This document provides a review of key algebra 1 concepts including equations of lines, solving various types of equations, factoring polynomials, expressions and equations involving perimeter, area, and geometry. Students are given examples to solve of each concept, including solving systems of equations, simplifying expressions, graphing lines, and determining equations of lines given points or other criteria. The review covers standard form, slope-intercept form, point-slope form of a line, solving linear and quadratic equations, factoring polynomials, perimeter, area, geometry relationships, graphing, and determining equations of lines from information provided.

1. Algebra II Name ______________________
Algebra I Review Period ______
Equations of a Line Slope Formula
Standard Form: Let and be two points in
Ax + By = C
the plane.
A and B are not both zero
Slope-Intercept Form: slope =
m = slope and b = y-intercept
Point-Slope Form:
m = slope,
Solve each equation.
1.  4(3  x)  8 x  2 x 8
4. 
5 3
2. 3x  2( x  1)  0
6 x
5. 
5 9
3. 3x  14  4( x  3) 6 3
6. 
b 8

2. Solve each system of equations using the method of your choice.
2 x  7 y  5
 2 x  y  8 5 x  4 y  2 
7.  8.  9.  7
 y  3x  2 4 x  2 y  2 y  2 x  2

Factor each polynomial completely.
10. x 2  x  72 11. a 2  10a  24 12. 10m3n 2  15m 2 n
13. x 2  12 x  36 14. x 2  64 15. 3 y 2  75
Determine each of the following:
16. Write an expression for the perimeter of a rectangle with length l = 2x + 3 and width w = x – 2
17. Write an expression for the area of a square with side s = 2x + 5
18. Find the diagonal of a rectangle with l = 40 and w = 55.
19. The length of each leg of an isosceles right triangle is 4 cm. What is the length of the hypotenuse?
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3. Simplify each of the following.
20. (3x 2  4 x  7)  (2 x 2  7 x  8) 21. (4a 3  2a 2  a  7)  (3a 3  2a 2  a  8)
22. ( x  7)( x  5) 23.  3xy 3 ( x  2 y)
24. (15a 4b 2 c) 0 25. (8a 3b 2 )(2a 4b5 )
3x3 y 2
26. 27. (x + 6)2
6 x 2 y 5
Graph each of the following.
3
28. y x4 29. y  3x 30. 2x  3 y  9
4
Determine each of the following:
31. Determine the slope of the line containing the points (6, -2) and (-1, 5).
1
32. Determine an equation for a line with slope and y-intercept at (0, -3).
2
33. Determine the equation of a line that passes through the points (3, 8) and (1, 4).
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