Prep for College Algebra Semester 1 Final Review

Name: _______________________ 1. Graph each linear equation. a. 𝑦 = −2 b. 3𝑥 − 2𝑦 = 6 2. Graph the solution to the system (i.e., the intersection of the graphs) a. 𝑦 < 2𝑥 − 1 𝑦 ≤ − !

!𝑥 + 5

b. 𝑦 > −1 𝑥 ≤ 8 𝑦 > !

!𝑥 − 3

Determine whether each pair of lines is parallel, perpendicular, or neither. 3. 𝑦 = 8𝑥 − 6 4. 𝑦 = !

!𝑥 + 1

𝑦 = 8𝑥 + 6 2𝑦 + 3𝑥 = 1

Prep for College Algebra Semester 1 Final Review

Find the equation of each line given the information below. Write in slope intercept 𝒚 =𝒎𝒙+ 𝒃 form. 5. Through (1, 6) and (5, 2) 6. Slope −4; through 5,−2 7. Slope = !

!; through (-6, 1) 8. Through (-6, 3) and (2, 7)

9. Thru (−1,−5); parallel to 𝑦 = 3𝑥 − 2 10. Thru (5,−2); perp. to  𝑦 = !

!𝑥 + 10

Solve each system of linear equations using the method of your choice.

11. 5𝑥 + 2𝑦 = 1𝑥 = 3𝑦 + 7     12.

𝑥 + 2𝑦 = 13𝑥 + 4𝑦 = 5    

Prep for College Algebra Semester 1 Final Review

13. 3𝑥 − 𝑦 = 11−6𝑥 + 2𝑦 = 2     14. 5𝑥 + 2𝑦 = −17

2𝑥 − 3𝑦 = −3    

Write a system of equations to represent the following scenarios and then solve. 15. Hilton Drama Club sold 311 tickets for a play. Student tickets cost $1.00 and Adult tickets cost $3.00. If

they collected $771 total for the play, how many student tickets and adult tickets were sold? 16. An office supply store sells 7 writing tablets and 4 pens for $6.40. Also, 2 tablets and 19 pens cost $5.40.

Find the price of each. 17. One number is 5 less than a second number. Two times one number plus 3 times a second number is 25.

What are the two numbers?

Prep for College Algebra Semester 1 Final Review

18. Solve each equation for the specified variable.

a. −3𝑥 + 4𝑦 = −12; 𝑓𝑜𝑟  𝑦 b. 𝐴 = 𝑃 𝑟 + 𝑡 ; 𝑓𝑜𝑟  𝑟

c. 𝑃 = 2𝑙 + 2𝑤; 𝑓𝑜𝑟  𝑤 d. 𝐶 = 2𝜋𝑑; 𝑓𝑜𝑟  𝑑 Solve the following linear equations and inequalities for  𝒙: (answers in interval notation when necessary) 19. 8𝑥 − 3 = −2𝑥 + 2 20. 9 𝑥 − 2 − 6 = 8 𝑥 − 3 + 𝑥 21. 2𝑥 − 4𝑥 − 3 = 3𝑥 − 2 22. 4 𝑥 − 1 ≤ 4𝑥 − 8 23. 7𝑥 + 9 > 7 𝑥 − 2 + 5 24. −3𝑥 − 8 < 4

Prep for College Algebra Semester 1 Final Review

25. Given 𝑔 𝑥 = 3𝑥 − 𝑥! a. 𝑔 3 = b. 𝑔 −2 = c. 𝑔 𝑐 + 2 Factor each polynomial. Remember first take out the GCF if there is one! 26. 𝑝! + 10𝑝 + 16 27. 2𝑥! + 3𝑥 − 5 28. 6𝑥! + 37𝑥 + 6 29. 𝑥! − 8𝑥! − 9𝑥 30. 6𝑣! + 33𝑣! + 15𝑣 31. 𝑛! − 4𝑛 − 12 32. Write a linear equation given the graph: ____________________________________

Prep for College Algebra Semester 1 Final Review

33. Answer the questions given the graph to the left: Southern Star Reality is an established real estate company that has enjoyed the constant growth in sales since 2000. a. What is the slope of the graph? b. What does the slope mean? c. Find 𝑓(2) d. What does the y-intercept mean according to the scenario? Solve for the given variable: 34. 𝑥! + 2𝑥 − 15 = 0 35. 3𝑦! − 2𝑦 − 16 = 0

36. 7𝑥 + 8 3𝑥 − 5 = 0 37. 2𝑥 2𝑥 − 1 = −𝑥! + 3

Years after 2000

(0, 170)

(7, 275)

Num

ber

of h

ouse

s sol

d

Prep for College Algebra Semester 1 Final Review

Perform the indicated operation. Be careful! Think about what is being asked…

38.   4𝑚! −𝑚! + (5𝑚! +𝑚!) 39. (2𝑥 − 4)(−𝑥! + 3𝑥 − 2)

40. 5+ 7𝑥! + 3𝑥! − (12− 5𝑥 − 6𝑥!) 41. 2𝑛 + 3 𝑛 − 2

42. Use the graphs below to answer the following questions.

A) Decide if the graphs are a function. Write “Function” or “Not Function” on the line

______________ ______________ ______________ ______________

B) Decide whether the graphs are linear. Write “Linear” or “Not Linear” on the line

______________ ______________ ______________ ______________

C) State the Domain in interval notation.

______________ ______________ ______________ ______________

D) State the Range in interval notation.

______________ ______________ ______________ ______________