Welcome to the 2015 Alabama School of Fine Arts Math Tournament!

• Silence all electronic devices at this time.• Respect cipherers by remaining quiet during

ciphering rounds

• Two minutes per question• Correct in 1st minute = five (5) points• Correct in 2nd minute = two (2) points.

• Five-second warning given before end of each time interval• Do not put your paper in the air until the warning is called.

• If you do not have your hand in the air before that time interval changes, you will not have your paper taken up.

• Runners are behind you to collect papers.• They will wait until the time interval has expired before collecting your paper.

• If you did not get your answer before the first time interval expires, please keep working. • ALL ANSWERS MUST BE WRITTEN IN THE ANSWER BOX ON YOUR ANSWER SHEET.

• CORRECT ANSWERS NOT IN THE ANSWER BOX WILL NOT BE COUNTED. • No units except for money (dollars and cents signs).

• However, if an incorrect unit is included in your answer, the answer will be marked wrong. • Reduce fractions

• Proper or improper• Mixed numbers

• Questions with percents as a solution should be written as a percent and not as the fraction or decimal equivalent.

• Leave π in your answers unless the problem tells you to substitute a value for π. • No radicals in the denominator when in fractional form• No fractions under a radical. • All radicals must be simplified.• All answers must be simplified,

Please send round 1

cipherers.

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

If you throw a standard 6 sided die, what is the

probability of rolling a 6?

6th

GRAD

EGE

OMET

RY

In tessellations, the sum of the interior angles at a point where several polygons meet

is _____.

166th G

RADE

GEOM

ETRY 360°

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

How many 2-digit prime numbers have a 1 in the unit’s

place?

6th

GRAD

EGE

OMET

RY

The side of the largest square in the diagram is 4 5. Assuming that each smaller square is created using the midpoints of the sides of each larger square, calculate the area of the shaded region. Express your answer in

decimal form.

5

52.5

6th

GRAD

EGE

OMET

RY

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

What is the next number in the sequence: 1, 31, 59, 85?

6th

GRAD

EGE

OMET

RY

A square is inscribed in a circle with radius 5

2. Find the area of

the region outside of the square but inside of the circle.

109

5𝜋𝜋 − 104

6th

GRAD

EGE

OMET

RY

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

A rectangle has a width of 46 cm. Its area is 92 cm2. Find the

perimeter.

6th

GRAD

EGE

OMET

RY

Find the area of the shaded circular segment if 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 120° and the radius

of ⨀𝑚𝑚 = 12.

96 𝑜𝑜𝑜𝑜 96𝑐𝑐𝑚𝑚6t

h GR

ADE

GEOM

ETRY 48𝜋𝜋 − 36 3

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

Juan has 5 shirts, 3 pants, 3 pairs of dress shoes, and 2 pairs of tennis shoes. How many different combinations of outfits can he make if an outfit consists of 1 shirt, 1 pair of pants,

and 1 pair of shoes? 6th

GRAD

EGE

OMET

RY

You are given the sides of a scalene triangle to be 6, 8, and 4. Let 𝑚𝑚 be the

area of the triangle, and 𝑚𝑚 be the sum of 𝑚𝑚 and the perimeter of the triangle. Find

𝑚𝑚 + 𝑚𝑚 in simplest form.

756t

h GR

ADE

GEOM

ETRY

6 15 + 18

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

Half of 60% of what number is 6?

6th

GRAD

EGE

OMET

RY

Find the ratio of the volume of a sphere to the volume of a cube

inscribed inside of that same sphere if the space diagonal of the cube is

18.

20

𝜋𝜋 32

6th

GRAD

EGE

OMET

RY

Please send round 2

cipherers.

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

Katlin saves a quarter a day, but spends a dollar a week. How much

money does she have after 4 weeks?

6th

GRAD

EGE

OMET

RY

A triangle has perimeter of 68. The length of one side is twice the length of the

smallest side. The remaining edge is 5 greater than twice the smallest side. Find the length of the longest side in improper

fraction form.

$3

1515

6th

GRAD

EGE

OMET

RY

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

6th

GRAD

EGE

OMET

RY

𝑃𝑃𝑃𝑃 is the diameter of ⨀𝑚𝑚. 𝑀𝑀𝑀𝑀is tangent to ⨀𝑚𝑚 at point 𝑃𝑃. The

measure of angle 𝑚𝑚𝑃𝑃𝑀𝑀 is 32.7°. Find the measure of angle 𝑚𝑚𝑚𝑚𝑃𝑃 in

degrees.

O

L

P

C

A

B

M N

The Grinch steals presents at a rate of 5 presents per minute.

How many presents can he steal in 2.5 hours?

750

114.6°

6th

GRAD

EGE

OMET

RY

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

Find the average of the first 5 composite numbers.

6th

GRAD

EGE

OMET

RY

What is the diameter of a circle if the circle’s area is equal to the area of a

triangle with an altitude of 4𝜋𝜋 and a base of 32?

375

16

6th

GRAD

EGE

OMET

RY

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

A machine makes 15 bottles per minute. How many bottles does the machine make in 1 1

3hour?

6th

GRAD

EGE

OMET

RY

Each corner of an inner square bisects the side of its outer

square. If the area of the innermost square in the diagram

is 15, what is the area of the outermost square?

1,200

3840

6th

GRAD

EGE

OMET

RY

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

(5 � 6 � (−3))(22(6) − 132)(4)(−3 � 20)(3)

6th

GRAD

EGE

OMET

RY

Find the number of diagonals of a regular

polygon with interior angle measures of 165°.

06t

h GR

ADE

GEOM

ETRY 252

Please send round 3

cipherers.

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

Simplify:2𝑏𝑏𝑎𝑎3𝑐𝑐

6𝑛𝑛𝑛𝑛𝑜𝑜𝑎𝑎2𝑏𝑏2

6th

GRAD

EGE

OMET

RY

Six congruent spheres of maximum size are packed in a box with dimensions of 6, 9,

and 3 inches. What is the volume, in cubic inches, inside of the box but outside of the

spheres?

𝑎𝑎𝑐𝑐3𝑛𝑛𝑛𝑛𝑜𝑜𝑏𝑏

162 − 27𝜋𝜋

6th

GRAD

EGE

OMET

RY

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

Find x:

𝑥𝑥 = 12[6 8 102

123

24]

560

6th

GRAD

EGE

OMET

RY

Square ABCD and rectangle ALMN are shown on the diagram,

along with a circular arc with center B. Let M be any point on the quarter circle having radius of 41 and 𝑀𝑀𝑀𝑀 = 6. Find the area

of ALMN.

A B

CD

MN

L

10

2 114

6th

GRAD

EGE

OMET

RY

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

If Vanessa is allowed 1.2 minutes to work each multiple choice question and 3.4 minutes to work each free response question, how many minutes is she allowed to complete a test with 7 multiple choice questions and 3 free response questions? 6t

h GR

ADE

GEOM

ETRY Find the area of a regular

hexagon inscribed inside of a circle with radius 1.

18.66t

h GR

ADE

GEOM

ETRY 3 3

2

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

Suppose for a math tournament the first place trophies are 18 inches tall, the second place trophies are 16 inches tall, and the third place trophies are 14 inches tall. Suppose a particular math team manages to get 3 first place trophies, 3 second place trophies, and 3 third place trophies. How many inches in height of trophies did they win? 6t

h GR

ADE

GEOM

ETRY

The coordinates of the vertices of triangle ABC are A(56, 35), B(6, 6), and C(16, 16).

What is the length of median AM?A

B

CM

144 𝑜𝑜𝑜𝑜 144 𝑖𝑖𝑛𝑛𝑐𝑐𝑖𝑖𝑖𝑖𝑖6t

h GR

ADE

GEOM

ETRY 51

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

Simplify the following:4(3−2)

6− 6 8−4 −2�11

6÷36th

GRAD

EGE

OMET

RY Find the altitude to side BC.

A

B C

15

98

10°6t

h GR

ADE

GEOM

ETRY 16 14

15

Please send round 4

cipherers.

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

Diagonals of a polygon are interior line segments connecting non-adjacent vertices. How many distinct diagonals can be drawn within a hexagon? 6th

GRA

DEGE

OMET

RY

Three congruent circles are tangent as shown. Their centers lie on the same line 𝑃𝑃𝑃𝑃. Line 𝑃𝑃𝑃𝑃 is drawn from point P on the left circle and tangent to the right circle at point T. Find the ratio of the length of chord XY of the

middle of the circle to the length of the radius of the middle circle.

P Q

T

YX

9

85

6th

GRAD

EGE

OMET

RY

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

Victor wants to buy a new ASFA sweatshirt. The sweatshirt is on sale for 75% off the original price of $16 before tax. If sales tax is 10%, how much will Victor spend on the sweatshirt?

6th

GRAD

EGE

OMET

RY

Two coplanar circles have radii of 17 and 34, and the distance between their centers is 36. Find the length of the

common external tangent of the two circles.

$4.40

1007

6th

GRAD

EGE

OMET

RY

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

The hypotenuse of a right triangle is 13 cm. One leg is 12 cm. Find the area of the right triangle.6th

GRA

DEGE

OMET

RY

Square ABCD has a side length of 32. M and N are midpoints of sides AD and CD respectively. Fine the

area of triangle BMN.D

A B

C

M

N

𝑚𝑚 = 306t

h GR

ADE

GEOM

ETRY 384

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

What is 30% of 135?6t

h GR

ADE

GEOM

ETRY

The area of the smaller base of a frustum of a right circular cone is 16𝜋𝜋, and the

height of the frustum is 3. If the diameter of the larger base of the frustum is 2 64,

what is the volume of the frustum?

40.5

112𝜋𝜋

6th

GRAD

EGE

OMET

RY

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

Find the surface area of a cube with a side length of 6 inches? 6th

GRAD

EGE

OMET

RY Find the area of a square inscribed in a semicircle having a diameter of

10.

216 in26t

h GR

ADE

GEOM

ETRY

20

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

Solve for x:−15𝑥𝑥 + 7 = 32

6th

GRAD

E

−1256t

h GR

ADE

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

6th

GRAD

E Krishna and Jacob are both driving motorcycles to New York along the same route. If they start from the same location and Jacob leaves at 2:00PM with a constant speed of 72mph and Krishna leaves 20 minutes later at a constant speed of 75mph, how far ahead of Krishna is Jacob at 5:20 PM?

15 𝑚𝑚𝑖𝑖𝑚𝑚𝑖𝑖𝑖𝑖6t

h GR

ADE

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

6th

GRAD

E Simplify the following expression:62 − 2 − 5 − 4 32 + 4 32 + 7 − 2 5 + 3

36 − 12 36t

h GR

ADE

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

6th

GRAD

EPriya, Jasmin and Cordy go to their favorite Mexican restaurant. Priya gets queso and a drink for $5.50, Jasmin gets queso and taco for $7.50 and Cordy gets two tacos for $7.00. How much is a meal consisting of queso, a taco and a drink at their favorite Mexican restaurant?

$9.006t

h GR

ADE

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

6th

GRAD

E If x! denotes x(x-1)(x-2)(x-3)…(2)(1), the find 6!4!

2!3!5!.

126t

h GR

ADE

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

What is the positive geometric mean between 53 and 123?

GEOM

ETRY

6519

GEOM

ETRY

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

An octahedron has a side length of 5. Find its

volume.GEOME

TRY

GEOM

ETRY 125 2

3

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

Find the smaller angle formed by the minute and

hour hands of a clock at 3:16.GE

OMET

RY

2°

GEOM

ETRY

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

A person starts at (6, 3) moves up 1, right 5 and down 4. Find the line

between the initial point and final point in slope-intercept form.GE

OMET

RY

𝑦𝑦 =−35𝑥𝑥 +

335GEO

METR

Y

2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End

Simplify completely: 117𝑥𝑥2 − 13

GEOM

ETRY

13(3𝑥𝑥 − 1)(3𝑥𝑥 + 1)

GEOM

ETRY

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