Algebra II L2 Name: ____________________________ Date: _______

Midterm Review Study the following problems to prepare for your midterm exam. You will be allowed to use a calculator

on all parts of the midterm. Use your tests from class as well to review.

Simplify each of the expressions.

1. 2 + 3(4 + 6)3 − 10 2. 4 − (5𝑥 + 6) − 8𝑥

Solve the equation or formula for the indicated variable.

3. 𝑆 = 4𝑟3𝑡, for 𝑡 4. 2𝐵 =5𝑀

𝑊, for M

Solve each equation for 𝒚.

5. 9𝑥 + 5𝑦 = −30 6. 0 = 3 + 2𝑥 − 4𝑦

Solve for x:

7. 10𝑥 − 3 + 2𝑥 = 12𝑥 + 1 8. 5(2𝑥 − 5) − 3(𝑥 + 1) = 12

Solve each absolute value equation.

8. |𝑥 − 2| = 15 9. 2|𝑥 + 3| − 4 = 10

Solve the inequality. Graph the solution set.

10. −2𝑘 + 3 ≥ 11 11. 4(𝑏 − 1) < −16 + 16𝑏

12. −18 ≤ 3𝑥 − 6 < 12 13. 7𝑥 − 8 < −36 or 6𝑥 + 7 > 19

14. x36 > 33 15. 54 x − 3 14

16. Write the equation of the line that:

a) is parallel to x + 2y = -4 and passes through the point (-6, 5)

b) is perpendicular to x + 2y = -4 and passes through the point (-6, 5).

17. Determine if the following relationships represent functions. Explain why or why not.

a) { (-3, 2) (4, 5) (-1, 2) (0, 3)} d)

b) y = 3x -5

c)

18. State the domain and range of a, b, & d above and the following:

a) b) c) d)

D: ______________ D: _______________ D:_______________ D:______________

R: ______________ R: _______________ R:_______________ R:______________

19. Solve and classify each system using either substitution or elimination method.

a) x – 2y = -24 b) 4x – 5y = -19

4x + 2y = 4 12x - 15y = -57

20. You ride an express bus from the center of town to your street. You have two payment options.

Option A is to buy a monthly pass and pay $1 per ride. Option B is to pay $2.50 per ride. A monthly pass

costs $30. After how many rides will the total costs of the two options be the same?

21. Solve the system, show all work. 𝑥 + 𝑦 + 4𝑧 = 2

2𝑦 + 5𝑧 = 4 3𝑥 + 2𝑦 + 4𝑧 = −7

22. Graph the absolute value functions.

a) y = 3x - 1 b) 𝑦 = −2 4x c) 𝑦 =1

2x + 3

23. Graph each inequality.

a) 5𝑥 – 2𝑦 > −8 b) – 𝑦 5

24. Graph the system of inequalities. Clearly indicate the solution area.

−𝑥 + 𝑦 > −4 𝑥 + 𝑦 < 3

25. Classify the polynomials by term and degree.

a) 2𝑥 + 1 b) 3 c) 𝑥2 + 2𝑥 + 3

______________________ ______________________ ________________________

______________________ ______________________ ________________________

26. Simplify and write your answers in standard form:

a) (𝑥 + 4)(𝑥 − 2) b) (3𝑥2 − 4𝑥 + 2) + (7𝑥 − 6)

c) (10𝑥2 − 4𝑥 + 5) − (2𝑥2 + 3𝑥 + 1) d) (𝑥 − 5)2

e) 3(𝑥 + 2)(𝑥 + 8) f) (𝑥 − 1)(−2𝑥2 − 9𝑥 + 2)

27. If 𝑓(𝑥) = 5𝑥2 − 6𝑥 + 2 , then 𝑓(−1) = ________

28. Factor each expression completely. If not factorable, write “prime”

a) 𝑥2 + 2𝑥– 63 b) 25𝑎2– 64 c) 3𝑚2 + 20𝑚– 7

d) 9𝑦2– 24𝑦 + 16 e) 𝑟3– 4𝑟 + 2𝑟2– 8 f) 30𝑎𝑏5 − 12𝑎2𝑏

g) 𝑥2 + 5𝑥 − 9

PRIME

6 2015-2016 Midterm Review Algebra 2 L2

29. Solve each by factoring.

a) x2 – 5x – 14 = 0 b) 24x2 + 12x = 0

c) 9x2 = 36 d) 2x2 + 13x = −15

e) 4𝑥3 − 3𝑥2 − 28𝑥 + 21 = 0 f) 3𝑥2 = 9𝑥 + 30

Set up a quadratic equation for each and solve by factoring:

30. The sum of a number and its square is 272. Find the number(s).

31. The product of two consecutive even integers is 288. What are the integers?

32. A rectangular playground 40m by 60m is to be doubled in area by extending the length

and width by an equal amount. By how much should the length and the width be lengthened?

33. The length of a rectangular table is 5 ft greater than the width. The area of the table

is 24 𝑓𝑡2. Find the length and width.

7 2015-2016 Midterm Review Algebra 2 L2

Graph each:

34. 𝑓(𝑥) = {𝑥 + 2, 𝑥 ≥ 13, 𝑥 < −1

35. g(x) = ________________

𝑓(1) = ________ 𝑓(−8) = _________ 𝑓(6) = ________ 𝑓(2) = _________

Write the model for each given graph below.

36. ______________ 37. ________________