SAT PRATICE QUESTION USING ALGEBRAIC IDENTITIES

Problem 1 :

Which of the following is equivalent to 

(1/m)² - 2 (1/m) (1/n) + (1/n)²

(a) (1/√m - 1/√n)⁴     (b) (1/m  - 1/n)²

(c)  1/(m-n)²     (d)  2/(m² - mn +n²)

Solution

Problem 2 :

(3x + 2y)²

If the expression above can be written as

ax² + bxy + cy²

 where a, b and c are constants, what is the value a + b +c ?

Solution

Problem 3 :

x² + kx + 9 = (x + a)²

In the equation above k and a are positive constants. If the equation is true for all values of x, what is the value of k ?

Solution

Problem 4 :

2x (x - y) (x + y)

Which of the following is equivalent to the expression above ?

(a) 4x³ - 2xy²     (b)  2x³ + 2xy²

(c)  2x³ - 2xy²     (d)  2x³ - 4xy + 2xy²

Solution

Problem 5 :

If (x + 3) (x - 3) = 91, what is the value of x²?

Solution

Problem 6 :

The expression

(x + 1)/(x + 2) - (x - 2)/(x - 1)

is equivalent to which of the following ?

(a)  -5/(x + 2) (x - 1)    (b)  1/(x + 2) (x - 1)

(c)  3/(x + 2) (x - 1)    (b)  (2x²+3)/(x + 2) (x - 1)

Solution

Problem 7 :

Which of the following is equivalent to

(m + n - 1) (m + n +1) ?

 (a) m² + 2mn + n² - 1      (b) m² - 2mn + n² - 1

(c) m² - n² - 1  (d) m² - 2mn + n² - 1

Solution

Problem 8 :

(a + b)² - (a - b)²

The expression above is equivalent 

(a)  2ab     (b) 4ab     (c)  4ab + b²      (d)  2a² + 2b²

Solution

Problem 9 :

(x - c)² = x + 3

If c = 3, what is the solution set of the equation above ?

(a)  {1}    (b)  {6}     (c)  {1, 6}    (d)  {-3, 1, 6}

Solution

Problem 10 :

The following is equivalent form of 

(1.5x - 2.4)² - (5.2x² - 6.4) ?

Solution