3. Transformations
Identify the transformation and the rule. The
pre-image is marked with an “x”.
X
The transformation is a
“translation” that moves 3 units
left (x – 3) and 4 units up (y + 4).
The rule is:
(x - 3, y + 4)
4. • Solve for x
a || b
x
1
3
5
7
c
2 8
4
10
9
a
670
6
b
1050
d
5. • Solve for x
Angle 8 = 670 because it is vertical to
the 670 angle on transversal d.
a || b
x
1
3
5
7
c
2 8
4
1
0
9
a
670
6
b
1050
d
Angle 2 = 750 because it is
supplementary to the 1050 angle on
transversal c.
Angles 2, 8 and x add up to 1800
because the sum of the interior
angles of any triangle is 1800.
67 + 75 = 142
180 – 142 = 38, so x = 38
8. • Write the following in scientific notation
0.000000075
9. • Write the following in scientific notation
0.000000075
The coefficient in scientific notation must be greater than or
equal to one, and less than ten; so, the decimal must be
moved between the 7 and 5 to make a coefficient of 7.5
For numbers less than 1 (small numbers), each decimal place
is equal to a negative power of ten, so moving the decimal 8
places gives us a scientific notation value of:
7.5 x 10-8
10. • Write the following in scientific notation
9,520,000,000
11. • Write the following in scientific notation
9,520,000,000
The coefficient in scientific notation must be greater than or
equal to one, and less than ten; so, the decimal must be
moved between the 9 and 5 to make a coefficient of 9.52
For numbers greater than 1 (large numbers), each decimal
place is equal to a postive power of ten, so moving the
decimal 9 places gives us a scientific notation value of:
9.52 x 109
13. • Simplify
This problem wants to know the
side lengths in a square with an
area of 256 square units.
The length of each side in a square
with 256 square units is 16,
because 16 x 16 = 256.
16
256
units2
16
21. • What are the square roots of 81?
Every square has 2 roots, a positive root and a negative root. The
square roots of 81 are 9 and -9, because 9 x 9 = 81, and -9 x -9 = 81.
24. • Mr. Langley has a square garden with an area
of 196 square feet. Mrs. Langley wants him to
put a fence around the garden to keep the
armadillos out
• How many feet of fence does Mr. Langley
need to buy?
25. • Mr. Langley has a square garden with an area of
196 square feet. Mrs. Langley wants him to put a
fence around the garden to keep the armadillos
out
• How many feet of fence does Mr. Langley need to
buy?
This is a two-part question. First you have to find
the square root of 196, which is 14 to find the
length of one side of the garden. Then you have to
multiply 14 x 4 to find the perimeter of the garden.
You need 56 feet of fence.
32. • Simplify. Write your solution with a positive
exponent:
When you divide exponents with the same base, keep the base and
subtract the exponents. 212 – (-3) = 215
34. • Simplify. Write your solution with a positive
exponent:
86 * 8-4
When you multiply exponents with the same base,
keep the base and add the exponents. 86 + (-4) = 82
36. Simplify. Write your solution in scientific
notation
Multiply your coefficients, then use the
properties of exponents to multiply the powers
of 10.
3 x 3 = 9 and 105 + (-3) = 102
9 x 102
47. • A golf ball has a radius of approximately 2
centimeters. Calculate the volume of the golf
ball.
•
48. • Soda is sold in cylindrical aluminum cans that
measure 15cm in height and 7cm in diameter.
Calculate the volume of a full soda can.
49. • A sno-cone cup has the dimensions listed
below. Calculate the volume of ice needed to
fill the cone to the top.
• height of cone: 12cm
radius of cone base: 5cm
50. • A cube has a side length of 6cm. What is the
longest piece of string you can fit in the cube?
Estimate to the nearest centimeter.
51. • Decide whether the relation is a function of x.
Write yes or no and explain your reasoning.
{(1, 0), (2, 0), (3, 0), (4, 0)}
52. • Decide whether the relation is a function of x.
Write yes or no and explain your reasoning.
53. • Decide whether the relation is a function of x.
Write yes or no and explain your reasoning.
Liz
Bob
Cara
Chris
Kayla
Jon
a
b
c
d
e
f
g
h
54. • Akil made a $75 down payment on a bicycle.
His monthly payments are $15.00 per month.
If he has 18 monthly payments, what is the
total cost of the bicycle?
55. • Your summer job is cutting lawns. You charge
a flat fee of $15 and an additional $5 per hour.
Write a function to determine how much you
earn.
56. • Determine whether the representations
below are linear functions, non-linear
functions, or not functions.
Months
1
2
3
4
5
6
Saved
1
4
9
16
25
36
y = x3 - 3
