PARCC Advanced Mathematics Practice Questions 1 — Questions and Answers
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?
- $5000
- $5500
- $4900
- $5050
- $4950 (Correct answer)
Correct answer: $4950
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?
- 10%
- 15%
- 20% (Correct answer)
- 25%
- 30%
Correct answer: 20%
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?
- 1400 miles
- 9210 miles (Correct answer)
- 4400 miles
- 4120 miles
- 8000 miles
Correct answer: 9210 miles
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?
- 68
- 69
- 71 (Correct answer)
- 73
- 76
Correct answer: 71
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?
- 15
- 45
- 54 (Correct answer)
- 64
- 84
Correct answer: 54
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.
Question 6: 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?
- 1/5 (Correct answer)
- 1/4
- 1/3
- 1/9
- 1/8
Correct answer: 1/5
This question is missing the image or specific dimensions for the cylinder. However, based on the provided correct answer of 226.20 and common problem values, it's highly probable the cylinder has a radius of 3 units and a height of 8 units (similar to Q18). The volume of a cylinder is calculated using the formula V = π * r^2 * h. With r=3 and h=8, V = π * (3^2) * 8 = π * 9 * 8 = 72π, which approximates to 226.19 cubic units.
Question 7: 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?
- 10
- 50
- 22 (Correct answer)
- 18
- 16.5
Correct answer: 22
The volume of a cube is found by multiplying its length, width, and height. Since all sides of a cube are equal, if the width is 5 inches, then the length and height are also 5 inches. Therefore, the volume is 5 inches * 5 inches * 5 inches = 125 cubic inches.
Question 8: 8. A blouse normally sells for $138, but is on sale for 25% off. What is the cost of the blouse?
- $67
- $103.50 (Correct answer)
- $34.50
- $113
- $125
Correct answer: $103.50
To find the total material, add the measurements for each unit separately: inches, feet, and yards. Total inches: 6 + 5 + 8 = 19 inches. Since 12 inches = 1 foot, 19 inches is 1 foot and 7 inches. Total feet: 2 + 1 + 2 + (1 carried from inches) = 6 feet. Since 3 feet = 1 yard, 6 feet is 2 yards and 0 feet. Total yards: 1 + 2 + 4 + (2 carried from feet) = 9 yards. Combining these, Sally has 9 yards, 0 feet, and 7 inches of material.
Question 9: 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?
- 330 lbs
- 990 lbs (Correct answer)
- 700 lbs
- 1100 lbs
- 2310 lbs
Correct answer: 990 lbs
The volume of a cylinder (can) is calculated using the formula V = π * r^2 * h. Given the diameter is 3 inches, the radius (r) is half of that, so r = 1.5 inches. The height (h) is 8 inches. Plugging these values into the formula: V = π * (1.5)^2 * 8 = π * 2.25 * 8 = 18π. Using π ≈ 3.14159, the volume is approximately 18 * 3.14159 = 56.54862, which rounds to 56.55 cubic inches.
Question 10: 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?
- $20
- $120.20
- $92.80 (Correct answer)
- $91
- $90
Correct answer: $92.80
For a square, the area is calculated by side * side (s^2). If the area is 16 square feet, then the side length (s) is the square root of 16, which is 4 feet. The perimeter of a square is calculated by 4 * side. So, the perimeter is 4 * 4 feet = 16 feet.
PARCC Advanced Mathematics Practice Questions 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?