2004 PSAT Corrections Math 4
25. In the figure, which of the following line
segments has a slope of 2?
B
C
• A. PA
• B. PB
• C. PC
• D. PD
• E. PE
A
P
D
E
This slopes UP
2 and over 1.
PD
goes
up
5
PB slopes down
and overof1up.
instead
PC isPA
a slopes down
instead of up.
vertical line
59%
26. When the 3 Adams children went to
31%
school one morning, they each took one of
the other’s lunches. In how many ways
could the 3 children have been paired with
the lunches so that no one took his or her
Child 1 Child 2 Child 3
own?
• A. One
• B. Two
• C. Three
• D. Six
Lunch 1
X
O
X
Lunch 2
X
X
O
Lunch 3
O
X
X
26. When the 3 Adams children went to
31%
school one morning, they each took one of
the other’s lunches. In how many ways
could the 3 children have been paired with
the lunches so that no one took his or her
Child 1 Child 2 Child 3
own?
• A. One
• B. Two
• C. Three
• D. Six
Lunch 1
X
X
O
Lunch 2
O
X
X
Lunch 3
X
O
X
27. If x and y are positive, which of the 30%
following represents x percent of y?
The
?
One way toxthink
about
this
i ?
=
represents
the
• A. 0.01xy is as individual
percents.
1%
y
100
equation we are
equals .01, so a certain
Cross
xyof =y would
100?be looking for
• B. 0.1xy
percent (x)
multiply
xyvariablesDivide
both of those
times both
=
?
100
• C. xy
1%
or 0.01.
sides by
100
0.01xy
=
?
Dividing
by
100
is
the
• D. 10xy
same as multiplying
by
hundredth.
• one
E. 100xy
35%
28. In the xy-plane below, the circle has
center O. Which of the following lines will
divide the circle into two semicircles?
✔
•I. The line with equation y = x
✔
•II. The line with equation y (0,
= 3)4x y = 4x
y=x
•III. The line with equation y = 1
O
• A. I only
• B. III only
• C. I and II only
y=1
4
5
(x )
a
x
29. If
= for all values of x, what is the
value of a? 20
4(5) = 20
When you raise an
exponent to
another power, you
just MULTIPLY
them.
34. In a straight line, the distance between
Rockfield and Nearburg is 18 miles;
between Nearburg and Carbonville the
distance in a straight line is 13.4 miles.
What is the least possible distance, in 4.6
miles
miles,Carbonville
from Rockfield13.4
to Carbonville?
Rockfield
18 miles
18 - 13.4 = 4.6
Nearburg
35. Let x△y be defined as x△y = - (x + y) for
all positive integers x and y. What is the
value of (4△2)△3? 987
Funky symbol
x =x10
=4
Order ofproblem!
operations
10y =y△=3 3
stays the same
2
y
x
42 - (4 + 2)
103 - (10 + 3)
16 - 6 = 10
1000 - 13 = 987
36. The figure shows some circles, each
measuring 2 inches in diameter, placed at
one end of a 50-inch line segment. If there
are 1-inch spaces between consecutive
circles and the center of each circle is on the
segment, what is the maximum number of
17
circles that can be placed on the 50-inch line
2
1
2
1
2
segment?
2
1
2
1
Each circle and space
unit is 3 inches
50 ÷ 3 = 16⅔
16 x 3 = 48
17
2
Sixteen FULL units will fit
on a 50 inch line
We will have 2
inches left over...
… which is just
enough room to fit
one more circle!
37. In the figure, each of the 16 small squares is
2
to be colored red, blue, or green.
•
All squares in row 1 will be the same color.
•
All squares in column 1 will be red.
•
There will be an even number of blue
squares.
•
There will be an even number of green
squares.
•
No green square will share a common side
or vertex with a red square.
•All squares in row 1 will be the same color.
2
•All squares in column 1 will be red.
•There will be an even1 number
2
3of blue
4
squares.
1
One
of
these
has
to
•There will
an even
number of green
Webeneed
a
be red since there 2
couple of blues
squares.
is an even number
to separate 3the
of blue & green
greens
from will
the share a common side
•No green
square
squares
reds.
or vertex with a red square.
4
38. In the sequence above, each term after the
first is equal to ⅓ the term immediately before
it. What is the value of the first tem
in
the
1/45
sequence that is less than 1/20?
1 = 3
5
15
3 ÷
1
=
3
15
15
27 9 3 1
1
5 , 5 , 5 , ...
5 , 15
Rewrite this so
This isn’t
⅓ of this is ⅕.
it’s easy to
smaller than
divide by 3
1/20
38. In the sequence above, each term after the
first is equal to ⅓ the term immediately before
it. What is the value of the first tem
in
the
1/45
sequence that is less than 1/20?
1 = 3
15 45
3 ÷ =
3
45
1
45
27 9 3 1
1
5 , 5 , 5 , ...
5 , 15
Rewrite this so
it’s easy to
divide by 3