Name_______________
PRACTICE AIMS QUESTION #11
The effect of dilations on Area and Perimeter
5) Which of the following would not be a possible scale factor for the linear measurement
if the smaller triangle has a height of 12 cm and the larger triangle has a height of 48.
a) 1/4
b) 4
c) 1/16
Dilations – a transformation that produces an image that is the same
shape as the original, but it is a different size.
What does this mean?
Remember the scale factor will tell how big or small the shape will become. If the
scale factor is a fraction the image will be smaller. If the scale factor is greater
than 1, then the image will be bigger. This means you will multiply or divide.
Remember that dilations create similar figures. Don forget, if the ratio of the
corresponding sides is a/b, then the ratios of the:
perimeters is a/b
areas is a2/b2
The ratio of the sides is also a scale factor.
1. Determine the length of the sides of a new triangle created be dilating the sides of a
triangles with side lengths 3,6, and 7 using a scale factor of 2.
a)
b)
c)
d)
6,12, 3.5
6,12,14
1.5,3, 3.5
1.5,3, 3.5
2. Determine the area of a new triangle if the original triangle had an area of 27 square
feet using a scale factor of 1/3.
a)
b)
c)
d)
3 square feet
81 square feet
9 square feet
36 square feet
3. Determine the perimeter of a new rectangle if the original rectangle had a perimeter of
21 m and is dilated by a factor of 7.
a)
b)
c)
d)
4.
5m
3m
154 m
147 m
The ratio of the corresponding sides of two rectangles is 1/3. If the area of the larger
rectangle is 108m2 , what would be the area of the smaller rectangle?
a)
b)
c)
d)
18
12
36
52
m2
m2
m2
m2
6) If a circle is dilated by 5/3 and the area of the larger circle is 100pi square cm, then
what would be the area of the smaller circle?
a)
b)
c)
d)
36
18
60
40
square
square
square
square
cm
cm
cm
cm
Answers: 1.b
2. a
3. d
4. b
5.c 6. a
Name_______________
PRACTICE AIMS QUESTION #12
Similarity
If two figures are similar, then their corresponding sides have the same
ratio and their corresponding angles are congruent.
What does that mean?
If the ratio of the sides is a/b, then the ratio of the:
perimeters is a/b.
areas is a2/b2.
volume is a3/b3.
1. The perimeter of a large square is 6 times the perimeter of a small square. How many
times as long is the base of the bigger than the base of the smaller square?
a)
b)
c)
d)
5. If the ratio of the volumes between two cones is 27/8 and the height of the larger cone
is 27 m, what is the height of the smaller cone?
b)
c)
d)
e)
9m
16 m
3m
18 m
6. Annie works in a magazine’s advertising department. A client has request that his 5
cm – by – 12 cm ad be enlarged: “Double the length and double the width, then send
me the bill.” The original ad cost $1500. How much should Annie charge for the
larger ad?
a)
b)
c)
d)
$3000
$4000
$2000
$6000
2 times as long
4 times as long
6 times as long
10 times as long
Answers: 1.c
2. If the sides of a square are made seven times longer, how many times the area of the
original figures is the area of the new figure?
a)
b)
c)
d)
seventy times
seven times
forty-nine times
twenty-eight times
3. There are two rectangular prisms. The length of one side on the larger prism is 3 and
the length of the corresponding side on the smaller prism is 2. Find the ratio of their
surface areas.
e)
f)
g)
h)
3/2
27/8
6/4
9/4
4. True/False. If two similar cones have radii in the ratio m/n, then their heights are in
the ratio m/n.
e) True
f) False
2. c
3. d
4. a
5.d 6. d
Name_______________
PRACTICE AIMS QUESTION #13
Absolute Value
AIMS Review Question #14 Combinations
Absolute Value – the difference between two numbers
Example: The distance between -2 and 7
−2 − 7 = −9 = 9 or 7 − (−2) = 7 + 2 = 9 = 9
In Combinations, order does not matter.
The formula for a combination is n Cr =
What does that mean?
Find the difference of two numbers by subtracting and then take the absolute
value of the answer.
1. What is the distance between 3 and -5?
a) 8
b) -2
c) 2
d) 0
−9 + 6 − 6k = 3
b) no solution
c) -1 and 3
d) -1 and -3
3. Perry High school has five different types of discuses. They are wooden, steel,
plastic, rubber, and iron. How many different combinations exist if three are
randomly chosen?
a. 5
b. 10
c. 120
d. 60
3. Solve the inequality.
−3 −2 + 6n ≥ −78
4. Baskin Robbins has 31 flavors, or so they say. ☺ If you only have enough
money to buy two scoops, how many combinations could you order?
a. 2
b. 930
c. 465
d. 404
i) n ≤ −3 or n ≥ −1
j) −4 ≤ n ≤ 14 / 3
k) n ≥ 14 / 3 or n ≥ −1
l) n > 2 or n < -4
4. What is the distance between -3/4 and 5/2?
g) 8/3
b) 3/2
c) 13/4
d) 4/13
5) If the temperature in Phoenix, AZ is 70 degrees and the temperature in Dayton, Ohio
is 20 degrees below freezing, what is the change in temperature?
f)
g)
h)
i)
45
50
25
90
1. Ten different colored socks are in a drawer. Without looking, two socks are
removed. What is the total number of combinations?
a. 45
b. 90
c. 1
d. 60
2. Kate went to the store and bought a package of refrigerator magnets each with a
different word on them. The package contained fifteen words. How many ten
word sentences can be made using the magnets?
a. 360,360
b. 3003
c. 3,628,800
d. 120
2. Solve the equation.
e) 1,3
degrees
degrees
degrees
degrees
5. Five different countries are in the medal rounds for men’s ice skating. They are
the USA, Jamaica, South Africa, Uganda, and Tonga. Three of the countries will
medal. What is the total number of combinations that include the USA? (Hint:
Since the USA is already included, that will change your total number of choices)
a. 6
b. 10
c. 120
d. 5
Answers: a. b. b. c. a.
Answers: 1.a
n!
r !( n − r )!
2. c
3. b
4. c
5.d
AIMS Review Question #15 Dependent Events
A dependent event “changes” or “depends” on a previous event.
Decide whether the event is dependent or independent.
1. Flip a coin, and then flip the same coin.
2. You have three pairs of shoes. Pick a pair of shoes, and then pick another pair.
3. Roll a dice, and then roll the same dice.
4. Roll a dice, and then flip a coin.
5. Select pair of shoes, put them back, and pick another pair.
6. Pick a card from a deck, return it, and then pick another card.
7. Select a card from a deck, keep it, and pick another card.
8. Mrs. Dominguez loves to play the lottery. Every Tuesday night she watches as the
winning numbers are drawn. Five numbers are chosen. Four of the chosen numbers
are dependent events. Which four are dependent events?