1. A ball is thrown into the air from an initial height of 10 feet. Its height above the ground, in feet, t seconds after it is thrown is given by the function h(t) = -16t2 + 27t + 10. How long will it take (in seconds) for the ball to hit the ground after it is thrown?
2. Kelly has 25 coins worth $5.20. The coins are all either dimes or quarters. How many dimes does she have?
3. A carpenter wants to cut a two-foot board into segments that are each 5 inches long. How many full segments can he cut?
4. An artist makes a replica of The Starry Night for a postcard. The scale factor of the replica to the original is 1:12. If the original painting is about 30 in. × 36 in., what are the dimensions of the replica?
5. Jerry goes to the grocery store and spends $2.25 for milk, $3.59 for oranges, and $3.29 for eggs. If he gives the cashier a $20 bill, what will his change be?
6. A school has 240 boys and 360 girls. What percentage of the student body are boys?
7. Susan buys a used car for $6,500 and finances it by making monthly payments of $325. How long will it take her to pay for the car?
- 16 months
- 17 months
- 18 months
- 19 months
- 20 months
8. A recipe calls for ½ cup of butter and two eggs (among other ingredients) to make 16 brownies. Assuming that you have enough of all of the other ingredients on hand, how many brownies can you make with sixteen eggs?
9. Mark works as a librarian and makes $17 per hour. However, if he works more than 40 hours in a week, he makes time-and-a-half for every hour over the initial 40. How much will he make in a week (before taxes) if he works 52 hours?
10. Christina makes $480 per week working as a cashier. She saves half of her salary toward buying a new laptop. If the laptop costs $1,200, how long will it take her to save enough money to buy it?
1. B. The ball will hit the ground when its height is zero. In mathematical notation, this will happen when h(t) = 0. Therefore, to answer the question, set the given function equal to zero.
Now solve the resulting equation for t. Factor the left side, and then use the zero-product property.
The answer only makes sense when t is positive, so discard the negative value. Thus, the ball will hit the ground exactly 2 seconds after it is thrown.
2. A. First translate the information in the word problem into two mathematical equations. Let the variables d and q represent the number of dimes and the number of quarters, respectively. Translate the information given in the problem into a system of equations using these variables.
d + q = 25
10d + 25q = 520
Solve the system of equations using elimination. First, eliminate q by multiplying the first equation by 25, and then subtract the resulting equations.
25(d + q = 25) ⇒ 25d + 25q = 625
10d + 25q = 520 – 10d + 25q = 520
15d = 105
Next, solve the resulting equation by dividing both sides by 15. The result is d = 7. Therefore, Sophie has 7 dimes.
3. A. There are 12 inches in a foot, so two feet is equal to 24 inches. Find the number of times 5 inches goes into 24 inches by dividing 24 by 5.
24 ÷ 5 = 4.8
Therefore, the carpenter can cut 4 full segments with some left over.
4. B. The scale factor given in the problem is the ratio of the side lengths of the replica to the side lengths of the original. Since the scale factor is 1:12, divide the dimensions of the original by 12 to find the dimensions of the replica.
Thus, the dimensions of the replica are in. × 3 in.
5. D. First add the costs of the three items together.
The total price is $9.13. Subtract this from $20.00 to find the change.
Thus, Jerry receives $10.87 in change.
6. B. First add the number of boys and girls to find the total number of students in the school.
240 + 360 = 600
So, there are 600 students. Divide the number of boys, 240, by 600 and convert the result to a percent.
240 ÷ 600 = 0.4
7. E. Divide the cost of the car, $6,500, by the amount of the payments, $325.
6,500 ÷ 325 = 20
Therefore, it will take Susan 20 months to pay for the car.
8. C. You have sixteen eggs and the recipe only calls for two; therefore, you have eight times the necessary ingredients and can make eight times as many brownies:
16 x 8 = 128
Therefore, you can make 128 brownies with 16 eggs.
9. C. First use multiplication to calculate how much he makes for the first 40 hours.
40 x $17 = $680
Next calculate his overtime hourly pay. To do this, multiply his regular pay by .
Thus, during overtime, he makes $25.50 per hour. Since he works a total of 52 hours, his overtime is 12 hours. Multiply to find his overtime pay.
12 x $25.50 = $306
Finally, add the pay from the first 40 hours to his overtime pay..
$680 + $306 = $986
10. D. First calculate the amount she saves per week by dividing her pay by 2.
$480 ÷ 2 = $240
Divide the cost of the laptop, $1,200, by the $240 she saves each week.
$1,200 ÷ $240 = 5
Thus, it will take Christina five weeks to save enough for the laptop.