Practice Test 1 - 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. Rectangle PQRS is congruent to rectangle TUVW. If rectangle PQRS has dimensions 5 by 12 and is positioned with its longer side horizontal, while rectangle TUVW is positioned with its longer side vertical, what transformation could map PQRS onto TUVW?
2. If the cost of 3.5 pounds of cheese is $14.70, what is the cost per pound?
3. The test scores in Mrs. Chen's class have a mean of 82, median of 85, and range of 36. If she curves the grades by multiplying each score by 1.1, what will be the new mean, median, and range respectively?
4. A store tracks weekly sales; what is the mean: 45.5, 50.0, 47.2, 52.3, 49.0, 46.0?
5. Using complementary angles, if $\triangle DEF$ is right at $E$ and $m\angle D=58^\circ$, find $m\angle F$.
6. A conveyor belt moves packages at 2 feet per second. If a worker walks on the belt in the same direction at 3 feet per second relative to the ground, how long does it take the worker to travel 120 feet along the belt?
7. A runner's distance follows input minutes $t$ to output miles $d$: 5→0.5, 10→1.0, 15→1.5. Which rule matches?​​
8. A ball is thrown upward from ground level. Its height $h$ (in feet) after $t$ seconds is $h = 40t - 16t^2$. What does the value of $t$ represent when $h = 0$ and $t > 0$?
9. Water flows from a pipe at a rate of 12 gallons per 8 minutes. At this rate, how many minutes will it take to fill a 45-gallon tank?
10. A trapezoid has parallel sides of lengths 8 cm and 14 cm, and the distance between these parallel sides is 6 cm. If the trapezoid is divided into two triangles by drawing a diagonal, what is the difference in areas between the two triangles?
11. Triangle XYZ has angles in the ratio 2:3:4. What is the measure of the largest angle?
12. The height $h$ (in feet) of a baseball $t$ seconds after being thrown is modeled by $h = 6 + 25t - 16t^2$. In this context, what does the term $6$ most likely represent?
13. The table shows the results of rolling two dice 50 times and recording the sum. Based on this experimental data, what is the experimental probability of rolling a sum of 7?
14. The number of books read by 10 students during summer vacation are: 3, 5, 6, 7, 8, 8, 9, 10, 12, 15. If each student reads 2 additional books, what will be the new median and new range?
15. A pizza parlor uses 3 ounces of cheese per pizza. If cheese costs $4.80 per pound and they make 64 pizzas in one day, what is the daily cost for cheese?
16. A concrete mixture contains cement, sand, and gravel in the ratio $1:3:4$. If a construction project uses 24 cubic yards of this mixture and requires an additional 6 cubic yards of sand to be added separately, what is the ratio of sand to the total volume of materials?
17. A real estate agent charges a 6% commission on home sales. Due to market conditions, the agent reduces the commission rate by 25%. If a house sells for $450,000, how much less commission does the agent earn compared to the original rate?
18. The graph shown represents a function $f(x)$. Based on the graph, what is the value of $f(f(2))$?
19. A triangle has sides of length $x$, $x+3$, and $2x-1$. Which expression represents the perimeter of the triangle?
20. The sum of the first $n$ terms of an arithmetic sequence is given by $S_n = 3n^2 + 2n$. What is the 5th term of this sequence?

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