Practice Test 11 - 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 store sells notebooks in packs of 5 for $8 and pens in packs of 12 for $15. If a school needs 85 notebooks and 156 pens, what is the minimum total cost?
2. A spring stretches 4.5 cm when a 12-newton force is applied. Assuming the stretch is proportional to the force, how much will the spring stretch when an 18-newton force is applied?
3. In a regular pentagon, what is the measure of each interior angle?
4. A sequence follows the pattern where the $n$th term is given by $a_n = \frac{(-1)^n}{n+1}$. What is the sum of the 5th and 6th terms?
5. A basketball coach evaluates a player's scoring to plan substitutions during games. Let $P$ represent the player's points scored in a game, and let $M$ represent the minutes the player is on the court. The coach defines scoring efficiency as $S = \frac{P}{M}$, which describes how many points the player scores per minute. If the player increases $P$ while playing the same $M$, then $S$ increases. If the player's $M$ increases but $P$ stays about the same, then $S$ decreases. The coach notices that when the player rests more, they sometimes return with higher intensity and score faster, changing both $P$ and $M$. In the given context, how are the variables $P$ and $M$ related?​
6. A farmer plants corn in a field that measures 120 feet by 80 feet. If each corn plant needs 4 square feet of space and seeds cost $0.25 each, what is the total cost for seeds?
7. A homeowner designs a rectangular garden that is 18 feet long and 12 feet wide, and plans to install fencing around the entire edge. The garden will be filled with soil to a uniform depth of 0.5 feet for planting. All measurements are in feet, and fencing covers only the perimeter. How much fencing is needed to enclose the garden?​
8. A taxi charges a flat fee of $3 plus $0.50 per mile. If a trip costs $8.50, how many miles was the trip?
9. A teacher reviews scores; find the median: 92.0, 85.5, 76.0, 88.5, 90.0, 81.5.
10. The population $P$ of a bacteria culture after $t$ hours is given by $P = 1000 \cdot 2^t$. In this exponential growth model, what does the base 2 indicate about the bacteria population?
11. A rectangular garden has length $l$ and width $w$. If the garden's perimeter is 50 feet, then $l + w = 25$. In this constraint equation, what does the variable $l$ represent when $w = 12$?
12. In a photography club, the ratio of film cameras to digital cameras is $3:7$. If there are 42 digital cameras, what is the ratio of film cameras to the total number of cameras?
13. The ratio of cats to dogs at a pet shelter is 7:4. If there are a total of 66 animals (only cats and dogs), how many cats are there?
14. A neighborhood bakery tracks its finances each week to decide whether it can expand its menu. Let $R$ be weekly revenue from selling breads and pastries, and let $E$ be weekly expenses, including ingredients, packaging, utilities, and wages. The bakery defines weekly profit as $P = R - E$. Revenue $R$ changes when the bakery sells more items, raises prices slightly, or adds a catering order for a school event. Expenses $E$ change when flour and butter prices rise, when the owner schedules extra staff for a busy weekend, or when electricity use increases during long baking days. One week, the bakery runs a discount that increases the number of customers, but it also buys higher-quality chocolate that costs more per batch. The owner uses the variables $R$, $E$, and $P$ to compare weeks and to decide whether the business is becoming more profitable over time. What does the variable $E$ represent in the context of this scenario?​
15. In rhombus ABCD, one angle measures 64°. What is the measure of the angle adjacent to it?
16. The stem-and-leaf plot shows test scores for Ms. Garcia's math class. What is the median score for the class?
17. A laboratory scale reads 0.0045 kilograms. What is this mass in milligrams?
18. The cumulative frequency graph shows the distribution of test scores for 80 students. How many students scored between 70 and 85 points?
19. Three fair coins are flipped simultaneously. Event A is "exactly two heads" and Event B is "at least one tail." What is P(A ∩ B)?
20. A construction crew lays bricks: $6, 12, 24, 48, 96$; which option completes the sequence correctly?

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