NOVEMBER 12, 2008
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#2 PYTHAGOREAN RELATIONS
ANSWERS:
1.
25
2.
72
2
3.
30.6
1. The hypotenuse and long leg of a right triangle have lengths 11 3 and 7 7 respectively.
Compute the length of the shorter leg.
2. Compute th
NOVEMBER 12, 2008
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#4
FRACTIONS
ANSWERS:
1.
2.
7
3
2 16 3 4
5
58 +71
2
2. Solve for x:
x 3 2x 8
3
2
=
x +1 x 1 x 1
3. If the integer n 1 and
( n + 1)!( 2n 2 )! = 2 , compute n.
( n 1)!( 2n )! 7
Recall: n ! = n ( n 1)(
NOVEMBER 12, 2008
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#6
EVALUATIONS
ANSWERS:
1.
2
2.
5
3.
16
1. Let the operation * be defined by a b c = a b bc + c a .
What is the value of 1 ( 1) 2 ?
2. Given:
Compute:
3 A + 5B
=2
4B 2 A
2 A 3B
A
3. a1 , a2 , a3 , a4
NOVEMBER 12, 2008
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#5
INEQUALITIES &
ABSOLUTE VALUE
ANSWERS:
1.
2.
10
3.
1. Find the area of the region defined by:
2
1 x <0 or 1< x 2
y x
x 2
x 1
y 0
2. Find the sum of all values of x if x 2 5 x = 6.
3. Determine th
OCTOBER 16, 2008
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#2 CREATIVE PROBLEM SOLVING
ANSWERS:
1.
27
2.
331
3.
289
1. Some boy scouts were out camping on a summers weekend. While sitting around the
campfire, one scout got up to check his flashlight, but ate
OCTOBER 16, 2008
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#3 TRIG: RT ANGLE PROBLEMS
ANSWERS:
1.
2.
Compute cos2 B.
2. Given:
Find:
15
3.
1. In right ABC with m C = 90, tan A =
16
27
45
4
.
11
Trapezoid ABCD with AD parallel to BC , E and F are right angles.
OCTOBER 16, 2008
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#4
SEQUENCES and SERIES
ANSWERS:
1.
57
2.
390
3.
40.5
1. 32 ,52 , 7 2 are the 2nd, 6th, and 12th terms of an arithmetic sequence. What is the 14th term?
2. Find the first term in the arithmetic sequen
OCTOBER 16, 2008
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#5
LOGIC & SET THEORY
ANSWERS:
1.
a
2.
butler
3.
zero
1. Which of the following conclusions make the argument valid? Supply a valid conclusion to
the following argument using all the premises.
If you
OCTOBER 16, 2008
CALCULATORS MAY BE USED ON THIS TOPIC
#6
PROBABILITY, STATISTICS,
and BINOMIAL THEOREM
ANSWERS:
1.
5
14
2.
71
3.
11
1. A container has 5 blue balls and 4 red balls. If balls are simultaneously chosen at random,
what is the probability tha
SEPTEMBER 24, 2008
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#1 CIRCLES
ANSWERS:
1.
3
2.
39
3.
24
1. In a circle with a 10-inch diameter, how many inches from the center is an 8-inch chord?
A
2. PA is tangent to circle O at A, PA = 5 x 3,
PB = 3x 1, BC = 7 x 11, and A
SEPTEMBER 24, 2008
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#2 QUADRATIC EQUATIONS
THEORY
ANSWERS:
1.
12
2.
b
3.
m < 1 or m > 2
1. Find all possible values of k in the equation x 2 + kx + 32 = 0 , given
that one root is twice the other.
2. Let a, b, and c, in some or
SEPTEMBER 24, 2008
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#3
ARITHMETIC
ANSWERS:
1.
12
2.
6
3.
20
1. One can of frozen juice concentrate, when mixed with 4 cans of water,
makes 2 quarts (64 oz.) of juice. Assuming no volume is gained or lost by mixing,
how many oz.
SEPTEMBER 24, 2008
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#4
EXPONENTS and RADICALS
ANSWERS:
1.
3
4
2.
(2, 1)
3.
161
1. Evaluate:
2. Given:
Find:
8
2
3
+
8
9
22 21
7
3y
52 y
and
1 = 27
= 625
x+ y
81x
25
( x, y)
3. Find all real values of x for which the following i
SEPTEMBER 24, 2008
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#5
ORDER of OPERATIONS
ANSWERS:
1.
81
2.
5
3.
6
1. Define the operation by a b = ab + b.
Compute (3 2) (2 3).
2. If McCain x = 2x + 4 and Obama x = 4x + 2, find
McCain(Obama 4) + (McCain 4 + Obama 4) Obama (
SEPTEMBER 24, 2008
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#6
ANALYTIC GEOMETRY
ANSWERS:
of the straight line
1.
3
2.
y = 2x 3
3.
0
1. L1 is a line with equation 2 x ay = 7. L2 is a line with equation ax 4 y 12 = 0.
L1 intersects L2 at the point P(8, a). Find a.
2.
OCTOBER 16, 2008
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#1 VOLUMES & SURFACES
ANSWERS:
1.
3773
2.
32
2
3
3.
343
1. A liter equals 1000 cubic centimeters. Find the number of liters in
a right circular cylinder of radius 49 cm and altitude of 500 cm, using =