HCF

Find the HCF of

x⁴ + x² + 1 and x¹⁰ + x⁵ + 1

Algebra

If 2b = a + c
then show that
(a - b)^2 + 2b^2 + (b - c)^2 = a^2 + c^2

Factorization

Resolve into factors:

Algebra

Algebra

Show that

x(x + 1)(x + 2)(x + 3) + 1 = (x^2 + 3x + 1)^2

Square root

Find the square root of 
3x/y (2 + 3x/y) + y/x (1 + y/4x) + 4

IPM MTSE test Papers STD. IV

IPM MTSE test Papers STD. IV

IPM MTSE test Papers STD. IV

IPM MTSE test Papers STD. IV

IPM MTSE test Papers STD. IV

IPM MTSE test Papers STD. IV

IPM MTSE test Papers STD. IV

IPM MTSE test Papers STD. IV

IPM MTSE test Papers STD. IV

IPM MTSE test Papers STD. IV

IPM MTSE test Papers STD. IV

IPM MTSE test Papers STD. IV

IPM MTSE test Papers STD. IV

IPM MTSE test Papers STD. IV

IPM MTSE practice paper STD. IV

IPM, MTSE practice test paper for Std IV

IPM and MTSE practice paper for Std. IV

IPM and MTSE practice paper for Std. IV

IPM and MTSE Practice test paper for Std. IV

IPM and MTSE Practice test paper for Std. IV

Math test paper STD IV

IPM / MTSE Practice test paper for Std. IV

ipm, mtse, question and answer STD IV

IPM and MTSE question and answer

ipm mtse STD IV

ipm, mtse, STD IV question and answer

IPM / MTSE STD IV

IPM / MTSE question and answer

IPM and MTSE test paper STD IV

IPM / MTSE test paper STD IV

IPM and MTSE test paper STD IV

IPM and MTSE test paper

IPM, MTSE test paper STD IV

IPM MTSE test Paper for STD IV

IPM / MTSE test Paper STD IV

Math Tes Paper IPM / MTSE STD IV

logarithm

Logarithm

Quadratic equation

solve the equation

(x² – 3x - 5)(x² – 3x + 3) + 7 = 0

Algebra

If xy = 3(x - 3) and yz = 3(y - 3), show that xz = 3(z -3)                   (Hall)

square root

Find the square root of 3x - 1 + 2√(2x² – 3x - 2)

Square root

Find the square root of 12a + 2b - 4√(6ab)         (Hall)

square root

Find the square root of 2m + 2√(m² – 9n² )      (Hall)

square root

Find the square root of 9m + 8n + 12√(2mn)

Square root

find the square root of √175 - √147

square root

Find the square root of  √32 - √24   (Hall)

square root

Find the square root of 4 +2√3   (Hall)

square root

Find the square root of 10 + 2√24            (Hall)

square root

Find the square root of 38 - 12√10      (Hall)

Helping Math student through exercise

Watch these videos for some invaluable insights for your kids


Why do kids do better in school after exercise? 
What happens to your brain after you exercise? 
A Program that has PE directly before MATH and ENGLISH Classes: LRPE 
What Steps Should a PE Teacher take to start a LRPE (Learning Readiness Physical Education) Prog
What is the Ideal PE class to help students physically and academically? 
There is tremendous value in heart rate monitors in school part 1 
There is tremendous value in heart rate monitors in school part 2 
There are challenges when implementing the LRPE prgram 
What a student should do BEFORE their Standardized Test. 
What roles do the Administrator and Classroom Teacher play in the LRPE program 

cube root

 ax³ + bx²+cx + d = 0 , is a perfect cube, if

b³ = 27 a²d and c³ = 27ad²

cube root

Find the cube root of:

27x⁶ - 27x⁵ + 171x⁴ – 109x³ + 342x² – 108x + 216

polynomial

If p, q, r are positive quantities, and the equation

If x⁴ +px³ + qx²+rx + 1 = 0, and

x⁴ +rx³ + qx²+px + 1 = 0, have a common root, then prove that

p + r = q + 2

Polynomial

If x³ + px²+qx + r = 0 , and s denotes their sum, prove that,

(s –a)(s – b)(s – c) = r - pq      (Hall)

remainder theorem

If x³ + px + r and 3x² + p have a common factor, 

then p³/27 + r²/4 = 0

Algebra

Algebra

if x + 1/y = 1 and y + 1/z = 1, then show that the value of z + 1/x  = 1

square root

If 9x⁴ – 12x³y + px²y² + 4xy³ + y⁴  is a perfect square then find the value of P

square root

If x⁴ – gx³ + kx² - px + 1 is a perfect square for all values of x, 

then g = p and g²/4 + 2 = k

square root

Find l and m so that

9x⁴ – 6x³ + 13x² + lx + m may be a perfect square?

square root

For what value of A will

25x⁴ – 30ax³ + 4a²x² – 24a³x + A , be a perfect square?

square root

Find the square root of the following expression

4 + 12x  - 7x² – 12x³ + 34x⁴ - 24x⁵ + 9x⁶

 

Square root

Find the value of A for which

25x⁴ – 30gx³ + 49g²x² – 24g³x + A is a perfect square

Square root

Find the square root of the expression

16x⁸ - 16x⁶ + 8x⁵ – 36x⁴ – 4x³ + 21x² – 10x + 25

Factorization

Show that: 

ab(x² + 1) – x (a² + b²) = (ax – b) (bx – a)

Algebraic Identity

If a + b + c = s

Then show that 

(s – 3a)³ + (s – 3b)³ +  (s – 3c)³ =  3(s – 3a)(s – 3b)(s – 3c)

Algebraic Identity

If a + b + c = 0

Then show that a (b – c)² + b(c – a)² + c (a – b)² + 9abc = 0

Algebraic Identity

If A = b +c – 2a, B = c + a – 2b and C = a + b – 2c

Find the value of A³ + B³ + C³ – 3ABC

algebraic identity

show that:

a² (b – c) + b² (c – a) + c² (a – b) + (b – c)(c – a)(a – b) = 0

Factorization

Show that:

(a + b + c)² – a(b + c – a) – b(a + c – b) – c(a + b – c) 

= 2(a² + b² + c²)

factorization

Show that: (ax + by)² + (ay – bx)² + c²x² + c²y² 

= (a² + b² + c²) (x² + y²)

factorization

Show that: (a + b)(a² – ab + b²) – (a + c)(a² – ac + c²) 

= (b – c)(b² + bc + c²)

Factorization

Show that: (ad + bc)² + (ac – bd)² = (a² + b²) (c² + d²)

Factorization

Factorize: 1 +27x³ – 8y³ + 18xy

Factorisation

Factorize: a³ + b³ + 8c³ - 6abc

factorization

Factorize: a³ – 27b³ + c³ + 9abc

Factorization

Factorize: a (b² + c² – a²) + b(a² + c² – b²)

Factorization

Factorize: m³ – n³ –(x² –mn)(m – n)

factorization

Factorize:

3x² – 2ab – x (b – 6a)

Factorization

Factorize: ab(x² + 1) – x(a² + b²)

Algebra

If x³ + y³ = 280 and x²y + y²x = 240, then find the ratio of x and y.

Arithmetic Progression

If p times the p^th term of an AP is q times the q^th term. Then show that the (p + q)^th term of the AP must be zero.

Quadratic equation - interesting way to solve

Solve for x:

(x + 5)² + (x + 3)² = 12

Divisibility

Show that  3¹ + 3² +... 3²⁰¹⁰ is divisible by 363.

algebra

 If x² + y² = 74 and xy = 35, find the value of x and y.

Remainder theorem

Show that: (c + a - 2b)d²+ (a + b - 2c) d + (b + c - 2a) is exactly divisible by (d - 1).

algebra

By means of the formula  (a + b)(a - b) = a² - b²

find the value of the expression
2117 x 1883 - 1113 x 887

Algebra

show that (y² - 3y)( y² - 3y + 2)+ 1 is a perfect square and find the square root.

Simultaneous equation

If 6x + 4y - 2z - 5 = 3x -2y + 4z + 10 = 5x - 2y + 6z + 13 = 0, then find x, y and z

Simultaneous equation

If p/x + q/y = 0 and px + qy = r then find the value of x and y.

simultaneous equation

if m/x + n/y = a and n/x + m/y = b, then find x and y

math for fun

 

(If you wish to know more about carbon dating, why don’t you take a peep at:

http://mathcentral.uregina.ca/beyond/articles/ExpDecay/Carbon14.html)

2-variations

The pressure of gas under constant heat condition is found to vary inversely with the volume raised to the power of γ, where γ is the ratio of specific heat of the gas under constant pressure to constant volume, and is found to be 1.14. A student observes that a certain gas occupies a volume of 22.4 litres under 3 kg /cm² pressure. What will be the pressure of gas if the same quantity of gas is reduced to 11.2 litres?

variation

For a free falling body, the instantaneous velocity is proportional to square of time taken. In 3.3 sec. the velocity of the body is 100 m/s. What will be the velocity after 10 sec.?

speed maths

Simple equations

More examples of the denominators being cyclical in the form AB, BC and CA.

Note the thin disguise in the problem:

 

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speed math

Simple equations 

More examples of the denominators being cyclical in the form AB, BC and CA, then

  

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