MANIPULATING AND SOLVING EQUATIONS SAT PRACTICE

Problem 1 :

If a + b = -2, then (a + b)³ = 

a)  4    b)  0   c)  -4   d)  -8

Solution

Problem 2 :

For what value of n is (n - 4)²  = (n + 4)²

Solution

Problem 3 :

If (1/a) x (b/c) = 1, what is the value of b - ac ?

(a)  -3    (b)  0     (c)  2    (d) it cannot be determined

Solution

Problem 4 :

If 3x - 8 = -23, what is the value of 6x - 7 ?

(a)  -5  (b)  -21    (c)  -30    (d)  -37

Solution

Problem 5 :

If 4/9 = 8m/3, what is the value of m ?

(a)  1/6   (b)  2/3   (c)  5/6   (d)  6

Solution

Problem 6 :

If 3x + 1 = -8, what is the value of (x + 2)³

Solution

Problem 7 :

If 4/(k + 2) = x/3, where  k ≠ -2, what is k in terms of x ?

(a)  (12 - 2x)/x   (b)  (12 + 2x)/x   (c)  x/(12 + 2x)   (d)  12x - 2

Solution

Problem 8 :

If (x - 3)² = 36 and  x < 0, what is the value of x²

Solution

Problem 9 :

f = p[ (1+i)ⁿ - 1 ] / i

The formula above gives the future value f of an annuity based on the monthly payment p, the interest rate i, and the number of months n. Which of the following gives p in terms of f, i and n.

Solution

Problem 10 :

If m/2n = 2, what is the value of n/2m ?

(a)  1/8   (b)  1/4   (c)  1/2  (d)  1

Solution

Problem 11 :

If x < 0 and x² - 12 = 4, what is the value of x ?

(a)  -16  (b)  -8   (c)  -4  (d)  -2

Solution

Problem 12 :

If x² + 7 = 21, then the value of x² + 3 ?

Solution

Problem 13 :

If x² + 5x - 24 = 0

If k is a solution of the equation above and k < 0, what is the value of |k| ?

Solution

Problem 14 :

x² (x⁴ - 9) = 8x⁴

If x > 0 for what real value of x is the equation above true ?

Solution

Problem 15 :

If [2 √(x + 4)] / 3 = 6 and x > 0, what is the value of x ?

Solution