Grade 9 Math Test #1 - Review Sheet
Topics:

Math terminology – review your notes

Integers (pg. A9)
o What is an integer? What is true of integers?

Adding and Subtracting Integers (pg. A10-A12)
o Three rules:
 Keep the first number the same (whether positive or negative)
 Look at the next two signs
 If same  ADD second number, if different  SUBTRACT second number

Multiplying and Dividing Integers (pg. A13-A14)
o If signs are the same, answer will be positive
o If signs are different, answer will be negative

Proper Fractions (pg. A15)
o The numerator is ________________ than the denominator
o Be able to write in lowest or most simple form
o Be able to find equivalent fractions

Improper Fractions (pg. A16)
o The numerator is _________________than the denominator
o Be able to convert from an improper fraction to a Mixed Number (eg. 23/4  5 ¾)

Common Denominators (pg. A17)
o Be able to find two common denominators given two fractions
o Also be able to find the lowest common denominator

Adding and Subtracting Fractions (pg. A18-A19)
o Rules:
 Make the denominators the same
 Once numerators are the same, create equivalent fractions for that denominator
 Add or subtract numerators
 Reduce to lowest form
 Check using calculator and the a b button
c

Multiplying Fractions (pg. A20)
o Rules:
 Multiply the numerators
 Multiply the denominators  denominators DO NOT have to be the same
 Reduce to lowest form

Dividing Fractions (pg. A21)
o Rules:
 Leave first fraction alone
 Change the sign from divide to multiply
 Invert or flip the second fraction
 Solve as a multiplication question

Powers with fractions:
o Apply the exponent to both the numerator and denominator
4
2 2 


   4 
3 3 
4
o
Example:

Powers with negative bases: (pg. 47-49, questions 2, 4, 5, 6, 7, 14)
o Recall: (-3)4 = (-3)(-3)(-3)(-3)
o Rules:
 A negative base to an ODD exponent  remains negative
 A negative base to an EVEN exponent  becomes positive

The power rules (pg. 52-55, questions 1-15; pg. 58-59, questions 1-12)
o Exponents with the SAME BASAE can be manipulated using the following rules”
 Multiplying powers
 Keep base same, add the exponents
 Dividing Powers
 Keep base same, subtract exponents
 Power to a Power, eg (34)7
 Keep base same, multiply the exponents

Zero Exponents: (pg. 61-62, questions pg. 63 #6,9)
o Anything to the power of zero, equals 1.
o Beware if the question asks =-40  remember that it means = (-1)(40), so it will equal -1

Negative Exponents: (pg 61-62, questions pg. 63 #1,2,3,4,5,7,9, 12)
o When you see a negative exponent, invert/flip it, and make the exponent positive
o

Eg: 4
2

1
1

2
4
16
Squares and Square Roots: (pg. 72-73, questions pg. 74 #1, 3-18)
o The length of each side of a square is the square root of its area
o Every number has both a positive and negative root, example 8 and -8 are roots of 64, as
8x8=64 and (-8)x(-8)=64
o
The radical sign(
) is used to represent the POSITIVE square root of a number

Order of operations:
o BEDMAS – Brackets Exponents Division Multiplication Addition Subtraction
o Questions 1 & 2, pg. 135

Pythagorean Theorem: (pg. 76-78, pg. 79 #1-5, pg. 80 #6-8, pg. 81 #14-15)
o It is a relationship between the size of RIGHT TRIANGLES
o The long side of a right triangle  Hypotenuse
o The two shorter sides Legs
o Equation: a2 + b2 = c2
NEW REVIEW QUESTIONS:
-
Integers and Fractions do not have review questions in the text book
-
pg. 71 - #1-6
-
pg. 87-89 - #1, 4, 6-15, 17, 25, 26, 27, 29** (a thinker), 30, 31