1.

1 Which statement is not always true?
(1) The product of two irrational numbers is irrational.
(2) The product of two rational numbers is rational.
(3) The sum of two rational numbers is rational.
(4) The sum of a rational number and an irrational number is
irrational.

Hint
Half-n-half Clue
2.

2 A satellite television company charges a one-time installation fee and
a monthly service charge. The total cost is modeled by the function
y = 40 + 90x. Which statement represents the meaning of each part
of the function?
(1) y is the total cost, x is the number of months of service,
$90 is the installation fee, and $40 is the service charge per
month.
(2) y is the total cost, x is the number of months of service,
$40 is the installation fee, and $90 is the service charge per
month.
(3) x is the total cost, y is the number of months of service,
$40 is the installation fee, and $90 is the service charge per
month.
(4) x is the total cost, y is the number of months of service,
$90 is the installation fee, and $40 is the service charge per
month.

Half-n-half Clue
3.

3 If 4x^{2} - 100 = 0, the roots of the equation are
(1) -25 and 25 (3) -5 and 5
(2) -25, only (4) -5, only

Half-n-half Clue
4.

U
4 Isaiah collects data from two different companies, each with four
employees. The results of the study, based on each worker’s age and
salary, are listed in the tables below.
Company 1 Company 2
Worker’s Salary Worker’s Salary
Age in in Age in in
Years Dollars Years Dollars
25 30,000 25 29,000
27 32,000 28 35,500
28 35,000 29 37,000
33 38,000 31 65,000
Which statement is true about these data?
(1) The median salaries in both companies are greater than $37,000.
(2) The mean salary in company 1 is greater than the mean salary in
company 2.
(3) The salary range in company 2 is greater than the salary range in
company 1.
(4) The mean age of workers at company 1 is greater than the mean
age of workers at company 2.

Half-n-half Clue
5.

5 Which point is not on the graph represented by y = x^{2} + 3x - 6?
(1) (-6,12) (3) (2,4)
(2) (-4,-2) (4) (3,-6)

Half-n-half Clue
6.

6 A company produces x units of a product per month, where C(x)
represents the total cost and R(x) represents the total revenue for the
month. The functions are modeled by C(x) = 300x + 250 and
R(x) = -0.5x^{2} + 800x - 100. The profit is the difference between
revenue and cost where P(x) = R(x) - C(x). What is the total profit,
P(x), for the month?
(1) P(x) = -0.5x^{2} + 500x - 150
(2) P(x) = -0.5x^{2} + 500x - 350
(3) P(x) = -0.5x^{2} - 500x + 350
(4) P(x) = -0.5x^{2} + 500x + 350

Half-n-half Clue
7.

7 What is one point that lies in the solution set of the system of
inequalities graphed below?
(1) (7,0) (3) (0,7)
(2) (3,0) (4) (-3,5)

Half-n-half Clue
8.

8 The value of the x-intercept for the graph of 4x - 5y = 40 is

Half-n-half Clue
9.

9 Sam and Jeremy have ages that are consecutive odd integers.
The product of their ages is 783. Which equation could be used to
find Jeremy’s age, j, if he is the younger man?
(1) j^{2} + 2 = 783 (3) j^{2} + 2j = 783
(2) j^{2} - 2 = 783 (4) j^{2} - 2j = 783

Half-n-half Clue
10.

10 A population that initially has 20 birds approximately doubles every
10 years. Which graph represents this population growth?

Half-n-half Clue
11.

11 Let f be a function such that f(x) = 2x - 4 is defined on the domain
2 ≤ x ≤ 6. The range of this function is
(1) 0 ≤ y ≤ 8 (3) 2 ≤ y ≤ 6
(2) 0 ≤ y < ∞ (4) -∞ < y < ∞

Half-n-half Clue
12.

12 Which situation could be modeled by using a linear function?
(1) a bank account balance that grows at a rate of 5% per year,
compounded annually
(2) a population of bacteria that doubles every 4.5 hours
(3) the cost of cell phone service that charges a base amount plus
20 cents per minute
(4) the concentration of medicine in a person’s body that decays by
a factor of one-third every hour

Half-n-half Clue
13.

13 Which graph shows a line where each value of y is three more than
half of x?

Half-n-half Clue
14.

14 The table below shows the average diameter of a pupil in a person’s
eye as he or she grows older.
Age Average Pupil
(years) Diameter (mm)
20 4.7
30 4.3
40 3.9
50 3.5
60 3.1
70 2.7
80 2.3
What is the average rate of change, in millimeters per year, of a
person’s pupil diameter from age 20 to age 80?
(1) 2.4 (3) -2.4
(2) 0.04 (4) -0.04

Half-n-half Clue
15.

15 Which expression is equivalent to x^{4} - 12x^{2} + 36?
(1) (x^{2} - 6)(x^{2} - 6) (3) (6 - x^{2} )(6 + x^{2} )
(2) (x^{2} + 6)(x^{2} + 6) (4) (x^{2} + 6)(x^{2} - 6)

Half-n-half Clue
16.

16 The third term in an arithmetic sequence is 10 and the fifth term is 26.
If the first term is a_{1} , which is an equation for the nth term of this
sequence?
(1) a_{n} = 8n + 10 (3) a_{n} = 16n + 10
(2) a_{n} = 8n - 14 (4) a_{n} = 16n - 38

Half-n-half Clue
17.

17 The graph of the equation y = ax^{2} is shown below.
(1) wider and opens downward
(2) wider and opens upward
(3) narrower and opens downward
(4) narrower and opens upward

Half-n-half Clue
18.

18 The zeros of the function f(x) = (x + 2)^{2} - 25 are
(1) -2 and 5 (3) -5 and 2
(2) -3 and 7 (4) -7 and 3

Half-n-half Clue
19.

19 During the 2010 season, football player McGee’s earnings, m, were
0.005 million dollars more than those of his teammate Fitzpatrick’s
earnings, f. The two players earned a total of 3.95 million dollars.
Which system of equations could be used to determine the amount
each player earned, in millions of dollars?
(1) m + f = 3.95 (3) f - 3.95 = m
m + 0.005 = f m + 0.005 = f
(2) m - 3.95 = f (4) m + f = 3.95
f + 0.005 = m f + 0.005 = m

Half-n-half Clue
20.

(1) 4 (3) 8
(2) 6 (4) 11

Half-n-half Clue
21.

21 The table below shows the number of grams of carbohydrates, x, and
the number of Calories, y, of six different foods.
Carbohydrates (x) Calories (y)
8 120
9.5 138
10 147
6 88
7 108
4 62
Which equation best represents the line of best fit for this set of data?
(1) y = 15x (3) y = 0.1x - 0.4
(2) y = 0.07x (4) y = 14.1x + 5.8

Half-n-half Clue
22.

22 A function is graphed on the set of axes below.

Half-n-half Clue
23.

23 The function h(t) = -16t^{2} + 144 represents the height, h(t), in feet, of
an object from the ground at t seconds after it is dropped. A realistic
domain for this function is
(1) -3 ≤ t ≤ 3 (3) 0 ≤ h(t) ≤ 144
(2) 0 ≤ t ≤ 3 (4) all real numbers

Half-n-half Clue
24.

24 If f(1) = 3 and f(n) = -2f(n - 1) + 1, then f(5) =
(1) -5 (3) 21
(2) 11 (4) 43

Half-n-half Clue