1

It \$ x + 1/x = 3\$, find the value of \$ x^3 + 1/x^3 \$.

A) 18

B) 23

C) 42

D) 12

2

Solve the nonlinear equation:

\$x^3 − 6x^2 + 11x − 6 = 0\$

A) x = -1, 2, 0

B) x = 1, -2, -9

C) x = -5, 2, 2

D) x = 1, 2, 3

3

Show that the following system of equations has an infinite solution:

y - 2x = 5
10x - 5y + 25 = 0

A) \$ (a_1)/(a_2) ne (b_1)/(b_2) ne (c_1)/(c_2) \$

B) \$ (a_1)/(a_2) = (b_1)/(b_2) = (c_1)/(c_2) \$

C) \$ (a_1)/(a_2) ne (b_1)/(b_2) = (c_1)/(c_2) \$

D) \$ (a_1)/(a_2) = (b_1)/(b_2) ne (c_1)/(c_2) \$

4

If there is no solution to the linear equation system 4x - ky = 13, 7x + 6y = 9, then find the value of k.

A) \$ k = - 3/7 \$

B) \$ k = 7/(24) \$

C) \$ k = - (24)/7 \$

D) \$ k = - (11)/2 \$

5

If the linear system 3x + 5y = 12 and 2x - ky = 8 has no solution, find the value of k.

A) \$(10)/3\$

B) \$3/(10)\$

C) \$-3/(10)\$

D) \$-(10)/3\$

6

Simplify the expression:

\$((3 a^2)-(9 a)+(6))/(a^2 - 4)\$

A) \$ (3(a+1))/(a-2) \$

B) \$ (3(a+1))/(a+2) \$

C) \$ (3(a-1))/(a+2) \$

D) \$ (3(a-1))/(a-2) \$

7

Solve the non-linear equation:

\$ 4 a^2 - 8 a + 3 \$ = 0

A) \$a = 3/2\$ and \$a = 1/2\$

B) \$a = 1/2\$ and \$a = 4/2\$

C) \$a = 1/2\$ and \$a = 3/2\$

D) \$a = 3/2\$ and \$a = 4/2\$

8

Solve the nonlinear equation:

\$ d^4 - 5 d^2 + 6 \$ = 0

A) \$ d^2 = 4\$ and \$ d^2 = 3\$

B) \$ d^2 = 2\$ and \$ d^2 = 3\$

C) \$d = 2 and d = 3\$

D) \$ d^2 = 2\$ and \$ d^2 = 4\$

9

Determine the number of solutions for the following system of linear equations:

2a + b = 5
4a + 2b = 10

A) Inconsistent

B) Independent

C) Dependent

D) Not enough information

10

If the linear system ax + by = 7 and cx + dy = 5 has no solution, find the relationship between a, b, c, and d.

A) \$a/b = c/d\$

B) \$a/c= b/d\$

C) 0

D) a = b = c = d