇𝑆𝑅 ?

(a) 50° (b) 80° (c) 100° (d) 160°

4. What is the measure of each exterior angle of a regular octagon?

(a) 22.5° (b) 45° (c) 67.5° (d) 135°

5. Two students are determining in which quadrilateral the measure of all interior angles can be calculated, given

the measure of one interior angle. Their response is as shown.

Student A: The quadrilateral will be a kite.

Student B: The quadrilateral will be an isosceles trapezium.

Whose response is correct?

(a) Only student A (b) Only student B (c) Both A and B (d) Neither A nor B

6. Gagan draws a quadrilateral with diagonals perpendicular to each other at a point O. Observe the following

figures to know what additional information is required to conclude that the quadrilateral drawn is a rhombus.

(a) Point O must be the midpoint of both the diagonals.

(b) Point O must be the midpoint of the longer diagonal.

(c) Point O divides both the diagonals in the ratio 1:2.

(d) Point O must be the midpoint of the shorter diagonal.

7. Find the measure of an interior angle of a regular polygon of 12 sides.

8. In the given figure, ABCD is a rhombus. Find the values of x, y and z.

9. In the given figure, ABCD is a parallelogram. Find x, y and z.

10. ABCD is a rhombus with ∠ABC = 126°, find the measure of ∠ACD.

11. Find the values of x and y in the following parallelogram.

12. Write true and false against each of the given statements.

(a) Diagonals of a rhombus are equal.

(b) Kite is a parallelogram.

(c) Sum of the interior angles of a triangle is 180°.

(d) A trapezium is a parallelogram.

(e) Diagonals of a rectangle are perpendicular to each other.

(f) In a parallelogram, the opposite sides are equal.

13. Find x, y, z in the given figures if AB ∥ CD.

14. The diagonal of a rectangle is thrice its smaller side. Find the ratio of its sides.

15. Find the number of sides of a regular polygon whose each exterior angle measure 72°.

16. How many diagonals are there in a polygon having 10 sides?

17. The interior angle of a regular polygon exceeds its exterior angle by 108°. How many sides does the regular

polygon have?

18. The angles of a pentagon are x, (x+20) , (x+40) , (x+60) and (x+80) . Find the smallest angle of the polygon.

19. The diagonals of a rhombus measure 16 cm and 12 cm. Find its perimeter.

DATA HANDLING

1. The histogram below shows the age of the participants in a play

How many participants are below the age of 25 years?

(a) 10 (b) 8 (c) 6 (d) 4

2. The table below shows different pets and the number of students that own the pet

Akhil wants to represent the data in a circle graph, where each sector of the graph represents number of

students that own a pet. Which of these is not a step to construct a circle graph?

(a) Find the total number of students

(b) Find the fraction or percentage that each sector represents

(c) Finding the degree of the central angle of each sector.

(d) Finding the area of each sector.

3. Jagat has 15 cards marked with 1 to 15 on it. Which of these is the list of all possible outcomes of getting a

card with a number divisible by 3?

(a) { 3,6, 9, 12} (b) { 3,6, 9, 12, 15} (c) { 3} (d) { 5, 10, 15}

4. The marks obtained by 40 students of class VIII in an examination are given below:

18, 8, 12, 0, 8, 16, 12, 5, 23, 2, 16, 23, 2, 10, 20, 12, 9, 7, 6, 3,

5, 5, 13, 21, 13, 15, 20, 24, 1, 7, 21, 16, 13, 18, 23, 7, 3, 18, 17, 10

Represent the data in the form of frequency distribution using the same class size, one such class being 15-20

(where 20 is not included). Also represent the data in a histogram.

5. A die is thrown once. Find the probability of getting a number lesser than 3.

6. A class consists of 11 boys and 9 girls. A student is to be selected for social work. Find the probability that

(i) a girl is selected

(ii) a boy is selected

7. The following pie chart depicts the percentage of students, nationwide. What is the percentage of

(i) Indian students (ii) African students?

8. Numbers 1 to 10 are written on ten separate cards such that one number on one slip. These are mixed well and

one slip is chosen from the box without looking into it. What is the probability of

(a) getting a card on which 6 is written?

(b) getting a card having two-digit number on it?

(c) getting a multiple of 5?

(d) getting a number more than 8?

9. In the month of August‟21, a housewife spent her monthly account amounting to ₹ 7200 on different items as

given below. Represent the information in the form of a pie-chart.

Item Food Clothing Rent Education Miscellaneous

Amount (in ₹) 3000 400 2000 600 1200

10. A bag contains 144 coloured balls represented by the following table. Draw a pie chart to show this

information.

11. Look at the following circle graph and answer the questions given below:

(a) Find the fraction of the circle representing each of these given information.

(b) What is the central angle corresponding to the activities “ Sleep”?

12. (a) What is the class of 30-40?

(b) What is the lower limit of class 25-35?

(c) What is the upper limit of class 40-45?

(d) What is the class mark of 15-20?

SQUARE AND SQUARE ROOTS

1. Which of the following are true statements?

(a) The number of digits in a perfect square is even.

(b) The square of a prime number is even.

(c) The sum of two perfect squares is a perfect square.

(d) The product of two perfect squares is a perfect square.

2. Find the greatest number of two digits which is a perfect square.

(a) 64 (b) 36 (c) 81 (d) 28

3. A perfect square number can never have the digits ____ at the units place.

(a) 0 (b) 7 (c) 4 (d) 9

4. Evaluate (105)2 - (104)

2

(a) 200 (b) 209 (c) 418 (d) 1

5. The greatest number that will divide 137, 182 and 422 leaving a remainder of 2 in each case is:

(a) 15 (b) 1 (c) 4 (d) 9

6. Find the value of

7. Write a Pythagorean triplet whose smallest member is 6.

8. What is the sum of first n odd natural numbers?

9. Express 144 as the sum of odd numbers.

10. Without adding, find the sum. (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17+ 19 + 21)

11. Find the square root of 144 by the method of repeated subtraction.

12. Find the smallest number by which 1800 must be multiplied so that it becomes a perfect square. Also find the

square root of the perfect square so obtained.

13. The area of a square field is 8281 m2. Find the length of its side.

14. Simplify:

15. 1225 plants are to be planted in a garden in such a way that each row contains as many plants as the number

of rows. Find the number of rows and the number of plants in each row.

16. Find the smallest number by which 3645 should be divided so as to get a perfect square. Also, find the square

root of the number so obtained.

17. What least number must be added to 6072 to make it a perfect square?

18. Given n = 12, find the difference between n2 and (n+1)

2.

19. Find the value of each of the following without calculating squares.

(a) 272 – 26

2

(b) 1182 – 117

2

20. What is the least number that must be subtracted from 3793 so as to get a perfect square? Also, find the square

root of the number so obtained.

CUBE AND CUBE ROOTS

1. Which of the following is cube of an odd number?

(a) 216 (b) 512 (c) 343 (d) 1000

2. By what least number should 324 be multiplied to get a perfect cube?

(a) 13310 (b) 133.1 (c) 133100 (d) 1331000

3. Which digit comes in the one‟s place in the result of the expression (21476 + 31520 + 41305 + 50697)3?

(a) 2 because 6 + 0 + 5 + 7= 18 and 8× 8 × 8 = 512

(b) 2 because 2 + 3 + 4 + 5 = 14 and 4 + 4+ 4 = 12

(c) 4 because 2 + 3 + 4 + 5 = 14 and 4 × 4 × 4 = 64

(d) 4 6 + 0 + 5 + 7= 18 and 8+ 8 + 8 = 24

4. Which of the following is a perfect cube?

(a) 216 (b) 512 (c) 343 (d) 1000

5. How many consecutive odd numbers must be added to get the sum equal to 243?

(a) 2 (b) 4 (c) 20 (d) 24

6. Is 392 a perfect cube? If not, find the smallest natural number by which 392 should be multiplied so that

the product is a perfect cube.

7. A metallic cuboid measuring 75 cm × 20 cm × 18 cm is melted to from a cube . Find the length of the

edge of the cube.

8. Simplify : 5

3× 25

3 × 1331

3

270 3 × 100 3

9. Find the cube root of each of the following numbers by prime factorisation method.

a. 148877

b. 35937

10. Find the smallest number by which 27648 may be multiplied so that the product is a perfect cube. Also find

the cube root of the number so obtained.

11. What is the smallest number by which 2916 should be divided so that the quotient is a perfect cube?

12. If one side of a cube is 15m, find the volume of the cube.

13. The volume of a cube is 17.576 cm3. What will be the volume of another cube whose sides are double of

this cube?

14. Evaluate :

(a) {√ ( 52 + 12

2) }

3 (b) 132 − 52

3

DIRECT AND INVERSE PROPORTIONS

1. Which of the following situations is an example of direct proportion?

(a) The perimeter p of a square and its side length a.

(b) The length l and the width w of a rectangle, given the area remain constant.

(c) The number of units of a product that can be purchased given a fixed amount of money.

(d) The number of rows m and the number of columns n in which a fixed number of marbles cab be arranged.

2. If 30 cupcakes are prepared using 500 grams of flour, how many cupcakes can be prepared by using 750 grams

of flour assuming each cupcake is equal in size?

(a) 15 (b) 25 (c) 36 (d) 45

3. To draw a model of a residential society, Jaya used a scale factor 1:300. If the height of the building in model is

12 cm, which of these can be actual height of the building?

(a) 20 m (b) 25 m (c) 30 m (d) 36 m

4. The weight of 12 sheets of a thick paper is 40 grams. How many sheets would weigh 1 kg?

(a) 480 (b) 360 (c) 300 (d) 366

5. A car takes 2 hours to reach a destination by travelling at 60 km/h. How long will it take while travelling at

80km/h?

(a) 1h 30 min (b) 1 h 40 min (c) 2 h 40 min (d) 2 h 30 min

6. A car is moving at a uniform speed of 90 km/h. How far will it travel in 20 minutes?

7. Complete the table if x and y vary directly.

8. If 25 workers can finish a job in 40 days, how many workers will do the same work in 25 days?

9. Teena types 540 words during half an hour. How many words would she type in 6 minutes?

10. A machine can fill 28 containers in 5 hours. How many containers can be filled in 28 hours?

11. The weight of zinc in 3 kg of the alloy is 1.8 kg. Find the weight of zinc in 10 kg of alloy.

12. If the mass of 56 sheets of paper is 280g, how many sheets will weigh 6 kg?

13. If 28 pumps can empty a reservoir in 15 hours, how long will 35 pumps take to do the same work?

14. A car is travelling at the average speed of 50km/hr. How much distance would it travel in 1hour 12 minutes?

15. Rajan has enough money to buy 30 cycles worth ₹ 600 each. How many cycles will he be able to buy if the cost

of each cycles increases by ₹ 150?

CASE STUDY BASED QUESTIONS

Q1. We are living in a society where parents proudly educate their daughters and give them equal opportunity and

rights as given to sons. A well educated farmer, Harish left his government job to take up Aloe Vera farming in

Rajasthan has a rectangular field of area 294 m2. He wants to divide it equally among his one son and two

daughters. Based on the given information answer the following question:

(a) Find the area of his daughter‟s share.

(i) 98000 cm2 (ii) 980000 cm

2 (iii) 9800 cm

2 (iv) 98 cm

2

(b) If the length and breadth of the field are in the ratio 3 : 2, then find the length of the field.

(i) 21m (ii) 14 m

(iii) 7 m (iv) 35 m

(c) How much wire will be required to fence the field to protect it from the cattle?

(i) 294 m (ii) 105 m

(iii) 70 m (iv) 35 m

(d) Find the cost of fencing the field at the rate of ₹ 30 per meter.

(i) ₹ 8820 (ii) ₹210

(iii) ₹ 2100 (iv) ₹ 1050

Q2. India is home to an extraordinary variety of climatic regions, ranging from tropical in the south to temperate

and alpine in the Himalayan north, where elevated regions receive sustained winter snowfall. The double bar

graph shown below represents the average monthly temperatures of two cities viz. Delhi and Dehradun, over

4 months period. Read the graph carefully and answer the questions given below:

(a) What does each 1 cm block on the vertical axis represent?

(i) 1 °C (ii) 10 °C (iii) 0 °C (iv) 5 °C

(b) What was the average monthly temperature in Dehradun in March?

(i) 30 °C (ii) 25 °C (iii) 5 °C (iv) 55 °C

(c) What was the average monthly temperature in Delhi for the whole 4 months?

(i) 130 °C (ii) 170 °C (iii) 135 °C (iv) 165 °C

(d) In which month was the difference between the temperature of Delhi and Dehradun maximum and how

much?

(i) March (ii) April (iii) May (iv) June

ASSERTION & REASONING QUESTIONS

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R).

Mark the correct choice as:

(a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

(b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

(c)Assertion (A) is true but reason (R) is false.

(d)Assertion (A) is false but reason (R) is true.

Q1. Assertion: The number of diagonals of a pentagon is 5.

Reason: Sum of all the exterior angles is always 180°.

Q2. Assertion: If three angles of a quadrilateral are 130°, 70° and 60° then the fourth angle is 100 °.

Reason: The sum of all the angles of a triangle is 180°.

Q3. Assertion: The product of two rational numbers is always a rational number.

Reason: Zero has no reciprocal.

Q4. Assertion: The sum of first „n‟ odd numbers is n2.

Reason: 1 + 3 + 5 + 7 + 9 = 52.

Q5. Assertion: 53240 is not a perfect cube.

Reason: The prime factors of 53240 can not be grouped in three.