Edition 18 math connect

1. If x=5+√3 find (x + (1/x)) and 

 (x - (1/x)).

2. If a=-30, b=18, c=12 find the value 

of a³+b³+c³.

3. What is 25% of 18000?

4.  Rationalise (√5+√2)/(√5-√2).

5. Write 26620 in terms of 

powers of its prime factors.

6. Multiply 30ab x 40bc x 50c x 2d.

7. If x = 8⁻¹ x 10⁴ and y = 15⁻¹ x 10⁴ find 

the value of (1/x²) + (1/y²).

8. Factorise 4x²-5x-6.

9. Evaluate (199)².

10. Evaluate 23 x 17 using identities.








1. APPRECIATION 

2. HUMANITY

3. GRATITUDE 

4. MINDFUL 

5. RESPECTFUL 

1. அலங்காரம் 

2. பொன்மொழிகள் 

3. மெய்யறிவு 

4. நீர்நிலைகள் 

5. மதிநுட்பம் 

1. A A E I I N T R P C P O

2. N I M A U Y H T 

3. T T I G E A U R D

4. L F I D N U M

5. S E E T P U R C L F 


1. அ ம் ங் ர கா ல

2. க பொ ழி ன் ள் மொ

3. றி ய வு ய் மெ 

4. லை ள் நீ நி க ர்

5. ம் தி ம ட் ப நு


1. What is 20% of 12000?

2. Rationalise (√3+√2)/(√3-√2)

3. Write 4096 in terms of 

     powers of its prime factors.

4. If a² +(1/a)²=23 then find a + (1/a)

5. Find the sum

     6+12+18+24+..........+600

6. Multiply 3a x 4b x 5c x 2d

7. (1x0.0001) + (2x0.001) + (3x0.01) +   

    (4x0.1) 

8. If 324÷2=162 then find 3.24÷2 and 

    0.0324÷0.2

9. Simplify (75xyz-150yz)/(x-2)

10. Find the value of (1/x²) + (1/y²)

     given x=0.5 and y=0.2


1. 20x12000/100=2400

2. (√3+√2)(√3+√2)/(√3-√2)(√3+√2)

=5+2√6

3. 2^11

4. (a + (1/a))²=a² +(1/a)²+2=23+2=25

5. 6(1+2+3+4+...+100)

=6(100)(101)/2

=100x303=30300

6. 120abcd

7. 0.4321

8.3.24÷2 = 1.62

0.0324÷0.2=0.162

9. (75xyz-150yz)/(x-2)

=75yz(x-2)/(x-2)= 75yz

10. x=0.5 and y=0.2

x=1/2 and y=1/5

(1/x²) + (1/y²)=2²+5²=4+25=29


1. E T M M N N A A E G

2. D E G P U R A 

3. R P E O E W M 

4. T M C N I E H R E N

5.  N T E A S L P A

1. கை பி ந க் ம் 

2. பி ம் ர ட் ப் பூ மி டு

3. ள ஞ் ய ம் க சி

4. ன ர மா பி ச கா

5. ய அ ல் வி றி


1. If x=2+√3 find (x + (1/x)) and 

     (x - (1/x)).

2. If a=-30, b=20, c=10 find the value 

     of a³+b³+c³.

3. If 264600= a³b³c²d² find a,b,c and d.

4. If (x/3)=(y/4) then find (x+3)/(y+4)

5. If x = 4⁻¹ x 10⁴ and y = 3⁻¹ x 10⁴ find 

    the value of (1/x²) + (1/y²).

6. If ab=1/3,bc=3/4,c=4 find (1/a) + (1/b) +

     (1/c).

7. If 2.56÷4=0.64 then find 0.0256÷4 and

     0.000256÷4 without actual division.

8.  If 12 pens and 6 pencils cost Rs.180 

     then find the cost of 30 pens and 15

     pencils.

9.  The cost of 18 kg sugar is 657 then

     what is the cost of 1000 kg sugar?

10. If a²+b²=35 and ab=6√6 then then      

      a³b+ab³

      

            


1. (1/x)= 1/(2+√3)= (2-√3)/ (2)²-(√3)²=2-√3

x + (1/x)) = 2+√3+2-√3=4

x - (1/x)).=2+√3-2+√3=2√3

2. a+b+c=-30+20+10=0

Therefore a³+b³+c³=3abc=3(-30)(20)(10)=-18000

3. 264600=2³x3³x5²x7²

a=2,b=3,c=5,d=7

4. x=3y/4

x+3=(3y/4)+3=(3/4)(y+4)

(x+3)/(y+4)=3/4

5. (1/x²) + (1/y²)=(4/10⁴)² + (3/10⁴)²=25x10⁻⁸

6. 

ab=1/3,bc=3/4,c=4

bx4=3/4

So, b=3/16

a=16/9

ac=64/9

abc=4/3

(1/a) + (1/b) + (1/c)

=(9/16)+(16/3)+(1/4)

=(27+256+12)/48

= (295/48)

7. 0.0256÷4=0.0064

 0.000256÷4=0.000064

8. Let x be the cost of 1 pen and 

     y that of a pencil.

So, 12x+6y=180

That is 6(2x+y)=180

(2x+y)= 180/6=30

30x+15y=15(2x+y)=15(30)=450

9. Cost of 1000 kg sugar= (657x1000)/18

     = 36500

10. a³b+ab³=ab(a²+b²)=6√6(35)=210√6

MATH CONNECT 


1. If a+b=5 and ab=6 find (a³+b³)

2. Given x+y=15 and xy=44 find (1/x) + (1/y)

3. Find (-120) - (-60) + (-45) - (100) - (-300)

4. Write the common factors of

     6x, 22xy, 38zx, 202yxz

5. Simplify √(.000256/.0004)

6. Express 25x100x128x81 as product 

    of prime factors in the exponential 

    form.

7. Simplify 9+(1/9)+(1/99)+(1/9999) and

    write the answer as a fraction.

8. If x²+y²=4 and xy=48/25 find (x+y)²

9. If a + (1/a) = 2.5 then what is a² +(1/a)²

10. If 3x+2y =14 and xy=4 find the value 

      of 18x²+ 8y²



1. H V N A I E E M C E T

2. I U U E T B L A F

3. O R E D A E V U N

4. I N L S U T O O

5. M Y R O E M


1. க பு ங் த ள் க த் 

2. ய ச ங் ணா ள் ல ர க

3. ர வ ங் ள் தி க த் ந ன

4. ற் ன் ம் ற னே மு 

5. ச் ழ ம் சா மா று ப



1. (a³+b³) = (a+b)³ -3ab(a+b)

= 5³ - 3(6)(5) = 125 - 90 = 35

2. (x+y)/xy = 15/44

3. 95

4. 2x

5. (.000256/.0004)

= √(2.56/4) = √0.64 = 0.8

6. 5³x(5x2)²x 2⁷ x 3⁴  

= 5⁵ x 2⁹ x 3⁴ 

7.  (9(9999) + 1111 + 101 + 1)/9999

= 89991 + 1111 + 101 + 1)/9999

= 91204/9999

8. 4 + (2(48)/25)= 196/25

9. Square it on both sides 

a² +(1/a)² + 2 = 6.25

a² +(1/a)²=4.25

10. (3x+2y)² =14²

9x²+ 12xy + 4y² = 196

9x²+ 12(4) + 4y² = 196

9x²+ 4y²=196-48=148

18x²+ 8y² =2(9x²+ 4y²)=2(148)=296


1. ACHIEVEMENT 

2. BEAUTIFUL 

3. ENDEAVOUR 

4. SOLUTION 

5. MEMORY 


1. புத்தகங்கள்

2. சரணாலயங்கள் 

3. நவரத்தினங்கள் 

4. முன்னேற்றம் 

5. மாம்பழச்சாறு 


 1. Find 79² - 21² without full calculation.

(79+21)(79-21)=(100)(58)=5800

 2. Simplify (225 x 5³ x 2² x 4³)/(3² x 10⁴)

     using exponent laws.

=5²x 3² x 5³ x 2² x 2⁶)/(3² x 5²x 2²)

=5³ x 2⁶=8000

 3. Find n if √(512) = n√2

√(256x2)=n√2

16√2=n√2

n=16

 4. Simplify 3√2 - 2√3 + 5√2 - 3√3

8√2-5√3

 5. Simplify (3x-24)(x²- x - 12)/(x² -5x-24)

3(x-8)(x-4)(x+3)/(x-8)(x+3)

=3(x-4)

 6. Find (4 x 10⁰ ) + 0.002 + (2 x 10⁻³)  +

     (40x10⁻³) + (400x10⁻³)

4+.002 + .002 + .04 + 0.4

= 4.444

 7. If A:B = 3:5 and B:C = 25:9 then find A:C

A/C= (A/B)(B/C)=(3/5)(25/9)=5/3

 8. If A:B = 2:7 and C:B =8:3 then find A:B:C

 A:B = 2:7 and B:C =3:8

A:B = 2x3 :7x3 and B:C =3x7 : 8x7

A:B:C = 6:21:56

 9. Simplify 3a - (2a +3 - 3b) - (4b - 3c +3a) +        5a +12  and find the value of the      expression at a=1, b=2and c = -3.

 3a - 2a +3 - 3b- 4b - 3c +3a+ 5a +12 

Rearranging,we get

3a-2a+3a+5a-3b-4b-3c+3+12

=9a-7b-3c+15

=9(1)-7(2)-3(-3)+15

9-14+9+15=19


10. Find x+y if x:y=7:4 and x-y=27

Let x=7k and y=4k

7k - 4k = 27

3k=27

k=9

x+y=7k+4k=11k=11(9)=99


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