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June 19th

June 19th

# 1999 Algebra II State Finals Solutions Manual

19. (D)

20. (E) . Let .

x = 2 because eb > 0 for all b.

21. (C)

No numerical method can be provided to solve the equation , but graphing
the functions reveals that the functions do intersect. Testing the
solutions provided, x = 7 works.

22. (A) Let b = the length of the base.

23. (B) The probability that the first card is an ace is . After the first
card is drawn and is an ace , the probability that the next card is also
an ace is . Then the probability that the next 3 cards are not aces is
.
There are combinations of drawing the 2 aces within the 5
card set. Thus the probability is 10 times greater, or

24. (E)

We can use a graph of f (x) = (x - 1)(x + 3)(x - 2) to predict that
f
(x) ≤ 0 when x ≤ -3 or 1 ≤ x ≤ 2. As a check, test the binomial
factors (x - 1), (x + 3), and (x - 2) to see if they are positive , 0, or
negative in the ranges x ≤ -3, -3 ≤ x ≤ 1, 1 ≤ x ≤ 2, and 2 ≤ x.

25. (C)

26. (C) Long division will find the answer, but since q(x) is a linear term ,
we can use a shortcut. Let

p(x) = q(x)h(x) + r

where r is the remainder and h(x) is the quotient polynomial produced
by long division. Let x = 2.

p(2) = q(2)h(2) + r

Since q(2) = 0,

r = p(2) = 17

27. (E)

N one of the given choices represent z.

28. (C)

Let y = x2 and b = c2.

29. (A)

30. (B) As suming lxl < 1,

, which agrees with our assumption.

31. (D)

32. (A)

33. (B) In the first 60 miles, R.C. has driven hours. In the next 60
miles, R.C. has only hours to drive, so he must go mph.

34. (A) The input of f(x) will be the output of f -1(x) and the output of
f(x) will become the input of f -1. This means that x = f-1(t) = 0.2
and t = f(x) = f(0.2) = -4.792

35. (C)

36. (B) Let f = the connection fee, and r = the charger per kwh. There
is a system of equations :

f + 980r = \$80.36

f + 910r = \$75.53

70r = \$4.83

r = \$0.069 = 6.9 cents

37. (D)

38. (C) Since all radii are congruent, the radius extending from the center,
(a, a) to (2, 16) and the radius extending from (a, a) to one of the axes
are congruent.

There is more than one circle that is tangent to the axes and contains
the point (2, 16), but the smaller of the 2 circles has a radius of 10 and
is centered at (10, 10).

39. (B) The line connecting the point and (4, 0) will be perpendicular to
y = 2x - 3. It has the equation . The point is located at
the intersection of the two lines .

40. (D) We can find the area of the triangle made by 3 points, (2, 16), (10, 10), (2, 1),
in the coordinate plane using the formula

where each row corresponds to a point. The first column contains x-
coordinates, the second column contains y-coordinates, and the third
column is 1.

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