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Grade 7
Arithmetic
Meet 2
2011-2012
1)
Evaluate and express your answer as a mixed number in lowest terms:
10 2  80
40  6 2

5 2  20 16  (24)  3
Answer: __________ (2 pts)
2)
The sum of four consecutive even integers is 236. What is the sum of the largest and
smallest of these four integers?
Answer: __________(3 pts)
3)
A * B  (A  B) 2  A  B. Find the value of 6*4.
Answer: __________(4 pts)
4)
The modes of 6 numbers are 9 and 12. The mean of these numbers is 13. If the difference
of the two remaining numbers is 26, what are the other two numbers?
Answer: _____, _____(5 pts)
5)
Sally works at a store that gives a 10% discount off the sale price to its employees.
During a store-wide sale where everything was 20% off, she bought an $80 sweater and a
$60 pair of shoes. After the two discounts and 6% sales tax, how much did Sally pay?
Answer: __________(6 pts)
Grade 7
Geometry
Meet 2
2011-2012
1)
The dimensions of a rectangular prism are 2 feet x 3 feet x 2 feet. What is the volume in
cubic inches of the rectangular prism?
Answer: ____________in3_ (2 pts)
2)
A solid rectangular prism of a certain metal with dimensions 4 feet x 5 feet x 2 feet is
worth $1120. How much would the same metal be worth if the dimensions changed to 3
feet x 6 feet x 4 feet?
Answer: $______________(3 pts)
3)
2
x . The sides of another rectangle are x and 1.5x.
3
The perimeter of the larger rectangle is 60 inches. What is the sum of the area of the
two rectangles?
The sides of one rectangle are x and
Answer: ____________sq. in. (4 pts)
4)
A regular hexagon, with side length x feet, shares four sides with four regular pentagons and
two sides with squares. What is the perimeter of this figure?
Answer:____________feet_(5 pts)
5)
Four circles all with radii of 2 inches are in a square whose perimeter is 32 inches. The
circles are all tangent to each other and to two sides of the square. How many times
larger is the area covered by the circles than the area not covered by the circles. Use 3.14
for pi and round you answer to the nearest hundredth.
Answer: ________________(6 pts)
Grade 7
Team
Meet 2
2011-2012
1)
Find the sum 312 4  554 6 and express your answer in base 8.
Answer: ____________8 (6 pts)
2)
The four interior angles of a quadrilateral are in the ratio of 1:3:5:6. In degrees, what is the measure
of the largest exterior angle?
Answer: _____________degrees(6 pts)
3)
A spinner is divided unequally into 4 colors: red, orange, purple and blue. The central angle for red
is 45 degrees, the central angle for orange is 135 degrees, and the central angle for purple is 60
degrees. What is the probability of landing on orange and then landing on blue and then landing on
red (in that exact order)? State your answer as a simplified fraction.
Answer: _______________(6 pts)
4)
A number is multiplied by itself. This product is doubled. 18 is added to the result. This newest
number is divided by 10. Then 39 is subtracted from this quotient. The absolute value of -20 is
added to this difference. This sum is equal to the positive square root of 49. What are the two
possible values of the original number?
Answer: ________, _______(6 pts)
5)
There are a total of 302 vehicles in a parking lot. The only two types of vehicles are motorcycles and
cars. There are 1030 tires in the parking lot. How many cars are there in the parking lot?
Answer: _______________(6 pts)
6)
Bill spent 12 minutes practicing guitar on Sunday, 30 minutes on Monday, 18 minutes on Tuesday,
21 minutes on Wednesday, 14 minutes on Thursday, 35 minutes on Friday and 48 minutes on
Saturday. What percent of the whole week did Bill spend practicing guitar? (Round your answer to
the nearest one-hundredth of a percent).
Answer: _______________(6 pts)
Grade 7
Solutions
Meet 2
2011-2012
Arithmetic
1) 8
2) 118
3) 552
4) 5 and 31
5) $106.85
Geometry
1) 20736 cu. in.
2) $2016
3) 312 sq. in.
4) 22x feet
5) 3.65 times
Team
1) 4148
2) 156º
3) 1/64
4) 11 and -11
5) 213 cars
6) 1.77%
20 4
10 2  80
40  6 2
=  8

2
5  20 16  (24)  3 5 8
236 = 56 + 58 + 60 + 62; 62 + 56 = 118.
(6  4) 2  6  4  24 2  24  576  24  552
If there are two modes in a set of six numbers, there must be two of each of
them. So the numbers are 9, 9, 12, 12, x, x + 26. The total is 6 x 13 = 78 =
(42 + 2x + 26) ; 2x = 10 so x = 5. The last number is 5 + 26 = 31.
The sale price is 0.8 x (80 + 60) = 112. Deduct the 10% discount to get
100.80. Multiply by 1.06 to get $106.85.
(2 x 12) x (3 x 12) x (2 x 12) = 20736
1120 / 40 = $28 per cubic unit; 3 x 6 x 4 = 72 units3 so 72 x 28 = $2016.
Perimeter = 60 = 2(x + 1.5x) = 5x so x = 12. Area #1 = 12 x 8 = 96. Area #2
= 12 x 18 = 216. 96 = 216 = 312.
The edges making up the perimeter include 4 sides each of four pentagons
plus three sides each of the two squares. 4 (4) + 3 ( 2 ) = 22.
Each of the four circles has an area of 4π, so the total area covered is 16π. If
the perimeter of the square is 32, each side is 8. The square’s area is thus 64,
16  3.14
 3.65
so the uncovered area is 64 - 16 π.
64  16  3.14
312 4  54; 554 6  214; 54  214  268; converted to base 8 is 4148
x + 3x + 5x + 6x = 15x; 15x = 360 so x = 24. The smallest angle of 24º
corresponds to the largest exterior of 156º .
Central angle for blue is 360 – (45 + 135 + 60) = 120. P(orange) = 135/360 =
3/8; P(blue) = 120/360 = 1/3. P(red) = 45/360 = 1/8. P(O then B then R) =
3 1 1 1
  
8 3 8 64
2 x 2  18
 39  20  7; 2 x 2  18  10  (26)  260; 2 x 2  242; x 2  121 so x   11
10
m + c = 302; 2m + 4c + 1030. m = 302 – c so 2(302 – c) + 4c = 1030; 604 +
2c = 1030 so 2c = 426 and c = 213.
(12 + 30 + 18 + 21 + 14 + 35 + 48) / (7 x 24 x 60) = 0.017658 or 1.77%.