12
π π π ===
1
FTTS MATH CHALLENGE 2013 Grades 9 & 10
FT
TS M
AT
H C
HA
LLEN
GE 2
013 D
ecem
ber
13,
2013
INSTRUCTIONS
1. Do not open the booklet until you are instructed to do so.
2. The duration of the test is 75 minutes.
3. The test is composed of 30 multiple choice items. Use the information pro-
vided in each item to choose the best answer from the four possible options.
4. On the answer sheet, write your name, school, and other information cor-
rectly. Use only a mongol no. 2 pencil. Do not use a pen.
5. Completely shade the circle that corresponds to your answer on the answer
sheet.
6. Mark only one circle for each question on the answer sheet. If more than one
circle is shaded, it will automatically be considered an incorrect answer.
7. To change an answer, erase any error completely on the answer sheet and
mark your new answer.
8. Talking, cheating, and assisting others during the test are strictly prohibited.
These are grounds for disqualification. Leaving the room while the test is
going on is also prohibited.
10. Submit the answer sheet to the proctor assigned at the end of the test.
Grades 9 & 10
2
11
FTTS MATH CHALLENGE 2013 Grades 9 & 10
19 17
20 18
10
1
16
49
256
81
128
65
128
On the dartboard below, the proba-
bility of hitting a certain region is pro-
portional to its corresponding area. The
outer circle has a radius of 4 and the
inner circle has a radius of 2. The two
diameters divide each circle into 4
equal parts. If two darts hit the board,
what is the probability that the score is
an even number?
a. b.
c. d.
Maria, Rai and Sharmaene have
their birthday today. The sum of
their ages is 30 and the product of
their ages is 270 more than the prod-
uct of their ages on their birthday
last year. What is the sum of the
squares of their ages?
a. 90 b. 109
c. 302 d. 810
30 29
16
S T O P
Check Your Work
3
FTTS MATH CHALLENGE 2013 Grades 9 & 10
1 12x y
x y
2
2
2
2
1
1
xx
yy
40 60
80 100
36003240
3420 3060
Solve
a. 1 b.
c. 0 d. – 1
If , then what is
the value of ?
a. 1 b. 2
c. 3 d. 4
3 1
What is the sum of the interior
angles of a polygon with 20 sides?
a. b.
c. d.
In the figure below, AB DE.
Solve for the value of x.
a. b.
c. d.
4 2
1 1 1 1 1 1...
2 3 4 9 8 27
1
2
A B
D
E x
4
3 2 5 6 0x kx x
6 2
4
6 2
4
1
2
1
4
The symbol m e a n s
”older than”. For example, if
Grace Liz
,then Grace is older than Liz. Based
on the illustration below, who is the
oldest?
a. Ali b. Patrick
c. Muktar d. Qas
If one root of
is 2, then what is the sum of the
other two roots?
a. 2 b. 1
c. 0 d. – 1
7 5
Fatima wants to make a bracelet,
composed of beads, for her friend
Nor. If she has blue, yellow, red,
orange, and green beads, in how
many ways can the beads be ar-
ranged in the bracelet?
a. 3 b. 6
c. 9 d.12
Calculate
a. b.
c. d.
8 6
sin15
9
FTTS MATH CHALLENGE 2013 Grades 9 & 10
3
3
1 1( )f x x
x x ( )f x
1x
x
3
3
1x
x
3 3x x
3 3x x
4 3
3 2
42 3
3
55 3
3 2
Kath has a broken calculator. If
the + (addition) key is pressed, it
adds 46; when the – (subtraction) key
is pressed, it adds –46; if the ×
(multiplication) key is pressed, it
adds 69; and when the ÷ (division)
key is pressed, it adds –69. If the oth-
er keys do not function, what number
closest to 2013 can Kath get from the
calculator which, when turned on,
displays 0?
a. 2001 b. 2012
c. 2018 d. 2024
Sorted numbers are positive
numbers, with two or more digits,
such that the digits from left to right
are strictly in increasing order. 34,
123 and 479 are examples of sorted
numbers but 122, 63, and 294 are
not. If the sorted numbers are listed
in increasing order, what is the 64th
sorted number?
a. 149 b. 169
c. 189 d. 239
27 25
If , find .
a. b.
c. d.
In the figure below, the circles
are arranged in such a way that 1/6 of
the circumference of one circle is in-
side another circles. If all the circles
are of radius 1, what is the total area
of the shaded regions?
a. b.
c. d.
28 26
8
7 12
4 15
3 B
4 6
2
2 1
A
(12 2 12)cm
(12 2 12)cm
12 2cm
12cm
2 4 ... 0.125x x 2
1 ... 1.4 16
x x
30 2 15 2
30 5 15 5
In the figure, B and D are centers of
two circles. If ABCD is a square and
the area of the shaded region is 36 π
cm2, what is the length of |DE|?
a.
b.
c.
d.
What is the area of the triangle
below?
a. b.
c. d.
23 21
Solve for x if
and
.
a. – 3 b. 3 and – 3
c. – 2 and – 1 d. 0
Based on the figure above, what is
the value of A + B + C?
a. 19 b. 24
c. 25 d. 28
24 22
11
10
C
B
A
9
5
11 3
4 2
C
5
FTTS MATH CHALLENGE 2013 Grades 9 & 10
2( )f x ax bx c
21 1 1f x f x f x x
2f
5
3
7
9
13
9
13
3
22 a
2a log 5
In a certain city, all telephone num-
bers are composed of 7 digits and
always start with either 9 or 8. If a
telephone has its 2 and 5 buttons
defective, how many phone num-
bers can it dial?
a. 40,320 b. 524,288
c. 10,080 d. 2,097,152
In the figure, |O1O2| = 5 cm and
r1 + r2 = 17 cm. Find the values
of r1 and r2.
a. r1 = 11cm, r2 = 6 cm
b. r1 = 6 cm, r2 = 11 cm
c. r1 = 12 cm, r2 = 5 cm
d. r1 = 4 cm, r2 = 13 cm
11 9
If and
, what is the value of ?
a. b.
c. d.
Calculate if . .
a. 5 b. 25
c. 32 d. 16
12 10
6
ln(2 1) log10 1x xe
In the figure above, What is the val-
ue of tan x if all the squares are con-
gruent and of side 1 unit?
a. 4 units b. 3 units
c. 2 units d. 1 unit
Solve for x if .
a. 0 b. 1
c. 2 d. 3
15 13
How many two – digit positive in-
tegers xy can satisfy the equation
(x – 2)2 + (y – 1)2 = 0?
a. 4 b. 3
c. 2 d. 1
A ball is dropped from a height of 5
meters. It falls and bounces by 3/5
of its previous height. On which
bounce will it first not rise to a
height of more than 1/2 meter?
a. 4th bounce b. 5th bounce
c. 6th bounce d. 7th bounce
16 14
7
FTTS MATH CHALLENGE 2013 Grades 9 & 10
2 2
2 2
6 6 632 32 32...
(5k – 4)x – ky + 3 = 0 and
y = (k+1)x – 3 are equations of
lines. If these lines are parallel, what
is the value of k?
a. b.
c. d.
Find the remainder when 20132013
is divided by 15.
a. 3 b. 6
c. 9 d. 12
19 17
Cesar went to a mall to buy school
supplies he needed for the entire
school year. He bought three types
of school supplies: notebooks, pen-
cils, and erasers.
All he bought except 18 are
notebooks.
All he bought except 21 are
pencils.
All he bought except 19 are
erasers.
How many notebooks did he buy?
a. 8 b. 9
c. 10 d. 11
Solve .
a. 0 b. -1
c. -2 d. undefined
20 18
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