Ch 1Numbers
5-Mark Questions
Draw a number line and represent the following rational numbers on it. (i) \(\frac{9}{4}\) (ii) \(\frac{-8}{3}\) (iii) \(\frac{-17}{-5}\) (iv) \(\frac{15}{-4}\)
(i) \(\frac{9}{4}\) \(\frac{9}{4}=2 \frac{1}{4}\) ∴ \(\frac{9}{4}\) lies between 2 and 3(ii) \(\frac{-8}{3}\) \(\frac{-8}{3}=-2 \frac{2}{3}\) \(-2 \frac{2}{3}\) lies between -2 and 3(iii) \(\frac{-17}{-5}\) \(\frac{-17}{-5}=3 \frac{2}{5}\) \(3 \frac{2}{5}\) lies between 3 and 4 in the number line.(iv) \(\frac{15}{-4}\) \(\frac{15}{-4}=-3 \frac{3}{4}\) \(-3 \frac{3}{4}\) lies between -3 and -4
List any five rational numbers between the given rational numbers. (i) 2 and 0 (ii) \(\frac{-1}{2}\) and \(\frac{3}{5}\) (iii) \(\frac{1}{4}\) and \(\frac{7}{20}\) (iv) \(\frac{-6}{4}\) and \(\frac{-23}{10}\)
(i) 2 and 0 i.e., \(\frac{-2}{1}\) and \(\frac{0}{1}\)∴ Five rational number between \(\frac { -20 }{ 10 }\) (= -2) and \(\frac { 0 }{ 10 }\) (= 0) are(ii) \(\frac{-1}{2}\) and \(\frac{3}{5}\) LCM of 2 and 5 = 2 × 5 = 10∴ Five rational number between(iii) \(\frac{1}{4}\) and \(\frac{7}{20}\)∴ Five rational number between(iv) \(\frac{-6}{4}\) and \(\frac{-23}{10}\)∴ Five rational number between
2-Mark Questions
The points S, Y, N, C, R, A, T, I and O on the number line are such that CN=NY=YS and RA=AT=TI=IO. Find the rational numbers represented by the letters Y, N, A, T and I.
Write the decimal form of the following rational numbers. (i) \(\frac{1}{11}\) (ii) \(\frac{13}{4}\) (iii) \(\frac{-18}{7}\) (iv) \(1 \frac{2}{5}\) (v) \(-3 \frac{1}{2}\)
(i) \(\frac{1}{11}\) \(\frac{1}{11}\) = 0.0909….(ii) \(\frac{13}{4}\) \(\frac{13}{4}\) = 3.25(iii) \(\frac{-18}{7}\) \(\frac{-18}{7}\) = -2.571428571428….(iv) \(1 \frac{2}{5}\) \(1 \frac{2}{5}=\frac{7}{5}\) = 1.4(v) \(-3 \frac{1}{2}\) \(-3 \frac{1}{2}=-\frac{7}{2}=-3.5\)
Use the method of averages to write 2 rational numbers between \(\frac{14}{5}\) and \(\frac{16}{3}\)
The average of a and b is \(\frac { 1 }{ 2 }\)(a + b)
1-Mark Questions (MCQ)
The number which is subtracted from \(\frac{-6}{11}\) to get \(\frac{8}{9}\) is _________ .
(B) \(\frac{-142}{99}\) Hint: Let x be the number to be subtracted \(\frac{-6}{11}-x\) = \(\frac{8}{9}\) \(\frac{-6}{11}-\frac{8}{9}\) = x
Ch 2Measurements
5-Mark Questions
For the sectors with given measures, find the length of the arc, area and perimeter. (π = 3. 14) (i) central angle 45° r = 16 cm
(i) central angle 45° r = 16 cm Length of the arc l = \(\frac{\theta^{\circ}}{360^{\circ}}\) × 2πr units l = \(\frac{45^{\circ}}{360^{\circ}}\) × 2 × 3.14 × 16 cm l = \(\frac{1}{8}\) × 2 × 3.14 × 16 cm l = 12.56 cm Area of the sector = \(\frac{\theta^{\circ}}{360^{\circ}}\) × πr 2 sq. units A = \(\frac{45^{\circ}}{360^{\circ}}\) × 3.14 × 16 × 16 A = 100.48 cm 2 Perimeter of the sector P = l + 2r units P = 12.56 + 2(16) cm p = 44.56 cm (ii) central angle 120°, d = 12.6 cm ∴ r = \(\frac{12.6}{2}\) cm r = 6.3cm Length of the arc l = \(\frac{\theta^{\circ}}{360^{\circ}}\) × 2πr units l = \(\frac{1 …
From the measures given below, find the area of the sectors. (i) Length of the arc = 48 m, r = 10 m
Area of the sector A = \(\frac{l r}{2}\) sq. units l = 48m r = 10m = \(\frac{48 \times 10}{2}\) m 2 = 24 × 10m 2 = 240 m 2 Area of the sector = 240 m 2 (ii) length of the arc = 50 cm, r = 13.5 cm Length of the arc l = 12.5 cm Radius r = 6 cm Area of the sector A = \(\frac{l r}{2}\) sq. units A = \(\frac{12.5 \times 6}{2}\) A = 12.5 × 3cm 2 A = 37.5 cm 2 Area of the sector A = 37.5 cm 2
2-Mark Questions
\(\frac{22}{7}\) and 3.14 are rational numbers. Is ‘π’ a rational number? Why?
\(\frac{22}{7}\) and 3.14 are rational numbers π has non-terminating and non-repoating decimal expansion. So it is not a rational number. it is an irrational number.
Ch 3Algebra
5-Mark Questions
Find the product of the terms. (i) -2mn, (2m) 2 , -3mn (ii) 3x 2 y , -3xy 3 , x 2 y 2
(i) (-2mn) × (2m) 2 × (-3mn) = (-2mn) × 2 2 m 2 × (-3mn) = (- 2mn) × 4m 2 × (- 3mn) = (-) (+)(-) (2 × 4 × 3) (m × m 2 × m) (n × n) = +24 m 4 4n 2 (ii) (3x 2 y) × (-3xy 3 ) × (x 2 y 2 ) = (+) × (-) × (+) × (3 × 3 × 1)(x 2 × x × x 2 ) × (y × y 3 × y 2 ) = -9x 5 y 6
Find the missing term. (i) 6xy × ______ = -12x 3 y
6xy × (-2x 2 ) = -12x 3 y (ii) ______ × (-15m 2 n 3 p) = 45m 3 n 3 p 2 -3mp × (-15m 2 n 3 p) = 45m 3 n 3 p 2 (iii) 2y(5x 2 y – ____ + 3____ ) = 10x 2 y 2 – 2xy + 6y 3 2y(5x 2 y – x + 3y 2 ) = 10x 2 y 2 – 2xy + 6y 3
2-Mark Questions
Statement A: If 24p 2 q is divided by 3pq, then the quotient is 8p. Statement B: Simplification of \(\frac{(5 x+5)}{5}\) is 5x. (i) Both A and B are true (ii) A is true but B is false (iii) A is false but B is true (iv) Both A and B are false
(ii) A is true but B is false Hint:
Find the simple interest on Rs. 5a 2 b 2 for 4ab years at 7b% per annum.
Plot the following points in a graph sheet. A(5, 2), B(-7, -3), C(-2, 4), D(-1, -1), E(0, -5), F(2, 0), G(7, -4), H(-4, 0), I(2, 3), J(8, -4), K(0, 7).
1-Mark Questions (MCQ)
The missing terms in the product -3m 3 n × 9(_) = _______ m 4 n 3 are
(A) mn 2 , 27
Ch 4Life Mathematics
5-Mark Questions
Rewrite each underlined part using percentage language. (i) One half of the cake is distributed to the children.
50% of the cake is distributed to the children Hint: One half is nothing but \(\frac { 1 }{ 2 }\) as percentage, we need to multiply by 100 ∴ \(\frac { 1 }{ 2 }\) × 100 = 50% (ii) Aparna scored 7.5 points out of 10 in a competition. Aparna scored 75% in a competition Hint: 7.5 points out of 10 is \(\frac{7.5}{10}\) = 0.75 For percentage, we need to multiply by 100 We get 0.75 × 100 = 75% (iii) The statue was made of pure silver . …
If the difference between 75% of a number and 60% of the same number is 82.5, then find 20% of that number.
Given that 75% of number less 60% of number is 82.5 Let the number be ‘x’ ∴ \(\frac{75}{100}\) x x – \(\frac{60}{100}\) x x = 82.5 ∴ 0.75 x – 0.60 x = 82.5 ∴ 0.15 x = 82.5 ∴ x = \(\frac{82.5}{0.15}=\frac{8250}{15}\) = 550 Required to find 20% of number ie 20% of x.
2-Mark Questions
48 is 32% of which number?
Let the number required to be found be ‘x’ Given that 32% of x is 48 i.e., \(\frac{32}{100}\) × x = 48∴ x = 150
What is 25% of 30% of 400?
Required to find 25% of 30% of 400The percentage decrease calculator determines the change from one amount to a lesser amount in terms of percent decrease.
A number when increased by 18% gives 236. Find the number.
Let the number be x. Given that when it is increased by 18%, we get 236.
1-Mark Questions (MCQ)
12% of 250 litre is the same as ________ of 150 litre.
(C) 20% Hint: 12% of 250 = \(\frac{12}{100}\) × 250 = 30 lit. Percentage: \(\frac{30}{150}\) × 100 = 20%
Ch 5Geometry
5-Mark Questions
Check whether given sides are the sides of right-angled triangles, using Pythagoras theorem. (i) 8, 15, 17
Take a = 8 b = 15 and c = 17 Now a 2 + b 2 = 8 2 + 15 2 = 64 + 225 = 289 172 = 289 = c 2 ∴ a 2 + b 2 = c 2 By the converse of Pythagoras theorem, the triangle with given measures is a right angled triangle. ∴ Ans: yes(ii) 12, 13, 15 (ii) 12, 13. 15 Take a = 12,b = 13 and c = 15 Now a 2 + b 2 = 12 2 + 13 2 = 144 + 169 = 313 15 2 = 225 ≠ 313 By the converse of Pythagoras theorem, the triangle with given measures is not a right angled triangle. ∴ Ans: No. …
An isosceles triangle has equal sides each 13 cm and a base 24 cm in length. Find its height.
In an isosceles triangle the altitude dives its base into two equal parts. Now in the figure, ∆ABC is an isosceles triangle with AD as its height In the figure, AD is the altitude and ∆ABD is a right triangle. By Pythagoras theorem, AB 2 = AD 2 + BD 2 ⇒ AD 2 = AB 2 – BD 2 = 13 2 – 12 2 = 169 – 144 = 25 AD 2 = 25 = 5 2 Height: AD = 5cm
2-Mark Questions
Find all integer-sided right angled triangles with hypotenuse 85.
(x + y) 2 – 2xy = 85 2Think (Text Book page No. 173)
1-Mark Questions (MCQ)
Two similar triangles will always have _______ angles
(D) matching
Ch 6Statistics
5-Mark Questions
Form a continuous frequency distribution table for the marks obtained by 30 students in a X std public examination. 328, 470, 405, 375, 298, 326, 276, 362, 410, 255, 391, 370, 455, 229, 300, 183, 283, 366, 400, 495, 215, 157, 374, 306, 280, 409, 321, 269, 398, 200.
Maximum mark obtained = 495 Minimum marks obtained = 157 Range = Maximum value – Minimum value Range = 495 – 157 = 338 If we take the class size as 50 then the number of class intervals possible= \(\frac{338}{50}\) = 6.76 ≅ 7The percentage difference calculator is here to help you compare two numbers.
A paint company asked a group of students about their favourite colours and made a pie chart of their findings. Use the information to answer the following questions. (i) What percentage of the students like red colour? (ii) How many students liked green colour? (iii) What fraction of the students liked blue? (iv) How many students did not like red colour? (v) How many students liked pink or blue? (vi) How many students were asked about their favourite colours?
Total percentage of students = 100 % ∴ 50students = 100% – (30% + 20% + 25% + 15%) = 100% – 90% 50 students = 10% 10% of total students = 50 ∴ \(\frac { 10 }{ 100 }\) (Total students) = 50 Total students = \(\frac{50 \times 100}{10}\) = 500. Total students = 500. (i) 20% of the students like red colour. (ii) 15% of the students liked green colour. \(\frac{15}{100}\) × 500 = 75 students liked green colour.(iii) 25% students liked blue students liked blue. ⇒ \(\frac{25}{100}\) students liked blue. ⇒ \(\frac{1}{4}\) students liked blue. …
2-Mark Questions
Represent the following data in ungrouped frequency table which gives the number of children in 25 families. 1, 3, 0, 2, 5, 2, 3, 4, 1, 0, 5, 4, 3, 1, 3, 2, 5, 2, 1, 1, 2, 6, 2, 1, 4
The data given is raw data. Ascending order : 0, 1, 2, 3, 4, 5, 6∴ Tabulating in frequency distribution table we get
The data on modes of transport used by the students to come to school are given below. Draw a pie chart for the data.
Converting the percentage into components parts of 360°. we haveMode of Transport by students.
A rupee spent in a cloth manufacturing company is distributed as follows. Represent this in a pie chart. Particulars Paise Farmer 20 Spinner 35 Dyer 15 Weaver 15 Printer 05 Salary 10
1 Rupee = 100 paise.Expenditure of a cloth manufacturing company.
1-Mark Questions (MCQ)
Which of the following data can be represented in a histogram? (i) The number of mountain climbers in the age group 20 to 60 in TamilNadu.
Yes (ii) Production of cycles in different years. No(iii) The number of students in each class of a school. No (iv) The number votes polled from 7 am to 6 pm in an election. Yes (v) The wickets fallen from 1 over to 50th over in a one day cricket match. Yes
Ch 7Information processing
5-Mark Questions
You want to have an ice cream or a cake. There are three flavours (chocolate, strawberry and vanilla) in ice creams, and two flavours (orange and red velvet) in the cakes. In how many possible ways can you choose an ice cream or a cake?
We are going to have either a ice cream or a cake. Ice cream can be selected from 3 flavors and cake from two flavors. Both the events cannot occur simultaneously selecting ice cream and cake. ∴ Number of possible ways = 3 + 2 = 5 ways
In a Higher Secondary School, the following groups are available in XI standard (i) Physics, Chemistry, Biology and Mathematics (ii) Physics, Chemistry, Mathematics and Computer Science. (iii) Physics, Chemistry, Biology and Home Science Il. Arts Group: (i) Accountancy, Commerce, Economics and Business Maths (ii) Accountancy, Commerce, Economics and Computer Science (iii) History, Geography, Economics and Commerce (i) Biology, Nursing Theory, Nursing Practical I and Nursing Practical II (ii) Home Science, Textiles and Dress Designing Theory, Textiles and Dress Designing Practical I and Textiles and Dress Designing Practical Il In how many possible ways, can a student choose a group?
The student either select any one of science group in 3 ways or any of the arts group in 3 ways or any of the vocational group in 2 ways. ∴ Total possible ways = 3 + 3 + 2 = 8 ways
2-Mark Questions
Shanthi has 5 chudithar sets and 4 frocks. In how many possible ways, can she wear either a chudithar or a frock?
Shanthi her 5 chudidhar sets and 4 frocks. She wear either chudidhar or a frock. ∴ Total possible ways = 5 + 4 = 9 ways
Using the given picture find the total special offer price of fresh sweets and bakery products to buy \(\frac { 1 }{ 2 }\) kg laddu, 1 kg cake, 6 pockets of bread.
When you plan to buy a shirt, one shop offers a discount of ₹ 200 on MRP ₹ 1000 and another shop offers 15% discount on the same MRP. Where would you buy?
Price in 1 st shop = ₹ 1000 – ₹ 200 = ₹800In shop 1.
1-Mark Questions (MCQ)
What is the eleventh Fibonacci number?
(c) 89 Hint:∴ 11 th Fibonacci number is 89
Frequently asked questions
- Draw a number line and represent the following rational numbers on it. (i) \(\frac{9}{4}\) (ii) \(\frac{-8}{3}\) (iii) \(\frac{-17}{-5}\) (iv) \(\frac{15}{-4}\)
- (i) \(\frac{9}{4}\) \(\frac{9}{4}=2 \frac{1}{4}\) ∴ \(\frac{9}{4}\) lies between 2 and 3(ii) \(\frac{-8}{3}\) \(\frac{-8}{3}=-2 \frac{2}{3}\) \(-2 \frac{2}{3}\) lies between -2 and 3(iii) \(\frac{-17}{-5}\) \(\frac{-17}{-5}=3 \frac{2}{5}\) \(3 \frac{2}{5}\) lies between 3 and 4 in the number line.(iv) \(\frac{15}{-4}\) \(\frac{15}{-4}=-3 \frac{3}{4}\) \(-3 \frac{3}{4}\) lies between -3 and -4
- List any five rational numbers between the given rational numbers. (i) 2 and 0 (ii) \(\frac{-1}{2}\) and \(\frac{3}{5}\) (iii) \(\frac{1}{4}\) and \(\frac{7}{20}\) (iv) \(\frac{-6}{4}\) and \(\frac{-23}{10}\)
- (i) 2 and 0 i.e., \(\frac{-2}{1}\) and \(\frac{0}{1}\)∴ Five rational number between \(\frac { -20 }{ 10 }\) (= -2) and \(\frac { 0 }{ 10 }\) (= 0) are(ii) \(\frac{-1}{2}\) and \(\frac{3}{5}\) LCM of 2 and 5 = 2 × 5 = 10∴ Five rational number between(iii) \(\frac{1}{4}\) and \(\frac{7}{20}\)∴ Five rational number between(iv) \(\frac{-6}{4}\) and \(\frac{-23}{10}\)∴ Five rational number between
- Write the decimal form of the following rational numbers. (i) \(\frac{1}{11}\) (ii) \(\frac{13}{4}\) (iii) \(\frac{-18}{7}\) (iv) \(1 \frac{2}{5}\) (v) \(-3 \frac{1}{2}\)
- (i) \(\frac{1}{11}\) \(\frac{1}{11}\) = 0.0909….(ii) \(\frac{13}{4}\) \(\frac{13}{4}\) = 3.25(iii) \(\frac{-18}{7}\) \(\frac{-18}{7}\) = -2.571428571428….(iv) \(1 \frac{2}{5}\) \(1 \frac{2}{5}=\frac{7}{5}\) = 1.4(v) \(-3 \frac{1}{2}\) \(-3 \frac{1}{2}=-\frac{7}{2}=-3.5\)
- Use the method of averages to write 2 rational numbers between \(\frac{14}{5}\) and \(\frac{16}{3}\)
- The average of a and b is \(\frac { 1 }{ 2 }\)(a + b)
These important questions are selected from the Samacheer Kalvi Class 8 Maths textbook book-back exercises to help you revise the most useful questions. Mark weightage (5/2/1) follows the usual exam pattern and may vary by exam — always check your latest syllabus and question pattern. Open each chapter for the complete set of questions and answers.