Question 1

Which of the following expressions is equivalent to $a(4 - a) - 5(a + 7)$?

Accepted Answer

$-a^2-a-35$

Answer

$-2a+7$

Answer

$-a^2-a+7$

Answer

$-2a-35$

Question 2

Which of the following inequalities orders the numbers 0.2, 0.03, and $  1/4 $ from least to greatest?

Accepted Answer

$0.03 < 0.2 < 1/4 $

Answer

$0.2 < 0.03 < 1/4 $

Answer

$1/4 < 0.2 < 0.03 $

Answer

$0.03 > 0.2 > 1/4 $

Question 3

If $x^2+4=29$, then  $x^2-4=?$

Accepted Answer

21

Answer

33

Answer

5

Answer

25

Question 4

The vertices of a rectangle are $(-1,-2), (4,-2), (4,3),$ and $(-1,3)$. When the rectangle is graphed in the standard $(x,y)$ coordinate plane below, what percent of the total area of the rectangle lies in Quadrant III ?

Accepted Answer

$8%$

Answer

$12%$

Answer

$32%$

Answer

$12.5%$

Question 5

In 1985, the cost of clothing for a certain family was 620 dollars. In 1995, 10 years later, the cost of clothing for this family was 1,000 dollars. Assuming the cost increased linearly, what was the cost of this family's clothing in 1991 ?

Accepted Answer

$848

Answer

$812

Answer

$810

Answer

$908

Question 6

The square root of a certain number is approximately 9.2371. The certain number is between what 2 integers?

Accepted Answer

81 and 99

Answer

3 and 4

Answer

9 and 10

Answer

18 and 19

Question 7

A bag contains 10 pieces of flavored candy: 4 lemon, 3 strawberry, 2 grape, and 1 cherry. One piece of candy will be randomly picked from the bag. What is the probability the candy picked is NOT grape flavored?

Accepted Answer

$\frac{4}{5}$

Answer

$\frac{1}{5}$

Answer

$\frac{3}{4}$

Answer

$\frac{1}{2}$

Question 8

When points A and B $(-3,4)$ are graphed in the standard $(x,y)$ coordinate plane below, the midpoint of $\overline{AB}$will be $( 1,2)$. What will be the coordinates of point A ?

Accepted Answer

$(5,0)$

Answer

$(-7,6)$

Answer

$(-1,8)$

Answer

$(-2,1)$

Question 9

Andrea manages a company that currently has 116 customers, which is 8 more than twice the number of customers the company had I year ago. How many customers did the company have 1 year ago?

Accepted Answer

54

Answer

62

Answer

66

Answer

50

Question 10

Joseph will have a 200-foot-long fence installed around his yard. The A+ Fence Company charges a 500.00 dollar fee, plus a set amount per foot of fence. The A+ Fence Company has given Joseph an estimate of 2,200.00 dollars to install the fence around his yard. What is the set amount per foot of fence?

Accepted Answer

$8.50

Answer

$13.50

Answer

$4.50

Answer

$11.00

Question 11

For a math homework assignment, Karla found the area and perimeter of a room of her house. She reported that the area of her rectangular living room is
180 square feet and that the perimeter is 54 feet. When drawing a sketch of her living room the next day, she realized that she had forgotten to write down the dimensions of the room. What are the dimensions of Karla's living room?

Accepted Answer

12 by 15

Answer

10 by 18

Answer

14 by 13

Answer

9 by 20

Question 12

Jeremy has 10.00  dollars in quarters to spend on candy. What is the maximum number of quarters he would have left after paying for a box of 25 candies at Tamika's Treat Shop?  (Note: Each quarter is worth $0.25.)

Accepted Answer

23

Answer

24

Answer

22

Answer

25

Question 13

At Tamika's Treat Shop, what is the average price per candy in a box of 20, to the nearest $0.01 ?

Accepted Answer

$0.19

Answer

$0.45

Answer

$0.17

Answer

$0.23

Question 14

Which of the following equations gives the relationship between the price in dollars, $c$, and the number of candies, $n$, in a box of candies at Carrie's Chocolate Shop?

Accepted Answer

$c=0.3n$

Answer

$c=0.2n+0.5$

Answer

$c=n-3.5$

Answer

$c=0.5n+1.5$

Question 15

Which of the following is a solution to the equation $x^2- 36x=0$ ?

Accepted Answer

36

Answer

-6

Answer

72

Answer

18

Question 16

In the figure below, vertices D and F of $	riangle{DEF} $lie on
$\overline{CG}$, the measure of $\angle{CDE}$ is 148°, and the measure of
$\angle{EFG}$ is 140°. What is the measure of $\angle{DEF}$?

Accepted Answer

108

Answer

89

Answer

90

Answer

100

Question 17

A company ships notepads in rectangular boxes that
each have inside dimensions measuring 9 inches long,
9 inches wide, and 12 inches tall. Each notepad is in
the shape of a cube with an edge length of 3 inches.
What is the maximum number of notepads that will fit
in I closed box?

Accepted Answer

36

Answer

11

Answer

22

Answer

12

Question 18

The function f is defined as $f(x) = -4x^3- 4x^2$. What is
$f(-4)$?

Accepted Answer

192

Answer

16

Answer

320

Answer

-192

Question 19

Which of the following $(x,y)$ pairs is the solution for the system of equations  $x + 2y = 4$ and $-2x + y = 7 $?

Accepted Answer

$(-2,3)$

Answer

$(4,0)$

Answer

$(2,1)$

Answer

$(-4,2.5)$

Question 20

Which of the following is a value of x that satisfies
$\log_x{36} = 2$?

Accepted Answer

6

Answer

8

Answer

2

Answer

4

Question 21

A 5-inch-by-7-inch photograph was cut to fit exactly into a 4-inch-by-6-inch frame. What is the area, in square inches, of the part of the photograph that was cut off?

Accepted Answer

11

Answer

7

Answer

10

Answer

12

Question 22

A line contains the points $A, B, C,$ and $D$. Point $B$ is
between points $A$ and $C$. Point $D$ is between points $C$
and $B$. Which of the following inequalities must be true
about the lengths of these segments?

Accepted Answer

$CD<BC$

Answer

$CD<AB$

Answer

$BD<AB$

Answer

$BD<CD$

Question 23

If $x$ and $y$ are positive integers such that the greatest
common factor of $x^2y^2$ and $xy^3$ is 45, then which of the
following could $y$ equal?

Accepted Answer

3

Answer

5

Answer

45

Answer

9

Question 24

To test a new medicine, each of 300 volunteers was
assigned a distinct number from l to 300. Next, a
calculator was used to simulate drawing 150 balls from
among 300 congruent balls. The balls were numbered
the same way as the volunteers so that 150 volunteers
to receive the new medication would be chosen without
bias. The other volunteers received a placebo. Weeks
later, the 2 groups were compared. Which of the
following phrases best describes the company's testing?

Accepted Answer

randomized experiment

Answer

randomized census

Answer

nonrandomized experiment

Answer

randomized sample survey

Question 25

One caution sign flashes every 4 seconds, and another
caution sign flashes every 10 seconds. At a certain
instant, the 2 signs flash at the same time. How many
seconds elapse until the 2 signs next flash at the same
time?

Accepted Answer

20

Answer

40

Answer

7

Answer

14

Question 26

For all nonzero values of a and b, the value of which of the following expressions is always negative?

Accepted Answer

$-|x|-|y|$

Answer

$|x|-|y|$

Answer

$|x|+|y|$

Answer

-$|x|+|y|$

Question 27

Graphed in the same standard $(x,y)$ coordinate plane
are a circle and a parabola. The circle has radius 3 and
center $(0,0)$. The parabola has vertex $(-3,-2)$, has a
vertical axis of symmetry, and passes through $(-2,-1)$.
The circle and the parabola intersect at how many
points?

Accepted Answer

2

Answer

0

Answer

3

Answer

1

Question 28

40% of 250 is equal to 60% of what number?

Accepted Answer

166$\frac{2}{3}$

Answer

170

Answer

160

Answer

150

Question 29

Which of the following inequalities is equivalent to
$-2x - 6y > 2y - 4 $?

Accepted Answer

$x <-4y+ 2$

Answer

$x < -4y -2$

Answer

$x > -4y + 2$

Answer

$x > -4y -2$

Question 30

For an angle with measure $	heta$ in a right triangle,
$\sin 	heta = \frac{40}{41} $and $	an 	heta = \frac{40}{9}$. What is the value of
$\cos 	heta$?

Accepted Answer

$\frac{9}{41}$

Answer

$\frac{40}{9}$

Answer

$\frac{9}{40}$

Answer

$\frac{41}{9}$

Question 31

The perimeter of rectangle ABCD is 96 cm. The ratio
of the side lengths AB:BC is 3:5. What is the length, in
centimeters, of $\overline{AB}$ ?

Accepted Answer

18

Answer

30

Answer

9

Answer

36

Question 32

For $	riangle{ABC} $ shown below, base $\overline{AC}$ has a length of
16 inches and altitude $\overline{BD} $ has a length of 8 inches. The
area of a certain square is equal to the area of  $	riangle{ABC}$.
What is the length, in inches, of a side of the square?

Accepted Answer

8

Answer

6

Answer

12

Answer

10

Question 33

The length of $\overline{EH}$ is what percent of the length of $\overline{AD}$ ?

Accepted Answer

30%

Answer

50%

Answer

40%

Answer

20%

Question 34

What is the length, in meters, of $\overline{JD}$ ?

Accepted Answer

13

Answer

17

Answer

18

Answer

19

Question 35

What is the length, in meters, of arc ${CD}$ ?

Accepted Answer

5$\pi$

Answer

2.5$\pi$

Answer

10$\pi$

Answer

6.25$\pi$

Question 36

The figure will be placed in the standard $(x,y)$
coordinate plane so that $K$ is at the origin, $\overline{AB}$ is
parallel to the x-axis, and 1 meter equals 1 coordinate
unit. Which of the following values could be the
y-coordinate of H ?

Accepted Answer

8.4

Answer

12

Answer

3.6

Answer

10

Question 37

What is the length, in coordinate units, of the altitude
from $C$ to $\overline{AB}$ in $	riangle{ABC}$ shown in the standard $(x,y)$
coordinate plane below?

Accepted Answer

3

Answer

7

Answer

6

Answer

5

Question 38

At a local post office, on average, 3 customers are in
line when the post office closes each day. The
probability, P, that exactly n customers are in line
when the post office closes can be modeled by the
 equation $P =  \frac{3^n e^{-3}}{n!}$ Given that $ e^{-3} = 0.05$, which of the following values is closest to the probability that
exactly 2 customers are in line when the post office
closes?

Accepted Answer

0.23

Answer

0.15

Answer

0.45

Answer

0.11

Question 39

What is the amplitude of the function
$f(x) = \frac{1}{2} \cos(3x + \pi)$ ?

Accepted Answer

$\frac{1}{2}$

Answer

$\frac{1}{3}$

Answer

$\frac{3}{2}$

Answer

$\frac{2}{3}$

Question 40

License plates on cars in a certain state consist of
3 letters taken from the 26 letters, A through Z,
followed by 3 digits taken from the 10 digits,
0 through 9. Which of the following expressions gives
the number of distinct license plates that are possible
given that repetition of both letters and digits is
allowed?

Accepted Answer

$10^3*26^3$

Answer

$(10+26)^3$

Answer

$2(26!)^3(10!)^3$

Answer

$(26*10)^3 * (26*10)^3$

Question 41

For 20 quiz scores in a typing class, the table below
gives the frequency of the scores in each score interval.
Which score interval contains the median of the
scores?

Accepted Answer

81-85

Answer

96-100

Answer

76-80

Answer

91-95

Question 42

In the complex numbers, where $i^2  = -1,$
$\frac{1}{1+i} * \frac{1-i}{1-i}$

Accepted Answer

$\frac{1-i}{2}$

Answer

i - 1

Answer

$\frac{1+i}{2}$

Answer

1+i

Question 43

Temperatures measured in degrees Fahrenheit (F) are
related to temperatures measured in degrees Celsius (C)
by the formula $F = \frac{9}{5}c + 32$. There is 1 value of x for
which $x$ degrees Fahrenheit equals x degrees Celsius.
What is that value?

Accepted Answer

-40

Answer

0

Answer

-32

Answer

-70

Question 44

The table below gives experimental data values for
variables$ x $and$ y$. Theory predicts that$ y$ varies directly
with $x$. Based on the experimental data, which of the
following values is closest to the constant of variation?
(Note: The variable y varies directly with the variable x
provided that $y = kx$ for some nonzero constant $k$,
called the constant of variation.)

Accepted Answer

.05

Answer

-2.61

Answer

15.9

Answer

3.61

Question 45

Diana is baking bread, and the original recipe calls for
I½ teaspoons of yeast and 2½ cups of flour. Diana will
use the entire contents of a packet that contains
2¼ teaspoons of yeast and will use the same ratio of
ingredients called for in the original recipe. How many
cups of flour will Diana use?

Accepted Answer

3 $\frac{3}{4}$

Answer

3 $\frac{1}{2}$

Answer

1 $\frac{7}{8}$

Answer

4

Question 46

For all nonzero values of $x,$ $ \frac {12x^6-9x^2}{3x^2}$

Accepted Answer

$4x^4-3$

Answer

$4x^3-3$

Answer

$4x^3-3x$

Answer

$4x^4-3x$

Question 47

Which of the following matrix products is undefined?

Accepted Answer

XZ

Answer

WX

Answer

WX

Answer

YZ

Question 48

The 3 parabolas graphed in the standard $(x,y)$
coordinate plane below are from a family of parabolas.
A general equation that defines this family of
parabolas contains the variable n in addition to x and y.
For one of the parabolas shown, $n = 1$; for another,
$n = 2$; and for the third, $n = 3$. Which of the following
could be a general equation that defines this family of
parabolas for all n$\geq$1 ?

Accepted Answer

$y = nx^2+1$

Answer

$y = x^2+n$

Answer

$y = \frac{1}{2}nx^2+1$

Answer

$y = -nx^2+1$

Question 49

After polling a class of 20 music students by a show of
hands, you find that 8 students play the guitar and
9 students play the piano. Given that information, what
is the minimum number of students in this music class
who play both the guitar and the piano?

Accepted Answer

0

Answer

1

Answer

9

Answer

8

Question 50

A teacher assigns each of her 18 students a different
integer from 1 through 18. The teacher forms pairs of
study partners by using the rule that the sum of the pair
of numbers is a perfect square. Assuming the 9 pairs of
students follow this rule, the student assigned which
number must be paired with the student assigned the
number 1 ?

Accepted Answer

15

Answer

9

Answer

16

Answer

8

Question 51

Lucky found $8.25 in pennies, nickels, dimes, and
quarters while walking home from school one week.
When she deposited this money in the bank, she
noticed that she had twice as many nickels as pennies,
1 fewer dime than nickels, and 1 more quarter than
nickels. How many quarters did Lucky find that week?

Accepted Answer

21

Answer

16

Answer

3

Answer

9

Question 52

Given $10^{\frac{2x-1}{x}} =1, x =? $

Accepted Answer

$\frac{1}{2}$

Answer

$-\frac{1}{8}$

Answer

$\frac{10}{19}$

Answer

$-\frac{1}{2}$

Question 53

According to the results, what is the probability that a
randomly selected person who was surveyed likes to
read, given that the person plays a musical instrument?

Accepted Answer

$\frac{5}{9}$

Answer

$\frac{1}{5}$

Answer

$\frac{9}{25}$

Answer

$\frac{5}{11}$

Question 54

Mario was riding a bicycle with wheels 26 inches in
diameter. During 1 minute of Mario's ride, the wheels
made exactly 200 revolutions. At what average speed,
in feet per second, was Mario riding during that
minute?

Accepted Answer

$\frac{65}{9}\pi$

Answer

$\frac{65}{18}\pi$

Answer

$\frac{845}{18}\pi$

Answer

$\frac{130}{9}\pi$

Question 55

Whenever j and k are positive integers such that $(\sqrt{3}) ^j = 27^k$ what is the value of $\frac{j}{k}$?

Accepted Answer

6

Answer

3

Answer

$\frac{1}{6}$

Answer

$\frac{3}{2}$

Question 56

A finite arithmetic sequence has 7 terms, and the first
term is ¾. What is the difference between the mean
and the median of the 7 terms?

Accepted Answer

0

Answer

$\frac{3}{4}$

Answer

4

Answer

3

Question 57

In the circle with center D shown below, the length of
radius $\overline{CD}$ is 4 cm, the length of $\overline{BC}$ is 1 cm, and $\overline{BC}$
is perpendicular to radius $\overline{AD}$ at B. When $\angle{ADC}$ is
measured in degrees, which of the following expressions
represents the length, in centimeters, of AC ?

Accepted Answer

$\frac{\pi}{45}\sin^{-1}{\frac{1}{4}}$

Answer

$\frac{2\pi}{45}\sin^{-1}{\frac{1}{4}}$

Answer

$\frac{2\pi}{45}\sin^{-1}{\frac{1}{4}}$

Answer

$\frac{\pi}{45}\cos^{-1}{\frac{1}{4}}$

Question 58

In scalene triangle $	riangle{GHI}$ shown below, point $J $ lies on
side $\overline{HI}$, $\overline{GJ}$ bisects $\angle{HGI}$ such that $\angle{HGJ}$ and $\angle{IGJ}$ each measure 9, and the given lengths $a , b, c, d, $and $e$
are in inches and are distinct. For all possible values of
$	heta$, the area of $	riangle{GHJ} $ is what fraction of the area of $	riangle{GHI}$?

Accepted Answer

$\frac{d}{d+e}$

Answer

$\frac{ad\sin{	heta}}{b(d+e)\sin{2	heta}}$

Answer

$\frac{a}{b}$

Answer

$\frac{1}{2}$

Question 59

The probability distribution of the discrete random
variable X is shown in the table below. What is the
expected value of X ?

Accepted Answer

$3\frac{1}{6}$

Answer

$\frac{1}{6}$

Answer

$\frac{1}{3}$

Answer

2

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