Lessons of Math

LESSON 3-1 TUNE - UP EXERCISES

Multiple Choice

1- If a = 9 x 23 and b = 9 x 124, what is the value of b – a?

(D) 909

2- By how much does the product of 8 and 25 exceed the product of 15 and 10?

B) 50

3- How many containers, each holding 16 fluid ounces of milk, are needed to hold 5 quarts of milk?( 1 quart = 32 fluid ounces. )

(C) 10

4- If the current odometer reading of car is 31,983 miles, what is the LEAST of number miles that the car must travel before the odometer displays four digits that are the same?

(B) 239

5- In store A a scarf costs $12, and store B the same scarf is on sale for $8. How many scarfs can be bought in store B with the amount of money, excluding sales tax, needed to buy o scarfs in store A?

(C) 15

6- Let * represent one of the four basic arithmetic operations such that, for any nonzero real number r,

r * 0 = r and r * r = 0

Which arithmetic operation(s) does the symbol * represent?

(B) - only

7- Kurt has saved $160 to buy a stereo system that costs $400 including taxes. If he earns $8 an hour after all payroll deductions have been made, how many hours will he have to work in order to have exactly enough money to buy the stereo system?

(D) 30

8- If the present time is exactly 1:00 P.M., what was the time exactly 39 hours ago?

(E) 10:00 P.M.

9- Let # represent one of the four basic arithmetic operations such that, for any nonzero real numbers r and s,

r # 0 = r and r # s = s # r

(A) + only

10- If w = (6)(6)(6), x = (5)(6)(7), and y = (4)(6)(8), which inequality statement is true?

(D) y < x < w

11- If x and y are positive integers, 2x + y < 29, and y > 4, what is the greatest possible value of x – y?

(B) 6

LESSON 3-2 TUNE - UP EXERCISES

Multiple Choice

1- If x = 3 and y = Ö1 + 7x – 2x2, then y =

(B) 2

2- If x = 32 – 16 ¸ 2 x 4, then x =

(B) 2

3- What is the greatest number of positive integer values of x for which 1 < x2 < 50?

(B) Six

4- If 2 = p3, then 8p must equal

(C) p10

5- If 5 = ax, then 5/a =

(B) ax 1

6- If b3 = 4, then b6 =

(D) 16

7- If w is a positive number and w2 = 2, then w3 =

(B) 2Ö2

8- If 8x+1 = 64, what is the value of 32x+1?

(D) 27

9- If 0 < y < x, which statement MUST be true?

(D) Öxy = (Öx) (Öy)

10- Given y = wx2 and y is not 0. If the values of x and w are each doubled, then the value of y is multiplied by

(E) 8

LESSON 3-3 TUNE - UP EXERCISES

Multiple Choice

1- If the sum of the factors of 18 is S and the sum of prime numbers less than 18 is P, then P exceeds S by what number?

(A) 19

2- When a whole number N is divided by 5, the quotient is 13 and the remainder is 4. what is the value of N?

(D) 69

3- If p is divisible by 3 and q is divisible by 4, then pq must be divisible by each of the following EXCEPT

(D) 9

4- Which number has the most factors?

(E) 100

5- Which number is divisible by 2 and by 3?

(B) 4308

LESSON 3-4 TUNE - UP EXERCISES

Multiple Choice

1- If 2b = -3, what is the value of 1 – 4b?

(E) 7

2- If a is a negative integer and b is a positive integer, which of the following statements must be true?

I. b + a > 0

II. b - a/a < 0

III. ab < 0

(C) II only

3- If the product of five numbers is positive, then, at most, how many of the five numbers could be negative?

(D) Four

4- For which value of k is the value of k(k – 2) (k + 1) negative?

(A) -2

5- p2 (2 – 5) + (- p)2 =

(C) –2p2

6- If a + 5 is an odd integer, then n could be which of the following?

C) -2

7- Which of the following statements must be true when a < 0 and b > 0?

I. a + b > 0

II. b – a > 0

III. a (a/b) > 0

(D) II and III only

8- (-2)3 + (-3)2 =

(D) 1

LESSON 3-5 TUNE - UP EXERCISES

Multiple Choice

1- What part of an hour elapses from 4:56 P.M. to 5:32P.M.?

(C) 3/5

2- If each of the fractions 3/k, 4/k, 5/k is in lowest terms, which of the following could be the value of k?

(B) 49

3- Which number has the greatest value?

(D) 0.2938

4- The elapsed time from 11:00 A.M. to 3:00 P.M. on Wednesday of the same day is what fraction of the elapsed time from 11:00 A.M. on Wednesday to 3:00 P.M. on Friday of the same week?

(C) 1/13

5- In which number is the digit 3 in the hundredths place?

(D) 0.030

6- In which arrangement are the fractions listed from least to greatest?

(A) 9/19, 1/2, 8/15

7- After the formula V = 4/3 pr3 has been evaluated for some positive value of r, the formula is again evaluated using onehalf of the original value of r. The new value of V is what fractional part of the original value of V?

(C) 1/8

8- Each inch on ruler A is marked in equal 1/8 inch units, and each inch on ruler B is marked in equal 1/12 –inch units. When ruler B is used, how many 1/12 –inch units will the same side measure?

(C) 18

9- 60 + 2 + 4/8 + 3/500 =

(C) 62.506

10- If N x 7/12 = 7/12 x 3/14, then 1/N =

(B) 14/3

11- If n = 2.5 x 10(25), then Ön =

(E) 5 x 10(12)

12- If y is real number and y = x - 2/x + 3, then x CANNOT equal which of the following numbers?

(E) 40

14 – A store sells 8-ounce containers of orange juice at $0.69 each and 12-ounce containers of orange juice at $0.95 each. How much money will be saved by purchasing a total of –8ounces of orange juice in in 12-ounce rather than 8-ounce containers?

(C) $0.34

15- In the repeating decimal

Ö0.3752 = 0.3175231752…

The set of digits 31752 repeats endlessly. Which digit is in the 968^th place to the right of the decimal point?

(E) 7

LESSON 3-6 TUNE UP EXERCISES

1- John completes a race in 9 minutes, and Steve finishes the same race in 7 minutes. How many seconds after Steve finishes the race dos John complete the race?

R= 95

2- Multiplying a number by and then dividing the result by is equivalent to performing which of the following operations on the number?

R= Multiplying by

3- ( )³+( )³+( )³=

R= 0.036

4- What is the of of 12?

R= 6

5- What is the of 3 X 5 X 7?

R= 10

6- For which value of is <> ?

R= 7/24

LESSON 3-7 TUNE UP EXERCISES

1- If of a number is 6, what is of the same number?

R= 14

2- After Claire has read the first of a book, there are 120 pages left to read. How many pages of the book has Claire read?

R= 200

3- of 27 is of what number?

R= 10

4- If of a class that includes 10 girls are boys, how many students are in the class?

R= 25

5- What is the sum of all two-digit whole numbers in which one digit is of the other digit?

R= 231

LESSON 3-8 TUNE UP EXERCISES

1- What is 20% of of 15?

R= 2

2- Which expression is equivalent to %?

R= 0.004

3- The fraction is equivalent to what percent?

R= 80%

4- In a movie theater, 480 of the 500 seats were occupied. What percent of the seats were NOT occupied?

R= 4%

5- After 2 months on a diet, John’s weight dropped from 168 pounds to 147 punds. By what percent did John’s weight drop?

R= 12 %

6- Which expression is equivalent to 0.01%?

R= 1/10⁴

7- If the result of increasing a by 300% of a is b, then a is what percent f b?

R= 25%

8- After a 20% increase, the new price of a radio is $ 78.00. What was the original price of the radio?

R= $65.00

9- After a discount of 15%, the price of a shirt is $51. What was the original price of the shirt?

R= $60.00

10- Three students use a computer for a total of 3 hours. If the first student uses the computer 28% of the total time. And the second student uses the computer 53% of the total time. How many minutes does the third student use the computer=

R= 36

11- What is the 20% of 25% of ?

R= 0.04

12- In a factory that manufactures light bulbs, 0.04% of the bulbs manufactured are defective. It is expected that there ill be one defective light bulb in what number of bulbs that are manufactured?

R= 2500

13- A discount of 25% on the price of a pair of shoes, followed by another discount of 8% on the new price of the shoes, is equivalent to a single discount of what percent of the original price?

R= 31%

14- If 8 Kilograms of alcohol are added to 7 kilograms of pure water, what percent by weight of the resulting solution is alcohol?

R= 32%

15- If a is 40% of b, then b exceeds a by what percent of a?

R= 250%