GMAS Review

Combining Terms

100

7x - 3x + 2

What is 4x + 2 ?

200

-5x + 3y +7y - 2x

What is -7x + 10y ?

300

-3 (x + 4)

What is -3x -4

400

3(4y - 2) + 5y - 7

What is 17y - 13 ?

Solution:

12y - 6 + 5y - 7
12y - 5y - 6 -7
17y - 13

500

0.5 (10x - 2) + -3 ( 4x - 3)

What is -7x + 8 ?

5x -1 + -12x + 9
-7x + 8

Integer Computation

100

 -7 - 3

What is -10 ?

200

-3  * - 4

What is 12 ?

300

 - 5 + 3 + (-2) - (7)

What is -11 ?

Solution:

-5 + 3 + (-2) - (7)
-2 + (-2) - (7)
-4 - 7
-4 + -7
-11

400

6 - (-3) + (-9)

What is 0 ?

6- (-3) + (-9)
6 + 3 + (-9)
9 + (-9)
0

500

-12 - (-7) - 3 - 7 * (-2)

What is 13  ?

-12 - (-7) - 3 - 7 * (-2)  
-12 - (-7) -3 + (-7 * -2)   (Multiply first)
-12 + 7 - 3 + 14  
-15 + 28
  13

ExponentsScientific Notation

100

This answer with positive exponents:
5² * 5⁵

What is 5⁷ ?

Solution:  Multiplying exponents-  add exponents

2 + 5 = 7
5⁷

200

This with a numeric answer:

2³ * 4

What is 32 ?

Solution:

2*2*2 * 4
4 * 2 * 4
8 * 4
32

300

  x⁴ 
-----
  x²

What is X² ?

Solution:

x^4-2= x²

400

(2x³ * 4y²)
-------------
  x⁴ * y²

What is   8/x ?

Solution:
x ^3-4 = x^-1
y^2-2= y⁰ = 1

500

3⁰ x^-4 y⁵ 
----------  
3  x² y^-2

What is   y⁷ 
           ------   ?
             3x⁶

Solution:

3⁰ = 1       x^-4-2 = x^-6 = 1/ x⁶ 
y^5--2= y⁵⁺²= y⁷ 

Equations

100

x - 2 = 7

  What is x = 9 ?

Solution:

x - 2 = 7
   +2    +2
      x = 9

200

-7 = x - 2x + 5

What is x = 12?

Solution:

-7 = x - 2x + 5
-7 =  -1x + 5
-5             -5
-12 = -1x
 12 = x

300

x/2 - 4 = 10

What is x = 28

Solution ?
x/2 - 4 = 10  
      +4    +4
___________
x/2    =  14
2(x/2) = (14) 2
     x = 28

400

-88 = 7 (3p + 1) - 2p 

What is p = -5 ?

Solution:
-88 = 7(3p + 1) - 2p
-88 = 21p +7 - 2p
-88 = 7 + 19p
  -7      -7
-95 = 19p
------------
19       19

-5 = p

500

2 (3a + 1) + 6a =-6 + 8a

What is a = -2

6a + 2 + 6a = -6 + 8a
12a + 2 = -6 + 8a
-8a                 -8a
----------------------
4a  + 2 = -6
      -2      -2
-----------------
4a   = -8
-----------
4           4
a = -2

Word Problems

100

Kenya's Kayaks charges a $20 fee for a lifejacket and a kayak plus $15 per hour.   This is the number of hours with a total of $65.

What is  3 hours ?

Solution:

15x + 20 = 65
       -20      -20
-------------------
15x = 45
-----   -----
15        15
x = 3 hours

200

  Hal's horse and Buggy charges $30 plus $2.50 an hour for the same service.  For this many hours you would pay $42.50

What is 5 hours ?

Solution:

2.50x + 30 = $42.50
           -30     -30
-------------------------
2.50x =      12.50
-------         -------
2.50              2.50
x = 5 hours

300

John spent $51 on movie tickets for 2 adults and 3 children.  Adult tickets were $12 each.  This was the cost of the child tickets.

What is $9 ?

Solution:
51= 2(12) + 3x
51 = 24 + 3x
-24      -24
----------------
27 = 3x
---     ---
3         3
$9 = x      Child's ticket is $9

400

Jennifer spent half of her weekly allowance playing arcade games.  To earn more money, her parents let her mow the lawn for $9.  Her weekly allowance would be this amount if she ended with $19.

What is $20 ?

Solution:

1/2 x + 9 = 19
         -9        -9
--------------------
1/2x    = 10
Divide by 1/2
x = 10 x 2
x = 20

500

I am this old if 500 reduced by 2 times my age is 396.

What is 52 ?

Solution:
500 - 2x = 396
-500         -500
---------------------
-2x = -104
-----   ------
  -2       -2
x = 52 years