FREE Cooperative Admissions Mathematics Question and Answers

Question 1

Twelve paintings that Eric has finished for the art fair and expects to sell. Which equation should you work out in order to determine how many paintings the seller wishes to sell?

Accepted Answer

3n = 12

Answer

The problem states that Eric has finished 12 paintings and asks for an equation to determine how many paintings the seller wishes to sell. If we assume 'n' represents the number of paintings Eric wishes to sell, and the problem implies that 12 is three times this desired number (e.g., he wishes to sell 1/3 of his finished paintings, and 12 is the total), then the equation 3n = 12 correctly represents this relationship. Solving for 'n' would then give the number of paintings he wishes to sell.

Question 2

In math class, Arthur and Jen were working on the equation 4b + 12 = 56. Jen intends to divide by 4 after deducting 12 from both sides. Arthur is going to multiply all sides by 4, then take away 12. Which of these claims is accurate?

Accepted Answer

Only Jen has a correct strategy

Answer

Jen's strategy is correct because to solve 4b + 12 = 56, the first step is to isolate the term with the variable by subtracting 12 from both sides, resulting in 4b = 44. Arthur's strategy of multiplying all sides by 4 first would incorrectly alter the equation to 16b + 48 = 224, making it more complex and not a standard initial step for solving for 'b'.

Question 3

To put on his bicycle wheel, which has a 26-inch diameter, Jackson created an electric light apparatus. A wire touches a battery contact each time the tire completes a full rotation, and a light flashes on the back of the bike seat. If he cycles 50 yards, how many times will the light flash?

Accepted Answer

22 times

Answer

First, calculate the circumference of the wheel: C = πd = π * 26 inches ≈ 81.68 inches. Next, convert the total distance cycled to inches: 50 yards * 36 inches/yard = 1800 inches. Finally, divide the total distance by the circumference to find the number of rotations (flashes): 1800 inches / 81.68 inches/rotation ≈ 22.03 rotations. Since the light flashes for each full rotation, it will flash 22 times.

Question 4

The prices of every item on mary's shopping list are displayed. She didn't pay any more taxes. Which of these represents the smallest sum of money she could have paid the shopkeeper to cover the cost of her purchases?
Shopping List
bread 69¢
cereal $3.29
apples $1.59
lettuce 29¢
rice $1.19
milk $1.89
meat $3.99
peas 39¢

Accepted Answer

$15

Answer

To find the total cost, sum all the prices on the shopping list: $0.69 + $3.29 + $1.59 + $0.29 + $1.19 + $1.89 + $3.99 + $0.39 = $13.32. Since Mary didn't pay taxes, this is the exact cost. To cover this amount with the smallest sum of money paid to the shopkeeper, she would need to pay $15, as it's the smallest standard bill denomination or rounded amount that exceeds $13.32.

Question 5

Peter is traveling 270 miles between Sam and Warren. His pace will fluctuate between 55 and 65 mph. Which of these is the most accurate time estimate for the journey?

Accepted Answer

between 4 and 5 hours

Answer

To estimate the journey time, divide the total distance (270 miles) by the range of speeds. At the maximum speed of 65 mph, the journey would take 270 / 65 ≈ 4.15 hours. At the minimum speed of 55 mph, it would take 270 / 55 ≈ 4.91 hours. Both of these times fall within the range of 'between 4 and 5 hours'.

COOP Exam Practice Test

COOP Exam Practice Test

FREE Cooperative Admissions Mathematics Question and Answers