Question
Draw an angle of $50^\circ $ with the help of protractor. Draw a ray bisecting this angle.
✓
Answer
Steps for construction:
$i.\ $Draw $\angle\text{BAC}=50^\circ$ with the help of protractor.
$ii.\ $With $A$ as the centre and any convenient radius, draw an arc cutting $AB$ and $AC$ at $Q$ and $P,$ respectively.
$iii.\ $With $P$ as the centre and radius more than half of $PQ$, draw an arc.
$iv.\ $With $Q$ as the centre and the same radius as before, draw another arc cutting the previously drawn arc at a point $S$.
$v.\ $Draw $SA$ and produce it to point $R.$
Then, ray $AR$ bisects $\angle\text{BAC}.$
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Given below is the bar graph indicating the marks obtained out of $50$ in mathematics paper by $100$ students. Read the bar graph and answer the following questions:
$i.\ $It is decidec to distribute work books on mathematics to the students obtaining less than $20$ marks, giving one workbook to each of such students. If a work book costs $₹ 5$, what sum is required to buy the work books?
$ii.\ $Every student belonging to the highest mark group is entitled to get a prize of $₹ 10$. How much amount of money is required for distributing the prize money?
$iii.\ $Every student belonging to the lowest mark-group has to solve $5$ problems per day. How many problems, in all, will be solved by the students of this group per day?
$iv.\ $State whether true or false.
$a.\ 17\%$ students have obtained marks ranging from $40$ to $49.$
$b.\ 59$ students have obtained marks ranging from $10$ to $29$.
$v.\ $What is the number of students getting less than $20$ marks?
$vi.\ $What is the number of students getting more than $29$ marks?
$vii.\ $What is the number of students getting marks between $9$ and $40$?
$viii.\ $What is the number, of students belonging to the highest mark group?
$ix.\ $What is the number of students obtaining more than $19$ marks?
→$i.\ $It is decidec to distribute work books on mathematics to the students obtaining less than $20$ marks, giving one workbook to each of such students. If a work book costs $₹ 5$, what sum is required to buy the work books?
$ii.\ $Every student belonging to the highest mark group is entitled to get a prize of $₹ 10$. How much amount of money is required for distributing the prize money?
$iii.\ $Every student belonging to the lowest mark-group has to solve $5$ problems per day. How many problems, in all, will be solved by the students of this group per day?
$iv.\ $State whether true or false.
$a.\ 17\%$ students have obtained marks ranging from $40$ to $49.$
$b.\ 59$ students have obtained marks ranging from $10$ to $29$.
$v.\ $What is the number of students getting less than $20$ marks?
$vi.\ $What is the number of students getting more than $29$ marks?
$vii.\ $What is the number of students getting marks between $9$ and $40$?
$viii.\ $What is the number, of students belonging to the highest mark group?
$ix.\ $What is the number of students obtaining more than $19$ marks?
The final marks in mathematics of 30 students are as follows:
(i) Arrange these marks in the ascending order. 30 to 39 one group, 40 to 49 second group, etc
(ii) What is the highest score?
(iii) What is the lowest score?
(iv) What is the range?
(v) If 40 is the pass mark how many have failed?
(vi) How many have scored 75 or more?
(vii) Which observations between 50 and 60 have not actually appeared?
(viii) How many have scored less than 50?
| 53 | 61 | 48 | 60 | 78 | 68 | 55 | 100 | 67 | 90 |
| 75 | 88 | 77 | 37 | 84 | 58 | 60 | 48 | 62 | 56 |
| 44 | 58 | 52 | 64 | 98 | 59 | 70 | 39 | 50 | 60 |
(ii) What is the highest score?
(iii) What is the lowest score?
(iv) What is the range?
(v) If 40 is the pass mark how many have failed?
(vi) How many have scored 75 or more?
(vii) Which observations between 50 and 60 have not actually appeared?
(viii) How many have scored less than 50?
The number of bottles of cold drinks sold by a shopkeeper on six consecutive days is as follows:
Prepare a pictograph of the data using one symbol to represent $50$ bottles.
→| Day: | Sunday | Monday | Tuesday | Wednesday | Thursday | Friday |
| Number of bottle: | $350$ | $200$ | $300$ | $250$ | $100$ | $150$ |
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Draw a right angle and construct its bisector.
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(a) -125 + (-30) = _________
(b) +105 – (-55) = _________
(c) +80 – (-150) = _________
(d) -99 – (-200) = _________
(a) -125 + (-30) = _________
(b) +105 – (-55) = _________
(c) +80 – (-150) = _________
(d) -99 – (-200) = _________
Draw a line segment $CD.$ Produce it to $CE$ such that $CE = 3CD.$
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