30. The sides of a square are 3 cm long. One
vertex of the square is at (2,0) on a square
coordinate grid marked in centimeter units.
Which of the following points could also be
a vertex of the square?
F. (−4, 0)
G. (0, 1)
H. (1, −1)
J. (4, 1)
K. (5, 0)
The Plan?
Plot and label everything (of course).
Unsure where to start, start with the answers.
(-4, 0)
(2, 0)
distance = 6
The distance is 6. I’m looking for
a distance of 3. Wrong answer.
But now I know what the problem
is asking for.
30. The sides of a square are 3 cm long. One
vertex of the square is at (2,0) on a square
coordinate grid marked in centimeter units.
Which of the following points could also be
a vertex of the square?
F. (−4, 0)
G. (0, 1)
H. (1, −1)
J. (4, 1)
K. (5, 0)
(0, 1)
(2, 0)
Wrong answer.
30. The sides of a square are 3 cm long. One
vertex of the square is at (2,0) on a square
coordinate grid marked in centimeter units.
Which of the following points could also be
a vertex of the square?
F. (−4, 0)
G. (0, 1)
H. (1, −1)
J. (4, 1)
K. (5, 0)
(2, 0)
(5, 0)
distance = 3
Right answer!
31. For ΔFGH, shown below,
which of the following is an
expression for y in terms of x ?
The Plan?
Pythagorean Theorem, of course.
H
4
F
y
x
y 2  x 2  42
y 2  x 2  16
y  x 2  16
G
32a. A bag contains 12 red marbles, 5
yellow marbles, and 15 green marbles. How
many additional red marbles must be
added to the 32 marbles already in the bag
so that the probability of randomly drawing
a red marble is 3/5?
(choices are 13, 18, 28, 32, 40)
The Plan?
What % is Red now?
Add some red marbles. How many? Try the answers!
p  red  
12
6
3


32 16 8
add 13: p  red  
12  13 25 5


32  13 45 9
Nope
add 18: p  red  
12  18 30 3


32  18 50 5
Yes!
32b. A bag contains 12 red marbles, 5
yellow marbles, and 15 green marbles. How
many additional red marbles must be
added to the 32 marbles already in the bag
so that the probability of randomly drawing
a red marble is 3/5?
(choices are 13, 18, 28, 32, 40)
A Quicker Way (maybe)
I like the first method many times
because it helps me “get the feel
of the problem”.
12  r 3

32  r 5
60  5r  96  3r
2r  36
r  18
33. What are the quadrants of the
standard (x, y) coordinate plane below
that contain points on the graph of the
equation 4x − 2y = 8 ?
Slope-Intercept Form:
The Plan?
Slope-Intercept Form - ALWAYS
What’s the question? What quadrants does the line go in?
Graph the line.
quadrant
quadrant
II
I
quadrant
quadrant
III
IV
y  mx  b
4x  2 y  8
2 y  4 x  8
y  2x  4
slope
y-intercept
34. The graph of y = −5x2 + 9 passes
through (1, 2a) in the standard (x, y)
coordinate plane. What is the value of a ?
y  5x2  9
If a point is on the
equation, it must
satisfy the
equation.
2a  5 1  9
2
2a  5  9
2a  4
a2
The Plan?
If the line passes through the point, then the point must
work in the equation.
34b. The graph of y = −5x2 + 9 passes
through (1, 2a) in the standard (x, y)
coordinate plane. What is the y-coordinate
of the point?
y  5x2  9
If a point is on the
equation, it must
satisfy the
equation.
2a  5 1  9
2
2a  5  9
2a  4
a2
The same problem, though now asking for something
different. Make sure you’re answering the question
asked!
The Plan?
If the line passes through the point, then the point must
work in the equation.
(1, 4)
35. Jerome, Kevin, and Seth shared a
submarine sandwich. Jerome ate 1 /2 of the
sandwich, Kevin ate 1/3 of the sandwich,
and Seth ate the rest. What is the ratio of
Jerome’s share to Kevin’s share to Seth’s
share?
The Plan?
I like drawing pies for fractions. Get a feel for the
problem before charging in.
Though it’s a submarine
sandwich, it’s easier for me
to think in terms of a pie.
Jerome at ½ of the “pie”.
Jerome
1/2
35. Jerome, Kevin, and Seth shared a
submarine sandwich. Jerome ate 1 /2 of the
sandwich, Kevin ate 1/3 of the sandwich,
and Seth ate the rest. What is the ratio of
Jerome’s share to Kevin’s share to Seth’s
share?
The Plan?
I like drawing pies for fractions. Get a feel for the
problem before charging in.
Now make sure you’re answering the question asked.
Kevin ate 1/3 of the “pie”.
Seth ate the rest.
Seth
?
Kevin
1/3
Pieces of Pie
Jerome
1/2
Jerome: 3
Kevin: 2
Seth: 1
Ratio of
Jerome to Kevin to Seth:
3:2:1
36. A particular circle in the standard (x,y)
coordinate plane has an equation of
(x − 5)2 + y2 = 36.
What are the radius of the circle, in
coordinate units, and the coordinates of the
center of the circle?
what happens
when y = 0
 x  5
2
 0  36
The Plan?
Always try to graph to get started. Though this may look
hard, make it look easy by setting something equal to 0.
What about the x-coordinate? How do I get y alone?
what happens
when x = 5
 5  5
2
 y 2  36
r=6
C(5,0)
 x  5
2
 36
x  5  6
x  11, 1
y 2  36
y  6
36b. A thought on circles in general …
Some Thoughts on the Circle
1. Draw a circle
2. Find any point on that circle.
3. How far is that point from the origin?
(x, y)
r
y
x
The equation for a circle with
Center (0,0) and Radius r :
r2 = x2 + y2
37. The figure below consists of a
square and 2 semicircles, with dimensions
as shown. What is the outside perimeter, in
centimeters, of the figure?
The Plan?
Outline what you’re looking for, labeling everything.
8cm
8cm
37. The figure below consists of a
square and 2 semicircles, with dimensions
as shown. What is the outside perimeter, in
centimeters, of the figure?
The Plan?
Outline what you’re looking for, labeling everything.
8cm
8cm
37. The figure below consists of a
square and 2 semicircles, with dimensions
as shown. What is the outside perimeter, in
centimeters, of the figure?
The Plan?
Outline what you’re looking for, labeling everything.
8cm
8cm
8cm
37. The figure below consists of a
square and 2 semicircles, with dimensions
as shown. What is the outside perimeter, in
centimeters, of the figure?
The Plan?
Outline what you’re looking for, labeling everything.
8cm
8cm
8cm
37. The figure below consists of a
square and 2 semicircles, with dimensions
as shown. What is the outside perimeter, in
centimeters, of the figure?
The Plan?
Outline what you’re looking for, labeling everything.
8cm
8cm
8cm
37. The figure below consists of a
square and 2 semicircles, with dimensions
as shown. What is the outside perimeter, in
centimeters, of the figure?
The Plan?
Outline what you’re looking for, labeling everything.
You need the radius of the circle to find its circumference.
How can you get it?
Remember to label everything!
C  2 r
 2  4 
 8
8cm
4
4
8cm
8cm
P  8  4  8  4
 16  8
4
38. In the figure below, points E and F are
the midpoints of sides AD and BC of
rectangle ABCD, point G is the intersection
of AF and BE , and point H is the
intersection of CE and DF. The interior of
ABCD except for the interior of EGFH is
shaded. What is the ratio of the area of
EGFH to the area of the shaded region?
The Plan?
1. This is a tricky one (for me). Because I don’t know
how to solve it, what can I do with it?
2. Since it’s asking for the area of the shaded vs. the
unshaded, part, and the shaded part is broken into
triangles, what if I break the unshaded into triangles.
3. Assume all the triangles are equal area. Why? It’s
better than doing nothing with the problem!
Triangles in
EGFH
2
Shaded
Triangles
6
Ratio = 2 : 6
=1:3
39. The coordinates of the endpoints of CD,
in the standard (x, y) coordinate plane, are
(−4, −2) and (14, 2).
What is the x-coordinate of the midpoint of
CD ?
The Plan?
1. Plot! Plot! Plot!
39. The coordinates of the endpoints of CD,
in the standard (x, y) coordinate plane, are
(−4, −2) and (14, 2).
What is the x-coordinate of the midpoint of
CD ?
The Plan?
1. Plot! Plot! Plot!
2. Label everything!
3. Even if you know the formula, quickly find where the
midpoint is – about.
(14,2)
(5,0)
(-4, -2)
39. The coordinates of the endpoints of CD,
in the standard (x, y) coordinate plane, are
(−4, −2) and (14, 2).
What is the x-coordinate of the midpoint of
CD ?
The Plan?
1. You don’t remember the formula, and approximating
doesn’t help. What then?
2. Plot (and label) two points where you know the
midpoint exactly, just by looking.
3. How do you get ‘4’ from ‘2’ and ‘6’? Add and divide
by two.
(4,1) is the midpoint
of (2,1) and (6,1).
How did you get it?
Midpoint =
(2,1)
add numbers together
2
(4,1)
(6,1)
40. What is the surface area, in square
inches, of an 8-inch cube?
A = 64
8
Areatotal   64  6 
8
front & back
2 sides
top & bottom
 384
41. The equations below are linear
equations of a system where a, b, and c are
positive integers.
ay + bx = c
ay − bx = c
Which of the following describes the graph
of at least 1 such system of equations in the
standard (x, y) coordinate plane?
I. 2 parallel lines
II. 2 intersecting lines
III. A single line
put equations in slopeintercept form
ax  by  c
ax  by  c
by  ax  c
by  ax  c
y
a
c
x
b
b
a
c
x
b
b
a
c
 x
b
b
y
Since the slopes
are different, the
lines intersect.
42. According to the measurements given
in the figure below, which of the following
expressions gives the distance, in miles,
from the boat to the dock?
opp
hyp
adj
I need "opp" and
have "adj".
`
SOH CAH TOA
tan 52 
opp
adj
tan 52 
opp
30
30tan52  opp
53. The determinant of a matrix
equals
ad − cb. What must be the value of x for the
matrix xx 8x to have a determinant of −16 ?
det
x 8
x x
 x2  8x
det
x2  8x  16
x2  8x  16  0
 x  4 x  4  0
x4
x 8
x x
 16
54. A formula for finding the value, A
dollars, of P dollars
invested at i% interest compounded
annually for n years is A = P(1 + 0.01i)n.
Which of the following is an expression for
P in terms of i, n, and A ?
A  P 1  0.01i 
A
1  0.01i 
n
n
P
58. What is the sum of the first 4 terms of
the arithmetic sequence in which the 6th
term is 8 and the 10th term is 13 ?
These are evenly spaced
(like 0,5,10,15,20)
this is halfway between the 6th and 10th
terms.
1.75
1
3
2
4.25
3
5.5
4
6.75
5
8
6
9.25
7
10.5
8
this is halfway
between the 6th
and 8th terms.
These are evenly spaced
(like 0,5,10,15,20)
9
13
10
59. In the equation x2 + mx + n = 0, m and
n are integers. The only possible value for x
is –3. What is the value of m ?
x = -3 is the only
solution.
x+3=0
x + 3 is the only
factor.
x2  mx  n  0
 x  3 x  3  x2  mx  n
x2  6 x  9  x2  mx  n
6m