Transcript firstQreview

1st quarter review
Test is Friday!!!
Number Patterns
• arithmetic patterns:
– have a common difference between all terms
• geometric patterns:
– common ratio between all terms
• think of it as:
– arithmetic: we add or subtract to get the next term
– geometric: we multiply or divide to get the next term
Example
• Give the next 5 terms in the patterns:
• 2, 4, 6, 8,…
• 2, 6, 18,…
Another sequence…
• What is the pattern?
• 1, 2, 9, 16, 25, 36, …
Primes & Composites
• prime number:
– has only two different factors, one and the
number itself
• composite number:
– has more than two factors
• the number one (1) is neither prime nor
composite!
Greatest Common Factor
• using two or more numbers
• find the prime factorization of both numbers
• find what they have in common, and that is the
GCF
• example:
190
360
Least Common Multiple
• find the GCF
• then, multiply in the leftover numbers
• example:
32
100
Fractions Vocabulary Review
• fraction:
• improper fraction:
• mixed fraction:
Least Common Denominator
• uses the least common multiple of the
denominators
• Example:
5
11
15
• What is the LCD for:
,
,
12 24 16
Adding/Subtracting Fractions
• must have common denominators
• adding mixed numbers:
– add fractions first
– add whole numbers
– reduce the fraction, if needed
• subtracting mixed numbers:
– subtract fractions first, borrowing if needed
– subtract whole numbers
– reduce the fraction, if needed
Examples
• Find the sum or difference:
7
5
3 2
9
9
1
3
6 4
2
10
Examples
• Find the sum or difference:
1
3
9 2
5
4
Multiplying/Dividing Fractions
• multiplying fractions:
– multiply numerators
– multiply denominators
– reduce, if needed
• dividing fractions:
– flip the second fraction
– multiply the fractions
– reduce, if needed
• mixed numbers:
– change into improper fractions
Examples
• Find the product or quotient:
2 6

3 7
5
3

12 4
Vocabulary Review
• Mean:
• Median:
• Mode:
Percents
• means per hundred or divided by 100
• you can change percents to a reduced
fraction or a decimal
• use multiplication to find the percent of a
number
Example
• Find 5% sales tax on a CD selling for
$12.95.
Example
• Estimate 74% of 840.
Example
• A sale sign says 20% off, save $30! What
is the original cost of the item?
Example
• Margo knows that the tax on the new coat
she bought was $12.60 and that the sales
tax rate was 7%. What was the cost of her
new coat?
Multiplication Properties of
Exponents
• When two powers have the
same base, add the exponents
and keep the base
x x
• When finding a power of a
power, multiply the exponents
x 
• When finding the power of a
product, “distribute” the power
to each part of the product
3
2
3 4
x y 
3
2 4
Negative & Zero Exponents
• Negative exponents
make the number or
variable a reciprocal
• Anything raised to a
zero exponent is 1
b
m
2
0
Division Properties of Exponents
8
• When dividing two
powers with the
same base, subtract
the exponents
x
3
x
• When finding a
power of a quotient,
“distribute” the power
to top and bottom
a 
 2 
b 
3
4
Scientific Notation
• Uses powers of 10 to write decimal
numbers
• Contains a number between 1 and 10 that
is multiplied by a power of 10
Example 1
• Write expressions for the perimeter and
the area of the rectangle:
3x+5
x
Example 2
• Evaluate each expression if m = 4, n = -3,
and t = 0:
• 2m + 3(4n)3
• (5n3 – 2s7)t
• 9m – 4m2 – m2 + m + 5n2
Example 3
• Write an expression for the perimeter of:
n
3n
n
n
Example 1
• Solve each equation:
1
3
x 2
3
4
 5x  85
Example 3
• Solve:
3x + 5 = 6
Example 5
• Solve:
x  13
 4x  3
3
Perimeter
• The distance around a polygon, shape,
object, etc.
• When you have a flat figure, add up all the
sides
• Circles: use the formula C = 2πr = πd
Area
• Area of square = (side)2
• Area of rectangle/parallelogram = base x height
• Area of triangle = ½ x base x height
• Area of trapezoid = ½ x height x (base + base)
• Area of circle = πr2
Surface Area
• Surface area is the sum of the areas of all
its bases and faces
• i.e. like wrapping a present
Formulas
• Surface Area of a Rectangular Prism
SA  2lw  lh  wh
• Surface Area of a Cylinder
SA  2r  2rh
2
• Surface Area of a Cone
SA  rs  r
2
Volume of a Prism
V  Bh
Height
Area of the base
Volume of a Pyramid
Height
1
V  Bh
3
Area of the Base
Volume of a Cylinder
V  r h
2
Volume of a Cone
1 2
V  r h
3
Volume of a Sphere
4 3
V  r
3