Algebra assessment

Introduction :


Algebra is a branch of mathematics. Algebra plays an important role in our day to day life. Algebra assessment will cover the four basic operations such as addition, subtraction, multiplication and division. The most important terms for algebra assessment are variables, constant,coefficients, exponents, terms and expressions. For Algebra assessment,we have to use the symbols and alphabets in place of unknown values to make a statement. Hence, algebra assessment causes the leads of Arithmetic.

Example problems for algebra assessment:


Example 1:

Solve the equation for x, 2(4x - 7) = 26.


Solution:

2(4x - 7) = 26

(2 * 4x) – (2 * 7) = 26

8x - 14 = 26(add 14 on both sides)

8x – 14 + 14 = 26 + 14

8x = 40 (divide both sides by 8)

`(8x) / 8="40" / 8`

x = 5


Example 2:

. If a="-3" and b="4," then -5ab4=?


Solution:

Put a="-3" and b="4" in -5ab4

-5ab4 = (-5 * -3) * 44

-5ab4 = -5 * -3 * (4 * 4 * 4 * 4)

-5ab4 = 15 (16 * 16)

-5ab4 = 15 * 256

-5ab4 = 3840


Example 3:

Solve (-3ab3) (4a2b3)


Solution:

(-3ab3) (4a2b3)

= (-3 * 4) * (a * a2) * (b3 * b3

 Note:

  • (am) (an) = am+n
  • a=a1

= -12 * ( a1+2) * (b3+3)

=-12a3b6 


Example 4:

Solve `(-3ab3)/(4a^2b^3)`


Solution:

`(-3ab^3) / (4a^2b^3)`

Note:

  • 1/a = a-1
  • a-1 = a
  • a0 = 1

`((-3 )* (a * a^(-2))* (b^3 * b^(-3)) ) /4 `

`(-3*a^(1+(-2))*b^(3-3))/4`

`(-3 * a^-1 * b^0) / 4`

`(-3 * a^-1 * 1) / 4`

`(-3* a^-1) / 4`

`-3/(4a)`


Example 5:

Use quadratic formula for solving x2 + 8x +7=0


Solution:

Here a = 1, b = 8 and c = 7

Discriminant: b2-4ac = 82 – 4 * 1 * 7 = 36

Discriminant (36) is greater than zero. The equation has two solutions.

x =`-b+-sqrt(b2-4ac)/(2a)`

x =`(-8+-sqrt(64-28))/(2*1) `

x1,2 = (-8 ± 6) / 2 * 1

or

 x1 = `-2 / 2` = -1

x2 = `-14 / 2 ` = -7

 or

 x1,2 = -1, -7


Practice problems for algebra assessment:


Problem 1:

Solve the equation for x, x-39=3.

The answer is x = 42


Problem 2:

Solve the inequality for x, 6x = 72

The answer is x = 12


Problem 3:

Solve 6x/2x2

The answer is x = 3/x


Problem 4:

Use quadratic formula solver 2x2+16x+14=0

The answer is x1 = -1 and x2=-7


Problem 5:

Use factorizing method for solving 2x2+16x+14=0

The answer is x1 = -1 and x2=-7