PreAlgebra Math Tourn. Practice

17th Annual 2004 8th Grade

Graph the inequality:388

6 1y x

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?

32 (3 8 )n n

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 mile marathon. If Dave runs

miles, Stephen runs miles, and Kevin runs miles. How many

miles does Juan run to finish the marathon?

145

586

388

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

What is the square root of ?900

225

Between which two consecutive integers would be found?550

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

6 18and

12 60

25 125and

4 45

15 160and

9 27

35 105and

Which of the following is not equal

to ?12

25

36

750.48 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?

2 15 2 7y 2

3 10 20x

4 35 25x 3(6 ) 63y

What is the solution of the equation?

2 81 45 10x x

What is the solution of the following inequality?

5(6 22) 12 40y y

What is the value of x in the system of equations?

6

3 24

y x

y x

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

to find the height of the rocket after 10 seconds.

2300 16h t t

During a basketball game, Brenda

scored of the points, Danny

scored 18% of the points, Joan

scored of the points, and Ted

scored .16 of the points. Who

scored the most points?

17

29

2002 8th Grade

Find the value of

4 32 4 3

Solve:3 28 46c

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 and22 3 5x x 2 5 8x x

Find the product of (3x+1) and (x+3).

Find the area of the parallelogram

Evaluate

if x = 6, y = 22, and z = 42xyz z

Find the GCF of 16, 56, and 64.

Express as a fraction in simplest form.0.4

Find the sixth term in the sequence 13, 11.7, 10.4, 9.1, ...

What is of 90?14%

Find the value of x.

Find

if( 3)f

2( ) 3 2f n n

Solve38 2

5r

Find the difference:(11 4 ) (13 2 )x y x y

Factor22 4x x

Solve.

5 314 6 4( 2 ) ( ) 1q

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

what is ?

( ) 7f x x

[ (2)]f f

Solve for m:32

3 41m

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 14 223

1 2 34

Find the GCF of2 3 484 120a b and ab

Evaluate

if a = 2, x = 3, and y = -1

2 3 22 3 21 9x y a

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: 2 23 (5 )a ab

Solve for x:

3 10.84 x

What is the probability that a family with six children will have all boys?

Find the value of 4 22 4

What is the sum of the prime factors of 80?

Solve for p:4 5 25p

What is the surface area of a cube that has a volume of 1 ?3yd

24 ?

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

Find the binomials that would represent the dimensions.

22 6 4x x

( 2)( 3)x x (2 1)( 4)x x

(2 4)( 1)x x ( 1)(2 4)x x

Let and .

Find

2( )f x x ( ) 2g x x

[ ( 2)]f g

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 from 62?

344

What is the diameter of a circle that has an area of

236 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:1414 0.07 2.65

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:

454 %

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?

Givenab = 2b – 3a

for all integers a and b, what is the value of

58?

The numerator and denominator of the common fraction are each

increased by 3. What is the positive difference between the resulting

fraction and ?

56

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 ?25

Solve for y:5 2 15y

Evaluate:25 80 5 7 3 10 (5 4 3) 5

What is the smallest positive integer that has 12 distinct, positive

factors?

The formula

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?

95 32F C

How many natural numbers are between 10 90and

1997 PreAlg Grade

Solve -6 + 4x = -30

Evaluate

if x = 5, z = 6, and m = -2

5zxm

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:4.6 146.9 a

Solve:

7{(29 11) 3(16 9)}

Evaluate:234

9 2( )

Solve the inequality:

12 8 9a

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 12 3y x

12 4y x

123y x

2 3y x 123y x

If the lengths of the legs of a right triangle are 3 in and 4 in, what is

the length of the hypotenuse?

Simplify:2 4(3 )( 2 )xy x y

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 27 3( 2 )(3 )n

Solve:4.64 + p = 3.96

Solve:

2 258 d

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:

3 54 65 2 2.5

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 ( 5)3x yz

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:

( ) ( 5 2 )p qr st

Mary has four more dimes than quarters. If the total value of her coins is $8.80, how many dimes

does she have?

If

, evaluate

2 2A B A AB B

5 3

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 , what is the value of ?

4 7 5x 14 5x

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:

6 17 8A

What is the area of a square that has a 15 inch side?

Find the slope of the line that contains the points

and5 42 5( , ) 1

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( 2 ) 9(2 3 ) 2[3 3( 4)] 5[7 2( 3)]a b a b a a

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:

6 5 40x

of 600 = n125 %

What is the prime factorization of 256?

A circle has an area of .What is its circumference?

225 m

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:343 . 7 . 2.25ft in ft ft

Multiply:5 28 32 ( )

Simplify:2 35(3 1) 3(3 ) 10

What is the next number in the sequence?

8, 27, 64, 125, ___

Simplify:8

31010

What is the value of x?5x – 6 = x + 18

Find the volume of the cube.

Change to a fraction in lowest terms.

1215 %

Hal spent of his savings. If his savings totaled $542.64, how much

did he spend?

58

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 and .112 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 = 5.2 2( )ab c abb

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 written as a fraction in simplest form?

2311 %

What mathematical property is shown by the equation

3 34 48 6 8 6 8

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.

12

12

1

1

If 3x = 21, then 21x = ?

1 130 20476 232

of what number is 26?2366 %

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:2 23(4 5) (12 9)

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?

343 ___yd ft

Write 210,000 using scientific notation.