Midterm

MA 106 Mid Term Exam Name_______________________________

Decide whether or not the ordered pair is a solution of the system.

1) (2, -3)

2x + y = 7

3x + 2y = 12

Solve the system by graphing. 2) 4x + y = -6

3x + 5y = 21

Solve the system by the substitution method. If there is no solution or an infinite number

of solutions, so state.

3) x - 3y = 0

-5x - 4y = -57

Solve the system by the addition method. If there is no solution or an infinite number of

solutions, so state.

4) x - 4y = 17

-7x - 4y = -23

Solve the problem. 5) Devon purchased tickets to an air show for 4 adults and 2 children. The total cost was $110.

The cost of a child's ticket was $5 less than the cost of an adult's ticket. Find the price of an

adult's ticket and a child's ticket.

Graph the solution of the system of linear inequalities. 6) x + 2y ≥ 2

x - y ≤ 0

Add or subtract as indicated.

7) (4𝑥2 − 3𝑥 + 2) + (−4𝑥2 + 3𝑥 − 2)

8) (6𝑥3 − 2𝑥2 − 4𝑥 + 5) − (5𝑥3 − 8𝑥2 − 5𝑥 + 3)

Perform the indicated operation. Simplify if possible.

9)   

     

   6y

9 y

10) 3𝑥(7𝑥 + 8)

11) (x + 2) (x +12)

12) 6

4 y 

 

  

13)  28x 

14)  216x 

15) (x + 1) (x - 1)

16) 4

x

8 x

17) 0

12

18) 2

4

a  

  



19) 3

5 

Write the number in decimal notation without the use of exponents.

20) 6

10 75.1 

Divide the polynomial by the monomial.

21) 2

2x-

5 18x

8 4x- 

Factor the following expression.

22) 42-x 2

x 

Factor out the Greatest Common Factor from the polynomial.

23) 5

x30 7

x5 

Factor by grouping.

24) 7-x7 2

x 3

x 

Factor the following expression.

25) 𝑥2 − 16