Download Jump Start 3000 Course-Pak

Learning Assistance Center
Schoolcraft College
Jump Start 3000
Course-Pak
Terri Lamb
Mathematics Learning Support Specialist
Learning Assistance Center
[email protected]
2011
1
Addition and Subtraction of Integers
When opposites are added, the result is
Ex:
-10+10
10 – 10
25 - 25
-25 + 25
Adding integers:
If the signs are the same
2 2
and keep the
25 25
286
If the signs are different
175
and keep the sign of the
12 2
45 20
75 280
*Note: Double negative = sign change
7 ( 3)
5 ( 1)
10 ( 10)
7 7
Multiplication and Division of Integers
Remember these:
To help you remember, you can use this:
Ex:
( 3)2
3 3
10
25 25=
3
9
5
-28
=
0
2(50)=
0
=
-28
2
Order of Operations with Integers
P
(8 6)32
65 5 23
E
M
D
A
S
3 2(4 32 )
(-2) 2 13 ( 7)
50
3 47
5 ( 6) 3 16
7(22 )
4(1 23 )
5(23 32 ) 5
=
4 10 5 3
3
Variables and Expressions
A variable is a letter or symbol used to represent some unknown quantity. Ex:
An expression is a collection of variables, symbols and/or numbers. Ex:
Evaluating Expression
Plug in value for the specified variable using parenthesis.
Evaluate the following expressions for x= -15, y= -21, z=3
z ( x 2) y
z x y
2 z 3 3z 1
4
Combining Like Terms
You can only add or subtract terms that are (exactly) alike
Combine like terms:
3x 2 x
12 r 2 2r r 2
a a
2 x 9 5 x 18
7+5x 11x 15
Multiplying Integers, Clearing Parenthesis & Combining Like Terms
Distribute to clear parenthesis
4 5n
9( 5 y )
3(2 x)
4 9x
3(3 x)
5(2 x 3)
7(8 4 x)
5( x 1) 3 x
2n 4(8 3n)
Equation Solving
Expression:
Equation:
5 Steps to Equation Solving
Never forget your goal!
1.
2.
3.
4.
5.
5
AND the QUEEN MOTHER of all algebra rules!!
Single Step Equation Solving
Solve for the given variable:
x 2 10
y 7 9
2 x 12
5 x 25
x
=5
3
y
=40
7
Two-Step Equation Solving
Solve for the given variable:
4x
12
3
15
3e
9
w
12
3
c
4
8
3
30
9
6
Multi-Step Equation Solving
3x – 9 + 5x = 15
11y – 3 = 4y+11
– 9n = 5n – 56
7a + 15 = 4a +37
19b – 14 – 21b = – 2
2(x+5) – x = –7
7
JumpStart! 3000 Practice Quest
Evaluate and simplify.
1. 21 + 9
5.
2.
14
2
3 ( 4)
3. 8
15
3
7. ( 3) 2
8.
4 1
11. 5 32 23 ( 2)2
6. 5
9. 24 ÷ 2 3=
10.
8(2 3)
7
4. 6(9)
4
0
Evaluate for x = 2, y = 3, z = 1
13. y x 2
12. x y
14. z 2 y 2 x
Solve for x
15. 2 x 10
18. 2 x 3
16.
17
x
3
7
19. 3x 5 x 1
17. x 3
20.
x
5 x 3
2
8
JumpStart! 3000 Practice Quest
Evaluate and simplify.
1. 21 + 9
5.
14
2
12
-7
2.
3 ( 4)
6. 5
15
3
5
10.
8(2 3)
9. 24 ÷ 2 3= 36
1
3. 8 7
7. ( 3) 2
4 1
56
4. 6(9)
9
8.
4
0
54
undefined
11. 5 32 23 ( 2) 2 0
3
Evaluate for x = 2, y = 3, z = 1
12. x y
13. y x 2 7
5
14. z 2 y 2 x
11
Solve for x
15. 2 x 10
16.
x=5
x
7
3
17. x 3 8
x=21
18. 2 x 3
17
x= 7
19. 3x 5 x 1
x=3
x=11
20.
x
5 x 3
2
x=16
9