Name_______________
PRACTICE AIMS QUESTION #17
Solving Formulas for a given variable
AIMS Review Question #16 Inverse Statements.
Statements are given in “If _____, then ______ “ form.
In fancy math language we say If p, then q where “p” is just words/statement and “q” is
just words/statement.
If “blah blah,” then “blah blah blah.”
The inverse is found by adding a not (or does not, whatever fits) in front of the “p” and
the “q.”
1) Use the rules for solving an equation
2) Remember you goal is to get the indicated variable (letter) alone on
one side.
1
1) a = bh for h
2
1
b
a) h =
b) h = ab
2a
2
a
5) D = (2t − 1) for a
2
(2t − 1)
2t
a) a =
b) a =
−1
2D
2D
2D
D
=a
c)
d) a =
(4t − 2)
(2t − 1)
If not “blah blah,” then not “blah blah blah.”
c) h =
Or
2a
b
d) h =
2b
a
If not p, then not q.
The truth value (a fancy math way of saying true or false) of the original statement will
usually be opposite of the inverse. Meaning, if the original is a true statement then the
inverse is usually false. If the original statement is false, then the inverse is usually true.
Here is an example:
If you live in Chandler, then you live in Arizona.
If you do not live in Chandler, then you do not live in Arizona.
Truth Value: True
Truth Value: False
6)
2) I = prt for t
a) t = I − pr
c) t =
pr
I
I
pr
pI
d) t =
r
3aw + 1 = aw − 7 for a
a) a = w − 4
b) t =
c) a =
−4
w
b) a =
w
−4
d) a = −4w
Write the inverse of each statement below and determine its truth value.
1. If you study hard, then you will do well in class.
2. If you live in Arizona, then you live in Mesa.
3. If you go to Perry, then you rock Bashas’ socks!
4. If you do not have a cell phone, then you have no friends.
A=
mv 2
r
C
a) m = 2
vr
v2
c) m =
Cr
4) C =
5. If you do not pass the AIMS test, then you will not graduate.
n
(a + 1) for a
2
2S
2n
a) a =
b) a =
−1
n −1
S
n
2n − 1
c) a =
d) a =
S
2( s − 1)
7) S =
1
h ( b + c ) fo r h
2
2A
2 (b + c )
a) h =
b) h =
(b + c )
A
(b + c )
c) h =
d ) h = 2 A (b + c )
2A
3)
for m
b) m = v 2 rC
d) m =
Cr
v2
Answers:
1.C
2.B
3.A
4. D
5.D
6.C
7.A
Practice Aims Question #19 Probability
Name_______________
PRACTICE AIMS QUESTION #18
Midpoint and Distance
Remember: Probability is the likelihood that something will happen.
It is usually written as a fraction(ratio) and sometimes as a decimal(percentage).
Midpoint is the point in the middle, it creates two equal segments.
the formula is on the AIMS reference sheet, do you know where?
P(E) = # of favorable outcome
Total # of outcomes
x +x y +y 
Midpoint =  1 2 , 1 2 
2 
 2
Distance is also called length. This formula is also on the AIMS reference sheet.
1. If a dart hits the target at random,
what is the probability that it will land
in the shaded region?
distance = ( x2 − x1 ) 2 + ( y2 − y1 ) 2
3.2 in
For #1-2 Find the midpoint of the line segment with the given endpoints.
1. (-11,1), ( -4,0)
2. (-8,-1), (-8,-6)
a) (17,-3)
c) (-7,1)
a) (0,2.5)
c) (-8,-11)
b) (-4,0)
d) (-5,1)
a)
c)
3.2 in
a) 5
c) 13
5 in
10 in
b) (-8,-3.5)
d) (-4.5,-7)
2
1
a.
c.
3
2
1
1
b.
d.
3
4
2. If a dart hits the target at random,
what is the probability that it will land
in the shaded region?
4. (3,4), (1,-7)
b) 15
d) 17
7
23
14
15
1
b.
15
b) 3
d) 5 5
15
56
15
b.
64
2 in
7
a)
b)
15
b)
c)
5
c) 3
d)
15
For #7-8 given the midpoint and one endpoint of a line segment, find the other endpoint.
7. Endpoint: (-6,0) midpoint: (6,-3)
a) (-18,3)
c) (6,-2)
Answers:
8. Endpoint: (-3,2), midpoint: (-4,2)
b) (0,-1½)
d) (18,-16)
1.B
2.B
3.D
a) (-2,2)
c) (-5,2)
4.D
5.D
6.D
7.D
8.C
c.
17
d) 3 5
13
5
3
3
d.
5
a.
6.
a)
c.
5. A bag contains 3 green marbles
and 5 purple marbles. One marble is
drawn at random and not replaced.
Then a second marbles is drawn.
What is the probability that the first
marble is purple and the second one is
green?
6 in
5.
1
16
15
d.
16
a.
For #3-6 find the distance between each pair of points.
3. (6,8), (-2,-7)
4. What is the probability that a
randomly dropped marker will fall in
the unshaded region?
b) (-1,-5)
d) (-3½, 2)
1
a.
3
7
b.
16
6. If the spinner is spun twice, what is
the probability that the arrow will
stop on a consonant both times?
1
c.
9
1
d.
4
G
3. A drawer contains 7 black socks, 3
gray socks, and 2 blue socks. Without
looking, you draw out a sock and then
draw out a second sock without
returning the first. What is the
probability that the two socks are a
matching pair?
49
144
7
b.
22
a.
O
N
25
66
25
d.
72
c.
R
I
H
4
9
19
b.
36
a.
5
12
7
d.
18
c.
Answers : d. c. c. d. a. a
Name_______________
PRACTICE AIMS QUESTION #20
Surface Area
The surface area is the sum of the areas of all the faces and bases of a
three-dimensional figure.
What does that mean? There are two ways to find it…
3) Find the area of all the faces and bases and add them together
4) Use the formulas on the AIMS reference sheet.
1.
3.
2.
a =
b =
c =
6m
10m
30m
a) 1800 m2
b) 1200 m2
c) 1080 m2
d) 540 m2
a =
b =
c =
5 km
6 km
12 km
a =
b =
a) 704 cm2
b) 224π cm2
c) 224 cm2
d) 704π cm2
a) 240 km2
b) 234 km2
c) 210 km2
d) 150 km
5
4.
a =
b =
a)
b)
c)
d)
18π
21π
24 π
40π
6 cm
16 cm
Answers:
3
4
5m
Find the surface area of the
square pyramid.
a)
b)
c)
d)
60 m2
75 m2
95 m2
165m2
1. C
2. A
3. B
4. C
5. C