PARCC Advanced Mathematics Practice Questions

Question 1

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?

Accepted Answer

$4950

Answer

Initially, the stock price is $100 per share. After a 10% increase, the price becomes $100 * 1.10 = $110 per share. When the price drops by 10% from this new value, it becomes $110 * 0.90 = $99 per share. John sold his remaining 50 shares at this price, so he received 50 shares * $99/share = $4950.

Question 2

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?

Accepted Answer

20%

Answer

The teacher has 3 hours (180 minutes) to grade 35 papers. She graded the first 5 papers in 30 minutes, leaving 30 papers to grade in 180 - 30 = 150 minutes. Her initial rate was 5 papers / 30 minutes = 1/6 paper per minute. To grade 30 papers in 150 minutes, she needs a rate of 30 papers / 150 minutes = 1/5 paper per minute. The required rate (1/5) is 20% faster than the initial rate (1/6), calculated as ((1/5) - (1/6)) / (1/6) = (1/30) / (1/6) = 6/30 = 1/5 = 20%.

Question 3

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?

Accepted Answer

9210 miles

Answer

First, calculate the radius of the satellite's orbit: Earth's radius (4000 miles) + altitude (400 miles) = 4400 miles. The circumference of this orbit is C = 2 * π * r = 2 * π * 4400 miles ≈ 27646 miles. Since the satellite completes one orbit in 120 minutes, in 40 minutes it travels (40/120) = 1/3 of the total circumference. Therefore, the distance traveled is (1/3) * 27646 miles ≈ 9215.33 miles, which is approximately 9210 miles.

Question 4

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

Accepted Answer

71

Answer

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. We need to check numbers after 67: 68 is divisible by 2, 69 is divisible by 3, 70 is divisible by 2. The next number, 71, is not divisible by any prime numbers up to its square root (which is about 8.4), meaning it's not divisible by 2, 3, 5, or 7. Thus, 71 is the next prime number after 67.

Question 5

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

Accepted Answer

54

Answer

To solve this, first convert the total length of the line to inches. There are 3 feet in a yard and 12 inches in a foot, so 1 yard = 3 * 12 = 36 inches. Therefore, 4.5 yards is 4.5 * 36 = 162 inches. To find how many 3-inch segments fit into 162 inches, divide 162 by 3, which equals 54 segments.

PARCC Practice Test

PARCC Practice Test

PARCC Advanced Mathematics Practice Questions