Practice Test 10 - 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. Which algebraic expression represents the total distance? A runner completes $x$ laps of a $0.4$ mile track and then runs $y$ additional miles on a trail. No other distances are included in the workout. Write an expression for the total miles run.
2. If $\angle PQR$ and $\angle SQT$ are vertical angles and $m\angle PQR=128^\circ$, what is $m\angle SQT$?
3. A book club orders $b$ books at $12 each and pays a shipping fee of $5 per order plus $1.50 for each book. After receiving a discount of $3 per book, which expression represents their total cost?
4. A subscription service increases its monthly fee by 30%, then offers existing customers a "grandfathered" rate that is 20% less than the new rate. What is the percent change in monthly fees for existing customers compared to the original rate?
5. A laptop's price is reduced by 20% for a sale, then an additional 10% is taken off the sale price for a student discount. If the final price is $576, what was the original price?
6. A square garden is surrounded by a walkway of uniform width. The garden itself has an area of 144 square feet, and the total area including the walkway is 256 square feet. What is the width of the walkway?
7. A model tower is 9 inches tall at a scale of 1 inch to 12 feet; what is the actual height?
8. A baker uses $1\frac{1}{4}$ cups of flour for each batch of cookies. If she has $3.75$ cups of flour, what percent of the flour needed for 4 batches does she have?
9. A phone plan charges $25 per month for unlimited talk and text, plus $10 per gigabyte of data used. If a customer uses $g$ gigabytes in a month and pays a $5 activation fee only in the first month, which expression represents their total cost for the first $n$ months?
10. In a fitness plan, a barbell was labeled 150 lb, but the coach recorded mass in kilograms. Using $1\text{ kg}=2.205\text{ lb}$, the coach used $\text{kg}=\text{lb}\div2.205$. What was 150 lb in kilograms, rounded to one decimal place?
11. A rectangle has length $3y + 2$ and width $y - 1$. If the area of the rectangle is equal to the area of a square with side length $s$, which equation relates $y$ and $s$?
12. A farmer plants corn in a rectangular field that is $50$ feet longer than it is wide. He also plants soybeans in a square field whose side length equals the width of the corn field. If the width of the corn field is $w$ feet, which expression represents the total area planted?
13. In the coordinate plane shown, triangle ABC has vertices at A(2,1), B(6,1), and C(4,5). Triangle DEF is similar to triangle ABC with vertex D at (1,2). If the scale factor from ABC to DEF is 1/2, what are the coordinates of vertex E?
14. Two pipes fill a tank in the ratio $3:5$ regarding their flow rates. If the faster pipe can fill the tank alone in 15 hours, how long would it take both pipes together to fill $\frac{2}{3}$ of the tank?
15. The membership fee for a gym increased by 25% in 2022 and then increased by another 20% in 2023. If the fee in 2023 was $180, what was the fee in 2021?
16. An arithmetic sequence has a common difference of -4. If the 6th term is 23, what is the 12th term?
17. A pump can fill a tank in 8 hours. At the same rate, how long would it take the same pump to fill a tank that is 2.5 times larger?
18. A machine produces 180 bolts in 45 minutes. How many bolts can 4 such machines produce in 2 hours?
19. What is the algebraic expression for the total cost? A student buys $x$ packs of index cards for $4$ dollars each and $y$ binders for $6$ dollars each, then uses a $10$ dollar coupon. Write an expression for the amount paid after the coupon is applied.
20. The price of gasoline increased from $3.42 per gallon to $3.89 per gallon. A driver who typically buys 12 gallons per week wants to quickly estimate the additional weekly cost using prices rounded to the nearest ten cents. Which calculation is most appropriate?

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