# PARCC Advanced Mathematics Practice Questions

#### 1. John buys 100 shares of stock at $100 per share. The price goes up by 10% and he sells 50 shares. Then, prices drop by 10% and he sells his remaining 50 shares. How much did he get for the last 50?

1. E: The stock first increased by 10%, that is, by $10 (10% of $100) to $110 per share. Then, the price decreased by $11 (10% of $110) so that the sale price was $110-$11 = $99 per share, and the sale price for 50 shares was 99 x $50 = $4950.

#### 2. A teacher has 3 hours to grade all the papers submitted by the 35 students in her class. She gets through the first 5 papers in 30 minutes. How much faster does she have to work to grade the remaining papers in the allotted time?

2. C: She has been working at the rate of 10 papers per hour. She has 30 papers remaining and must grade them in the 2.5 hours that she has left, which corresponds to a rate of 12 papers per hour. of her previous rate, or 20% faster.

#### 3. A satellite in a circular orbit rotates around the Earth every 120 minutes. If the Earth's radius is 4000 miles at sea level, and the satellite's orbit is 400 miles above sea level, approximately what distance does the satellite travel in 40 minutes?

3. B: The radius, R, of the satellite's orbit is the sum of the Earth's radius plus the satellite's orbital altitude, or R = 4400 miles. The circumference of the circular orbit is thereforeC = 2Π = 2Π(4400) = 8800Π miles. Since 40 minutes is one third of the satellite's 120-minute orbital time, it traverses one third of this distance in that time. So the distance, D = 2Πx4400 = 9210.66 miles, using 3.14 for Π.

#### 4. What is the next-highest prime number after 67?

4. C: Prime numbers are those that are only evenly divisible by one and themselves.

#### 5. How many 3-inch segments can a 4.5-yard line be divided into?

5. C: There are 12 inches in a foot and 3 feet in a yard. Four and a half yards is equal to 162 inches. To determine the number of 3-inche segments, divide 162 by 3.

#### 6. Sheila, Janice, and Karen, working together at the same rate, can complete a job in 3 1/3 days. Working at the same rate, how much of the job could Janice and Karen do in one day?

6. A: If it takes 3 people 3 1/3 days to do the job, then it would take one person 10 days:

#### 7. A box of laundry detergent contains 16.5 oz of product. What is the maximum number of loads that can be washed if each load requires a minimum of 3/4 oz of detergent?

7. C: 16.5 x 4/3 = 22.

#### 8. A blouse normally sells for $138, but is on sale for 25% off. What is the cost of the blouse?

8. B: 25% off is equivalent to , so the sale price becomes $138 - $34.50 = $103.50.

#### 9. A crane raises one end of a 3300 lb steel beam. The other end rests upon the ground. If the crane supports 30% of the beam's weight, how many pounds does it support?

9. B: 30% 0f 3300 = 0.3 x 3300 = 990

#### 10. A taxi service charges $5.50 for the first 1/5th of a mile, $1.50 for each additional 1/5th of a mile, and 20 cents per minute of waiting time. Joan took a cab from her place to a flower shop 8 miles away, where she bought a bouquet, then another 3.6 miles to her mother's place. The driver had to wait 9 minutes while she bought the bouquet. What was the fare?

10. C: The total distance traveled was 8 + 3.6 = 11.6 miles. The first 1/5th of a mile is charged at the higher rate. Since 1/5th = 0.2, the remainder of the trip is 11.4 miles. Thus the fare for the distance traveled is computed as . To this the charge for waiting time must be added, which is simply 9 x 20 cents = 180 cents = $1.80. Finally, add the two charges, $91 + $1.80 = $92.80. Since this value is unique, all other answers are incorrect.