Astb Math Skills Test (Mst) [Comprehensive]

Front 1

-2²[(-4-6⁰)(5-3⁰)] ÷ |-6|-[-(-2)]

a. -5
b. 10
c. 20
d. -20

Back 1

c. 20

Front 2

12½ × 1/5 = ?

a. 2½
b. 4
c. 5¼
d. 6

Back 2

a. 2½

Front 3

If the hypotenuse of a right triangle is 5 inches long and one of the sides is 4 inches long, how long is the remaining side?

a. 2 inches
b. 3 inches
c. 4 inches
d. 9 inches

Back 3

b. 3 inches

Front 4

If (a+1)(a-1) = 3, then a² =

a. √2
b. √3
c. 4
d. 9

Back 4

c. 4

Front 5

Which statement is equivalent to 2 + 2log(x) - (3/2)log(y)?

a. log (4x/(3/2)y)
b. log (x⁴/y^(3/2))
c. log (100x²/y^(3/2))
d. 2log (x²/y^(3/2))

Back 5

c. log (100x²/y^(3/2))

Front 6

√¼ + √(1/16)

a. 1/64
b. 17/256
c. 5/16
d. 3/4

Back 6

d. 3/4

Front 7

A basketball player averages 21 points per game for the first 8 games of the season. If he is held scoreless in the next two games, how many average points per game must he score in his final 6 games in order to complete the season with an overall average of 21 points per game?

a. 21
b. 28
c. 32
d. 42

Back 7

b. 28

Front 8

If n is a positive even integer, which of the following must also be an even integer?

a. 3n-2
b. 4n+1
c. 5n+5
d. 6n-1

Back 8

3n-2

Front 9

A coin purse contains coins with values of 1 cent, 5 cents, 10 cents, 25 cents, and 50 cents. Using each coin at least once, what is the minimum number of coins required to equal the highest possible total less than $2?

a. 10
b. 11
c. 12
d. 13

Back 9

b. 11

Front 10

Assume the probability of having a boy is 50% and a girl is 50%. If a family has four children, what is the probability the family has at least two girls?

a. 5/16
b. 1/2
c. 5/8
d. 11/16

Back 10

d. 11/16

Front 11

If you flip a coin three times, what is the probability of getting three tails in a row?

a. .0625
b. .10
c. .125
d. .333

Back 11

c. .125

Front 12

A man is paddling a canoe upstream. Assuming he can paddle at 6 miles per hour and the stream is flowing at a rate of 3 miles per hour, after one hour of paddling, how many miles will he have traveled?

a. 2
b. 3
c. 12
d. 18

Back 12

b. 3

Front 13

What is the area equation for a triangle?

Back 13

A = ½bh

b = base
h = height

Front 14

What is the area equation for a rectangle/parallelogram?

Back 14

A = bh

b = base
h = height

Front 15

What is the area equation for a trapezoid?

Back 15

A = ½(b₁+b₂)h

b₁ = base 1
b₂ = base 2
h = height

Front 16

What is the area equation for a circle?

Back 16

A = πr²

r = radius

Front 17

What is the circumference equation for a circle?

Back 17

C = 2πr or C = πd

r = radius
d = diameter

Front 18

What is the Pythagorean Theorem?

Back 18

a² + b² = c²

Front 19

What are the three commonly used trigonometric functions?

Back 19

sine (sin), cosine (cos), and tangent (tan)

sin = opposite leg / hypotenuse
cos = adjacent leg / hypotenuse
tan = opposite leg / adjacent leg

use mnemonic SOHCAHTOA

Front 20

What is the equation for simple interest?

Back 20

I = prt

I = interest
p = principal amount
r = rate
t = time

Front 21

What is the formula for compound interest?

Back 21

A = P(1 + (r/n))^nt

A = amount accumulated after n years
P = principal amount
r = rate
n = number of times interest is compounded
t = time

Front 22

What is the order of operations?

Back 22

parentheses, exponent, multiply, divide, add, subtract

use mnemonic PEMDAS

Front 23

If 5x + 3y = 29 and x - y = 1, then x equals?

a. 1
b. 2
c. 3
d. 4
e. 5

Back 23

d. 4

Front 24

Solve for x: 2x/7 = 2x²

a. 1/7
b. 2/7
c. 2
d. 7
e. 14

Back 24

a. 1/7

Front 25

If x is an odd integer, which one of the following is an even integer?

a. 2x + 1
b. 2x - 1
c. x² - x
d. x² + x - 1
e. none of the above

Back 25

c. x² - x

Front 26

10^x divided by 10^y equals

a. 10^(x/y)
b. 10^xy
c. 10^(x+y)
d. 10^(x-y)
e. none of the above

Back 26

d. 10^(x-y)

Front 27

(x-2) / (x²-6x+8) can be reduced to

a. 1/(x-4)
b. 1/(x-2)
c. (x-2)/(x+2)
d. 1/(x+2)
e. 1/(x+4)

Back 27

a. 1/(x-4)

Front 28

If 3^n = 27, what is the value of 4^n +1?

a. 24
b. 48
c. 65
d. 108
e. none of the above

Back 28

c. 65

Front 29

The expression √28 - √7 reduces to

a. √4
b. √7
c. 3√7
d. √21
e. -√35

Back 29

b. √7

Front 30

You need eight barrels of water to spring ½ mile of roadway. How many barrels of water do you need to spring 3½ miles of roadway?

a. 7
b. 15
c. 50
d. 56
e. 28

Back 30

d. 56

Front 31

A snapshot 8 inches long and 6 inches wide is to be enlarged so that its length will be 12 inches. How many inches wide will the enlarged snapshot be?

a. 8
b. 6
c. 9
d. 10
e. 12.5

Back 31

c. 9

Front 32

Heather Marie has an ordinary life insurance policy with a face value of $10,000. At her age, the annual premium is $24.00 per thousand. What is the total premium paid for this policy every six months?

a. $100
b. $120
c. $240
d. $400
e. $480

Back 32

b. $120

Front 33

If 2 pounds of cottage cheese cost $3.20, what is the cost of a 3-ounce portion of cottage cheese?

Back 33

$0.30

Front 34

Jonathan drove for 12 hours at an average speed of 55 miles per hour. If his car covered 22 miles for each gallon of gas consumed, how many gallons of gas did he use?

Back 34

30 gals.

Front 35

Gus earns $7.50 per hour. If he works from 8:45 AM until 5:15 PM, with one hour off for lunch, how much does he arn in one day?

Back 35

$56.75

Front 36

If five shirts and three ties cost $52 and each tie costs $4, what is the cost of a shirt?

Back 36

$8.00

Front 37

What is the fifth term in this series: 5; 2; 9; 6; ____?

Back 37

13

Front 38

In a theater audience of 500 people, 80% were adults. How many children were in the audience?

Back 38

100

Front 39

A brand-name dining room table usually sells for $240, but because it has the display model and is a little shopworn, the store manager lets it go for $210. What is the percent of reduction?

Back 39

12½%

Front 40

Mr. and Mrs. Bailey bought a repossessed house for an investment for $55,000. It was assessed at 80% of the purchase price. If the real estate tax was $4.74 per $100, how much tax did the Baileys pay?

Back 40

$2,085.60

Front 41

The scale on a particular map is 1 inch = 50 miles. On this map, two cities are 2½ inches apart. What is the actual distance between the two cities?

Back 41

125 miles

Front 42

A shipment of 2,200 pounds of fertilizer is packed in 40-ounce bags. How many bags are needed for the shipment?

Back 42

880

Front 43

A TV set priced at $400 was reduced 25% during a weekend sale. In addition, there was a 10% discount for cash. What was the cash price of the TV set during the sale?

Back 43

$270

Front 44

In a store, four clerks each receive $255 per week, and two part-timers each earn $120. What is the average weekly salary paid to these six workers?

Back 44

$210.00

Front 45

The perimeter of a rectangle is 40 feet. If the length is 15 feet, 6 inches, what is the width of the rectangle?

Back 45

4 ft., 6 in.

Front 46

What is the result of dividing 0.675 by 0.9?

Back 46

0.75

Front 47

Two planes leave the same airport, traveling in opposite directions. One is flying at a speed of 340 miles per hour, the other at 260 miles per hour. In how many hours will the two planes be 3,000 miles apart?

Back 47

5

Front 48

What is the cost of 5 feet, 3 inches of plastic slipcover material that sells for $8 per foot?

Back 48

$42.00

Front 49

If 1 gallon of milk costs $3.84, what is the cost of 3 pints?

Back 49

$1.44

Front 50

A man left $72,000 in his will to his wife and son. The ratio of the wife's share to the son's share was 5:3. How much did his wife receive?

Back 50

$45,000

Front 51

A recipe calls for 2½ ounces of chocolate and ½ cup of corn syrup. If only 2 ounces of chocolate are available, how much corn syrup should be used?

Back 51

2/5 cup

Front 52

A ship sails x miles the first day, y miles the second day, and z miles the third day. What was the average distance covered per day?

Back 52

(x+y+z) ÷ 3

Front 53

A man invests $6,000 at 5% annual interest. How much more must he invest a 6% annual interest so that his annual income from both investments is $900?

Back 53

$10,000

Front 54

Which of these is an example of similar figures?

a. a plane and a scale model of that plane
b. a pen and a pencil
c. a motorcycle and a car
d. an equilateral triangle and a right triangle
e. an isosceles triangle and a right triangle

Back 54

a. a plane and a scale model of that plane

Front 55

Find the numerical value of 5a²b - 3ab² if a = 7 and b = 4.

Back 55

644

Front 56

If the circumference of a circle is divided by the length of its diameter, what is the result?

Back 56

π

Front 57

A businesswoman spends 1/5 of her small company's gross income for office rent, and 3/8 of the remainder of the company's income for salaries. What part of her income does she spend for salaries?

Back 57

3/10

Front 58

Using the following formula, find the value of C when F = 50.

C = (5/9)(F-32)

Back 58

10

Front 59

What is the average of these temperature reading, taken on a cold day last winter?

6 AM = -12 degrees
7 AM = -7 degrees
8 AM = -2 degrees
9 AM = 0 degrees
10 AM = +6 degrees

Back 59

-3 degrees

Front 60

Jonathan earns $350 (before taxes) every two weeks at his part-time job. His withholdings are $27. 75 for federal income taxes, $5.65 for Social Security (FICA), and $12.87 for Medicare tax. How much will his net paycheck be?

Back 60

$303.73

Front 61

A computer-generated award certificate 9 inches long a 6 inches wide has to be enlarged so that its length will be 12 inches. How many inches wide will the enlarged certificate be?

Back 61

8

Front 62

June C. has a certificate of deposit for $10,000 at an annual interest percentage rate of six percent. How much interest will she gain if she does not touch the CD for two years?

Back 62

$1,236

Front 63

If 2 pounds of jellybeans cost $3.20, what is the cost of 3 ounces?

Back 63

$0.30

Front 64

Mrs. H.B. drove her Volvo S80 four-door sedan from Waco to San Antonio at an average speed of 60 miles per hour, including two rest stops of 10 minutes each. Her car gets average highway mileage of 30 miles per gallon. If her car used 7 gallons of gas, how many hours did she travel?

Back 64

3.5 hours

Front 65

Mike earns $17.50 per hour. If he works from 7:45 AM until 5:30 PM, with 1 hour off for lunch, about how much does he earn in one day?

Back 65

$153.13

Front 66

A basketball team won 70% of the 40 games it played. How many games did it lose?

Back 66

12

Front 67

EconoAir Flight 1776 is scheduled for departure at 3:50 PM. If the flight takes 2 hours and 55 minutes, at what time is it scheduled to arrive at its destination?

Back 67

6:45 PM

Front 68

How many 4-ounce candy bars are there in a 3-pound package of candy?

Back 68

12

Front 69

What is the fifth term of the series 2 5/6, 3 1/2, 4 1/6, 4 5/6, ...?

Back 69

5 1/2

Front 70

In a steakhouse, a guest orders a small steak entree with vegetables for $12.50, dessert for $3.50, and coffee for $1.25. If the tax on meals is 8%, what tax should be added to his check?

Back 70

$1.38

Front 71

A mechanic's warehouse is going to use a 55-gallon drum of oil to fill cans that hold 2 quarts each. How many cans can be filled from the drum?

Back 71

110

Front 72

On production line 2A in the Lee County wooden product factory, a lathe operator takes 45 minutes to do the finish work on 9 spindles. How many hours will it take him to finish 96 spindles at the same rate?

Back 72

8

Front 73

A triangle has two equal sides. The third side has a length of 13 feet, 2 inches. If the perimeter of the triangle is 40 feet, what is the length of one of the equal sides?

Back 73

13 ft., 5 in.

Front 74

A lawn is 21 feet wide and 39 feet long. How much will it cost Jan to weed and feed it if a gardening service charges $0.40 per square yard for this treatment?

Back 74

$36.40

Front 75

The perimeter of a rectangle is 40 feet. If the length is 15 feet, 6 inches, what is the width of the rectangle?

Back 75

4 ft., 6 in.

Front 76

Two partners operate a business that shows a profit for the year equal to $63,000. Their partnership agreement calls for them to share the profits in the ratio 5:4. How much of the profit should go to the partner who gets the larger share?

Back 76

$35,000

Front 77

A purchaser paid $17.16 for an article that had recently been increased in price by 4%. What was the price of the article before the increase?

Back 77

$16.50

Front 78

In a clothing factory, 5 workers finish production of 6 garments each per day, 3 others turn out 4 garments each per day, and one worker turns out 12 per day. What is the average number of garments produced per worker per day?

Back 78

6

Front 79

Travis makes a 255-mile trip by car. He drives the first 2 hours at 45 miles per hour. At what speed must he travel for the remainder of the trip in order to arrive at his destination 5 hours after he started the trip?

Back 79

55 mph

Front 80

A contractor bids $300,000 as his price for erecting a building. He estimates that 1/10 of this amount will be spent for masonry materials and labor, 1/3 for lumber and carpentry, 1/5 for plumbing and heating, and 1/6 for electrical and lighting work. The remainder will be his profit. How much profit does he expect to make?

Back 80

$60,000

Front 81

The list price of a TV set is $325, but the retailer offers successive discounts of 20% and 30%. What price does a customer actually pay?

Back 81

$182.00

Front 82

A certain brand of motor oil is regularly sold at a price of 2 quart cans for $1.99. On a special sale, a carton containing 6 of the quart cans is sold for $5.43. What is the saving per quart if the oil is bought at the special sale?

Back 82

$0.09

Front 83

A worker earns $7.20 an hour. She is paid time and a half for overtime beyond a 40-hour week. How much will she earn in a week in which she works 43 hours?

Back 83

$320.40

Front 84

A tree 36 feet high casts a shadow 8 feet long. At the same time, another tree casts a shadow 6 feet long. How tall is the second tree?

Back 84

27 ft.

Front 85

Find the numerical value of 5a2b - 3ab2 if a =7 and b = 4.

Back 85

112

Front 86

If the circumference of a circle is divided by the length of its diameter, what is the result?

Back 86

π

Front 87

For a special mission, 1 soldier is to be chosen at random from among 3 infantrymen, 2 artillerymen, and 5 tank crewmen. What is the probability that an infantryman will be chosen?

Back 87

3/10

Front 88

A naval task force is to be made up of a destroyer, a supply ship, and a submarine. If 4 destroyers, 2 supply ships, and 3 submarines are available from which to choose, how many different combinations are possible for the task force?

Back 88

24

Front 89

The base of a cylindrical can is a circle whose diameter is 2 inches. Its height is 7 inches. How many cubic inches are there in the volume of the can?

Back 89

22 cu. in.

Front 90

How many ounces in 1 pound?

Back 90

16 ounces

Front 91

How many pints in 1 gallon?

Back 91

8 pints

Front 92

How many quarts in 1 gallon?

Back 92

4 quarts

Front 93

How many pounds in 1 ton?

Back 93

2000 pounds

Front 94

If 2 times r exceeds one-half of t by 5, what equation represents the relationship between r and t?

Back 94

2r - ½t = 5

Front 95

If 3 times x exceeds 1/3 of y by 9, what equation represents the relationship between x and y?

Back 95

3x - (1/3)y = 9

Front 96

One recruiter can complete a certain assignment in 40 minutes; another can complete the same assignment in one hour. How long would it take to complete the assignment if they worked together?

Back 96

24 minutes

Front 97

How much pure acid must be added to 12 ounces of a 40% acid solution in order to produce a 60% acid solution?

Back 97

6 ounces

Front 98

Subject A can complete a project in 20 days and Subject B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project by completed?

Back 98

18 days

Front 99

A businesswoman spends 1/5 of her income for rent, and 3/8 of the remainder goes towards salary. How much does she have remaining?

Back 99

3/10

Front 100

A purchaser paid $17.16 for an article that had recently been increased in price by 4%. What was the price before the increase?

Back 100

$16.50

Front 101

A naval detachment has enough rations to feed 16 people for 10 days. If 4 more people join the detachment, for how many fewer days will the rations last?

Back 101

2 less days (8 days total)

Front 102

A field can be plowed by 9 machines in 5 hours. If 3 machines are broken and cannot be used, how many hours will it take to plow the field?

Back 102

7.5 hours

Front 103

In a 3 hour examination of 320 questions, there are 40 mathematics problems. If twice as much time should be allowed for each mathematics problem as each of the other questions, how many minutes should be spent on the mathematics problems?

Back 103

40 minutes

Front 104

A tank that holds 450 gallons of water can be filled by 1 pipe in 15 minutes, and emptied by another in 30 minutes. How long would it take to fill the tank if both pipes are open?

Back 104

30 minutes

Front 105

If a driver completes a trip of 120 miles at a rate of 30 mph, at what rate would the driver have to travel on the return trip in order to average 40 mph for the round trip?

Back 105

60 mph

Front 106

A bridge crosses a river that is 1520 feet wide. One bank of the river holds 1/5 of the bridge and the other holds 1/6. How long is the bridge?

Back 106

2400 feet long