March 31, 2009
2009 State Math Contest
Wake Technical Community College
Algebra I Test
1. A popular platform in skateboarding is the half-pipe pictured to the right.
Assume a skateboarder begins on one side and skates to the other side. Which
of the following graphs is the best representation of total distance travelled
versus time?
a.
b.
c.
d.
e.
2. Tom rode his bike 3.5 miles in 12 minutes. What was his average speed in miles per hour?
a. 16.5 mph
b. 17 mph
c. 17.5 mph
1
d. 18 mph
e. 18.5 mph
2009 State Math Contest
Wake Technical Community College
Algebra I Test
3. Chris paid $51.84 for a dress. From the tag she saw that first the store had marked it down 20%, and
then decided to mark it down an additional 40%. What was the original price of the dress?
a. $162.00
b. $108.00
c. $129.60
d. $172.80
e. $86.40
4. Line L has equation y = 2 x + 3 . Line M is perpendicular to line L and has the same y-intercept as L.
Which of the following points lies on line M?
a.
(− 4,5)
5. A recipe calls for
make?
a.
1
2
b. (− 2,5)
1
2
c. (− 1,5)
cup of sugar. You only have
b.
1
c.
3
1
d. (1,5)
3
2
3
e. (4,5)
cup of sugar. What fraction of the recipe can you
d.
1
e.
6
5
6
6. Jamie can mow the yard in 75 minutes and it takes her brother only 50 minutes. If they borrow the
neighbor’s mower how many minutes to the nearest minute would it take if they worked together?
a. 36
b. 33
c. 32
d. 31
e. 30
7. A classroom contains twice as many boys as girls. If 8 girls leave, four times as many boys as girls
remain. What was the original number of students present?
a. 48
b. 40
c. 36
d. 32
2
e. 24
2009 State Math Contest
Wake Technical Community College
Algebra I Test
8. If a 2 = a + 2 , then which of the following represents a 3 ?
a. a + 4
b. 2a + 2
c. 27 a + 8
d. 3a + 2
e. 4a + 8
9. Robin thinks of three numbers. If they are added in pairs the results are 38, 44, and 52. What is the
largest of these numbers?
a. 27
b. 29
c. 31
d. 24
e. 28
10. Office Depot provides an online copy service for 9¢ per page. I could print from home where the cost is
4.8¢ per page, but I must also purchase printer ink which costs $63. How many copies would I have to
make in order for the costs to be the same?
a. 1600
b. 1550
c. 1500
d. 1450
e. 1400
11. If x = −1 is one solution of ax 2 − bx − c = 0 , what is the other solution?
a.
x=−
a
b
b. x = −
b
a
c. x = −
c
a
d. x =
c
a
e. x =
b
a
12. Ryan told Sam that he had 9 coins worth 45¢. Sam said, “There is more than one possibility. How
many are pennies?” After Ryan answered truthfully, Sam said, “Now I know what coins you have.”
How many nickels did Ryan have?
a. 0
b. 3
c. 4
d. 5
e. 9
13. Ted scored 96 on his last test in History and raised his test average from 82.5 to 84. What does he need
to score on his next test to increase his test average to 85?
a. 93
b. 94
c. 95
d. 96
3
e. 97
2009 State Math Contest
Wake Technical Community College
Algebra I Test
14. Mrs. Smith required her students to bring 8 colored pencils to art class each day. One day she noticed
that all the girls had their 8 pencils and all the boys had lost one of their pencils. In total the students
had 118 colored pencils that day. What is the ratio of girls to boys in the art class?
a. 7:8
b. 5:6
c. 3:4
d. 2:3
e. 3:5
15. On April 12, 1790, the colony of Jamestown had among its remaining rations 10,840 kilograms of pork
at the end of the day. There were 590 people to feed and it was estimated that this pork would last until
August 26, 1790. Which of the following best approximates the average daily ration of pork per person?
a. 135 grams
b. 0.135 grams
c. 184 grams
d. 13.5 grams
e. 18.4 grams
16. A pizza parlor offers 4 toppings. How many different pizzas can a customer order, assuming there is a
choice of 0 to 4 toppings?
a. 16
b. 24
c. 29
d. 32
e. 120
17. If Samantha loses 20% of an investment during the first year and gains 25% of what is left the following
year, what is her net gain over the two years?
a. 5%
b. 2%
c. 4%
d. 1%
e. 0%
18. If x > 7 , which of the following is smallest?
a.
7
x
b.
7
x +1
c.
x +1
7
d.
7
x −1
e.
x
7
19. How many prime numbers less than 200 have 7 as the units digit?
a. 10
b. 11
c. 12
d. 13
4
e. 14
2009 State Math Contest
Wake Technical Community College
Algebra I Test
20. At a party there were 20 students. Shirley danced with seven boys, Diane with eight boys, Debby with
nine boys, and so on for all the girls until the last girl Kathy who danced with all the boys. How many
boys were at the party?
a. 14
b. 13
c. 12
d. 11
e. 10
21. An upholsterer purchased some fabric for $240. She found the same material selling for $4 a yard more
at another store. If she had purchased the fabric at the higher price, she would have received 3 yards less
material for her $240. How many yards did she purchase?
a. 16 yd
b. 10 yd
c. 12 yd
d. 15 yd
e. 14 yd
22. An energy-conscious homeowner makes three successive improvements that save, in turn, 20%, 25%,
and 55% on the heating costs of the house. What is the overall percentage saved?
a. 33%
b. 97.25%
c. 68%
d. 73%
e. 100%
23. Before a basketball game, the five starting players on the team are going to be weighed. After each
player is weighed, the average weight of players already weighed is calculated. How much heavier is
the heaviest player than the lightest one if after every weighing the average weight of the players
increases by one pound?
a. 12 lb
b. 10 lb
c. 8 lb
d. 6 lb
e. 4 lb
24. Summit Plummet at Disney World is billed as the most thrilling freefall waterslide in the country. It is
120 feet high and the slide is 351 feet long. Daredevil Drop, the freefall waterslide at Emerald Point, is
76 feet high. What would the length of the slide need to be to have the same slope as Summit Plummet?
a. 222.3 ft
b. 235.4 ft
c. 228.6 ft
5
d. 236.2 ft
e. 228.5 ft
2009 State Math Contest
Wake Technical Community College
Algebra I Test
25. Thom was bored one snow day and decided to make up what he called Phone Math. He told his Mom
that BAT + NET = TON. She asked what BAG + KID equaled. Using your knowledge of the phone
which of the following words would be possible?
a. PUP
b. PEP
c. RIP
6
d. POP
e. SAP
2009 State Math Contest
Wake Technical Community College
Algebra I Test
SHORT ANSWER
Place the answer in the appropriate space.
66. A farmer loads his wagon with 1000 kilograms of watermelons to take to the market. At the start of the
trip they are 99% water but partly dry out through evaporation on the trip. At the end of the trip the
watermelons are only 98% water. How much do the watermelons weigh at the end of the trip?
67. What is the second smallest whole number to be squared that yields a 7 as one of the digits of its
product?
68. The sum of eleven consecutive whole numbers is 1,358,024,688,642,030. What is the difference
between the largest and the smallest of these numbers?
69. The schools in an athletic conference compete in a cross-country meet to which each school sent three
participants. Eric finished the race in the middle position; Joe finished after Eric, in 19th position; and
Sam finished 29th. How many schools are there in the conference?
70. A bracelet is made by threading 3 identical red beads and 3 identical yellow beads onto a hoop. How
many different arrangements of the 6 beads can be made?
7
2009 State Math Contest
Wake Technical Community College
Algebra I Test
1. e
2. c
3. b
4. a
5. c
6. e
7. a
8. d
9. b
10. c
11. d
12. e
13. b
14. e
15. a
16. a
17. e
18. b
19. c
20. b
21. d
22. d
23. c
24. a
25. d
66. 500 kg
67. 26
68. 10
69. 11
70. 3
8
2009 State Math Contest
Wake Technical Community College
Algebra I Test
1. Graph a would only be appropriate if the skateboarder was travelling at a constant speed. The
skateboarder’s speed is fastest in the middle of the half-pipe; hence the graph should be the steepest in
the middle of the graph. Graph e is the only graph that has this property.
2.
3.5
= 17.5
0.2
3. 0.6(0.8 x ) = 51.84 ⇒ 0.48 x = 51.84 ⇒ x = 108
4. Line M has equation y = −0.5 x + 3 . The only point lying on this line is (− 4,5) .
1
5.
6.
1
3
2
=
2
3
x
x
+
= 1 ⇒ 50 x + 75 x = 3750 ⇒ x = 30 .
75 50
7. Let x be the number of girls in the class, then 2x is the number of boys. Using the second sentence this
gives 4( x − 8) = 2 x ⇒ 4 x − 32 = 2 x ⇒ x = 16 . Hence there were 32 boys in the room originally.
8. a 3 = a (a 2 ) = a(a + 2) = a 2 + 2a = a + 2 + 2a = 3a + 2
9. Let x, y, and z be the three numbers. Then x + y = 38 , x + z = 44 , and y + z = 52 . Solving this system
of equations the numbers are 15, 23, and 29.
10. 0.09 x = 0.048 x + 63 ⇒ x = 1500 .
11. If x = −1 is a solution then one of the factors is (x + 1) . The other factor must be (ax − c ) . Hence the
c
other solution is x = .
a
12. The only possibilities are 5 pennies and 4 dimes; 5 pennies, 3 nickels, and a quarter; and 9 nickels.
Since Sam knew the answer after knowing how many pennies, then Ryan must have 9 nickels.
82.5 x + 96
= 84 . Solving this
x +1
equation we get that x is 8 tests. To be able to have an 85 average on 10 tests then Ted must score
85 * 10 − 84 * 9 = 94 on his tenth test.
13. Let x be the number of tests that Ted took before he made the 96, then
14. Everyone in class has seven pencils. 118 divided by 7 is 16 with a remainder of 6. That means there are
6 girls and 16 total students. Hence the ratio of girls to boys is 3:5.
15. There are 136 days between April 12, 1790 and August 26, 1790.
grams.
9
10840
= 0.135 kilograms or 135
136(590)
2009 State Math Contest
Wake Technical Community College
Algebra I Test
16. There is one pizza with no toppings; 4 different pizzas with one topping; 6 different pizzas with two
toppings; 4 different pizzas with 3 toppings; and one pizza with all four toppings. That makes 16
different pizzas.
17. Let x be Samantha’s initial investment amount, then 1.25(0.8 x ) = x . So her net gain is 0%.
18. Since x > 7 , choices b and e are greater than 1. When comparing choices a, b, and d, since the
numerators are all the same we need the fraction with the largest denominator which is x + 1 or choice b.
19. They are 7, 17, 37, 47, 67, 97, 107, 127, 137, 157, 167, and 197.
20. Girl 1 danced with 7 boys; Girl 2 danced with 8 boys; Girl 3 danced with 9 boys; Girl 4 danced with 10
boys; Girl 5 danced with 11 boys; Girl 6 danced with 12 boys; and Girl 7 danced with 13 boys. That
gives 20 students so there are 13 boys.
21. Let x be the price per yard at store one and y be the number of yards purchased, then xy = 240 and
(x + 4)( y − 3) = 240 . Solving these equations simultaneously gives y = 15 yds.
22. Let x be the original heating costs of the house, then the new heating costs are 0.45(0.75(0.8 x )) = 0.27 x .
This is a 73% overall savings.
23. Let x be the weight of the first player, then the second player must weigh x + 2 to give an average of x +
1. Similarly, the third player must weigh x + 4 to give an average of x + 2. Continuing in this manner
we find that the fifth player must weigh x + 8. That gives a difference of 8 pounds between the first and
last player.
24. Let x be the length of the slide, then
351 x
=
. So the length of the slide is 222.3 ft.
120 76
25. BAG = 224 and KID = 543 so BAG + KID = 767 and the only word possible is POP.
66. The non-water weight is 10 pounds. At the end that makes up 2% of the total weight
10
= 500 kg.
0.02
67. 24 is the first one with a square of 576. 26 is the second one with a square of 676.
68. The difference between the first and last numbers of eleven consecutive whole numbers is 10.
69. The total number of participants must be an odd number (there was a middle position), must be a
multiple of three, and must be greater than 29. The first possible one is 33 which works because the
middle position is 17th which is before 19th. The next possible value is 39 which will not work since the
middle position is 20th which after 19th. Hence, there were 11 schools.
70. There are only 3 possibilities. All three beads of the same color together; no bead next to another bead
of the same color; and two beads of the same color together. The reason there are so few is because it is
a bracelet and can be flipped and turned.
10