Download Mastery Test 2A Review

Mastery Test #2 - Study Guide
Math: Grade 7
Rules for combining (adding or subtracting) integers:
1. Look for any double signs and change them:
If they are the same, make a big +
If they are different, make a big –
2. After that :
a. Same signs: add and keep the sign
b. Different signs: subtract and use the sign of the bigger #
Rules for multiplying or dividing integers:
1. Same signs = answer is ALWAYS a  (positive)
2. Different signs = answer is ALWAYS a ─ (negative)
Evaluating:
1. If given a problem like this: A + B if A = 2 and B = -6
2. Plug the numbers in place of the letter and follow integer rules:
2 + -6 = -4
Scientific Notation and Standard Numerals:
1. Scientific notation is a way of writing numbers using 2 parts:
a. Part 1 is a number between 1 and 9.9
b. Part 2 is “times 10 to some power (exponent)”
2. Examples:
Standard Numeral
Scientific Notation
730,000
7.2 x 105
5,402,000,000
5.402 x 109
.00075
7.5 x 10-4
4.12
4.12 x 100
3. To write a number in scientific notation you have to move the decimal
between the first two whole numbers. Then you have to count the number of
times the decimal was moved (from the right to left is a positive exponent;
from left to right is a negative exponent).
4. To write scientific notation as a standard numeral, just move the decimal the
number of times indicated by the exponent (negative exponent = move
decimal to the left; positive exponent = move the decimal to the right)
Order of Operations:
1. Used to solve problems that have more than 1 operation (+, -, x, ÷)
2. Start with any ( ) , [ ] , or { }
3. Next solve any exponents
4. Next do multiplication or division (for a tie go left to right)
5. Finally do addition or subtraction (for a tie go left to right)
Negative Exponents:
1. Given a problem like this: 10-4, change to a fraction and a decimal:
2. For the fraction: change to this __1__ (make the exponent positive)
104
Next solve 104, which means 10 x 10 x 10 x 10; which is 10,000
Finally write the answer as a fraction ___1___
10,000
3. For the decimal: think scientific notation: 1 x 10-4
Write the 1 and move the decimal 4 times to the left
The answer is : .0001
Laws of exponents for multiplication and division:
1. Multiply any whole numbers and add all exponents (REMEMBER the “1” is
invisible as an exponent)
Examples:
A2 ‧ A4 ‧ A = A7
(4B3) (3B5) = 12B8
2. Divide any whole numbers and subtract the exponents (REMEMBER…
the “1” can be an invisible exponent)
Examples:
A6
A2 = A 4
12a9 ÷ 3a3 = 4a6
Proving Statements about Integers:
1. Decide if the person is correct or incorrect
2. Write a sentence explaining why (use the question to get started)
3. Give 2 examples of what you are saying
Examples:
A. Candy says “the sum of any 2 negative numbers is always
a negative number.”
ANSWER: Candy is correct because the sum of any 2 negative
numbers is always a negative number.
-1 + -2 = -3
-5 + -1 = -6
B. Danny says “the sum of a positive number and a
negative number is always a positive number.”
ANSWER: Danny is incorrect because the sum of a positive
number and a negative number may be positive or negative
depending on the sign of the bigger digit.
+5 + -2 = +3
+4 + -8 = -4
Vocabulary you need to know for this:
SUM = + (addition)
DIFFERENCE = - (subtraction)
PRODUCT = x (multiplication)
QUOTIENT = ÷ (division)
Klink / Greenberg - Fall 2009