Practice Test 2 - ISEE Upper Level Quantitative Reasoning

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. A model airplane is built to a scale of 1:48. If the model's wingspan is 9.5 inches, what is the wingspan of the actual airplane?
2. Water flows into a tank at 8 gallons per minute for the first 15 minutes, then at 12 gallons per minute for the next 20 minutes. If the tank was initially empty, what is the average rate of water flow for the entire 35-minute period?
3. A printing press can print 1,500 pages in 20 minutes. Due to a mechanical issue, its efficiency drops to 75% of its original rate. How many pages can it print in 45 minutes at the reduced rate?
4. A recipe calls for 2.5 cups of flour. If 1 cup equals 240 milliliters, and you only have a measuring container marked in fluid ounces where 1 fluid ounce equals 30 milliliters, how many fluid ounces of flour do you need?
5. A pipe can fill a swimming pool in 6 hours. A drain can empty the same pool in 8 hours. If both the pipe and drain are operating simultaneously, how long will it take to fill the empty pool?
6. A machine produces defective items at a rate of 3 defective items for every 125 items produced. If the machine produces 2,000 items, how many defective items should be expected?
7. The frequency table shows the distribution of student heights in a physical education class. What percentage of students are 66 inches or taller?
8. A student argues that $0.\overline{571428} = \frac{4}{7}$ and therefore $0.\overline{571428} > 57\%$. Is this argument valid?
9. In track practice, what is the mean time: 12.4, 12.8, 13.1, 12.6, 12.9?
10. The sequence 100, 50, 25, 12.5, 6.25, ... represents a geometric progression. What is the 8th term of this sequence?
11. For a travel itinerary, a museum was 3.2 km from the hotel, but the student wanted miles. Using $1\text{ mi}=1.609\text{ km}$, he computed $\text{mi}=\text{km}\div1.609$. What was 3.2 km in miles, rounded to two decimals?
12. A rectangular room is 16 feet long and 13 feet wide, with walls 8 feet high. A designer plans to place trim along the floor edges and order carpet for the floor. All measurements are in feet, and the room is a perfect rectangle when viewed from above. Perimeter determines trim length, and area determines carpet needed. Determine the perimeter of the rectangle based on the provided dimensions.​
13. A water tank is being filled at a rate of 15 gallons per minute. After 8 minutes, the rate increases to 20 gallons per minute for the next 12 minutes. What is the average rate of water flow for the entire 20-minute period?
14. A chemical reaction produces heat at a rate of 850 calories per minute. What is this rate in joules per second? (Note: 1 calorie = 4.184 joules)
15. A recipe from Italy called for 200 g of flour, but Lina measured in ounces. She used $1\text{ oz}=28.35\text{ g}$ and wrote $\text{oz}=\text{g}\div28.35$. How many ounces of flour was 200 g, rounded to one decimal place?
16. A shopper compares flour prices: $3.60 for 2 lb, $5.10 for 3 lb, and $7.20 for 4 lb. Prices are in dollars and weights are in pounds. She wants the lowest cost per pound. Which option is the best buy?
17. A factory makes 200 items in 4 hours, then 180 items in 3 hours; what is overall rate?
18. Line segments AB and CD intersect at point P. If angle APC measures 3x + 20° and angle BPD measures 5x - 12°, what is the value of x?
19. In a garden, plants per row are $7, 11, 15, 19, 23$; calculate the 10th term.
20. A function $w(t)$ represents the weight (in pounds) of a puppy after $t$ weeks, where $w(t) = 2t + 5$. If the puppy currently weighs 15 pounds, how much will it weigh 3 weeks from now?

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