IMSA
1)
Solve for x:
2)
Find
MI-3
Prob. Set #7
DUE: Tuesday, March 20
Spring '12
2x  4 – x  4 < 8
8
 (3k  2) [recall ∑ means sum]
k 3
3)
Let S = { a1, a2, a3, . . . , an, . . . } be a sequence of numbers. S is called an arithmetic sequence
if an+1 – an = d, a constant, for all n > 0.
Give the next term in each arithmetic sequence:
a. 3, 11, 19, 27, ____
b. 10, 3, -4, -11, ____
c.
1 1 7 5
, , , , ____
12 3 12 6
d. 5.5, 4.9, 4.3, 3.7, ____
4)
5)
The angles of a hexagon form an arithmetic sequence. If the smallest angle is 20°, find the
measures of the other five angles.
if n  0
1
Recall: n! = n(n – 1)(n – 2) . . . 2 • 1 = 
 n(n  1)! if n  0
Simplify:
6)
7)
a.
10! 9!
9!
b.
91! 90!
90!
c.
(n  2)! (n  3)!
(n  3)!
A Master padlock has a dial with 31 numbers. How many different 3 number combinations are
there where no two consecutive numbers can be the same?
Find the area under the graph shown.
P.S. 7.1
8)
ABCD is a square.
AB = 6
B is center of a circle with radius AB and arc AC.
D is center of a circle with radius AD and arc AC.
Find the area of the shaded region. Leave answer in terms
of  .
9)
Determine the measure of A .
8x - 40
A
x + 43
10)
3x + 21
Determine the value of a.
33
22
a
11)
x2 + y2 = 36 is an equation for a circle.
a. Sketch it. Label all x and y-intercepts
c.
12)
30
a.
Graph the following equations: (Label all intercepts.)
ii.
x2 y 2

0
49 16
ii.
x2 y 2

0
36 25
Graph the following equations:
i.
c.
Verify that ( 2, 4 2) lies on the circle.
Find an equation of the line that is tangent to the circle at this point.
[Hint: A tangent to a circle at a point (x,y) is perpendicular to the radius of the
circle from its center to the point (x,y).]
x2 y 2

1
i.
49 16
b.
b.
x2 y 2

 1
36 25
Describe a relationship between each pair of graphs.
P.S. 7.2
13)
The legs of right triangle ABC are trisected as shown such that BC = 3 EC and AB = 3 AD.
AE = 109 and DC = 2 41 . Determine AC.
A
D
B
14)
a.
E
C
Determine g(8).
1
y = g(x) =
b.
If the domain of g is restricted and
written x  8  4 , determine the
resulting restrictions on y = g(x).
Write your answer in the form:
x ?  ?
3
g(8) = ?
4
4
8
15)
The function y = f(x) = x2 + 2 is graphed to
the right. The slope of the secant PQ can
be found by evaluating
m=
y f (1  h)  f (1)
=
.
x
(1  h)  1
Let m(h) =
f (1  h)  f (1)
h
a. Find m(1), m(–1), and m(2).
b. Graph y = m(h)
16)
If f (x) =
x
2 x3  x 2  23x  20
2 x3  x 2  71x  140
a.
Determine all zeros of f (x).
b.
Determine all values of x for which f is not defined.
P.S. 7.3
13
3
17)
a. If a coin is tossed, then the probability of a head is .52 and of a tail is .48. What is the
probability of getting 6 heads, if this coin is tossed 10 times?
b. Show that 4 C1  4 C2  5 C2 (this the triangle addition feature of the Pascal Triangle)
18)
Determine k and solve the equation x3 – kx2 + 3x – 54 = 0, if one of its zeros is the triple of
another.
P.S. 7.4
17)
19)
Solve for x:
1
1
1
1
+
+
+
= 3
log 2 x log 3 x
log 4 x
log9 x
Find the domain of the function: f(x) =
x2  6x  7
x2
20)
Find the area of the 7th triangle
if the triangles are continued on
the x-axis.
21)
Given the graph of y = f(x) below, sketch each of the following:
a. y = f(2x)
b. y = f  x 
y = f(x)
22)
Complete the square to find the center and the radius of the circle:
4x2 + 4y2 – 16x + 40y + 36 = 0
23)
Write the equations of the parabolas with the following conditions:
a. with vertex (-2,-4) and passing through (0,-8)
b. passing through the points (2, 1), (–1, 6) and (5, 1)
The arithmetic mean of two numbers is 15. Their geometric mean is 12. Find the sum of the
square roots of the two numbers.
16)
P.S. 7.5