Download Grade 6

Grade 8
Arithmetic
Meet 2
2009-2010
1)
If
2 
2 
3
3
x
= 2 , what is the value of x?
Answer: _________________ (2 pts)
2)
For integers x and y,
x  y  16 and x – y = -128. What is the value of x?
Answer: _________________(3 pts)
3)
The mean of five positive integers is 7. If the set of data has a unique mode, what is the greatest
possible integer in the set?
Answer: _________________(4 pts)
4)
Five hundred raffle tickets were sold at the 8th grade fundraiser for $5 each. Eight winning
tickets paid as follows: one ticket at $750, two tickets at $250, and five tickets at $125 each. The
revenue from the ticket sales that was not used to pay off the prizes was considered profit. What
percent of the revenue from the ticket sales was profit?
Answer: ______________% (5 pts)
5)
Jamia's science project grade has 2 parts. The oral presentation is worth 30 points and the
written report is worth 70 points. Jamia earned 84% of the possible points for her written report.
To earn at least 87% of the possible points for the entire project, what percent of the possible
points for the oral project presentation must she earn?
Answer: _________________(6 pts)
Grade 8
Geometry
Meet 2
2009-2010
1)
A triangle has sides with measures of 10, 23, and 27 units. The perimeter of a square is 60% of
the triangle's perimeter. What is the area of the square?
Answer: _________________(2 pts)
2)
If a || b , find the value of x.
Answer: ________________ (3 pts)
(4x + 11)
a
3)
(8x + 1)
b
The measure of an interior angle of a regular polygon is 170°. Find the number of sides in the
polygon.
Answer: _________________(4 pts)
4)
Quadrilateral ABCD is a rectangle, and its length is twice the width. The perimeter of the
rectangle is 60 units. Points P, Q, R, and S are midpoints of each side. What is the area of
quadrilateral PQRS?
Answer: _________________ (5 pts)
5)
Find the area of the smaller sector. Use 3.14 for π and round your answer to the nearest tenth.
12 cm 92∘
12 cm
Answer: _________________ (6 pts)
Grade 8
Team
Meet 2
2009-2010
1)
The number 839 can be written as 19q + r, where q and r are positive integers. What is the
greatest possible value of q – r?
Answer: _________________ (6 pts)
2)
Use the given clues to figure out which integer I am : 1) If I am not a multiple of 4, then I am
between 60 and 69. 2) If I am a multiple of 3, I am between 50 and 59. 3) If I am not a
multiple of 6, I am between 70 and 79. What integer am I?
Answer: _________________ (6 pts)
3)
Using one drain, a swimming pool can be emptied in 45 minutes. Using a different drain, the job
takes 1 hour and 15 minutes. How long will it take if both drains are opened?
Answer: _________________(6 pts)
4)
Sixty jelly beans are placed into boxes V, W, X, Y, and Z. Together boxes V and W contain 24
jelly beans. Together boxes W and X contain 15 jelly beans. Together boxes X and Y contain
18 jelly beans. Together boxes Y and Z contain 30 jelly beans. How many jelly beans are in box
V?
Answer: _________________(6 pts)
5)
If a # b = a² + b and a @ b = b – a, what is the value of ( ( 1 # 3) @ 2)?
Answer: _________________(6 pts)
6)
From a regular hexagon, three vertices are selected at random. What is the probability that these
three vertices form an equilateral or isosceles triangle? Express your answer as a common
fraction.
Answer: _________________(6 pts)
Grade 8
Solutions
Meet 2
2009-2010
Arithmetic
1) 24
2) 16
3) 31
4) 25
5) 94
Geometry
1) 81
8
24
(2 3 ) = 2
Using guess and check: for x, 16 = 4 and for y, 144 = 12., 16 – 144 = -128.
The sum of the integers is 5*7 = 35. Minimize the values of the other 4 numbers to 1 and
that leaves 1,1,1,1, 31. The mode is unique (1) from the mean of 31.
Ticket Sales = $2500. Prize money was $1875. The remaining $2500 - $1875 = $625
was profit. $625 / $2500 = .25 or 25%.
The oral presentation is 30 points, and the written piece is 70 points. In order to earn
87% of total points, 87 points are needed. 84% of 70 = 58.8 points and Jamia still needs
87-58.8 = 28.2 points out of the 30 points. 28.2/30 =.94 or 94%.
The perimeter of the triangle is 60 units. If the square's perimeter is 60% of this, it is .60
x 60=36 units. Each of the four sides is x, so x = 36/4 =9, 9² =81.
2) 14
(4x+11) + (8x+1) = 180, 12x = 168, x=14
3) 36
180(n-2)/n = 170, 180n -360 = 170n, 10n = 360, n=36
4) 100
AD = x and AB =2x, so x + 2x + +x +2x = 60, which means x = 10. AP =PB=CR=RD
=10 units and BQ=QC=DS=SA=5 units. PS, SR, RQ, and QP are congruent because
they are all hypotenuses of right triangles. PQRS is a rhombus with diagonals PR=10
and SQ=20. Use A=½(d1 d2), PQRS is ½ of 200 = 100 units squared.
5) 115.6 cm² Area of the circle = 452.16 cm², 92 / 360 = .2555, 452.16 * .2555 = 115.6
Team
1) 41
2)
3)
4)
5)
6)
The greatest value of q-r is found if we divide 839 by 19. We get a (q)quotient of 44 with
a (r)remainder of 3. The greatest value of q-r is 44-3=41.
76
If a multiple of 3, it must be 51, 54, or 57. But, these 3 numbers are not a multiple of 4.
So this means the mystery number is a multiple of 4 and not 3 or 6. Therefore the
number must be 71, 73, 74, 75, 76, 77, or 79. Of these numbers, only 76 is a multiple of
4.
28 1/8 min. Drain #1 can do 4/3 x in one hour. Drain #2 can do 4/5 x in one hour. 4/3 x + 4/5 x =
32/15 x. x = 1 * 15/32 = 0.46875 of an hour ≈ 28 1/8 minutes.
15
V must have 24-15=9 more marbles than X. Z must have 30-18=12 more marbles than
X. Z must have 3 more marbles than V. V+2W+2X+2Y+Z=87 marbles. Extra W, X, Y
account for 87-60=27 marbles, V+Z=60-27=33 marbles. Z is 3 more than V, remove the
3 marbles and 30/2=15 marbles.
-2
(2 - (1² + 3))=2 - 4= -2
2
/5
6 C 3 = 6!/[3!(6-3)!]=20 Triangles, 8 of the triangles are equilateral or isosceles, 8/20=2/5