The post 10th Math Periodic Test I (2018-19) appeared first on Class Notes Education Online.

]]>2

4

6

10

p+5

3

2

3

1

2

Kx + 3y – (k – 3) = 0

12x + ky – k = 0

60 – 100

100 – 150

150 – 250

250 – 350

350 – 450

5

16

12

2

3

a^{2 }b^{2
—– – —— = 0
}^{X Y}

a^{2 }b^{2
—– – —— = a+b; x, y ≠ 0
X Y}

20 – 30

30 – 40

40 – 50

50 – 60

60 – 70

30 – 40

40 – 50

50 – 60

60 – 70

8

40

58

90

83

40

58

90

83

100 – 120

120 – 140

140 – 160

160 – 180

180 – 200

12

14

8

6

10

Convert the distribution above to a less than type cumulative frequency distribution and find median graphically.

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]]>The post 10th Maths Periodic Test II (2018-19) appeared first on Class Notes Education Online.

]]>- All questions are compulsory.
- The question paper consists of 30 questions divided into four sections A, B, C and D. Section A compares of 6 questions of 1 mark each, Sections B comprises of 6 questions of 2 marks each, Section C comprises of 10 questions of 3 marks each and Section D comprises of 8 questions of 4 marks each.
- Use of calculator is not permitted.

1. The points P (2,0), Q (- 6, -2), R (a, a) and S (4, – 2) are the vertices of a parallelogram (in order). Find the co-ordinate of the point R.

2. Find the value of k for which the pair of linear equation 4x + 6y – 1 = 0 and 2x + ky – 7 = 0 represents parallel lines.

3. Write whether the rational number 7/75 will have terminating decimal expansion or a non – terminating repeating decimal expansion.

4. In Δ DEW, AB||EW. If AD = 4 cm, DE = 12 cm and DW = 24 cm, then find the value of DB.

5. A ladder of length 15√2 m reaches a window 15 m high. Find the inclination of the ladder with the ground.

6. If sec 2A = cosec (A – 36°), find A.

7. E is any point on produced side BC of Δ ABC in which AB = AC. If AD ⊥ BC and EF ⊥ AB, then prove that ΔACD ˜ ΔEBF.

8. Find the first term if k + 2, 4k – 6 and 3k – 2 are the three consecutive terms of an A.P.

9. Find the value of k, for which the given quadratic equation has equal roots:

4x^{2} + kx + 6 = 0.

10. Given that √2 is irrational, prove that (5 + 3√2) is an irrational number.

11. Find the ratio in which P(4, m) divides the line segment joining the points A(2,3) and B(6,- 3). Hence find m.

12. In the figure, ABCD is a rectangle. Find the values of x and y.

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]]>- The H.C.F of two number is 145 and their L.C.M is 2175. If one number is 725, then find the other number.
- Find the nature of roots of ax
^{2 }+ bx + c = 0, a > 0, b = 0, c > 0. - Find whether the given lines representing the following pair of liner equations intersect at a point, are parallel or coincident.

2x – 3y = 8

4x – 6y = 9 - Given 2 cos 3θ = √3, find the value of θ.
- Given that cos (A – B) = cos A cos B + sin A sin B, find the value of cos 15° by taking suitable values of A and B.
- For what value of k will the following pair of linear equations have no solution?

2x + 3y = 9

6x + (k – 2)y = (3k – 2) - Find a quadratic polynomial with zero 3 + √2 and 3 – √2.
- Without actually performing the long division, state whether 257/500 has a terminating decimal expansion or not. Also write the terminating decimal expansion if it exists.
- Find the zeroes of the polynomial 5x
^{2 }– 8x – 4 and verify the relationship between the zeroes and the coefficients. - Solve the following system of linear equations graphically
5x – 7y = 50

5x + 7y = 20

Also write the coordinates of the points where they meet x axis. - Solve the equation + 6 = 0 by method of completing the square.
- Simplify
tan 28° 1

————- + ——– (tan 20°. tan 60°. tan 70°)

cot 62° + 1 √3 - Find the positive value of k for which x
^{2 }+ kx + 64 = 0 and x^{2 }– 8x + k = 0 will have real roots. - Prove that:
cot

^{3 }θ. sin^{3 }θ tan^{3 }θ. cos^{3 }θ sec θ cosec θ – 1

——————- + ——————— = ———————-

(cos^{ }θ. + sin^{ }θ)^{2 }(cos^{ }θ. + sin^{ }θ)^{2 cosec θ + sec θ} - A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank is 60°. When he retires 40 metres from the bank, he finds the angle of elevation to be 30°. Find the width of the river.
- A man has certain notes of denomination of Rs. 20 and Rs. 5 which amount to Rs. 380. If the number of the each king are interchanged, they amount Rs. 60 less than before. Find the number of notes of each denomination.

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]]>The post NCERT 5th Class (CBSE) Mathematics: Introduction To Algebra appeared first on Class Notes Education Online.

]]>**Can you give the mathematical expressions for these words?**

- Seventy three minus forty -two
- Twelve less two
- Six times fifteen
- Thirty plus eleven take away nine

Sometimes, in a mathematical expression, we use letters to represent numbers we do not know.

If we say that there were some people at a party and 7 people left, we can show this as an expression, n-7, where n represents the number of people in the party.

If there were 12 people at the party, then n would represent 12. If there were 20 people at the party, then n would represent 20.

**These letters are called variable because they can represent any number.**

**CHECKPOINT:** When we write an expression using variables, words and/or operations, it is called an algebraic expression.

Let *p* be the number of pencils in your pencil box. Study the algebraic expressions for each:

12 pencils more than the number of pencils in your box → *p* + 12 or 12 + *p*

4 pencils less than the number of pencils in your box → *p* – 4

Three times the number of pencils in your box. → 3 × *p* also written as 3*p*

The number of pencils in your box divided by 4 → *p* ÷ 4 also written as p/4

**Here, the expressions have been put into words. The unknown number or the variable is ***w.*

18 + *w *→ *w* added to 18

10 – *w *→ *w* subtracted from 10

7*w *→ The product of *w* and 7

6 ÷ *w *→ 6 divided by *w*

If we know that *w* = 3, Then expressions above can be simplified and a value can be obtained for each expression.

If we substitute 3 in place of *w*, we get

18 + *w* = 18 + 3 = 21

10 – *w = *10 – 3 = 7

7*w* = 7 × 3 = 21

6 ÷ *w = *6 ÷ 3 = 2

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]]>The post NCERT 5th Class (CBSE) Mathematics: Area And Volume appeared first on Class Notes Education Online.

]]>This stamp has been stuck on centimeter-squared paper. Take each square to have a side of 1 cm.

So, the perimeter of the stamp is 14 cm.

Perimeter = 2 × (l + b)

We can say that the stamp covers an area of 12 square centimeters or 12 sq. cm.

You can count half squares and add them to make full squares while finding the are of shapes like this. 9 full squares, 8 half squares = 4 full squares, 9 + 13, Area = 13 sq. cm

This is the image of a thumbprint. It does not have a regular shape. We have to estimate the area of shapes like this. Complete squares = 5, Incomplete squares combining to make complete squares = about 5 squares, 5 + 5 = 10 squares, Area of thumbprint = about 10 sq. cm

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]]>The post NCERT 5th Class (CBSE) Mathematics: Polygons And Circles appeared first on Class Notes Education Online.

]]>The word triangle means three angles. The given triangle has three angles ∠A, ∠B and ∠C. Points A, B and C are the vertices of triangle ABC. The sides of the triangle are AB, BC and CA.

A quadrilateral is a closed shape with 4 straight sides.

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]]>The post NCERT 5th Class (CBSE) Mathematics: Lines And Angle appeared first on Class Notes Education Online.

]]>**CHECK IN**

A protractor is used to measure angles.

This angle is measured on the inner scale as the baseline arm point to 0° on the inner scale. The other arm crosses 50° showing that ∠ AOB = 50°.

Angles are named according to their measures.

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]]>The post NCERT 5th Class (CBSE) Mathematics: Graphical Representation appeared first on Class Notes Education Online.

]]>- Pictograph use pictures or symbols to represent information.
- It has a title.
- It gives the definition of the symbol or the key. The key is defined such that it represents the entire data.
- pictographs help you understand the information by allowing you to compare the data shown.

(a) The table shows the number of magazines published for children.

Weekly magazines

50

Fortnightly magazines

30

Monthly magazines

100

Quarterly magazines

50

This pictograph shows the same information.

(b) Represent the following information in the form of a pictograph. Give the pictograph a title and show what your symbol stands for

Favorite TV channels in Class V:

Comedy – 15 children, Cartoons – 25 children, Sports – 10 children, Adventure – 5 children.

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]]>The post NCERT 5th Class (CBSE) Mathematics: Application Of Percentage appeared first on Class Notes Education Online.

]]>Mr Gupta makes very good rocking chairs. It coast him Rs. 795 to make one rocking chair. He sells it in his furniture shop at Rs. 900.

Rs. 795 is the Cost Price (CP) of the chair.

Rs. 900 is the Selling Price (SP) of the chair.

Since he sells it for more than it costs to make, he earn money by doing so. This is called his **profit**.

Rs. 900 SP

Rs. – 795 CP

Rs. 105 **Profit**

Formula to calculate profit → **SP – CP = Profit**

There is one rocking chair with a small scratch on it. Mr Gupta sells this particular chair for Rs. 715. Since he sells it for less than what it costs him to make it, he loses money on the sale. This is called his **loss**.

Rs. 795 CP

Rs. – 715 SP

Rs. 80 **Loss**

Formula to calculate Loss → **CP**** – SP = Loss**

**CHECKPOINT**

- When SP > CP the difference (SP – CP) is Profit.
- When SP < CP the difference (CP – SP) in Loss.

Mr Gupta delivered one rocking chair to another town. It costs him Rs. 105 to do so. The cost price of this particular chair is now Rs. 975 + Rs. 105 = Rs. 900. If he sell this chair at Rs. 1000 what is his profit or loss on the chair?

SP = Rs. 1000

CP = Rs. 900

Comparing the SP and CP, we see that SP > CP , so there is a profit.

SP – CP = Profit

1000 – 900 = 100

Mr Gupta makes a profit of Rs. 100 on the chair.

Ramu bought apples from a farmer and sold them in the market. He sells them at Rs. 70 for a kilo and makes a profit of Rs. 23 on each kilo. How much did Ramu pay per kilo apples?

He also bought oranges from the farmer. He sold them in the market at Rs. 95 per dozen. This was at a loss of Rs. 12 per dozen. What did 1 dozen oranges cost him?

Selling price of one kilo apples = Rs. 70

Selling price of one dozen oranges = Rs. 95

Profit = Rs. 23

Loss = Rs. 12

Cost price = ?

Cost price = ?

CP = SP – Profit

CP = SP + Loss

CP = Rs. 70 – Rs. 23 = Rs. 47

CP = Rs.95 + Rs. 12 = Rs. 107

SP – CP = Profit

CP – Sp = Loss

Rs. 70 – Rs. 23 = Rs. 47

Rs. 107 – Rs. 95 = Rs. 12

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]]>The post NCERT 5th Class (CBSE) Mathematics: Percentage appeared first on Class Notes Education Online.

]]>Using fractions we can say 43/100 of her coins are Indian coins.

Using decimals we can say 0.43 coins of her collection are Indian coins. We can also express this as a percentage. The word per cent means ‘per one hundred’. We use the sign % to represent per cent.

43% of Anisha’s coins collection is Indian.

We use percentage very often in our every day lives. Sometimes we use it to compare numbers, sometimes just to understand them. If you see a sale sign that says 20% off it means that for every item that costs Rs. 100 you have to pay Rs. 20 less. If we say that 9% of people were spectacles it means that for every 100 people 9 people were spectacles.

So, 1% means 1 out of 100 or 1/100.

99% means 99 out of 100 or 99/100.

This is a page out of Sunil’s stamp album. The page has 100 stamps. He has stuck them according to their color.

Blue

50/100

0.5

50%

Yellow

15/100

0.15

15%

Red

30/100

0.3

30%

Green

5/100

0.05

5%

**CHECK POINT**

- Any number that can be written as a fraction or decimal can also be written as a percent.
- We use per cent to compare a number with hundred.

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