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Algebra has always been a subject that serves as a building block for other high school math courses. Without a fundamental understanding of algebra and its applications, high school students will struggle and may need in home tutoring. In the middle of this page, we have put together some key formulas most students should understand by the time they have completed their algebra class. In addition, at the bottom of the page we’ve included sample problems so students can have more practice. You can contact a San Diego Tutor representative to help you go over those problems at the number above. At San Diego Tutor, we understand how crucial it is to have an in home tutor that knows how to teach algebra. We are available everyday of the week to help. CONTACT US today for more information on getting a algebra tutor in the Del Mar, La Jolla, Carmel Valley, Poway, Rancho Santa Fe and Scripps Ranch areas.
Helpful Algebra Formulas
Equation of a Straight Line
Straight-line equation in "slope-intercept form"
y = mx + c Equation
1
Where:
m = slope
c = y-intercept (where the line crosses the y axis)
Slope = y / x = Rise / Run
If the line goes through the origin (0,0) then the straight line equation simplifies to
y = mx Equation 2
By comparing Equation 1 with Equation 2 one can see that when a line goes through the origin, c becomes zero. This is also evident by looking at Figure 1. As the line moves up toward the origin, c becomes less negative and approaches zero.
Laws of Exponents for Algebra
- (xm)(xn) = xm+n
- (xy)m = xmym
- (xm)n = xmn
- x0 = 1
- (xm)/(xn) = xm-n
- x-m= 1/(xm)
- x1 = x
- x-1 = 1/x
- (x/y)n = xn/yn
Binomial Theorem for Algebra
- (a + b)1 = a + b
- (a + b)2 = a2 + 2ab + b2
- (a + b)3 = a3 + 3a2b + 3ab2 + b3
Difference of Squares for Algebra
- a2 - b2 = (a - b)(a + b)
Sample Problems
Below you will find some sample algebra problems you may see on one of your exams. If you would like one of our San Diego Tutor educational specialists to go over the answers with you, please send your answers to practiceproblems@sandiegotutor.com and one of our representatives will contact you.
Solve for the unknown variable(s)
1.) - 7x = - 14
2.) 7x - 4 = - 4
3.) 63 = - 7x - x - 1
4.) 3x - 2 = - 6x - 20
5.) 3(7x - 2) = - 174
6.) - 3x + 3y
= 12
3x + 3y = 6
7.) x + 5y = 21
x + 2y = 3
8.) - x + 2y = 2
- x + 3y = 6
9.) 2x + 4y
= 30
- 2x - 8y = - 66
10.) 3x + y = 16
- x - 5y = - 10
11.) x = - 4y + 0
- 3x + 2y =
0
12.) x2 + 3x - 10 = 0
13.) - 8x2 - 10x - 2 = 0
14.) 9x2 + 19x + 10 = 0
15.) 9x2
+ 12x + 5 = 0
Figure 1: Equation of a straight line
Pythagoras was a Lonian Greek Philosopher and a Mathematician