2005 Lassiter Invitational JV Math TournamentPage 1 of8
1) Given .
A)
B)
C)
D)
E)
2) If and , then what is the domain of f(g(x))?
A) x > 3
B) x > 0
C) x > 1
D) x > 2
E) x > 3
3) If Mr. Slater rolls a standard, 6-sided, fair die 3 times, what is the probability
that he gets 3 threes?
A)
B)
C)
D)
E)
4) The area of a right triangle is equal to its perimeter, and the length of each
side is an even integer. What is the perimeter?
A) 24
B) 26
C) 28
D) 30
E) 32
5) If the repeating decimal .36 is expressed as a rational number a/b, where a
and b are integers, in reduced form, then a + b is equal to
A) 14
B) 15
C) 17
D) 18
E) 36
6) What is the minimum value of f(x) = x2 2x 24?
A) 27
B) 25
C) 24
D) 9
E) 1
7) How many different arrangements of 2 letters or more can be made from the
letters in “ROHAN”?
A) 10
B) 20
C) 26
D) 120
E) 320
8) Find mBC given mA = 10 and mDE = 90.
A) 10
B) 30
C) 45
D) 70
E) 80
9) What is the probability that a four-digit number will have repeated digits?
A)
B)
C)
D)
E)
10) Nathan is going to walk from home to school using the map below. If he
can only walk north or east and only along the lines drawn, how
many different routes can Nathan take from home to school?
A) 32
B) 120 N
C) 252W E
D) 1024 S
E) 3628800
11) The number 101023 is equal to the number 134n. What does n equal?
A) 6
B) 7
C) 8
D) 9
E) 11
12) If y = mx + b is the equation of the perpendicular bisector between (5, 2)
and (9,7), find the value of b.
A) 10
B) 10.1
C) 10.2
D) 10.4
E) 10.5
13) In how many ways can Phillip choose 4 people from a selection of 10
people to write the Junior Varsity Test?
A) 40
B) 210
C) 256
D) 5040
E) 151200
14) The measure of ABC is60, and BA and BC are tangent to ʘK at points
A and C. If the diameter of ʘK is 12, find the area of the ∆ABC.
A)
B)
C)
D)
E) 36
15) Find the sum of all solutions inthe set of complex numbers to:
.
A) 5
B)
C) 0
D)
E) 1
16) Suppose that # is an operation applied to positive real numbers such that:
a # b = ab-1. What is 3 # (2 # 3)?
A) 3
B) 8
C) 9
D) 27
E) 81
17) A ball is dropped from a height of 30 feet. It bounces to a height of 10 feet,
falls again, and bounces to a height of feet. If this pattern (the ball
bouncing to the previous height) continues indefinitely, what is the total
distance that the ball will travel (in feet)?
A) 45
B) 60
C) 90
D) 120
E)
18) Ekta ran p miles in b hours, and then she walked q miles in d hours. How
many hours would it take her to travel 10 miles if she maintains this
average rate?
A)
B)
C)
D)
E)
19) Find .
A) 100
B) 150
C) 5050
D) 5150
E) 1009950
20) What is the distance between the points of intersection of the graphs of
x y = 1 and y = x2 − 2x − 1?
A)
B)
C)
D)
E)
21) What is the surface area of a sphere with diameter 10?
A) 100
B) 200
C) 400
D)
E)
22) How many liters of water should be evaporated from 50liters of a 48%
saline solution in order to obtain a 60% saline solution?
A) 10
B) 12
C) 15
D) 18
E) 20
23) Of the three angles in a triangle, the sum of the two smallest angles is 40
less than the largest and the sum of the two largest angles is five times the
smallest. What is the measure of the middle-sized angle?
A) 50
B) 48
C) 45
D) 42
E) 40
24) If and g(x) = 2x, find(f◦g-1)(4).
A)
B)
C)
D)
E) 8
25) Given the figure below, where BEA is aright angle, find the area of the
entire figure.
A) 615
B) 984
C) 1080
D) 1380
E) 2160
Write the answers to these last 5 problems on the back of your GradeMaster form. (Free Response)
26) If p(x) = x3 31x + 30, write the smallest root of p(x).
27) Solve for all real values of p: .
28) The average test grade for a class of 30 students was 84. If the 18 girls
had an average of 90 for that test, what was the average of the boy’s test
grades?
29) A and B are points on a number line with coordinates at 3 and 5
respectively. If C also lies on that number line and AC:BC = 1:3, there are
2 possible locations for C. Find the positive distance between these two
locations.
30) If f(x) = x2, Evaluate and simplify the expression completely.