REVIEW OF BASIC ALGEBRA 2
PRECALCULUS
LINEAR EQUATIONS - Write the appropriate Linear Equation for each of the following.
1. The point-slope form given (−3, 10) with 𝑚 = −4.
2. The standard form given (−2, 6) & (5, 2).
3. The slope-intercept form given (−1, −5) & (6, 0).
4. The slope-intercept form given (6, −5) &
perpendicular to −5𝑥 − 7𝑦 = −17.
5. The standard form of the line parallel to the given
line 𝑦 = 3𝑥.
6. The horizontal and vertical lines going through the
point (2, 7), identifying which is which.
SOLVING EQUATIONS - Solve each equation for the stated variable.
7. Solve for 𝑥. 5𝑥 + 3(𝑥 − 2) = 4𝑥 + 1
8. Solve for 𝑚. 𝑔 = 4𝑐𝑚 − 3𝑚
9. Solve for 𝑥. −(1 + 7𝑥) − 6(−7 − 𝑥) = 36
11. Solve for y:
𝑥2
9
𝑦2
+ 25 = 1
10. Solve for x: 𝑦 =
2𝑥−1
𝑥+5
12. Solve for x: 𝑦 + 1 = √𝑥 − 2
QUADRATICS - Solve by completing the square.
13. 𝑥2 + 10𝑥 − 25 = 0
https://www.khanacademy.org/mat
h/algebra/quadratics/solving- quadratics-by-completing-thesquare/v/solving-quadratic- equations-by-completing-thesquare2
14. 𝑥 + 15 = 8𝑥
QUADRATICS - Solve the equation using the quadratic formula.
15. 2𝑥2 − 14𝑥 + 40 = 3𝑥2 − 16𝑥 + 32
https://www.khanacademy.org/math/algebra/quadr
atics/solving- quadratics-using-the-quadraticformula/v/quadratic-formula-1
16. 𝑥2 − 4 = 8𝑥
h/algebra/polynomial-factorization
QUADRATICS - Solve the equation by factoring.
17. 4𝑥2 − 1 = 0
18. 𝑥2 + 3𝑥 = 10
19. 5𝑥2 − 32𝑥 − 21 = 0
20. 2𝑥2 − 13𝑥 + 19 = −2
21. 27𝑥2 + 18𝑥 = 0
22. 2𝑥2 + 20𝑥 + 12 = 5𝑥 − 𝑥2
https://www.youtube.com/watch?v=JHUju_Qkqbg
QUADRATICS - Solve by using your Graphing Calculator.
Round answers to the nearest thousandths (3 decimal places).
23. 𝑥 2 − 8𝑥 = −18
24. 13𝑥 2 + 24𝑥 − 1 = 14
LINEAR SYSTEMS - Solve the following Linear Systems.
𝟑𝒙 + 𝟒𝒚 = 𝟏𝟐
https://www.khanacademy.org/mat h/algebra/systems-oflinear- equations
25. 𝟐𝒙 − 𝟑𝒚 = −𝟗
26.
𝟐𝒙 + 𝟗𝒚 − 𝟓 = 𝟎
𝟓𝒚 − 𝒙 = 𝟐𝟔
27. The school that Stephan goes to is selling tickets to a choral performance. On the first day of ticket sales the school
sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling
3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.
28. For what value of 𝑏 would the following system of equations have an infinite number of solutions?
9𝑥 + 12𝑦 = 21
6𝑥 + 8𝑦 = 𝑏
RATIONAL EXPRESSIONS: Simplify – Factor, reduce and/or complete the rational operation. In
addition, give the domain of the expression.
https://www.khanacademy.org/math/algebra2/rational-expressions- equations-and-functions
29.
31.
33.
𝑥 2 +𝑥−6
𝑥 2 −4
3
𝑥+5
−
𝑥2 −1
5𝑥
𝑥+1
5𝑥2 +10
30.
𝑥
5
32.
34.
𝑥 2 +𝑥−12
5𝑥−15
3𝑥 2 +7𝑥−6 15𝑥 2 +4𝑥−4
9𝑥 2 −4
6𝑥
𝑥 2 −4
−
∙
3
𝑥−2
9−𝑥 2