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In an A.P. the first term is – 5 and the last term is 45. If the sum of all numbers in the A.P. is 120, then how many terms are there? What is the common difference?
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
If the sum of first p terms of an A.P. is equal to the sum of first q terms then show that the sum of its first (p + q) terms is zero. (p ≠ q)
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
The first term of an A. P. is 5 and the common difference is 4. Complete the following activity and find the sum of the first 12 terms of the A. P.
a = 5, d = 4, s12 = ?
`s_n = n/2 [ square ]`
`s_12 = 12/2 [10 +square]`
`= 6 × square `
` =square`
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Market value of a share is Rs 200. If the brokerage rate is 0.3% then find the purchase value of the share.
Concept: Shares
The market value of a mutual fund is 400 crore rupees. Which is divided into 8 crore units.
(a) Suppose you invest Rs. 10,000 in the units, how many units will you get ?
(b) While selling the units if their market value is increased by 10%, how much amount will you get by selling them ?
Concept: Mutual Funds and Systematic Investment Plan
The marks scored by students in Mathematics in a certain Examination are given below:
| Marks Scored | Number of Students |
| 0 — 20 | 3 |
| 20 — 40 | 8 |
| 40 — 60 | 19 |
| 60 — 80 | 18 |
| 80 — 100 | 6 |
Draw histogram for the above data.
Concept: Histograms
Draw the frequency polygon for the following frequency distribution
| Rainfall (in cm) | No. of Years |
| 20 — 25 | 2 |
| 25 — 30 | 5 |
| 30 — 35 | 8 |
| 35 — 40 | 12 |
| 40 — 45 | 10 |
| 45 — 50 | 7 |
Concept: Histograms
Given below is the frequency distribution of driving speeds (in km/hour) of the vehicles of 400 college students:
| Speed (in km/hr) | No. of Students |
| 20-30 | 6 |
| 30-40 | 80 |
| 40-50 | 156 |
| 50-60 | 98 |
60-70 |
60 |
Draw Histogram and hence the frequency polygon for the above data.
Concept: Histograms
Represent the following data by Histogram:
|
Price of Sugar per kg (in Rs.) |
Number of Weeks |
| 18-20 | 4 |
| 20-22 | 8 |
| 22-24 | 22 |
| 24-26 | 12 |
| 26-28 | 8 |
| 28-30 | 6 |
Concept: Histograms
Draw a histogram of the following data.
| Height of student (cm) | 135 - 140 | 140 - 145 | 145 - 150 | 150 - 155 |
| No. of students | 4 | 12 | 16 | 8 |
Concept: Histograms
The following frequency distribution table shows marks obtained by 180 students in Mathematics examination.
| Marks | No. of students |
| 0 - 10 | 25 |
| 10 - 20 | x |
| 20 - 30 | 30 |
| 30 - 40 | 2x |
| 40 - 50 | 65 |
Find the value of x. Also draw a histogram representing the above information.
Concept: Histograms
Read the following poem and write an appreciation of it with the help of the given points in a paragraph format:
|
All the World’s a Stage All the world’s a stage, - William Shakespeare |
Points:
- The title and the poet of the poem (01)
- Rhyme scheme (01)
- Figures of speech (01)
- Central Idea/Theme (02)
Concept: All the World’s a Stage
Say whether the following sentence is Assertive (Statements), Imperative (Commands, Requests, etc.), Interrogative (Questions) or Exclamatory (Exclamations).
How utterly we have failed our children!
Concept: Types of Sentences
Say whether the following sentence is Assertive (Statements), Imperative (Commands, Requests, etc.), Interrogative (Questions) or Exclamatory (Exclamations).
How utterly we have failed our children!
Concept: Types of Sentences
Spot the error in the following sentence and rewrite it:
When I took the note, I saw it were still wet from the nights rain.
Concept: Spotting Errors
Write any 2 compound words of your own.
Concept: Vocabulary >> Compound Words
Write a word register of 8 words related to:
‘Music’.
Concept: Vocabulary >> Register
Change the voice:
Anil had already made the tea.
Concept: Change the Voice
Make two sentences by using the given word as a noun and as a verb:
dream
Concept: Parts of Speech
Spot the error in the given sentence and rewrite it:
The doctors give him two and half years to live.
Concept: Spotting Errors
