Transcript PreAlgebra Math Tourn. Practice

PreAlgebra Math Tourn.
Practice
17th Annual 2004 8th Grade
3
Graph the8inequality:
8
y  6x 1
What are two integers whose sum
is 12 and whose difference is -60?
The rectangle and isosceles
triangle have the same perimeters.
How long is each side of the
triangle?
At a football game, Joe carried the
ball four times. He had a loss of 15,
a gain of 2, a loss of 5, and a gain
of 7. What was his total yardage?
What is the value of the following
expression when n = -3?
2n(3n  8 )
3
Frankie received a Collie puppy for
his birthday. The puppy weighed
4 ½ lb. at his birth. Frankie read
that a Collie will weigh 8 times its
birth weight by the time the puppy
is 18 months old. How much will
the Collie weigh at 18 months old?
Dave, Stephen, Kevin, and Juan
are taking turns running in a 26
1
mile marathon. If Dave runs 5 4
miles, Stephen runs 6 85 miles, and
Kevin runs 8 83 miles. How many
miles does Juan run to finish the
marathon?
Listed below are the test scores
from Mr. Swinford’s math test. What
percent of the students scored
below the class average?
68, 92, 88, 70, 82, 99, 88, 77, 85,
93, 84, 98, 89, 86, 77, 70, 87, 90
900
What is the square root of
?
225
Between which two consecutive
integers would 550 be found?
What happens to the mean,
median, mode, and range of the
following set of data if the value 89
is added?
45, 67, 56, 50, 43, 46, 67
What are the measures of the
unknown angles of the isosceles
triangle?
Marina works in a factory. She
packs 65 ball caps in 20 minutes. If
she works a 6 hour shift, how many
ball caps can she pack during the
shift?
Mario is 75 inches tall. On a sunny
day his shadow is 110 inches. If the
shadow of a nearby oak tree is 80
feet, ABOUT how tall is the tree?
What is the surface area of the
triangular prism?
Which of the following ratios are
not in proportion?
5
15
and
6
18
12
60
and
25
125
4
45
and
15
160
9
27
and
35
105
Which of the following is not equal
12
to
?
25
36
75
0.48
24%
48%
The length of a model train is 8 cm
and the length of the actual train is
32 m. What is the scale
What is the sale price of a $575.00
stereo system that is marked 55%
off?
What is the probability of rolling two
fair number cubes and having the
sum of the numbers being greater
than 12?
A leather jacket is on the sale rack.
Each week it is on the sale rack, it
is reduced 10%. The original cost
of the jacket is $350. Is has been
on the sale rack for 4 weeks. How
much does it cost now?
Which equation has a solution of
15?
2y
5
 12  7
4 x  35  25
2
3
x  10  20
3(6  y )  63
What is the solution of the
equation?
2 x  81  45  10 x
What is the solution of the following
inequality?
5(6 y  22)  12 y  40
What is the value of x in the system
of equations?
y  x6
y  3 x  24
The number of people moving into
the city triples every five years. If
there are 2500 residents in the city
now, how many will live in the city
in 20 years?
A rocket is shot into the air at 300
feet per second. Use the function
2
h  300t  16t
to find the height of the rocket after
10 seconds.
During a basketball game, Brenda
1
7
scored
of the points, Danny
scored 18% of the points, Joan
scored
2
9
of the points, and Ted
scored .16 of the points. Who
scored the most points?
2002 8th Grade
Find the value of
2  4 3
4
3
Solve:
3c  28  46
Find the prime factorization of 897
Find the area of a triangle with
base, 2.4 m, and height, 5.8 m
10 is what percent of 50?
Find the distance between (2,-4)
and (-3,1). Round to the nearest
tenth.
Give two ordered pairs that are
solutions to y = -3x – 2
Find the coordinates of Q’ after a
reflection over the x-axis.
Find the area of a circle whose
diameter is 8 meters.
Find the volume of the cone.
Round to the nearest whole
number.
Find the value of P(7,3)
How many combinations are
possible for 6 things taken 4 at a
time?
Find the sum of
2
2
and
2 x  3x  5
x  5x  8
Find the product of (3x+1) and
(x+3).
Find the area of the parallelogram
Evaluate
xyz  2 z
if x = 6, y = 22, and z = 4
Find the GCF of 16, 56, and 64.
Express 0.4 as a fraction in
simplest form.
Find the sixth term in the sequence
13, 11.7, 10.4, 9.1, ...
1
4
What is % of 90?
Find the value of x.
Find
f (3)
if
2
f ( n)  3  2n
Solve
38
r

2
5
Find the difference:
(11x  4 y )  (13x  2 y )
Factor
2x  4x
2
Solve.
(2 14 )  ( 65 q)  1 43
Eighteen of the 56 businesses in a
town advertise in the Family
Magazine. Half of the others
advertise in the Gazette. The rest
do not advertise in either
magazine. How many don’t
advertise?
Find the surface area and the
volume of the prism to the nearest
tenth.
2000 8th Grade
Given
f ( x)  x  7
what is
f [ f (2)]?
Solve for m:
m  1 23  43
Find the largest of three
consecutive integers such that if
three times the smallest is
decreased by the sum of the other
two, the difference between them
will be 46.
Express the ratio of 150 miles in 3
hours as a unit rate.
Simplify:
1
1
1 4 2 2
2
3

3
4
Find the GCF of
2 3
84a b and 120ab
4
Evaluate
2
3
2
2 x  3 y  21  9a
if a = 2, x = 3, and y = -1
The sides of square X are ¼ as
long as the sides of square Y. How
much smaller is the area of square
X than of square Y?
What is the value of P(6,4)
Simplify:
3a (5ab)
2
2
Solve for x:
3
4

10.8
x
What is the probability that a family
with six children will have all boys?
Find the value of
2 4
4
2
What is the sum of the prime
factors of 80?
Solve for p:
4 p  5  25
What is the surface area of a cube
3
that has a volume of 1 yd ?
4 ?
2
You have $10 to purchase oranges
and bananas. The oranges sell for
$2 per pound while the bananas
sell for 2 pounds for a dollar. Write
an equation that best describes the
different amounts of oranges and
bananas you can purchase
The area of a rectangle is
2
2x  6x  4
Find the binomials that would
represent the dimensions.
( x  2)( x  3)
(2 x  1)( x  4)
(2 x  4)( x  1)
( x  1)(2 x  4)
Let
f ( x)  x
2
and g ( x)  2 x .
Find
f [ g (2)]
Express the square of x+2
The polar diameter of the earth is
about 7,900 miles. There is about
161,000 cm in one mile. What is
the polar diameter of the earth in
centimeters?
Simplify:
4(1.5)  2  1.7
The slope of the line that passes
through the point (1,3) is 1.5. If the
point (-3,y) lies on the line, find the
value of y.
The length of a rectangle is 5 cm
greater than 3 times its width. The
area of the rectangle is 22
centimeters squared. Find the
dimensions of the rectangle.
The product of two consecutive
integers is 18,360. What is the sum
of the two numbers?
The height of a triangle is 10 cm. If
the area of the triangle is at least
25 square centimeters, what is the
smallest possible centimeters in the
length of the base?
What is the arithmetic mean of the
sum of the first five prime numbers
and the sum of the cubes of the
first three prime numbers?
1998 PreAlgebra
The length of a rectangular field is
three times its width. The perimeter
of the field is 600 meters. How
many square meters is the area?
What is left when you take 4 34 from
62?
What is the diameter of a circle that
has an area of
2
36 cm
One dollar is worth 4.5 francs. A
quart of gas costs 2 francs. How
many dollars does a gallon of gas
cost? (round answer to the nearest
cent)
Solve: (-7 – 4) – 2
Write 0.047 in scientific notation.
What is the sum of two-thirds and
seven-tenths?
Kim walks every day for one hour.
If she walks at a rate of 1 kilometer
in 15 minutes, how many meters
will she walk in one hour?
What is the surface area of a cube
whose side has a length of 9 cm?
Find 12 ½% of 300
The third term of an arithmetic
sequence is 13 and the eighth term
is 38. What is the product of the
first and tenth term?
Compute:
14  0.07  2.65 
1
4
Nina wants to get to the airport in
plenty of time so she will not miss
her plane. If it takes her 35 minutes
to drive to the airport, 20 minutes to
park the car, and she plans to
check in 45 minutes early for her
8:20 am flight. What time should
she leave for the airport?
What is the supplement of a 40
degree angle?
Special stickers have been
attached to 1,000 cassette tapes in
Mr. Music’s stock. Ten out of every
250 stickers win a free cassette. If
all 1,000 are sold and you buy one
of them, what is the probability you
will win a free cassette?
Change to a fraction in simplest
form:
4 54 %
What is the area of an isosceles
trapezoid whose parallel sides
have measures 12 inches and 14
inches, respectively, and has a
height of 20 inches?
Extra: Can you find the perimeter?
What is the sum of the largest and
smallest prime factors of 990?
A 6% rate increase by a local
media cable company resulted in
an increase of $1.20 per month on
a family’s bill. How much was the
bill before the increase?
Given
aMb = 2b – 3a
for all integers a and b, what is the
value of
5M8?
The numerator and denominator of
the common fraction 56 are each
increased by 3. What is the positive
difference between the resulting
fraction and 56 ?
What is the sum of the mean,
median, and mode of the following
data set:
{42, 56, 48, 56, 53}
What is the result when the
reciprocal of 3 is divided by the
reciprocal of 52 ?
Solve for y:
5  2 y  15
Evaluate:
5  80  5  7  3  10  (5  4  3)  5
2
What is the smallest positive
integer that has 12 distinct, positive
factors?
The formula
F  95 C  32
can be used to convert temperature
between degrees Fahrenheit (F)
and degrees Celcius (C). How
many degrees are in the Celsius
equivalent of -22 degrees
Fahrenheit?
How many natural numbers are
between
10 and 90
1997 PreAlg Grade
Solve -6 + 4x = -30
Evaluate
5z
xm
if x = 5, z = 6, and m = -2
What property is illustrated?
5(x + 2a) = 5x + 10a
Write 47,500 in scientific notation
Write 1.55 as a fraction in simplest
form
Solve the proportion:
4.6
6.9

14
a
Solve:
7{(29  11)  3(16  9)}
Evaluate:
3 2
4
9
2
( )
Solve the inequality:
 a  8  9
1
2
If a ten-pound turkey takes 4 hours
to cook, how long will it take a 14
pound turkey to cook?
Mike’s savings account earned
$9.48 in interest. This is equal to
6% of his savings. What are his
savings?
19 is what percent of 76?
The point (-2,-3) is in what
quadrant?
Which line is parallel to
y  12 x  3
y  x4
y  2 x  3
y  3x 
y  3 x 
1
2
1
2
1
2
If the lengths of the legs of a right
triangle are 3 in and 4 in, what is
the length of the hypotenuse?
Simplify:
(3 xy )(2 x y )
2
4
If the area of a square is 81, what
is the length of each side?
Suppose you draw one card at
random from a standard deck of 52
playing cards. What is the
probability of drawing a Jack?
What is the mode of the following:
5, 6, 9, 11, 2, 11, 40?
Find the area of a circle if the
diameter is 8m in length.
Write 56.4% as a fraction.
Solve:
1
2
n  (2 7 )(3 3 )
Solve:
4.64 + p = 3.96
Solve:
8
2 d 2
5
Simplify:
5(3p + 2q) + 6(2p + q)
Find three consecutive integers
such that 3 times the least is 4
more than twice the greatest.
Solve:
5  2  2.5
3
4
5
6
The greater of two numbers is 7
more than the lesser. Three times
the greater is 5 more than 4 times
the lesser number. Find the
numbers.
1998 8th Grade
If x = 5, y = 2, and z = 3, find the
value of
3 x ( y 5)
3z
Find the LCM of 36 and 60
Name two consecutive integers
that have a product of 42 and a
sum of -13.
If p = -25, q = -19, r = 7, and s = -3,
evaluate:
( p  qr )  (5  2st )
Mary has four more dimes than
quarters. If the total value of her
coins is $8.80, how many dimes
does she have?
If
A  B  A  AB  B
2
, evaluate
53
2
Find the area of a circle with a
diameter of 16 meters.
Given a triangle with two sides 10
and 14, find the length of the
missing side x, if the perimeter of
the triangle is 45.
If 3x + 4 + 2x = 29, find x:
 196
In a right triangle with legs of length
15 and 20, find the length of the
hypotenuse.
What is the median of 80, 100, 70,
30, and 150?
Helen worked 40 hours at $3.35
per hour and made $85.75 in tips.
What was her weekly earnings?
Six less than twice a number is -14.
Find the number.
If 4 x  7  5, what is the value of
1
?
x

5
4
The longest side of a right triangle
is 13 cm and the shortest side is 5
cm. Find the length of the third side
of the triangle.
Solve:
A
6
 17  8
What is the area of a square that
has a 15 inch side?
Find the slope of the line that
contains the points
5 4
1
( 2 , 5 ) and ( 2 ,1)
How many different rectangular
arrangements can be made with a
36 member drill team? Each row
and column must have at least two
members.
Simplify:
3(a  2b)  9(2a  3b)  2[3  3(a  4)]  5[7  2( a  3)]
Linda plans to use 2 cups of flour in
a recipe which serves 5 people.
How many cups should she use in
the same recipe to serve 16
people?
What is the name of a polygon that
has seven sides?
A 6-foot ladder touches the side of
a building at a point 5 feet above
the ground. At what height would a
15 foot ladder touch the building if it
makes the same angle with the
ground as the short ladder?
12.8 mm = _____ m
What is the eighth term in the
following sequence:
1, 1, 2, 3, 5, ...
Given a regular hexagon, list the
measure of any angle AND the sum
of the measures of all the angles.
Suppose you draw one card at
random from a standard deck of 52
playing cards. What is the
probability of drawing a king or a
queen?
1997 8th Grade
Solve for x:
x
6  5  40
1
2
5 % of 600 = n
What is the prime factorization of
256?
A circle has an area of 25 m.
What is its circumference?
2
Change 33,792 feet to miles.
A video regularly sells for $28.48. It
is on sale at a discount of 25%.
Find the sale price.
Simplify:
[6  (5)][4  (8)]
Write 53,480 in scientific notation
What percent of 160 is 8?
Add:
3 ft. 7in.  34 ft  2.25 ft
Multiply:
2 85  ( 32 )
Simplify:
5(3  1)  3(3 )  10
2
3
What is the next number in the
sequence?
8, 27, 64, 125, ___
Simplify:
8
10
3
10
What is the value of x?
5x – 6 = x + 18
Find the volume of the cube.
Change 15 12 % to a fraction in
lowest terms.
5
8
Hal spent of his savings. If his
savings totaled $542.64, how much
did he spend?
One leg of a right triangle is 7 in.
long. The other leg measures 24 in.
long. What is the length of the
hypotenuse?
Find the measure of the third angle
of a triangle if two of the angles
measure 112 and 38 .
If there are 8 blue marbles, 5 red
marbles, and 10 yellow marbles,
what is the probability that a yellow
marble will be chosen if one is
drawn at random?
Ann borrows $700 for 4 ½ years.
The bank charges her 12% interest
per year. How much interest will
Ann have to pay?
650 mm = ___ hm
Cupcakes sell for 2 dozens for
$13.20. How much would you pay
for 5 cupcakes?
If Tom can drive 195 miles in 3
hours, how far can he drive in 5
hours at the same rate?
The three angles of a triangle equal
x, x+10, and 2x -14. Find the
measures of all three angles.
Find the area of the shaded region.
Solve if a = -2, b = -3, and c = 5.
ab c ( ab )
b
2
2
1994 8th Grade
Solve: 4x + 7 = 43.8
Find the area of the triangle
Find the area of a circle with a
diameter of 100 m.
Find the measure of the missing
angle of a triangle whose 2 known
angles are 49 degrees and 22
degrees.
What is 11 23 % written as a fraction
in simplest form?
What mathematical property is
shown by the equation
86  86  8
3
4
3
4
If -4d + 2 = 18, then solve for d.
What percent of 50 is 35?
Find x if (24 + 3.26) – 25 = x
Pineapple juice sells for 3 cans for
$1.35. How much would he pay for
7 cans.
1  12
1  12
If 3x = 21, then 21x = ?
476 301  232 201
66 23 % of what number is 26?
14  3  5  y
Solve for x:
-2.3 + 5.7 = x
The perimeter of a rectangular
painting is 24 in. It is 2 in. longer
than it is wide. How long is it?
Find the average of the first 4
multiples of 5.
The boss wants to ship 94 videos
in as few boxes as possible. Big
boxes hold one dozen videos, but
are used only when full, while little
boxes hold two videos. How many
boxes must be used in all?
Simplify:
3(4  5)  (12  9)
2
2
Solve:
4x + 2 = 14
Simplify:
36  6  5
Find the area of triangle ABC
At what point does the graph of
8x – 4y = 12 intersect the y-axis?
The number of students in a math
class increased from 20 to 26.
What was the percent of increase?
3 34 yd  ___ ft
Write 210,000 using scientific
notation.