Download Algebra and Functions

Algebra and Functions
1)
The price of a sweater went up 20% since last year. If last year’s price was x, what is this
year’s price in terms of x?
2)
One year ago an average restaurant meal costs $12. Today, the average restaurant meal costs
$15. By what percent has the cost of the meal increased?
3)
The average height ( arithmetic mean ) of 4 members of a 6-person volleyball team is 175
cm. What does the average height in cm of the other 2 players have to be if the average
height of the entire team equals 180 cm?
4)
A car travelling at an average rate of 55 Km/h made a trip in 6 hours. If it had travelled at an
average rate of 50 Km/h, the trip would have taken how many minutes longer?
5)
The number of juice packs that Rambling Pines Day Camp buys each day is directly
proportional to the number of children at the camp that day. If the camp bought 150 juice
boxes yesterday for 60 children, how many juice boxes will they buy today for 52 children?
6)
If c and d are inversely proportional and c=10 when d=6, what is d when c=30?
7)
What are the domain and range of f(x)=1+√x?
8)
If f ( x) 
a) 11/2
3  2x 2
for all nonzero x, then f(2)=
x
b) 7/2
c) -1/2
d) -5/2
9)
Let the operation  be defined by a  b 
a) 4
1  2  2  x , what is the value of x?
b) 3
c) 2
d) 1
e) -7
ab
for all numbers a and b where a≠b. If
ab
e) 0
10)
During a sale, a customer can buy one shirt for x dollars. Each additional shirt the customer
buys costs z dollars less than the first shirt. For example, the cost of the second shirt is x-z
dollars. Which of the following represents the customer’s cost, in dollars, for n shirts bought
during the sale?
x  ( x  z)
( x  z)
a) x  (n  1)( x  z ) b) x  n( x  z )
c) n( x  z )
d)
e) ( x  z ) 
n
n
11)
12)
x2
Let the function h be defined by h( x)  14 
. If h(2m)=9m, what is one possible value of
4
m?
Set X has x members and set Y has y members. Set Z consists of all members that are in
either set X or set Y with the exception of the k common members. Which of the following
represents the number of members in set Z?
a) x+y+k
b) x+y-k
c) x+y+2k
d) x+y-2k
e) 2x+2y-2k
h(t)=c-(d-4t)2
13)
At time t=0, a ball was thrown upward from an initial height of 6 feet. Until the ball hit the
ground, its height, in feet, after t seconds was given by the function h above, in which c and
d are positive constants. If the ball reached its maximum height of 106 feet at time t= 2.5,
what was the height, in feet, of the ball at time t=1?
14)
a) 1
Let x# be defined as x#=x2-x for all values of x. If a#=(a-2)#, what is the value of a?
b) ½
c) 3/2
d) 6/5
e) 3
15)
t
g(t)
-1
4
0
2
1
0
2
-2
The table above gives values of the linear function g(t) for selected values of t. Which of the
following defines g?
a) g(t)=1/2t+1 b) g(t)=-1/2t+1 c) g(t)=-t+1 d) g(t)=-t+2 e) g(t)=-2t+2
16)
a) 1
Luke purchased an automobile for $5,000, and the value of the automobile decreases by
20% each year. The value, in dollars, of the automobile n years from the date of purchase is
given by the function V, where V(n)=5,000(4/5)n. How many years from the date of
purchase will the value of the automobile be $3,200?
b) 2
c) 3
d) 4
e) 5
Questions 17-18 refer to the following functions g and h.
g(n)=n2+n
h(n)= n2-n
17)
a)0
g(5)-h(4)=
b) 8
c) 10
d) 18
18)
Which of the following is equivalent to h(m+1)?
a) g(m)
b) g(m)+1
c) g(m)-1
19)
e) 32
d) h(m)+1
e) h(m)-1
Let the function f be defined by f(x)= x2+18. If m is a positive number such that
f(2m)=2f(m). what is the value of m?
20)
Let the function h be defined by h(t)=2(t3-3). When h(t)=-60, what is the value of 2-3t?
a) 35
b) 11
c) 7
d) -7
e) -11