Math

5. Solve the following equation for A : 2A/3 = 8 + 4A A. -2.4 B. 2.4 C. 1.3 D. -1.3 E. 0

. A: In order to solve for A, both sides of the equation may first be multiplied by 3. This is written as 3(2A/3)=3(8+4A) or 2A=24+12A. Subtraction of 12A from both sides of the equation gives -10A=24. Division by -10 gives A = -2.4.

1. If Lynn can type a page in p minutes, what piece of the page can she do in 5 minutes? A. 5/p B. p - 5 C. p + 5 D. p/5 E. 1- p + 5

. A: The following proportion may be written: 1/p=x/5. Solving for the variable, x, gives xp = 5, where x=5/p. So, Lynn can type 5/p pages, in 5 minutes.

2. If y(x-1)=z then x= A. y-z B. z/y + 1 C. y(z-1) D. z(y-1) E. 1-zy

2. B: The equation may be solved by first distributing the y across the expression, x - 1, on the left side of the equation. Doing so gives: xy - y = Z. Adding y to both sides of the equation gives: xy = Z + y. Finally, division of both sides of the equation by y gives: x=(Z+y)/y or x=Z/y+1.

1. An instrument store gives a 10% discount to all students off the original cost of an instrument. During a back to school sale an additional 15% is taken off the discounted price. Julie, a student at the local high school, purchases a flute for $306. How much did it originally cost? A. $325 B. $375 C. $400 D. $408 E. $425

1. C: The equation, x-0.10x-0.15(x-0.10x)=306, may be used to solve the problem. Solving for x gives 0.90x - 0.15x + 0.015x = 306, where x = 400. Thus, the original price was $400.

10. A soda company is testing a new sized can to put on the market. The new can is 6 inches in diameter and 12 inches in height. What is the volume of the can in cubic inches? a. 339 b. 113 c. 432 d. 226

10. A. V = ?r2h. V = 3.14 x (32) x 12. 3.14 x 9 x 12 = 339.12.

10. A student receives his grade report from a local community college, but the GPA is smudged. He took the following classes: a 2 hour credit art, a 3 hour credit history, a 4 hour credit science course, a 3 hour credit mathematics course, and a 1 hour science lab. He received a "B" in the art class, an "A" in the history class, a "C" in the science class, a "B" in the mathematics class, and an "A" in the science lab. What was his GPA if the letter grades are based on a 4 point scale? (A=4, B=3, C=2, D=1, F=0) A. 2.7 B. 2.8 C. 3.0 D. 3.1 E. 3.2

10. C: The GPA may be calculated by writing the expression, ((3*2)+(4*3)+(2*4)+(3*3)+(4*1))/13, which equals 3, or 3.0.

12. Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color? A. 4 B. 8 C. 12 D. 13 E. 16

12. D: If she removes 13 jellybeans from her pocket, she will have 3 jellybeans left, with each color represented. If she removes only 12 jellybeans, green or blue may not be represented.

16. If 8x + 5x + 2x + 4x = 114, the 5x + 3 = A. 12 B. 25 C. 33 D. 47 E. 86

16. C: The given equation should be solved for x. Doing so gives x = 6. Substituting the x-value of 6 into the expression, 5x + 3, gives 5(6) + 3, or 33.

2. Kate got a 56 on her first math test. On her second math test, she raised her grade by 12%. What was her grade? a. 62.7 b. 67.2 c. 68.0 d. 72.3

2. A: First, calculate 12% of 56. 56 x 0.12 = 6.72 Then, add this value (the increase) to the original value of 56. 56 + 6.72 = 62.72 Rounding off, we get 62.7

3. Jason chooses a number that is the square root of four less than two times Amy's number. If Amy's number is 20, what is Jason's number? a. 6 b. 7 c. 8 d. 9

3. A: Jason's number can be determined by writing the following expression: ?(2x-4), where x represents Amy's number. Substitution of 20 for x gives ?(2(20)-4), which simplifies to ?36, or 6. Thus, Jason's number is 6. Jason's number can also be determined by working backwards. If Jason's number is the square root of 4 less than 2 times Amy's number, Amy's number should first be multiplied by 2 with 4 subtracted from that product and the square root taken of the resulting difference.

Enrique weighs 5 pounds more than twice Brendan's weight. If their total weight is 225 pounds, how much does Enrique weigh? a. 125 pounds b. 152 pounds c. 115 pounds d. 165 pounds

3. B. If E + B = 225, and E = 2B + 5, then 225 - B = 2B + 5. Solving for B, 3B = 220 and B = 73.3. 225 - 73.3 = 151.7.

3. Which of the following values is NOT equal to 34(58+9)? A. 34 x 67 B. 58(34+9) C. 34 x 58 + 34 x 9 D. 1,972 + 306 E. (9 + 58) 34

3. B: This problem illustrates the distributive property of multiplication over addition. The factor being distributed may not change.

4. In a square built with unit squares, which of the following would represent the square root of the square? a. The number of unit squares comprising a side b. The total number of unit squares within the square c. Half of the total number of unit squares within the square d. The number of unit squares comprising the perimeter of the square

4. A: The square root of a square is equal to the length of one of the sides, or the number of unit squares comprising a side. For example, a square representing 7 squared will have 7 unit squares on each side; 7^2=49, and 7 is the square root of 49. The square will contain 49 unit squares, with 7 unit squares comprising each side.

4. What is the missing number in the sequence: 4, 6, 10, 18, ___, 66. a. 22 b. 34 c. 45 d. 54

4. B. Double the number that is added to the previous number. So, 4+2=6, 6+4=10, 10+8=18, 18+16=34, and 34+32=66.

4. Penny drinks 8 glasses of water each day. The number of glasses of water she drinks over a 12-day time span can be determined, using the number sentence: Which number sentence would not show the number of glasses of water she drinks? a. ? / 8 = 12 b. 12 x 8 = ? c. ? / 12 = 8 d. 12 - 8 = ?

4. D: If she drinks 8 glasses of water each day, the number of glasses of water she drinks in 12 days can be determined by multiplying 8 by 12. This product is 96; thus she drinks 96 glasses of water in a 12-day time span. The relationship between the number of glasses of water she drinks per day and the total number of glasses of water she drinks in 12 days can be represented by an appropriate multiplication or division number sentence within the following fact family: Subtracting 8 from 12 will not reveal the number of glasses she drinks in a 12-day time span. The number sentence: , is not in this fact family.

4. Two angles of a triangle measure 15° and 85 °. What is the measure for the third angle? A. 50° B. 55° C. 60° D. 80° E. 90°

4. D: The measure of the third angle of the triangle is equal to 180°-(15° + 85°), or 80°.

5. Belinda draws a rectangle with a length of 6 cm. She draws a second rectangle with a length of 11 cm. Belinda continues drawing more rectangles, where for each rectangle drawn, she uses a length that is 5 more centimeters than the length of the previous rectangle. If this pattern continues, what will be the length of the 11th rectangle? a. 46 cm b. 54 cm c. 56 cm d. 61 cm

5. C: If each rectangle has a length that is 5 cm more than that of the previous rectangle, the lengths of the 3rd rectangle through the 11th rectangle can be found by adding 5 cm to the length of the second triangle and continuing for each next rectangle. So, the lengths of the rectangles will be as follows: 16 cm, 21 cm, 26 cm, 31 cm, 36 cm, 41 cm, 46 cm, 51 cm, and 56 cm.

6. A publishing company has been given 29 manuscripts to review. If the company divides the work equally amongst 8 editors, which of the following represents the number of manuscript each editor will review? a. 3 3/5 b. 3 5/8 c. 3 7/9 d. 3 2/3

6. B: In order to determine the number of manuscripts each editor will review, the total number of manuscripts should be divided by the number of editors; 29 / 8 can be written as 29/8, which simplifies to the mixed fraction 3 5/8. Notice that the quotient is 3 with a remainder of 5.

7. A lake near Armando's home is reported to be 80% full of water. Which fraction is equivalent to 80% and in simplest form? a. 1/80 b. 8/10 c. 4/5 d. 80/1

7. C: The 80% means 80 out of 100, which can be written as 80/100 . This fraction can be written in lowest terms by dividing both the numerator and denominator by the greatest common factor of 20, to get the fraction, 4/5.

8. Alma collected coins. In the bag where she kept only dimes, she had dimes from four different years. She had 20 dimes minted in 1942, 30 minted in 1943, 40 minted in 1944, and 10 minted in 1945. If Alma reached into the bag without looking and took a dime, what is the probability that she took a dime minted in 1945? a. 2/5 b. 3/10 c. 1/5 d. 1/10

8. D: By adding all of the dimes, we find that there are a total of 100 dimes in the bag. 10 of them were minted in 1945. The probability, then, of choosing a dime minted in 1945 is 10 out of 100, which is equivalent to the fraction 1/10.

9. Which of the following is equal to 5.93 x 10-2? A. 0.0593 B. 0.00593 C. 593 D. 5930 E. 59300

9. A: Movement of the decimal point two places to the left gives 0.0593.