4. BASE – tells what
factor is being
multiplied
EXPONENT – Tells
how many equal
factors there are
5. EXAMPLES
1. x • x • x • x = x4
2.6 • 6 • 6 = 63
3. -2 • p • q • 3 •p •q •p =
-6p3
q2
4.(-2) •b • (-4) • b = 8b2
6. ORDER OF OPERATIONS
1. Simplify expression within
grouping symbols
2. Simplify powers
3. Simplify products and
quotients in order from left
to right
4. Simplify sums and
differences in order from
left to right
10. DEFINITIONS
Monomial – an expression
that is either a numeral, a
variable, or the product of
a numeral and one or
more variables.
-6xy, 14, z, 2/3r, ab
34. Example 1
A helicopter leaves Central
Airport and flies north at 180
mi/hr. Twenty minutes later a
plane leaves the airport and
follows the helicopter at 330
mi/h. How long does it take
the plane to overtake the
helicopter.
35. Use a Chart
Rate Time Distance
helicopter 180 t + 1/3 180(t + 1/3)
plane 330 t 330t
37. Example 2
Bicyclists Brent and Jane
started at noon from points 60
km apart and rode toward
each other, meeting at 1:30
PM. Brent’s speed was 4 km/h
greater than Jane’s speed.
Find their speeds.
38. Use a Chart
Rate Time Distance
Brent r + 4 1.5 1.5(r + 4)
Jane r 1.5 1.5r
41. Examples
A rectangle is 5 cm longer
than it is wide. If its length
and width are both increased
by 3 cm, its area is increased
by 60 cm2
. Find the
dimensions of the original
rectangle.
44. Example 2
Hector made a rectangular fish
pond surrounded by a brick
walk 2 m wide. He had
enough bricks for the area of
the walk to be 76 m2.
Find the
dimensions of the pond if it
is twice as long as it is wide.
48. Examples
A lawn is 8 m longer than it
is wide. It is surrounded
by a flower bed 5 m wide.
Find the dimensions of
the lawn if the area of the
flower bed is 140 m2
#35:You must use 1/3 because the rate is in miles per hour, and the time must be in hours also. To get this you put 20minutes over 60 minutes in an hour.
To get the distance for each thing you have to multiply the rate and the time.
#36: We want to know when the plane overtakes the helicopter, which means they are the same distance from the airport. Therefore, you set the two distances equal and solve for t.
Once you get the answer 2/5, you must figure out how many minutes that is by multiplying 2/5 by 60.
This should give you the answer of 24 minutes.
#38: You get the time by counting how many hours it takes them to meet. Since they started at 12 and met at 1:30, they rode for 1.5 hours.
#39: We knew that they were 60 km apart when they started riding, so when they have met in the middle the total distance the two have traveled is 60 km.
To set up the equation, add the two distances and set it equal to 60.
The question asked for both speeds, so you take 18 and add 4 to get the speed of 22 for Brent.
#42: Always draw the rectangle, and label each side.
x + 3 and x + 8 are the dimensions of the larger rectangle, after you added 3 to each side
#43: Set up the equation with the original area increased by sixty equal to the larger area.
Solve for x, then find the dimensions of the original rectangle
#45: Label the length and width of the pond as x and 2x.
Label the length and width of the entire thing by adding the 2 meters to each end to get 2x + 4 and x + 4.
#46: Set up the equation so that you take the area of the entire rectangle, (2x+4)(x+4), and subtract the area of the pond, (2x)(x), to get the area of the walk, which is 76.
Solve for x by multiplying and then combining like terms.
Find the dimensions of the pond
