Practice Test 5 - 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 cell phone plan charges $0.15 per text message after the first 500 messages. If a user sends 847 messages in a month, approximately how much will the overage charges be?
2. The equation $\frac{x + a}{3} = \frac{x - a}{2}$ is satisfied when $x = 10$. What is the value of $a$?
3. If $u(x) = 3x + 7$ and $u^{-1}$ represents the inverse function of $u$, what is $u^{-1}(16)$?
4. In the diagram, triangles PQR and STU are congruent. The transformation that maps triangle PQR onto triangle STU includes a reflection across the y-axis followed by a translation. If P is at (-3, 2), what is the location of point P after the reflection across the y-axis?
5. While traveling, Elena read that a walk was 2.0 miles, but signs showed kilometers. Using $1\text{ mi}=1.609\text{ km}$, she used $\text{km}=\text{mi}\times1.609$. What was 2.0 miles in kilometers, rounded to one decimal place?
6. A piece of fabric is 3.6 meters long. A tailor needs to cut it into strips that are each 15 centimeters wide. Assuming no waste, how many strips can be cut from the fabric?
7. The sequence 3, 7, 15, 31, 63, ... follows the pattern $a_n = 2^{n+1} - 1$. What is the 8th term?
8. Triangle JKL is congruent to triangle MNO by the SAS postulate. If JK = MN = 8, angle K = angle N = 72°, and KL = NO = 5, what additional information would be sufficient to prove the triangles are congruent by SSS instead?
9. Based on weekly temperatures, what is the median: 71.2, 68.5, 70.0, 72.6, 69.4?
10. The sequence $\frac{1}{3}, \frac{1}{6}, \frac{1}{12}, \frac{1}{24}, ...$ is geometric. What is the 7th term?
11. Kevin's age is 4 years less than 3 times his sister's age. If Kevin is 14 years old, how old is his sister?
12. A 20-pound bag of fertilizer covers 800 square feet of lawn. How many pounds of fertilizer are needed to cover 1,200 square feet?
13. A taxi fare follows input miles $m$ to output cost $c$: 1→7, 2→9, 3→11. Which function rule is correct?​​
14. A pharmaceutical company produces medication in doses measured in micrograms (μg). If a patient needs 0.75 milligrams of medication per day, and each pill contains 250 micrograms, how many pills should the patient take daily?
15. Circles O and P are congruent with radius 6 cm. If circle O is centered at the origin and circle P is centered at (8, 6), what is the distance between the centers of these congruent circles?
16. Two quantities, $x$ and $y$, are in the ratio 5:8. If $x = 35$, what is the value of $y$?
17. A store offers a membership program where customers pay an annual fee of $50 and then receive a 20% discount on all purchases. If $x$ represents the total amount spent on purchases before the discount, and $C$ represents the total amount paid including membership, then $C = 50 + 0.8x$. What does the expression $0.8x$ represent?
18. A printer makes 30 pages per minute. If input is minutes, what is the output when input equals 7?​​
19. If $k(x) = \frac{x + 1}{x - 3}$ and $k(a) = 2$, what is the value of $k(2a)$?
20. Express $\frac{3}{8} \div 0.375$ as a decimal.

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