SAT Prep
A.) Terminology – Center – Radius – Diameter – Chord
– Secant – Tangent
Tangent
Radius
Secant
Center
Chord
Diameter
B.) Formulas: Be familiar with
  3.14
d  2r
C
C

or
d
2r
C  2 r or  d
A r
2
Ex. In the figure, if P and Q are points on circle O, what
is the value of x?
P
O
70
x
Q
2x  70  180
2x  110
110
x
 55
2
C.) Arcs – Semicircle – Central Angles
NOTE: Degree measure of an arc ≠ Length of an arc.
Arc Measure = Central Angle Measure
Arc Measure = x°
Arc Length =
x
(2 r )
360
Ex. In the figure, square ABCD is inscribed in circle O.
If the area of the square is 50, what is the
circumference of the circle?
B
C
A  s  50
2
s 5 2
O
d  AC  5 2  2  10
A
D
C   d  10
Ex. Find the area and the perimeter of the shaded
region?
C

Asector 
 r2
360

O
60
12
D
Atriangle

1
 bh
2
Ashaded  Asector  Atriangle
C
O
Ashaded  Asector  Atriangle
Asector
60
12
D
60
2


12
 24


360
Atriangle


1
 12  6 3  36 3
2
Ashaded  24  36 3
Ex. A is the center of a circle whose radius is 10, and B
is the center of a circle whose diameter is 10. If these
two circles are tangent to one another, what is the area
of the circle whose diameter is AB? d  10  5  15
A
B
15
r
2
A r
2
225
 15 
A   

4
 2
2
Ex. In the figure, square ABCD is inscribed in a circle
whose center is O and whose radius is 4. If EO ┴ AB
at F, what is the length of EF?
E
A
B
F
4
OF 
2 2
2
4
O
D
45
OBF is a 45  45  90 rt. 
C
EF  4  2 2
Ex.- In the figure, AB is tangent to circle O at point P. If
OB = 15 and PB = 12, what is QB?
A
P
9
12
B
Q
O
15
3  4  5 rt.   3
OP  9  OQ
A.) Rectangular Prisms, Cubes, and Cylinders
B.) Surface Area Formulas:
1.) Prism =
2.) Cube =
2(lw  wh  lh)
6s
3.) Cylinder =
2
2 rh  2B
C.) Volume Formulas:
1.) Prism =
2.) Cube =
lwh
3
s
3.) Cylinder =
r h
2
D.) Diagonal of a solid is the longest line segment that can
be drawn between two vertices.
Ex. What is the length of a diagonal of a cube whose
sides are 1?
d 1 
2
1
2
2
 2
d2  3
d 3
2
Ex. The volume of a cube and the volume of a cylinder
are equal. If the edge of the cube and the radius of
the cylinder are both 6, what is the height of the
cylinder?
s r h
3
2
6   6  h
3
2
6  6  h

2
2
6
6
3
2
6 h
6

h
A.) xy-plane
x-axis-horizontal y-axis-vertical
(x, y) is a COORDINATE
Ex. In the figure, all of the following equal except…
A.) ab
B.) ac
C.) ad
C.) ad
The only choice not equal to 0
D.) bc
( a, b)
E.) bd
(c, d )
Ex. In the figure, which of the following must be true?
I. rs < 0
II. r < s
III. r + s = 0
A.) None
B.) I only
D.) I and II only
r  0, s  0
r  s ????
D.) I and II only
C.) II only
E.) I, II, III
(r , s)
B .) Formulas
Distance Formula :
d  ( x2  x1 )2 ( y2  y1 )2
When all else fails – Pythagorean Theorem!!!
 x1  x2 y1  y2 
,
Midpoint Formula : 

2 
 2
Slopes –
Vertical lines – NO SLOPE
Horizontal lines - =0
Parallel lines – Slopes =
Perpendicular lines – Opposite reciprocals
Ex. What is the area and perimeter of
R
1
A   6  3  9
2
4
T (0, 4)
5
13
2
T
RST ?
2
3
4
(-2, 1) R
S
S (4,1)
6
P  6  5  13  11  13
5
Ex. - If A (2,3) and B (8,5) are the endpoints of the
diameter of a circle, what are the coordinates for the
center of the circle?
 28 35
Midpoint  
,

2 
 2
Midpoint   5, 4
Ex. - Find the slope of the line perpendicular to the
line containing (1,2) and (3,5).
52 3
slope 

3 1 2
2
 slope  
3