Download Things you Must know! The Distributive Property ab + ac = a(b + c

Things you Must know!
1.
The Distributive Property
a.
ab + ac = a(b + c)
2.
Combining Like Terms
3.
Order of Operations
4.
Properties:
a.
2x + 3x + 2 = 5x + 2
a.
Commutative:
a + b = b + a;
b.
Associative: a + (b+c) = (a+b) +c;
c.
Distributive: a(b + c) = ab + ac
d.
Identity:
a + 0 = a;
e.
Inverse:
a + (-a) = 0
5.
How to add and subtract a matrix
6.
Division of real numbers.
a.
a(1) = a
c
Rate – 2 quantities with different units
a.
8.
a(bc) = (ab)c
a + b = 1 (a + c)
c
7.
ab = ba
miles/hour (read miles per hour)
Ratio – 2 quantities with the same units
a.
Number of red m&m’s
Total number of m&m’s
Linear equations
9.
Whatever you do to one side of an equation you must do to the other side!
10. When you have an equations with 2 or more transformations
a.
Simplify the equation first – combine like terms
b.
Use inverse operations to isolate the variable
i. Start with addition or subtraction before you do multiplication or division
2x + x -6 = 12
3x – 6 = 12
combine like terms
+6 = +6
3x
= 18
3
divide by 3
3
x=3
check the answer
2(6) + 6 -6 = 12 Yes!
Graphing Linear Equations
11. Horizontal line equation
a.
y = a number
i. y = 2
every point on this line has y equal to the same number
(1, 2) (5, 2) (-2, 2)
12. Vertical line
a.
13.
x = a number
Table of values – choose values for x and solve the equations for y to get points on the line.
a.
y = 2x + 3
x y
03
1 5
-1 1
14. Intercepts of the line – where the graph of the linear equation crosses the x and y axes.
To find the intercepts:
a.
The x intercept is where y = 0
b.
The y intercept is where x = 0
15. Slope – slope is the change in y divided by the change in x or the rise
You need two coordinate points
run
y2 – y 1
x2 – x1
16. Slope – intercept form of the equation of a line
a.
y = mx + b where m is the slope of the line and b is where the line crosses the y axis (the y intercept)
MORE THINGS YOU MUST KNOW!
Reminder:
Graphing Absolute Value Equations
a.
Find the vertex
a.
ax+b +c
i. The x value of the vertex is found by making what is inside the absolute value sign = to 0 and
solving for x.
ii. The y value of the vertex is c
b.
Make a table of values – remember the absolute value sign
c.
Chose values for x and solve for the value of y
Linear Inequalities:
< less than, open circle of a graph
≤ less than or equal to – closed circle on the line graph
>greater than, open circle on the line graph
≥ greater than or equal to – closed, filled in circle on the line graph
When you multiply or divide an inequality by a negative number, you switch the inequality.
Example: -2x < 4 divide each side by -2 the inequality becomes x > 2
Compound inequalities:
x is between 2 and 5 is written 2 < x < 5. The graph is a line segment (remember to check whether the circles should
be open or closed, is there an equal component to the inequality.
Or problems have a line segment that is not part of the solutions, rather there is one side that goes on to the left (getting
smaller) and one that goes on to the right (getting bigger.)
Absolute value inequalities:
To take away the absolute value symbols you turn the equation into either a “between” inequality – this happens
when the absolute value inequality is less than: example x + 2 < 8 becomes – 8 < x + 2 < 8. If there is a greater than
inequality
x + 2 > 8 becomes an “or” problem x + 2 > 8 OR x + 2 < -8
Linear inequalities with 2 variables:
First graph the line (change the inequality into an equality and graph it as you would any other linear equation.) Before you
actually draw the line, decide if it should be a solid line (≤ or ≥) or dashed line if there is not an equal part to the inequality.
Second – decide which side of the line has all the answers to the inequality by choosing a point on one side, substituting the
values for x and y into the original inequality and see if it is true. If so, shade in that side of the graph, if not – shade the
other side.