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Grissom Math Tournament
Algebra I Test
April 11, 2009
1. Solve for x: 4( x y) 3( x 2 y) 0.
A. -10y
B. 10y
C. y
D. 4y
E. -2y
2. Which of the following is the y-intercept of the line with equation 4x – 3y = 12 ?
A.
0,
4
3
B.
0,
4
3
C. (0, 4)
3. The cost of a taxicab is $0.50 for the first
D. (0, 3)
E. (0, -4)
1
1
of a mile and $0.10 for each additional of a mile. How
5
5
far did you travel (in miles) in the taxi if the cost of the trip is $2.50 ?
A. 4
B. 4
1
5
C. 4
5 x 2 y3
4. Simplify completely:
5y 9
64
A.
D. 4
3
5
E. 4
4
5
3
6
5y9
B.
64
125 y 9
64
C.
5x 6
64 x
D.
E. None of these
P H K
=
where P, M, H, T, and K are positive real numbers, which of the following is (are) true ?
M T K
5. If
I.
II.
III.
If T > H , then M > P
If T = 2H, then M = 2P
If T = H, then M = P
A. II only
6. Find x :
A.
7. If
2x
2
5
A.
16
4
3x 1 1 3x
13
3
7
x
3
9
49
B. I only
C. II and III only D. I, II, and III
1.
B. - 7
3
y and y
7
E. I and III only
0 , then
B. 1
x
y
C.
19
3
D. 7
C.
7
3
D.
E. none of these
?
49
9
E.
3
7
8. Mr. Cecil wants his investments to earn 5% each year. He has invested $6000 at 4.5 % interest. How much
must he invest in a second account at 6% interest to realize 5% on his total investment?
A. $3000
B. $4500
C. $5000
D. $2500
a2
9. Perform the indicated operation and simplify completely:
a
A.
a b
a (a 4)
B.
a 2 b2
a 4
C.
a 2 ab
a 4
2
D.
b2
E. $3500
÷
3a 4
a 2 ab
a 4
a b
a2
a
.
E.
a 2 ab
a 4
10. Find the largest of three consecutive odd integers such that the sum of the first two is four times the last.
A. -7
B. -3
C. -1
D. 1
E. 11
D. x ≤ -2
E. x < 2
11. Solve for x in the inequality: 4 – 3x ≤ 12 + x.
A. x ≥ 8
B. x ≥ -8
C. x > -2
12. If the average of v and w is p, and the average of x, y, and z is q, what is the average of v, w, x, y, and z in
terms of p and q?
A. p + q
B.
p q
2
C.
2 p 3q
5
D.
3 p 2q
5
E.
p 2q
2
13. On a mathematics examination, short questions take 3 minutes each, and long questions take 8 minutes
each. If the test takes 70 minutes and there are twice as many short questions as long questions, how many
long questions are there?
A. 5
14. If S =
B. 6
a
1 r
C. 10
D. 4
E. 8
D. 1/2
E. -1/2
; S = 3/4 ; r = -1/2, then a = ?
A. -3/8
B. 3/8
C. 9/8
15. One more than three times the reciprocal of N is -5. Find 1 / N 2 .
A. -1/2
B. 2
C. 1/4
D. 4
E. 1/2
D. 6 xy 3 x
E. 18 x 2 y 3x
16. Simplify completely: 108x5 y 2 where y>0
A. x 2 y 108 x
B. 2 x 2 y 54 x
C. 6 x 2 y 3 x
17. If the distance a plane travels is decreased by 10% and the rate is decreased by 20%, by what percent has
the time been increased?
A. 10
B. 12 ½
C. 30
D. 25
E. 15
18. If x varies inversely as y and if x=12 when y=8, find x when y = 10.
A. 10
B. 9.6
C. 15
D. 12
E. none of these
19. If a certain number is decreased by its reciprocal, the result is 8/3. If the two possible values for the
number are a and b, find the value of
A.
8
3
2
3
B.
ab
.
a b
C.
3
8
D.
2
3
E.
3
8
20. Triangle ABC has sides with lengths that are consecutive multiples of three. If 7 more than twice the
perimeter of the triangle is 97, Q is the perimeter of the triangle, and P is the product of the largest and
smallest side lengths, find the value of Q + P.
A. 45
B. 180
C. 216
D. 261
E. 313
21. Which of the following is the equation of the line through (2 ,-4) and (-14, 4)?
A. x + 2y = 6
B. x = y - 10
C. x + 2y = -6
D. x – 2y = -6
E. x – 2y = 6
22. The ratio of boys to girls in a school is 3:2. If 2/3 of the boys and 3/4 of the girls vote in favor of a boatride,
what percent of the whole school voted in favor of a boatride?
A. 70
B. 50
C. 80
D. 60
E. None of these
23. Given that a, b, and c form a set of consecutive multiples of 4 such that the product of the two
largest minus the product of the two smallest is 256, find ac.
A. 324
B. 768
C. 896
D. 908
E. 1008
24. A fraction is equivalent to 3/7. If the numerator is increased by 6 and the denominator is increased by 2
and then doubled, the result equals 3/8. Which of the following is the denominator of the original fraction?
A. 2
B. 6
C. 7
D. 14
E. 28
25. Given two numbers, a and b, that are chosen from the set {1, 2, 3, . . . , 9, 10}, find the number of distinct
ordered pairs (a, b) such that:
A. 9
B. 10
a
b
b
a
4.
C. 18
D. 19
E. 20
TB1: ☼ (n) is defined as the number of positive integral divisors of n.
♣(n) is defined as the sum of the positive integral divisors of n.
Find the value of ☼(12) + ♣(12).
TB2: If 14 boys pick 294 crates of apples in 7 hours, how many boys does it take to pick 513 boxes in 3 hours
working at the same rate?
T B3: Solve for x:
x
3x 2
4. (If there is more than one solution, find the largest.)