1. What is the least value of integer x such 2.
In the figure below, if a = 2c, and b = 3a,
that the value of 2x − 5 is greater than 7? what is the value of c?
a) 7
b) 6
c) 5
d) 4
e) 3
Note: Figure not drawn to scale.
a) 18
b) 20
c) 28
d) 34
e) 36
3. A supermarket has brand A juice 6. In the figure below, points A and B lie
smoothie on sale every 8 days and has on circle O. If ∠AOB = 2yo, what is the
brand B juice smoothie on sale every 5 value of x in term of y?
days. Within a year (365 days), how
many times does this supermarket have
both brands of juice smoothie on sale on
the same day?
a) 9
b) 10 a) y
c) 12 b) 90 − y
d) 24 c) 180 − y
e) 26 d) 90 – y
y
4. If 2x + 3 = 11, then 6x − 2?
a) 20
√
b) 22 7. If then y = ?
√
c) 24 a) 1
d) 26 b) 3
e) 28 c) 5
d) 8
e) 9
5. In the figure below, what is the value of
a − b?
8. If x is a positive integer, then
50𝑜 o
a 3 × 10–x + 10–x must be equal to?
a)
60
o o b)
b
c)
a) 10
b) 15 d)
c) 20 e)
d) 25
e) 30
12. If 60 percent of x is 48, then what is 20
o
percent of x?
40
a) 30
2y+5 x+1
b) 20
o c) 16
70
d) 14
6
e) 12
9. In the triangle above, which of the
following must be true?
a) x = y
b) x = 5 13. How many positive three-digit integers
c) x < y have the hundreds digit equal to the
d) x = 2y + 4 multiple of 3 and the units digit (ones
e) x + 4 = 2y digit) is an even digit?
a) 150
b) 160
10. Kim spent 3 hours installing 600 square c) 162
feet of solar panels. At this rate, how d) 180
many hours will she require to install e) 200
4800 square feet of solar panels?
a) 15
b) 18 14. Let <I, J> be defined as any integer
c) 20 greater than I but less than J, such as
d) 21
<–3, 3> = { –2, –1, 0, 1, 2, }. Which of the
e) 24
following has the same elements as the
intersection of <–1, 4> and <1, 6>?
a) <–2, 2>
11. The average score of John’s 5 math tests
b) <–1, 3>
is 80. If the teacher decides not to count
c) <–3, 2>
his lowest score, which is 60, what will
d) <1, 4>
be John’s new average score?
e) <2, 6>
a) 80
b) 82
c) 85
d) 86
e) 87
15. In the figure below, the vertices of an b)
isosceles right triangle, an equilateral
triangle, and a regular pentagon
intersect at one point. What is the value
of a + b + c?
c)
a) 90 d)
b) 100
c) 135
d) 147
e) 188
e)
16. The figure above shows the graph of the
line y = mx + b, where m and b are
constants. Which of the following best
represents the graph of the line
y= − 2mx − b?
a)
A 19. If Bill can run as fast as Mitt. Sam can
run as fast as Bill. Mitt can run how
E F many times as fast as the average speed
of Bill and Sam?
a)
D
B
10
C b)
17. In isosceles right triangle ΔABC above, c) 1
EF BC and length of ̅̅̅̅ is half of the d)
length of ̅̅̅̅ . What is the area of the e)
rectangular legion?
a) 16
b) 25 20. What is the remainder of 20132014
c) 36
divided by 10?
d) 64
e) 100 a) 1
b) 3
c) 7
d) 9
e) 0
18. What is the area of quadrilateral as
shown above?
a) 12
b) 6 + √
c) 6 + 2√
d) 6 + 4√
e) It cannot be determined.
1. If x – y = 7, y = 2z +4, and z = 1, what is 2. If 0 < xy and y > 0, which of the
the value of x? following statements must be true?
a) –13 I. x < 0
b) –12 II. x < y
c) 11 III. x > 0
d) 12 a) I only
e) 13 b) III only
c) I and II
d) II and III
e) II only
3. If ax∙ a4 = a10 and (a4) y = a12, what is the 6. A company sells boxes of marbles in red
value of x + y? and green. Helen purchased a box of
a) 7 marbles in which there were half as
b) 8 many green marbles in the box as red
c) 9 ones and 15 marbles were green. How
d) 10
many marbles were in Helen’s box?
e) 12
a) 30
b) 40
4. If a movie is 100 minutes long, what c) 45
fraction of the movie has been d) 50
completed 25 minutes after it begins? e) 60
7. If set A = {1, 3, 8, 10, 15} and set B
consists of all the even positive numbers
less than or equal to 10, how many
elements are in the union of the two
sets?
a) 0
5. If f(x) = x2 + x3/2, what is the value of f(3)
b) 3
=?
c) 8
a) 3 × (1 + 3√ ) d) 9
b) (1 + 3√ ) e) 10
c) 3 × (1 + 3√ )
d) 3 × (3 + √ ) 8. For all numbers p and q, let p@q be
e) (1 + 3√ ) ÷ 3 defined by p@q = (p + 1)2 × (q – 2)2, what
is the value of 7@5?
a) 24
b) 576
c) 729
d) 884
e) 1024
9. If x +2 y = 5, what is the value of x + 2y – 11. If 2(x − 5) = 12, what does x 5 equal?
1? x5
10. If 4x = 3y2 = 12, what is the value of x2y?
1.313113111311113. . .
16. The decimal number above consists of
only 1s and 3s. The first 3 is followed
by one 1, the second 3 is followed by
two 1s, and the third 3 is followed by
12. A circle is tangent to two sides of a three 1s. If such a pattern goes on, how
parallelogram ABCD as shown in the many 1s are between the 94th 3 and the
above figure. If the circle has an area of 98th 3?
36𝜋, what is the area of the
parallelogram ABCD?
17. In a junior high school with seventh and
eighth grades, there is the same number
13. In the figure below, what is the value of of girls as boys. The eighth grade has
a + b + 2c + 2d? 220 students, and there are 5 boys for
every 6 girls. In the seventh grade there
are 5 boys for every 4 girls. How many
girls are in the seventh grade?
18. Ms. DePietro provides some markers to
Note: Figure not drawn to scale. her Arts class. If each student takes 3
markers, there will be 1 marker left. If 5
students take 4 markers each and the
14. In quadrilateral ABCD, m∠A = m∠B = rest of students take 2 marker each,
o
120°, and m∠D is l0 less than 4 times of there will be no markers left. How many
m∠C. Find m∠D. students are in Ms. DePietro’s Arts
class?
15. The cube shown above has edges of
length 5. If ̅̅̅̅ = ̅̅̅̅ = 2, what is the
length of ̅̅̅̅?
2. Ken, Justin, and Tiff have read a total of
100 books from the library. Justin read 3
times as many books as Ken and Tiff
read 2 times as many as Justin. How
many books did Ken read?
1. In the figure above, lines l1 and l2 are
a) 12
parallel. What is the value of x? b) 10
a) 40 c) 9
b) 46 d) 8
c) 75 e) 7
d) 80
e) 86
3. In all except one of the following, at
least one of the coordinates of the 5. In the figure below, what is the sum of
ordered pair, when squared, is equal to a, b, c, d, e, f?
the reciprocal of the other coordinate.
For which ordered pair does this not
hold true?
a) (1, 1)
b) ( −1, 1)
c) (2, )
d) (4, ) a) 360
b) 300
e) (9, ) c) 240
d) 180
e) It cannot be determined.
4. A box contains red, blue and green
pens. If one pen is chosen at random,
6. If 40 percent of 40 percent of a number
the probability that a red pen will be
is 64.96, what is the number?
chosen is three times the probability for
a) 0.205
a blue pen and four times the
b) 35.4
probability for a green pen. If there are
c) 192
24 red pens in the box, how many pens
d) 203
are in the box?
e) 406
a) 60
b) 48
c) 44
7. A parking lot charges $3.00
d) 40
maintenance fee per day to use its
e) 38
parking space. In addition, there is a
charge of $1.25 per hour. Which of the
following represents the total charge, in
dollars, to park a car in the parking lot
for m hours in one day?
a) 3 + 1.25m
b) 3m + 1.25
c) (3 + 1.25)m
d) 3 + 1.25 + m
e) 1.25m – 3
8. Given the set of integers that are greater 11. If x and y are positive integers and 22x +
than 0 and less than 1000, how many of 2(2x+2) = y, what is 2x in terms of y?
the integers are multiples of either 2 or a)
5? √
b)
a) 900 √
b) 898 c)
c) 600 d) √
d) 599 √
e)
e) 598 √
9. If x = √ +√ , what is the value of x2
a) 124
12. If |5 − 2x| ≦ 1, which of the fol1owing
b) 120
is a possible value of x?
c) 108
a) 3
d) 84 b) 4
e) 60 c) 5
d) −3
e) −2
13. The quadratic function f is given by f(x)
= ax2 + bx + c, where a is a negative real
number and c is a positive real number.
10. Find the surface area in square meter of
Which of the following is the possible
the half of a rectangular solid as shown
graph of f(x)?
above.
a)
a) 44
b) 36
c) 34
d) 32
e) 26
b)
15. If x and y are non-zero integers, what is
x percent of y percent of 2000?
a) xy
b) 5xy
c) c) 10xy
d)
16. July 4th, 2014 is a Friday. What day of
the week is July 4th, 2050?
a) Sunday
b) Monday
c) Thursday
e) d) Friday
e) Saturday
14. To get a job done, a machine needs to
produce x boxes of toys, in which each
box contains y toys. If this machine runs
10 hours per day and produces an
average of z toys per minute, how many
days will it take to finish the job?
