R - S - T (1982 F.) If are real and then find. 2. (1986 P.) If then find. 3. (1984 P.) If and then find and

R - S - T - 12 1. (1982 F.) If are real and then find . 2. (1986 P.) If then find . 3. (1984 P.) If and then find and . 4. (1977 J.) and are ...
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R - S - T - 12 1. (1982 F.) If

are real and

then find .

2. (1986 P.) If

then find .

3. (1984 P.) If

and

then find

and .

4. (1977 J.) and are positive integers. The sum of the digits of is and the sum of the digits of is . If the addition involves exactly carriers, find the sum of digits of . 5. (1964 J.) could do a job in 6 days, could do the job in 4 days. Together, how long would it take them to do the job? 6. (1985 G. adapt) The dimensions of a cube are tripled. How many of the original cube would fit in the new cube? 7. (1971 J.) Given trapezoid of trapezoid is . Find area

with . B

5

A

and height

E

9

D

C

8. (1968 J. - hard) In ratio

10

and

. Find the ratio of area

divides

to area of

.

A X

Z

Y B

internally in the

C

S - T - 12 1. (1984 P.) If

find

when

.

2. (1978 J.) is divided into 4 equal parts and semicircles on and creating paths from to as shown. Find the ratio of upper path to lower path.

3. (1983 P.) If the 4 digit number

A

D B

E

C

is a perfect square, then find

.

4. (1964 J. - adapt) A woman travels 100 km at km/hr, 400 km at km/hr and 600 km at km/hr. Find her average speed in km/hr for the entire trip. 5. (1982 J.) The sides of a triangle are 10, 24 and 26. Find the perpendicular distance from the midpoint of the shortest side to the longest side. 6. (1988 P.) If the reciprocal of ( 7. (1982 F. - hard) Find

) is

, then find .

in the parallelogram.

8. (1989 F.) A cable is formed of wires with radius 2 units as shown. A band is wrapped tightly around the system. What is the length of band?

Band

R - S - T - 13

1. (AMC-10 2001) If figure square √ and . What is the area of inner square A

is between ?

and

B E H

F G

D

C

2. (AMC-10 2001) How many positive cubes divide 3. (AMC-12 1981) For

, evaluate

?

.

4. (AHSME 1981) If 3 times the larger of two numbers is 4 times the smaller and the difference between the numbers is 8, then find the larger number. 5. (AHSME 1981 - adapt) The base representation of is . Write the base representation of . 6. (AHSME 1986) Find ( 7. (AHSME 1988) If 8. (AHSME 1984) Find

)(

)

and

(

then find .

)( .

).

S - T - 13

1. (AHSME 1984) If

and

, then find

2. (AHSME 1984) Find all (

)

.

if {

3. (AHSME 1984) Find the largest integer for which 4. (AHSME 1984) and

.

is a trapezoid with . Find . A

√ ,

and

B 3√

D

60°

45°

5. (AHSME 1979) Find

C

.

6. (AHSME 1990) is a parallelogram, Extend to with . If intersects E

D

A

7. (1990 - adapt) Find ( )

. to , then find

.

C

B

.

8. (AHSME 1990) How many positive integers less than 50 have an odd number of positive integer divisors?

R - S - T - 14

1. (2009 CTT) What is the LCM of positive even numbers less than fourteen? 2. (2009 CTT) What is the mean of the mode, median and range of the data }. set { 3. (2009 CTT - modified) Find the -intercept of the line the line hits -axis)

. (pt. where

4. (2009 CTT - modified) Find the -intercept of the line

.

5. (new) Find distance between answers in # 3 and # 4. 6. (2009 Dec. CNML) A shaded square has its vertices at points which divide the sides of a large square into segments whose lengths are in ratio 3 : 4. What is the ratio of the area of shaded square to the area of large square?

7. Find the equation of the line through (

) with slope 5.

8. (2009 CTT) Find the surface area of a right square pyramid with base lengths of 6 cm and height of 4 cm.

R - S - T - 14 1. (Open 2009) If negative integers, then find (

and

and

are non

).

2. (A&P 2009 Math League) The point ( ) is reflected in the line to ) to point . What are point . Then the point is reflected in -axis ( the coordinates of ? P 3. (Open 2009) In . If the area determine the length of

and is , . Q

4. (A&P 2009 Math League) If √

√ what is

R

T

?

B C

A

5. (Open 2009) A polygon is called regular if all its sides and all its angles are equal in size. In the diagram a portion of a regular polygon is shown. If how many sides does the polygon have?

120° D

6. (Cayley 2004) Find the value of

7. (Cayley 2004) In the diagram, lie in straight line, with and Find .

.

A

and .

100°

B

D

C P

8. (Cayley 2004) In the diagram, and . Find

T

. Q

128°

R

S - T - 14

1. (CTT 2009) If four people can build nine widgets in 25 minutes, how many people would you need to build 45 widgets in 10 minutes? 2. (CTT 2009) What value(s) of

satisfy

.

3. (CTT 2009) What is the largest possible volume in cubic centimeters by rolling a 6 cm by 8 cm piece of paper into a cylinder. 4. (CNML Dec. 2009) If

what is the value of

?

5. (New) When 3 fair six sided dice are rolled, what is the probability that the total of the up faces is six? 6. (CNML Dec. 2009) The 6-digit number ends in a 6. Transferring the 6 from the last place to the first place, and leaving the other digits unchanged relative to one another, results in the same number that one ) would get by multiplying the original number by 4, i.e. ( . Find . 7. (Cayley 1997) Find .

8. (Cayley 1997) In a convex polygon, exactly five of the interior angles are obtuse. Find the largest possible number of sides.

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