Learning Assistance Center
Schoolcraft College
Jump Start 4000
Course-Pak
Terri Lamb
Mathematics Learning Support Specialist
Learning Assistance Center
[email protected]
2014
1
Evaluating Expression & Order of Operations with Integers
P
E
M
D
A
S
Evaluate the following expressions for x= 3, y= -2, z= - 4
Plug in value for the specified variable using parenthesis.
y2
( y )2
x2  y
z  x2
5 Steps to Equation Solving
1. Clear parenthesis and/or fractions
Never forget your goal!
2. Combine like terms on each side
3. Get all variables on one side (L)
AND the QUEEN MOTHER of all algebra rules!
4. Get all constants on the other side (R)
5. Solve for x, usually by division
2(x  5) 1
 =4
3
5
2x
3 1

=
 x
3
4 2
2
Exponent Rules (with like bases)
Multiplying exponents:___________________
32 34
x5 x 4
Power to a Power ______________________
(24 )3
(x 3 ) 8
Dividing exponents: _____________________
34
33
x5
x9
Negative exponents:_____________________
x
x 3
2 -3
Putting it all together:
1.
2.
3.
a 2b3c 2
a 4b 5c 2
 3x 5y 2z 1 


2 2
 6x y z 
2
Polynomials
F.O.I.L.:______________________________________________________________________
( x  2)( x  1)
( x  3) 2
Factoring Polynomials **1ST STEP IN ALL FACTORING: ______________________!!**
4x 12
3a2  24a
3
4 Terms:__________________________________________
2 xy  6 x  3 y  9
3ab  3b  2a  2
3 Terms: ___________________________________________________________________
x 2  3x  4
2 x2  8x  8
4 x 2  14 x  6
4 x2  8x  3
4
2 Terms: ____________________________________________________________
x2  9
2a 2  50
Cubes - remember the formulas
a 3  b3  (a  b)(a 2  ab  b2 )
OR Clean 'em up!
1.
2.
AND
3.
a 3  b3  ( a  b)(a 2  ab  b 2 )
4.
x 3  27
8x3  1
5
Graphing linear equations
The intro: _____________________________________
x+y=7
X
Y
The TWEAK:
x-cept:
y-cept:
3x + 4y = 12
6
Until finally! The algebra students BFF:
1.
2.
3.
2x ‒3y = 9
y = 1‒ x
x=3
y = ‒7
7
JumpStart! 4000 Practice Quest
1. Simplify for x=  3 and y =  1
a. - x 2
b. x 2  3 x  4
c.
y ( x  2)
5y
2. Solve for x
a. 2 x  3  17
3. Simplify completely
x5
a. 9
x
b. 3x  5  x  1
b. y 4 y 3
4. Factor completely
a. x 4  x
b. 4 x 2  8 x  12
e. 20 x3  34 x 2  6 x
5. Graph
1
a. y  x
2
f. 25  x 2
c.
c.
x3
x 3
x
1
5  x
2
3
d . (3 x 2 yz 2 )3
c. ab  6a  7b  42
g. 14x 3  21x 2  14 x  21
b. 5 x  2 y  10
d. 12 x 2  22 x  20
h. 3x 3  81
c. x  3
8
JumpStart! 4000 Practice Quest
1. Simplify for x=  3 and y =  1
a.  9
b. 14
c.  1
2. Solve for x
a. x  7
b. x  3
3. Simplify completely
1
a. 4
x
4. Factor completely
a. x( x  1)( x 2 +x+1)
e. 2 x(5 x  1)(2 x  3)
5. Graph
1
a. y  x
2
b. y 7
c. x  
28
9
c. x 6
b. 4( x  3)( x  1)
f. (5  x)(5  x)
b. 5 x  2 y  10
d.
27 x 6 y 3
z6
c. (a  7)(b  6)
d. 2(2 x  5)(3 x  2)
g. 7(2 x  3)( x  1)( x  1)
h. 3(x  3)( x 2  3x  9)
c. x  3
9