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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